WO2025212655A1

WO2025212655A1 - Multiple priming for on-support nucleic acid amplification

Info

Publication number: WO2025212655A1
Application number: PCT/US2025/022551
Authority: WO
Inventors: Tuval Ben-Yehezkel; Pedro Belda FERRE; Kyle METCALFE; Marielle KRIVIT
Original assignee: Element Biosciences Inc
Current assignee: Element Biosciences Inc
Priority date: 2024-04-02
Filing date: 2025-04-01
Publication date: 2025-10-09
Anticipated expiration: 2026-10-02

Abstract

The present disclosure provides compositions, apparatus and methods for generating a plurality of concatemer template molecules immobilized on a support for conducting massively parallel sequencing runs. In some embodiments, the concatemer template molecules can be generated by conducting rolling circle amplification reactions on a support comprising a mixture of immobilized capture and pinning primers. The rolling circle amplification reaction comprises a plurality of circularized polynucleotide molecules and soluble amplification primers which generates concatemer template molecules that collapse to form compact DNA nanoballs that are stably immobilized to a support.

Description

MULTIPLE PRIMING FOR ON-SUPPORT

NUCLEIC ACID AMPLIFICATION

CROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application claims priority to, and benefit of, U.S. Provisional Application No. 63/573,392, filed on April 2, 2024, the contents of which are incorporated by reference in their entirety.

INCORPORATION BY REFERENCE OF SEQUENCE LISTING

[0002] The contents of the electronic sequence listing (ELEM_026_001WO_SeqList_ST26.xml; Size: 158,086 bytes; and Date of Creation: March 28, 2025) are herein incorporated by reference in their entireties.

TECHNICAL FIELD

[0003] The present disclosure provides compositions, apparatus and methods for generating a plurality of concatemer template molecules immobilized on a support for conducting massively parallel sequencing runs.

BACKGROUND

[0004] Massively parallel sequencing methods have applications in biomedical research and healthcare settings as they allow for analyzing large quantities of biological samples. However, when conducting massively parallel sequencing runs, it is challenging to achieve high sequencing quality across the entire length of library sequences of large size, e.g., larger than 200 bases, because the sequencing quality drops in part due to a decrease in signal intensity. Achieving high sequencing quality in pairwise sequencing runs is particularly challenging because the signal intensity can drop precipitously when sequencing the second strand. Thus, there exists a need for improved methods for performing massively parallel sequencing.

SUMMARY

[0005] In some aspects, provided herein is a method for generating and sequencing a plurality of compact DNA nanoballs immobilized to a support, comprising: providing a support comprising: a plurality of capture primers immobilized to the support, wherein individual capture primers comprise a 3’ extendible end; a plurality of pinning primers immobilized to the support, wherein individual pinning primers comprise a 3’ non-extendible end; and a plurality of covalently closed circular polynucleotide molecules, wherein individual covalently closed circular polynucleotide molecules are hybridized to individual capture primers, thereby forming a plurality of immobilized circular molecule-capture primer duplexes; contacting the plurality of immobilized circular molecule-capture primer duplexes with a plurality of soluble amplification primers under a condition suitable for hybridizing at least one soluble amplification primer to an individual immobilized circular molecule-capture primer duplex thereby forming a plurality of immobilized circular molecule-capture primer duplexes; conducting a rolling circle amplification (RCA) reaction on the plurality of immobilized circular molecule-capture primer duplexes of step (b) in the presence of a plurality of compaction oligonucleotides, thereby generating a plurality of compact DNA nanoballs immobilized to the support, wherein individual compact DNA nanoballs comprise (i) a concatemer template molecule generated by RCA-extension of an immobilized capture primer and (ii) at least one concatemer template molecule generated by RCA-extension of a soluble amplification primer, wherein at least a portion of individual compact DNA nanoballs is hybridized to a pinning primer, thereby generating a plurality of compact DNA nanoballs immobilized to the support; removing the plurality of covalently closed circular polynucleotide molecules and retaining the plurality of compact DNA nanoballs; and sequencing the plurality of the compact DNA nanoballs.

[0006] In some embodiments, the support comprises glass, plastic and/or a polymer material. In some embodiments, the support is passivated with at least one hydrophilic polymer coating.

[0007] In some embodiments, the plurality of capture primers and the plurality of pinning primers are covalently joined to the at least one hydrophilic polymer coating. In some embodiments, the at least one hydrophilic polymer coating has a water contact angle of no more than 45 degrees.

[0008] In some embodiments, the plurality of capture primers are immobilized to the support at random locations or immobilized to the support at pre-determined locations.

[0009] In some embodiments, the plurality of pinning primers are immobilized to the support at random locations or immobilized to the support at pre-determined locations.

[0010] In some embodiments, the plurality of capture primers are immobilized to the support at a density of about 10² - 10¹⁵ capture primers per mm². [0011] In some embodiments, the plurality of pinning primers are immobilized to the support at a density of about 10² - 10¹⁵ pinning primers per mm².

[0012] In some embodiments, the support lacks partitions or barriers that separate regions of the support.

[0013] In some embodiments, the plurality of covalently closed circular polynucleotide molecules comprises RNA or DNA, optionally wherein the DNA comprises complementary DNA (cDNA).

[0014] In some embodiments, individual covalently closed circular polynucleotide molecules comprise a sequence of interest that is 200 - 2000 nucleotides in length.

[0015] In some embodiments, individual covalently closed circular polynucleotide molecules comprise a sequence of interest and lack a universal adaptor sequence.

[0016] In some embodiments, individual covalently closed circular polynucleotide molecules comprise a sequence of interest and any one or any combination of two or more of: a universal sequence for binding a pinning primer or a complementary sequence thereof, a universal sequence for binding a capture primer or a complementary sequence thereof, at least one universal sequence for binding a first sequencing primer or a complementary sequence thereof, at least one universal sequence for binding a second sequencing primer or a complementary sequence thereof, at least one universal sequence for binding a soluble amplification primer or a complementary sequence thereof and/or a universal sequence for binding a compaction oligonucleotide or a complementary sequence thereof.

[0017] In some embodiments, individual soluble amplification primers bind to any one or more of: the sequence of interest, the universal sequence for binding a pinning primer or a complementary sequence thereof, the universal sequence for binding a capture primer or a complementary sequence thereof, the universal sequence for binding a first sequencing primer or a complementary sequence thereof, the universal sequence for binding a second sequencing primer or a complementary sequence thereof, the universal sequence for binding a compaction oligonucleotide or a complementary sequence thereof; or a combination thereof.

[0018] In some embodiments, individual covalently closed circular polynucleotide molecules are further hybridized to 1, 2, 3, 4, 5, 6, 7, 8, 9 or 10 soluble amplification primers. [0019] In some embodiments, the at least one soluble amplification primer is hybridized to any one or more of: the sequence of interest, the universal sequence for binding a capture primer or a complementary sequence thereof, the universal sequence for binding a pinning primer or a complementary sequence thereof, the universal sequence for binding a first sequencing primer, the universal sequence for binding a second sequencing primer, and/or the universal sequence for binding a compaction oligonucleotide or a complementary sequence thereof; or a combination thereof.

[0020] In some embodiments, the RCA reaction comprises contacting the plurality of the immobilized circular molecule-capture primer duplexes with a plurality of strand displacing polymerases, and a plurality of nucleotides.

[0021] In some embodiments, the plurality of nucleotides comprises at least one nucleotide having a scissile moiety that can be cleaved to generate an abasic site in the immobilized compact DNA nanoball. In some embodiments, the at least one nucleotide having a scissile moiety comprises uridine, 8-oxo-7,8-dihydrogunine or deoxyinosine. [0022] In some embodiments, the plurality of compaction oligonucleotides comprises at least a first and a second compaction oligonucleotide, wherein the first compaction oligonucleotide comprises a first binding region that hybridizes to a first portion of the concatemer template molecule generated, and a second binding region that hybridizes to a second portion of the same concatemer template molecule thereby pulling together distal portions of the concatemer molecule causing compaction of the concatemer template molecule, and the second compaction oligonucleotide comprises a first binding region that hybridizes to a first portion of the concatemer template molecule generated, and a second binding that hybridizes to a second portion of the same concatemer template molecule thereby pulling together distal portions of the concatemer molecule causing compaction of the concatemer template molecule.

[0023] In some embodiments, the first and the second compaction oligonucleotides comprise the same sequence or different sequences.

[0024] In some embodiments, the plurality of compact DNA nanoballs are immobilized to the support at a high density, wherein at least some of the immobilized compact DNA nanoballs comprise nearest neighbor compact DNA nanoballs that touch each other and/or overlap each other when viewed from any angle of the support including above, below or side views of the support.

[0025] In some embodiments, the sequencing comprises contacting individual compact DNA nanoballs with a plurality of sequencing primers, a plurality of sequencing polymerases and a plurality of detectably labeled multivalent molecules, individual detectably labeled multivalent molecules comprising a core and a plurality of nucleotide arms and wherein individual polymer arms comprise at least one nucleotide moiety. [0026] In some embodiments, the sequencing comprises: binding the concatemer template molecules with a plurality of sequencing primers, a plurality of sequencing polymerases, and a plurality of detectably labeled multivalent molecules, and/or binding the concatemer template molecules with a plurality of sequencing primers, a plurality of sequencing polymerases, and a plurality of detectably labeled multivalent molecules, thereby generating a compact DNA nanoball immobilized to the support that emits a detectable signal.

[0027] In some embodiments, individual detectably labeled multivalent molecules comprise a core; and a plurality of nucleotide arms comprising a core attachment moiety, a spacer, a linker, and a nucleotide moiety, wherein the core is attached to the plurality of nucleotide arms via their core attachment moiety, wherein the core attachment moiety is attached to the spacer, wherein the spacer is attached to the linker, and wherein the linker is attached to the nucleotide moiety.

[0028] In some embodiments, individual nucleotide arms comprise a core attachment moiety, a spacer and a nucleotide moiety, wherein the core is attached to the plurality of nucleotide arms via their core attachment moiety, wherein the core attachment moiety is attached to the spacer, wherein the spacer is attached to the nucleotide moiety.

[0029] In some embodiments, the linker comprises an aliphatic chain having 2-6 subunits or an oligo ethylene glycol chain having 2-6 subunits.

[0030] In some embodiments, the plurality of nucleotide arms attached to an individual core has the same type of nucleotide moiety selected from the group consisting of dATP, dGTP, dCTP, dTTP and dUTP.

[0031] In some embodiments, individual detectably labeled multivalent molecules have the same type of nucleotide moiety selected from the group consisting of dATP, dGTP, dCTP, dTTP and dUTP.

[0032] In some embodiments, the plurality of detectably labeled multivalent molecules comprises a mixture of two or more types of detectably labeled multivalent molecules, individual types of detectably labeled multivalent molecules having nucleotide moieties selected from the group consisting of dATP, dGTP, dCTP, dTTP and dUTP.

[0033] In some embodiments, individual detectably labeled multivalent molecules in the plurality comprise a core attached to a fluorophore, a nucleotide arm attached to a fluorophore, and/or a nucleotide moiety attached to a fluorophore.

[0034] In some embodiments, the sequencing further comprises contacting individual compact DNA nanoballs with a plurality of non-catalytic divalent cations that inhibit polymerase-catalyzed nucleotide incorporation, wherein the non-catalytic divalent cations comprise strontium, calcium or barium.

[0035] In some embodiments, the sequencing comprises: binding a first sequencing primer, a first sequencing polymerase, and a first multivalent molecule to a first portion of the concatemer template molecule thereby forming a first binding complex, wherein a first nucleotide moiety of the first multivalent molecule binds to the first sequencing polymerase; and binding a second sequencing primer, a second sequencing polymerase, and the first multivalent molecule to a second portion of the same concatemer template molecule thereby forming a second binding complex, wherein a second nucleotide moiety of the first multivalent molecule binds to the second sequencing polymerase, and wherein the first and second binding complexes which include the same multivalent molecule form an avidity complex.

[0036] In some embodiments, the sequencing comprises: contacting different portions of the concatemer template molecule with a first plurality of sequencing polymerases and a first plurality of sequencing primers to form at least a first and a second polymerase complex on the same concatemer template molecule; contacting a plurality of detectably labeled multivalent molecules with the at least first and second polymerase complexes on the same concatemer template molecule to bind a single multivalent molecule to the first and the second polymerase complexes, wherein at least a first nucleotide moiety of the single multivalent molecule is bound to the first polymerase complex thereby forming a first binding complex, and wherein at least a second nucleotide moiety of the single multivalent molecule is bound to the second polymerase complex thereby forming a second binding complex, wherein the contacting is conducted under a condition suitable to inhibit polymerase-catalyzed incorporation of the bound first and second nucleotide moieties in the first and second binding complexes, and wherein the first and second binding complexes which are bound to the same multivalent molecule form an avidity complex; detecting the first and the second binding complexes on the same concatemer template molecule; and identifying the first nucleotide moiety in the first binding complex thereby determining the sequence of the first portion of the concatemer template molecule, and identifying the second nucleotide moiety in the second binding complex thereby determining the sequence of the second portion of the concatemer template molecule.

[0037] In some embodiments, contacting individual compact DNA nanoballs with a plurality of labeled nucleotides comprises: binding the concatemer template molecule of step (c) with a plurality of sequencing primers, a plurality of sequencing polymerases, and a plurality of detectably labeled nucleotides, and binding the concatemer template molecule of step (c) with a plurality of sequencing primers, a plurality of sequencing polymerases, and a plurality of detectably labeled nucleotides, thereby generating a compact DNA nanoball immobilized to the support that emits a detectable signal.

[0038] In some embodiments, individual detectably labeled nucleotides in the plurality comprise an aromatic base, a five-carbon sugar, and 1-10 phosphate groups.

[0039] In some embodiments, the plurality of detectably labeled nucleotides comprises one type of nucleotide selected from the group consisting of dATP, dGTP, dCTP, dTTP and dUTP.

[0040] In some embodiments, the plurality of detectably labeled nucleotides comprises two or more types of nucleotides selected from the group consisting of dATP, dGTP, dCTP, dTTP and dUTP.

[0041] In some embodiments, at least one detectably labeled nucleotide in the plurality is labeled with a fluor ophore.

[0042] In some embodiments, at least one nucleotide in the plurality lacks a fluorophore label.

[0043] In some embodiments, at least one of the detectably labeled nucleotides comprises a removable chain terminating moiety attached to the 3’ carbon position of the sugar group, wherein the removable chain terminating moiety comprises an alkyl group, an alkenyl group, an alkynyl group, an allyl group, an aryl group, a benzyl group, an azide group, an azido group, an O-azidomethyl group, an amine group, an amide group, a keto group, an isocyanate group, a phosphate group, a thio group, a disulfide group, a carbonate group, a urea group, an acetal group or a silyl group, and wherein the removable chain terminating moiety is cleavable with a chemical compound to generate an extendible 3 ’OH moiety on the sugar group.

[0044] In some embodiments, the sequencing further comprises contacting individual compact DNA nanoballs with a plurality of catalytic divalent cations that promote polymerase-catalyzed nucleotide incorporation, wherein the catalytic divalent cations comprise magnesium or manganese.

[0045] In another aspect, provided herein is method for generating a plurality of compact DNA nanoballs, comprising: providing a support comprising: a plurality of capture primers immobilized to the support, wherein individual capture primers comprise a 3’ extendible end; a plurality of pinning primers immobilized to the support, wherein individual pinning primers comprise a 3’ non-extendible end; and a plurality of covalently closed circular polynucleotide molecules, wherein individual covalently closed circular polynucleotide molecules are hybridized to individual capture primers, thereby forming a plurality of immobilized circular molecule-capture primer duplexes; contacting the plurality of immobilized circular molecule-capture primer duplexes with a plurality of soluble amplification primers under a condition suitable for hybridizing at least one soluble amplification primer to individual immobilized circular molecule-capture primer duplexes; conducting a rolling circle amplification (RCA) reaction on the plurality of immobilized circular molecule-capture primer duplexes of step (b) in the presence of a plurality of compaction oligonucleotides, thereby generating a plurality of compact DNA nanoballs immobilized to the support, wherein individual compact DNA nanoballs comprise a concatemer template molecule generated by RCA-extension of an immobilized capture primer and at least one concatemer template molecule generated by RCA-extension of a soluble amplification primer, wherein at least a portion of individual compact DNA nanoballs is hybridized to an immobilized pinning primer; removing the plurality of covalently closed circular polynucleotide molecules and retaining the plurality of compact DNA nanoballs immobilized to the support.

[0046] In some embodiments, the method further comprises sequencing the plurality of immobilized compact DNA nanoballs.

BRIEF DESCRIPTION OF THE DRAWINGS

[0047] The features of the disclosure are set forth with particularity in the appended claims. A better understanding of the features and advantages of the present disclosure will be obtained by reference to the following detailed description that sets forth illustrative embodiments, in which the principles of the disclosure are utilized, and the accompanying drawings of which: [0048] FIG. 1 is a schematic of various exemplary configurations of multivalent molecules. Left (Class I): schematics of multivalent molecules having a “starburst” or “helter-skelter” configuration. Center (Class II): a schematic of a multivalent molecule having a dendrimer configuration. Right (Class III): a schematic of multiple multivalent molecules formed by reacting streptavidin with 4-arm or 8-arm PEG-NHS with biotin and dNTPs. Nucleotide moieties are designated ‘N’, biotin is designated ‘B’, and streptavidin is designated ‘SA’. [0049] FIG. 2 is a schematic of an exemplary multivalent molecule comprising a generic core attached to a plurality of nucleotide-arms.

[0050] FIG. 3 is a schematic of an exemplary multivalent molecule comprising a dendrimer core attached to a plurality of nucleotide-arms. [0051] FIG. 4 is a schematic of an exemplary multivalent molecule comprising a core attached to a plurality of nucleotide-arms, where the nucleotide arms comprise biotin, spacer, linker and a nucleotide moiety.

[0052] FIG. 5 is a schematic of an exemplary nucleotide-arm comprising a core attachment moiety, spacer, linker and nucleotide moiety.

[0053] FIG. 6 shows the chemical structure of an exemplary spacer (top), and the chemical structures of various exemplary linkers, including an 11 -atom Linker, 16-atom Linker, 23- atom Linker and an N3 Linker (bottom).

[0054] FIG. 7 shows the chemical structures of various exemplary linkers, including Linkers 1-9.

[0055] FIG. 8 shows the chemical structures of various exemplary linkers joined/attached to nucleotide moieties.

[0056] FIG. 9 shows the chemical structures of various exemplary linkers joined/attached to nucleotide moieties.

[0057] FIG. 10 shows the chemical structures of various exemplary linkers joined/attached to nucleotide moieties.

[0058] FIG. 11 shows the chemical structure of an exemplary biotinylated nucleotide-arm. In this non-limiting example, the nucleotide moiety is connected to the linker via a propargyl amine attachment at the 5 position of a pyrimidine base or the 7 position of a purine base. [0059] FIG. 12 is a schematic of an exemplary low binding support comprising a glass substrate and alternating layers of hydrophilic coatings which are covalently or non- covalently adhered to the glass, and which further comprises chemically-reactive functional groups that serve as attachment sites for oligonucleotide primers (e.g., capture oligonucleotides). The support can be made of any material such as glass, plastic or a polymer material.

[0060] FIG. 13A is a pair of schematics of exemplary supports having a plurality of nucleic acid capture primers arranged thereon, (i) depicts a schematic of an exemplary support having a plurality of nucleic acid capture primers arranged on the support in a nonpredetermined and random manner. The capture primers can be attached to the support such that some of the nearest neighbor capture primers touch each other and/or overlap each other when viewed from any angle of the support including above, below or side views of the support. The dotted lines that surround the four capture primers represent nearest neighbor capture primers that touch each other, (ii) depicts a schematic of the same support shown in (i), where individual nucleic acid capture primers are attached to a nucleic acid template molecule having one of four different batch sequences. The different batch sequences of the template molecules are represented by horizontal stripes, vertical dashed, brick or solid black. The template molecules can attach to the support (e.g., via attachment to the capture primers) such that some of the nearest neighbor template molecules touch each other and/or overlap each other when viewed from any angle of the support including above, below or side views of the support. The dotted lines that surround the four template molecules represent nearest neighbor template molecules that touch each other.

[0061] FIG. 13B is a pair of schematics of exemplary supports having a plurality of template molecules immobilized thereon, (iii) is a schematic of an exemplary support having a plurality of template molecules immobilized to the support (e.g., via attachment to the capture primers) where the template molecules are arranged on the support in a predetermined manner. The template molecule comprise one of four different batch sequences. The different batch sequences of the template molecules are represented by horizontal stripes, vertical dashed, brick or solid black. For example, the template molecules can be immobilized to the support to form spots arranged in row and columns, (iv) is a schematic of an exemplary support having a plurality of template molecules immobilized to the support (e.g., via attachment to the capture primers) where the template molecules are arranged on the support in a predetermined manner. The template molecule comprises one of four different batch sequences. The different batch sequences of the template molecules are represented by horizontal stripes, vertical dashed, brick or solid black. For example, the template molecules can be immobilized to the support to form stripes.

[0062] FIG. 14A is a schematic of a guanine tetrad (e.g., G-tetrad).

[0063] FIG. 14B is a schematic of an exemplary intramolecular G-quadruplex structure. [0064] FIG. 15 is a schematic showing an exemplary workflow where a covalently closed circular library molecule is distributed onto a support comprising an immobilized capture primer and an immobilized pinning primer. The covalently closed circular library molecule can comprise: a surface capture primer binding site sequence (130), a right sample index sequence (170), a reverse sequencing primer binding site sequence (150), an insert (110), a forward sequencing primer binding site sequence (140), a left sample index sequence (160), and a surface pinning primer binding site sequence (120). The surface capture primer binding site sequence (130) of the covalently closed circular library molecule can hybridize to the immobilized capture primer thereby generating an immobilized circular molecule-capture primer duplex. The covalently closed circular library molecule shown in FIG. 15 can be generated by the workflow shown in FIG. 25 using padlock probes. Alternatively, the covalently closed circular library molecule shown in FIG. 15 can be generated by the workflow shown in FIGS. 26A-26C using single-stranded splint strands (200). As a further alternative, or in addition, the covalently closed circular library molecule shown in FIG. 15 can be generated by the workflow shown in FIGS. 27A-27C using double-stranded adaptors (500).

[0065] FIG. 16 is a schematic showing an exemplary workflow where the immobilized circular molecule-capture primer duplex shown in FIG. 15 is hybridized with a soluble amplification primer which can hybridize to any universal adaptor sequence (e.g., 150) in the covalently closed circular library molecule thereby generating an immobilized circular molecule-capture primer duplex. The immobilized circular molecule-capture primer duplex is subjected to a rolling circle amplification (RCA) reaction, thereby generating a compact DNA nanoball immobilized to the support. The compact DNA nanoball can comprise (i) a concatemer template molecule generated by RCA-extension of an immobilized capture primer and (ii) at least one concatemer template molecule generated by RCA-extension of a soluble amplification primer. The rolling circle amplification reaction can be conducted in the presence of a plurality of compaction oligonucleotides.

[0066] FIG. 17 is a schematic showing an exemplary workflow where the immobilized circular molecule-capture primer duplex shown in FIG. 15 is hybridized with first and second soluble amplification primers which can hybridize to any universal adaptor sequence (e.g., a reverse sequencing primer binding site sequence (150) and/or a forward sequencing primer binding site sequence (140)) in the covalently closed circular library molecule thereby generating an immobilized circular molecule-capture primer duplex. The immobilized circular molecule-capture primer duplex is subjected to a rolling circle amplification (RCA) reaction, thereby generating a compact DNA nanoball immobilized to the support. The compact DNA nanoball can comprise (i) a concatemer template molecule generated by RCA- extension of an immobilized capture primer and (ii) at least one concatemer template molecule generated by RCA-extension of a soluble amplification primer. The rolling circle amplification reaction can be conducted in the presence of a plurality of compaction oligonucleotides.

[0067] FIG. 18 is a schematic showing an exemplary workflow where the immobilized circular molecule-capture primer duplex shown in FIG. 15 is hybridized with four soluble amplification primers including a first, a second, a third and a fourth soluble amplification primer which can hybridize to any universal adaptor sequence (e.g., a reverse sequencing primer binding site sequence (150) and/or a forward sequencing primer binding site sequence (140)) in the covalently closed circular library molecule thereby generating a immobilized circular molecule-capture primer duplex. The immobilized circular molecule-capture primer duplex can be subjected to a rolling circle amplification (RCA) reaction, thereby generating a compact DNA nanoball immobilized to the support. The compact DNA nanoball can comprise (i) a concatemer template molecule generated by RCA-extension of an immobilized capture primer and (ii) at least one concatemer template molecule generated by RCA- extension of a soluble amplification primer. The rolling circle amplification reaction can be conducted in the presence of a plurality of compaction oligonucleotides.

[0068] FIG. 19 is a schematic showing an exemplary workflow where a covalently closed circular library molecule is distributed onto a support comprising an immobilized capture primer and an immobilized pinning primer. The covalently closed circular library molecule can comprise a sequence of interest (e.g., an insert (110)) and a forward sequencing primer binding site sequence (140). The covalently closed circular library molecule can lack a surface capture primer binding site sequence (130). The covalently closed circular library molecule can lack a surface pinning primer binding site sequence (120). The immobilized capture primer can comprise a target-specific sequence that can hybridize to a portion of the sequence of interest of the covalently closed circular polynucleotide molecule thereby generating an immobilized circular molecule-capture primer duplex. The immobilized circular molecule-capture primer duplex is hybridized with a soluble amplification primer which can hybridize to a portion of the sequence of interest in the covalently closed circular library molecule thereby generating a immobilized circular molecule-capture primer duplex. The immobilized circular molecule-capture primer duplex can be subjected to a rolling circle amplification (RCA) reaction, thereby generating a compact DNA nanoball immobilized to the support. The compact DNA nanoball can comprise (i) a concatemer template molecule generated by RCA-extension of an immobilized capture primer and (ii) at least one concatemer template molecule generated by RCA-extension of a soluble amplification primer. The RCA reaction can be conducted in the presence of a plurality of compaction oligonucleotides. The immobilized pinning primer can comprise a target-specific sequence that can hybridize to a portion of the sequence of interest of the concatemer template molecules, wherein the sequences of the immobilized capture primer and the immobilized pinning primer are different.

[0069] FIG. 20 is a schematic showing an exemplary workflow where a covalently closed circular polynucleotide molecule is distributed onto a support comprising an immobilized capture primer and an immobilized pinning primer. The covalently closed circular polynucleotide molecule can comprise a sequence of interest (e.g., an insert(HO)) and can lack a universal adaptor sequence. The covalently closed circular polynucleotide molecule can lack a surface capture primer binding site sequence (130). The immobilized capture primer can comprise a target-specific sequence that can hybridize to a portion of the sequence of interest of the covalently closed circular library molecule thereby generating an immobilized circular molecule-capture primer duplex. The immobilized circular moleculecapture primer duplex is hybridized with a soluble amplification primer which can hybridize to a portion of the sequence of interest in the covalently closed circular library molecule thereby generating an immobilized circular molecule-capture primer duplex. The immobilized circular molecule-capture primer duplex can be subjected to a rolling circle amplification (RCA) reaction, thereby generating a compact DNA nanoball immobilized to the support. The compact DNA nanoball can comprise (i) a concatemer template molecule generated by RCA-extension of an immobilized capture primer and (ii) at least one concatemer template molecule generated by RCA-extension of a soluble amplification primer. The rolling circle amplification reaction can be conducted in the presence of a plurality of compaction oligonucleotides. The immobilized pinning primer can comprise a target-specific sequence that can hybridize to a portion of the sequence of interest of the concatemer template molecules, wherein the sequences of the immobilized capture primer and the immobilized pinning primer are different.

[0070] FIG. 21 is a schematic showing an exemplary concatemer template molecule generated from RCA-extension of an immobilized capture primer wherein at least a portion of the concatemer template molecule is hybridized to an immobilized pinning primer. The concatemer template molecule can be generated by conducting a workflow shown in any of FIGS. 15-18.

[0071] FIG. 22 shows two histograms that plot normalized intensities during pairwise sequencing of compact DNA nanoballs (e.g., polonies) generated by the methods described herein. FIG. 22A compares normalized intensities during a forward sequencing run (Rl) of compact DNA nanoballs generated using 1 or 3 soluble amplification primers. FIG. 22B compares normalized intensities during a reverse sequencing run (R2) of compact DNA nanoballs generated using 1 or 3 soluble amplification primers.

[0072] FIG. 23 shows two boxplots of quality scores at each base position during pairwise sequencing of compact DNA nanoballs (e.g., polonies) generated by the methods described herein. The x-axis indicates the base position in the forward reads. The y-axis indicates the quality scores. FIG. 23A shows the quality scores during a forward sequencing run (Rl) of compact DNA nanoballs generated using 1 soluble amplification primer. FIG. 23B shows the quality scores during a forward sequencing run (Rl) of compact DNA nanoballs generated using 3 soluble amplification primers.

[0073] FIG. 24 shows two boxplots of quality scores at each base position during pairwise sequencing of compact DNA nanoballs (e.g., polonies) generated by the methods described herein. The x-axis indicates the base position in the reverse reads. The y-axis indicates the quality scores. FIG. 24A shows the quality scores during a reverse sequencing run (R2) of compact DNA nanoballs generated using 1 soluble amplification primer. FIG. 24B shows the quality scores during a reverse sequencing run (R2) of compact DNA nanoballs generated using 3 soluble amplification primers. FIGS. 23A and 24A show quality scores from forward (FIG. 23 A) and reverse (FIG. 24A) pairwise sequencing of the same experiment. FIGS. 23B and 24B show quality scores from forward (FIG. 23B) and reverse (FIG. 24B) pairwise sequencing of the same experiment.

[0074] FIG. 25 is a schematic showing an exemplary workflow where a target sequence of interest is hybridized with a padlock probe thereby forming a circularized padlock probe with a nick or gap. The exemplary padlock probe can comprise: a surface pinning primer binding site sequence (120) (e.g., a batch-specific surface pinning primer binding site sequence); a left sample index sequence (160); a forward sequencing primer binding site sequence (140) (e.g., a batch-specific forward sequencing primer binding site sequence); a sequence of interest (e.g., an insert (110)); a reverse sequencing primer binding site sequence (150) (e.g., a batch-specific reverse sequencing primer binding site sequence); a right sample index sequence (170); a surface capture primer binding site sequence (130) (e.g., a batch-specific surface capture primer binding site sequence); and an optional unique identification sequence (e.g., UMI). The nick or gap can be enzymatically closed to generate a covalently closed padlock probe.

[0075] FIG. 26A is a schematic of an exemplary workflow of a linear single stranded library molecule (100) hybridizing with a single-stranded splint molecule/ strand (ss-splint strand) (200) thereby circularizing the library molecule to form a library-splint complex (300) with a nick. The exemplary library molecule (100) can comprise: a surface pinning primer binding site sequence (120) (e.g., a batch-specific surface pinning primer binding site sequence); a left sample index sequence (160); a forward sequencing primer binding site sequence (140) (e.g., a batch-specific forward sequencing primer binding site sequence); a sequence of interest (e.g., an insert (110)); a reverse sequencing primer binding site sequence (150) (e.g., a batch-specific reverse sequencing primer binding site sequence); a right sample index sequence (170); a surface capture primer binding site sequence (130) (e.g., a batchspecific surface capture primer binding site sequence); and an optional unique identification sequence (e.g., UMI). The single-stranded splint strand (200) can comprise a first region (210) that hybridizes with the surface pinning primer binding site sequence (120) of the linear single-stranded library molecule (100), and a second region (220) that hybridizes with the surface capture primer binding site sequence (130) of the linear single-stranded library molecule (100).

[0076] FIG. 26B is a schematic of an exemplary workflow of a library-splint complex (300) shown in FIG. 26A where the nick is enzymatically ligated to generate a covalently closed circular library molecule (400) (also referred to herein as a “covalently closed circular polynucleotide molecule”).

[0077] FIG. 26C is a schematic showing an exemplary linear single-stranded library molecule (100) hybridizing with a single-stranded splint molecule/ strand (ss-splint strand) (200) thereby circularizing the library molecule to form a library-splint complex (300) with a nick. The library molecule (100) can comprise: a first left junction adaptor sequence (121); a surface pinning primer binding site sequence (120); a second left junction adaptor sequence (125); a left sample index sequence (160); a third left junction adaptor sequence (165); a forward sequencing primer binding site sequence (140); a fourth left junction adaptor sequence (145); a sequence of interest (e.g., an insert; (110)); a fourth right junction adaptor sequence (155); a reverse sequencing primer binding site sequence (150); a third right junction adaptor sequence (175); a right sample index sequence (170); a second right junction adaptor sequence (135); a surface capture primer binding site (130); and a first right junction adaptor sequence (131). The single-stranded splint strand (ss-splint strand) (200) comprises a first region (210) that hybridizes with one end of the linear single stranded library molecule (100) including at least a portion of the surface pinning primer binding site sequence (120) and/or at least a portion of the first left junction adaptor sequence (121). The single-stranded splint strand (200) comprises a second region (220) that hybridizes with the other end of the linear single-stranded library molecule (100) including at least a portion of the surface capture primer binding site sequence (130) and/or at least a portion of the first right junction adaptor sequence (131). For the sake of simplicity, the library-splint complex (300) does not show any of the junction adaptors. The skilled artisan will recognize that the library-splint complex (300) can include any one or any combination of two or more of the junction adaptors that are depicted in the exemplary library molecule (100). [0078] FIG. 27A is a schematic of an exemplary workflow of a linear single-stranded library molecule (100) hybridizing with a double-stranded adaptor (ds-splint adaptor) (500) thereby circularizing the library molecule to form a library-splint complex (800) with two nicks. The exemplary library molecule (100) can comprise: a surface pinning primer binding site sequence (120) (e.g., a batch-specific pinning primer binding site sequence); a left sample index sequence (160); a forward sequencing primer binding site sequence (140) (e.g., a batchspecific forward sequencing primer binding site sequence); a sequence of interest (e.g., an insert (110)); a reverse sequencing primer binding site sequence (150) (e.g., a batch-specific reverse sequencing primer binding site sequence); a right sample index sequence (170); and a surface capture primer binding site sequence (130) (e.g., a batch-specific surface capture primer binding site sequence); and an optional unique identification sequence (e.g., UMI). The double-stranded adaptor can comprise a first splint strand (600) hybridized to a second splint strand (700). In the double-stranded adaptor, the first splint strand (600) comprises a first region (620), an internal region (610), and a second region (630), wherein the internal region (610) of the first splint strand is hybridized to the second splint strand (700). The second splint strand (700) can comprise a first, a second, and a third subregions, and the internal region (610) of the first splint strand (600) can comprise a fourth, a fifth, and a sixth subregions. In some embodiments, the first region of the first splint strand (620) can hybridize to at least a portion of the surface pinning primer binding site sequence (120) of a single-stranded nucleic acid library molecule (100), and the second region of the first splint strand (630) can hybridize to at least a portion of the surface capture primer binding site sequence (130) of the same single-stranded nucleic acid library molecule (100).

[0079] FIG. 27B is a schematic of an exemplary workflow of a library-splint complex (800) shown in FIG. 27A where the two nicks are enzymatically ligated to generate a covalently closed circular library molecule (900) (also referred to herein as a “covalently closed circular polynucleotide molecule”).

[0080] FIG. 27C is a schematic showing an exemplary linear single-stranded library molecule (100) hybridizing with a double-stranded splint molecule (ds-splint adaptor) (200) thereby circularizing the library molecule to form a library-splint complex (500) with two nicks (solid arrowheads). The library molecule (100) can comprise: a first left junction adaptor sequence (121); a surface pinning primer binding site sequence (120); a second left junction adaptor sequence (125); a left sample index sequence (160); a third left junction adaptor sequence (165); a forward sequencing primer binding site sequence (140); a fourth left junction adaptor sequence (145); a sequence of interest (e.g., an insert; (HO)); a fourth right junction adaptor sequence (155); a reverse sequencing primer binding site sequence (150); a third right junction adaptor sequence (175); a right sample index sequence (170); a second right junction adaptor sequence (135); a surface capture primer binding site sequence (130); and a first right junction adaptor sequence (131). The double-stranded splint adaptor (500) comprises a first splint strand (600) having a first region (620) that hybridizes with one end of the linear single stranded library molecule (100) including at least a portion of the surface pinning primer binding site sequence (120) and/or at least a portion of the first left junction adaptor sequence (121). The double-stranded splint adaptor (500) comprises a first splint strand (600) having a second region (630) that hybridizes with the other end of the linear single-stranded library molecule (100) including at least a portion of the surface capture primer binding site sequence (130) and/or at least a portion of the first right junction adaptor sequence (131). The double-stranded splint adaptor (500) comprises a second splint strand (700) that is hybridized with an internal region (610) of the first splint strand (600). For the sake of simplicity, the library-splint complex (800) does not show any of the junction adaptors. The skilled artisan will recognize that the library-splint complex (800) can include any one or any combination of two or more of the junction adaptors that are present in the library molecule (100).

[0081] FIG. 28 is a graph showing the nucleotide base diversity of a right sample index sequence (170) including universal right sample index and a 3-mer random sequence (NNN). The graph shows a nucleotide diversity of the 3-mer random sequence (NNN) of approximately 30% for A and T base calls, and approximately 20% for C and G base calls. [0082] FIG. 29 is a graph showing the nucleotide base diversity of a left sample index sequence (160) which lacks a 3-mer random sequence (NNN). The graph shows a nucleotide diversity of approximately 40% for A and T base calls, approximately 15% for C base calls, and approximately 5% for G base calls.

[0083] FIG. 30 shows schematics of several embodiments of linear compaction oligonucleotides each comprising a first binding region, an intervening linker, and a second binding region. For instance, a compaction oligonucleotide can comprise a first binding region arranged in a 5’ to 3’ orientation and a second binding region arranged in a 5’ to 3’ orientation (i). Alternatively, or in addition, a compaction oligonucleotide can comprise a first binding region arranged in a 3’ to 5’ orientation and a second binding region arranged in a 3’ to 5’ orientation ( (ii). Alternatively, or in addition, a compaction oligonucleotide can comprise a first binding region arranged in a 3’ to 5’ orientation and a second binding region arranged in a 5’ to 3’ orientation (iii). Alternatively, or in addition, a compaction oligonucleotide can comprise a first binding region arranged in a 5’ to 3’ orientation and a second binding region arranged in a 3’ to 5’ orientation (iv). The 5’ to 3’ orientation of a binding region of a compaction oligonucleotide, or the 3’ to 5’ orientation of a binding region of a compaction oligonucleotide, refers to the orientation of the sugar-phosphate backbone of the binding region.

[0084] FIG. 31 A shows schematics of several embodiments of linear compaction oligonucleotides each comprising a first binding region, a first intervening linker, a second binding region, a second intervening linker, and a third binding region. For instance, a compaction oligonucleotide can comprise a first binding region arranged in a 5’ to 3’ orientation, a second binding region arranged in a 5’ to 3’ orientation, and a third binding region arranged in a 5’ to 3’ orientation i). Alternatively, or in addition, a compaction oligonucleotide can comprise a first binding region arranged in a 5’ to 3’ orientation, a second binding region arranged in a 5’ to 3’ orientation, and a third binding region arranged in a 3’ to 5’ orientation ii). Alternatively, or in addition, a compaction oligonucleotide can comprise a first binding region arranged in a 5’ to 3’ orientation, a second binding region arranged in a 3’ to 5’ orientation, and a third binding region arranged in a 3’ to 5’ orientation (iii). The 5’ to 3’ orientation of a binding region of a compaction oligonucleotide, or the 3’ to 5’ orientation of a binding region of a compaction oligonucleotide, refers to the orientation of the sugar-phosphate backbone of the binding region.

[0085] FIG. 31B shows schematics of several embodiments of linear compaction oligonucleotides each comprising a first binding region, a first intervening linker, a second binding region, a second intervening linker, and a third binding region. For instance, a compaction oligonucleotide can comprise a first binding region arranged in a 5’ to 3’ orientation, a second binding region arranged in a 3’ to 5’ orientation, and a third binding region arranged in a 5’ to 3’ orientation iv). Alternatively, or in addition, a compaction oligonucleotide can comprise a first binding region arranged in a 3’ to 5’ orientation, a second binding region arranged in a 5’ to 3’ orientation, and a third binding region arranged in a 5’ to 3’ orientation v). Alternatively, or in addition, a compaction oligonucleotide can comprise a first binding region arranged in a 3’ to 5’ orientation, a second binding region arranged in a 3’ to 5’ orientation, and a third binding region arranged in a 5’ to 3’ orientation (vi). The 5’ to 3’ orientation of a binding region of a compaction oligonucleotide, or the 3’ to 5’ orientation of a binding region of a compaction oligonucleotide, refers to the orientation of the sugar-phosphate backbone of the binding region. [0086] FIG. 31C shows schematics of several embodiments of linear compaction oligonucleotides each comprising a first binding region, a first intervening linker, a second binding region, a second intervening linker, and a third binding region. For instance, a compaction oligonucleotide can comprise a first binding region arranged in a 3’ to 5’ orientation, a second binding region arranged in a 5’ to 3’ orientation, and a third binding region arranged in a 5’ to 3’ orientation (vii). Alternatively, or in addition, a compaction oligonucleotide can comprise a first binding region arranged in a 3’ to 5’ orientation, a second binding region arranged in a 3’ to 5’ orientation, and a third binding region arranged in a 5’ to 3’ orientation (viii). Alternatively, or in addition, a compaction oligonucleotide can comprise a first binding region arranged in a 3’ to 5’ orientation, a second binding region arranged in a 5’ to 3’ orientation, and a third binding region arranged in a 3’ to 5’ orientation (ix). The 5’ to 3’ orientation of a binding region of a compaction oligonucleotide, or the 3’ to 5’ orientation of a binding region of a compaction oligonucleotide, refers to the orientation of the sugar-phosphate backbone of the binding region.

[0087] FIG. 32A shows schematics of several embodiments of compaction oligonucleotides each comprising three binding arms linked together by at least one inner intervening linker, wherein individual binding arms comprise a binding region. For instance, a compaction oligonucleotide can comprise: (1) an inner intervening linker and a first binding region arranged in a 5’ to 3’ orientation where the 3’ end of the first binding region is directed away from the inner intervening linker; (2) an inner intervening linker and a second binding region arranged in a 5’ to 3’ orientation where the 3’ end of the second binding region is directed away from the inner intervening linker; and (3) an inner intervening linker and a third binding region arranged in a 5’ to 3’ orientation where the 3’ end of the third binding region is directed away from the inner intervening linker (i). Alternatively, or in addition, a compaction oligonucleotide can comprise: (1) an inner intervening linker and a first binding region arranged in a 3’ to 5’ orientation where the 5’ end of the first binding region is directed away from the inner intervening linker; (2) an inner intervening linker and a second binding region arranged in a 3’ to 5’ orientation where the 5’ end of the second binding region is directed away from the inner intervening linker; and (3) an inner intervening linker and a third binding region arranged in a 3’ to 5’ orientation where the 5’ end of the third binding region is directed away from the inner intervening linker (ii). The 5’ to 3’ orientation of a binding region of a compaction oligonucleotide, or the 3’ to 5’ orientation of a binding region of a compaction oligonucleotide, refers to the orientation of the sugar-phosphate backbone of the binding region. [0088] FIG. 32B shows schematics of several embodiments of compaction oligonucleotides each comprising three binding arms linked together by at least one inner intervening linker, wherein individual binding arms comprise a binding region. For instance, a compaction oligonucleotide can comprise: (1) an inner intervening linker and a first binding region arranged in a 5’ to 3’ orientation where the 3’ end of the first binding region is directed away from the inner intervening linker; (2) an inner intervening linker and a second binding region arranged in a 5’ to 3’ orientation where the 3’ end of the second binding region is directed away from the inner intervening linker; and (3) an inner intervening linker and a third binding region arranged in a 3’ to 5’ orientation where the 5’ end of the third binding region is directed away from the inner intervening linker (iii). Alternatively, or in addition, a compaction oligonucleotide can comprise: (1) an inner intervening linker and a first binding region arranged in a 5’ to 3’ orientation where the 3’ end of the first binding region is directed away from the inner intervening linker; (2) an inner intervening linker and a second binding region arranged in a 3’ to 5’ orientation where the 5’ end of the second binding region is directed away from the inner intervening linker; and (3) an inner intervening linker and a third binding region arranged in a 3’ to 5’ orientation where the 5’ end of the third binding region is directed away from the inner intervening linker (iv). The 5’ to 3’ orientation of a binding region of a compaction oligonucleotide, or the 3’ to 5’ orientation of a binding region of a compaction oligonucleotide, refers to the orientation of the sugar-phosphate backbone of the binding region.

[0089] FIG. 33 shows a schematic of an embodiment of a compaction oligonucleotide comprising three binding arms linked together by at least one inner intervening linker, wherein individual binding arms comprise a first binding region, an intervening linker, and a second binding region. A compaction oligonucleotide can comprise three binding arms where each binding arm comprises: an inner intervening linker, a first binding region arranged in a 5’ to 3’ orientation, an intervening linker, and a second binding region arranged in a 5’ to 3’ direction, where the 3’ end of each of the first and second binding region is directed away from the inner intervening linker. The 5’ to 3’ orientation of a binding region of a compaction oligonucleotide, or the 3’ to 5’ orientation of a binding region of a compaction oligonucleotide, refers to the orientation of the sugar-phosphate backbone of the binding region.

[0090] FIG. 34 shows schematics of several embodiments of compaction oligonucleotides each comprising four binding arms linked together by at least one inner intervening linker, wherein individual binding arms comprise a binding region. For instance, a compaction oligonucleotide can comprise: (1) an inner intervening linker and a first binding region arranged in a 5’ to 3’ orientation where the 3’ end of the first binding region is directed away from the inner intervening linker; (2) an inner intervening linker and a second binding region arranged in a 5’ to 3’ orientation where the 3’ end of the second binding region is directed away from the inner intervening linker; (3) an inner intervening linker and a third binding region arranged in a 5’ to 3’ orientation where the 3’ end of the third binding region is directed away from the inner intervening linker; and (4) an inner intervening linker and a fourth binding region arranged in a 5’ to 3’ orientation where the 3’ end of the fourth binding region is directed away from the inner intervening linker (i). Alternatively, or in addition, a compaction oligonucleotide can comprise: (1) an inner intervening linker and a first binding region arranged in a 3’ to 5’ orientation where the 5’ end of the first binding region is directed away from the inner intervening linker; (2) an inner intervening linker and a second binding region arranged in a 3’ to 5’ orientation where the 5’ end of the second binding region is directed away from the inner intervening linker; (3) an inner intervening linker and a third binding region arranged in a 3’ to 5’ orientation where the 5’ end of the third binding region is directed away from the inner intervening linker; and (4) an inner intervening linker and a fourth binding region arranged in a 3’ to 5’ orientation where the 5’ end of the fourth binding region is directed away from the inner intervening linker (ii). The 5’ to 3’ orientation of a binding region of a compaction oligonucleotide, or the 3’ to 5’ orientation of a binding region of a compaction oligonucleotide, refers to the orientation of the sugar-phosphate backbone of the binding region.

[0091] FIG. 35A shows a schematic of an embodiment of a double-sided comb shaped compaction oligonucleotide comprising a plurality of binding arms linked to a linker moiety, wherein individual binding arms comprise a binding region and an inner intervening linker. The compaction oligonucleotide can comprise at least three binding arms. The compaction oligonucleotide can comprise a plurality of binding arms having the same sequence. Individual binding arms can comprise a first binding region arranged in a 5’ to 3’ orientation where the 3’ end of the first binding region is directed away from the linker moiety. Individual binding arms can be joined to the linker moiety by the inner intervening linker. The 5’ to 3’ orientation of a binding region of a compaction oligonucleotide, or the 3’ to 5’ orientation of a binding region of a compaction oligonucleotide, refers to the orientation of the sugar-phosphate backbone of the binding region.

[0092] FIG. 35B shows a schematic of an embodiment of a double-sided comb shaped compaction oligonucleotide comprising a plurality of binding arms linked to a linker moiety, wherein individual binding arms comprise a binding region and an inner intervening linker. The compaction oligonucleotide can comprise at least three binding arms. The compaction oligonucleotide can comprise a plurality of binding arms having one of two different sequences. For instance, individual binding arms can comprise a first binding region arranged in a 3’ to 5’ orientation where the 5’ end of the first binding region is directed away from the linker moiety. Individual binding arms can comprise a second binding region arranged in a 3’ to 5’ orientation where the 5’ end of the second binding region is directed away from the linker moiety. Individual binding arms can be joined to the linker moiety by the inner intervening linker. The first binding regions and the second binding regions can be arranged to be on different sides of the double-sided comb shaped compaction oligonucleotide. The 5’ to 3’ orientation of a binding region of a compaction oligonucleotide, or the 3’ to 5’ orientation of a binding region of a compaction oligonucleotide, refers to the orientation of the sugar-phosphate backbone of the binding region.

[0093] FIG. 35C shows a schematic of an embodiment of a double-sided comb shaped compaction oligonucleotide comprising a plurality of binding arms linked to a linker moiety, wherein individual binding arms comprise a binding region and an inner intervening linker. The compaction oligonucleotide can comprise at least three binding arms. The compaction oligonucleotide can comprise a plurality of binding arms having one of three different sequences, such as a first binding region, a second binding region, and a third binding region. For instance, individual binding arms can comprise a first binding region arranged in a 5’ to 3’ orientation where the 3’ end of the first binding region is directed away from the linker moiety. Individual binding arms can comprise a second binding region arranged in a 5’ to 3’ orientation where the 3’ end of the second binding region is directed away from the linker moiety. Individual binding arms can comprise a third binding region arranged in a 5’ to 3’ orientation where the 3’ end of the third binding region is directed away from the linker moiety. Individual binding arms can be joined to the linker moiety by the inner intervening linker. The first binding regions, the second binding regions, and the third binding regions can be arranged to be on the same side of the double-sided comb shaped compaction oligonucleotide. The 5’ to 3’ orientation of a binding region of a compaction oligonucleotide, or the 3’ to 5’ orientation of a binding region of a compaction oligonucleotide, refers to the orientation of the sugar-phosphate backbone of the binding region. DETAILED DESCRIPTION

INTRODUCTION

[0094] When conducting massively parallel sequencing runs, it is challenging to achieve high sequencing quality across the entire length of library insert regions larger than 200 bases, because the sequencing quality drops in part due to a decrease in signal intensity. Achieving high sequencing quality in pairwise sequencing runs is particularly challenging because the signal intensity drops precipitously when sequencing the second strand.

[0095] In some aspects, the present disclosure provides compositions, apparatus and methods for generating concatemer template molecules immobilized on a support for conducting massively parallel sequencing runs, including pairwise sequencing, and achieving high sequencing quality of Q30 or Q40 across the length of the library insert regions on both strands.

[0096] In some aspects, the present disclosure provides compositions, apparatus and methods for generating a plurality of concatemer template molecules (sometimes referred to herein as “concatemer template molecules” and the like) which form compact DNA nanoballs that are stably immobilized to a support. In some embodiments, the compact DNA nanoballs can be generated by conducting rolling circle amplification (RCA) reactions on a support comprising a mixture of immobilized capture and pinning primers. The RCA reaction comprises a plurality of circularized polynucleotide molecules and soluble amplification primers. Without wishing to be bound by theory, it is hypothesized that individual compact DNA nanoballs have increased DNA content compared to DNA nanoballs generated without the plurality of soluble amplification primers, because the immobilized capture primers and soluble amplification primers generate RCA-extension products. The immobilized capture primers can serve to capture circularized polynucleotide molecules, the rolling circle amplification reaction generates concatemer template molecules, and the immobilized pinning primers serve to hybridize to portions of the generated concatemers to produce compact DNA nanoballs that are stably immobilized to the support and retain their compact shape and size after multiple cycles of nucleic acid sequencing reactions. The RCA reaction can be conducted with compaction oligonucleotides which hybridize to portions of the concatemer template molecule to pull together distal portions of the concatemer template molecule which causes compaction of the concatemer template molecule to form compact DNA nanoballs. The resulting compact DNA nanoballs can then be sequenced in a massively parallel sequencing workflow using detectably labeled nucleotide reagents to yield increased signal intensity at any given sequencing cycle. For example, the compact DNA nanoballs exhibit increased signal intensity in long sequencing runs even beyond 300 sequencing cycles. In some embodiments, the compact DNA nanoballs also exhibit increased signal intensity in pairwise sequencing runs where the forward and reverse sequencing runs include more than 300 sequencing cycles. In some embodiments, the compact DNA nanoballs can be subjected to batch-sequencing and/or re-iterative sequencing.

Definitions

[0097] The headings provided herein are not limitations of the various aspects of the disclosure, which aspects can be understood by reference to the specification as a whole. [0098] Unless defined otherwise, technical and scientific terms used herein have meanings that are commonly understood by those of ordinary skill in the art unless defined otherwise. Generally, terminologies pertaining to techniques of molecular biology, nucleic acid chemistry, protein chemistry, genetics, microbiology, transgenic cell production, and hybridization described herein are those well-known and commonly used in the art. Techniques and procedures described herein are generally performed according to conventional methods well known in the art and as described in various general and more specific references that are cited and discussed throughout the instant specification. For example, see Sambrook et al., Molecular Cloning: A Laboratory Manual (Third ed., Cold Spring Harbor Laboratory Press, Cold Spring Harbor, N.Y. 2000). See also Ausubel et al., Current Protocols in Molecular Biology, Greene Publishing Associates (1992). The nomenclatures utilized in connection with, and the laboratory procedures and techniques described herein are those well-known and commonly used in the art.

[0099] Unless otherwise required by context herein, singular terms shall include pluralities and plural terms shall include the singular. Singular forms “a”, “an” and “the”, and singular use of any word, include plural referents unless expressly and unequivocally limited on one referent.

[00100] It is understood the use of the alternative term (e.g., “or”) is taken to mean either one or both or any combination thereof of the alternatives.

[00101] The term “and/or” used herein is to be taken mean specific disclosure of each of the specified features or components with or without the other. For example, the term “and/or” as used in a phrase such as “A and/or B” herein is intended to include: “A and B”; “A or B”; “A” (A alone); and “B” (B alone). In a similar manner, the term “and/or” as used in a phrase such as “A, B, and/or C” is intended to encompass each of the following aspects: “A, B, and C”; “A, B, or C”; “A or C”; “A or B”; “B or C”; “A and B”; “B and C”; “A and C”;

“A” (A alone); “B” (B alone); and “C” (C alone).

[00102] As used herein and in the appended claims, terms “comprising”, “including”, “having” and “containing”, and their grammatical variants, as used herein are intended to be non-limiting so that one item or multiple items in a list do not exclude other items that can be substituted or added to the listed items. It is understood that wherever aspects are described herein with the language “comprising,” otherwise analogous aspects described in terms of “consisting of’ and/or “consisting essentially of’ are also provided.

[00103] As used herein, the terms “about” and “approximately” refer to a value or composition that is within an acceptable error range for the particular value or composition as determined by one of ordinary skill in the art, which will depend in part on how the value or composition is measured or determined, i.e., the limitations of the measurement system. For example, “about” or “approximately” can mean within one or more than one standard deviation per the practice in the art. Alternatively, “about” or “approximately” can mean a range of up to 10% (i.e., ±10%) or more depending on the limitations of the measurement system. For example, about 5 mg can include any number between 4.5 mg and 5.5 mg. Furthermore, particularly with respect to biological systems or processes, the terms can mean up to an order of magnitude or up to 5-fold of a value. When particular values or compositions are provided in the instant disclosure, unless otherwise stated, the meaning of “about” or “approximately” should be assumed to be within an acceptable error range for that particular value or composition. Also, where ranges and/or subranges of values are provided, the ranges and/or subranges can include the endpoints of the ranges and/or subranges.

[00104] The term “polymerase” and its variants, as used herein, comprises an enzyme comprising a domain that binds a nucleotide (or nucleoside) where the polymerase can form a complex having a template nucleic acid and a complementary nucleotide. The polymerase can have one or more activities including, but not limited to, base analog detection activities, DNA polymerization activity, reverse transcriptase activity, DNA binding, strand displacement activity, and nucleotide binding and recognition. A polymerase can be any enzyme that can catalyze polymerization of nucleotides (including analogs thereof) into a nucleic acid strand. Typically, but not necessarily such nucleotide polymerization can occur in a template-dependent fashion. Typically, a polymerase comprises one or more active sites at which nucleotide binding and/or catalysis of nucleotide polymerization can occur. In some embodiments, a polymerase includes other enzymatic activities, such as for example, 3' to 5' exonuclease activity or 5' to 3' exonuclease activity. In some embodiments, a polymerase has strand displacing activity. A polymerase can include without limitation naturally occurring polymerases and any subunits and truncations thereof, mutant polymerases, variant polymerases, recombinant, fusion or otherwise engineered polymerases, chemically modified polymerases, synthetic molecules or assemblies, and any analogs, derivatives or fragments thereof that retain the ability to catalyze nucleotide polymerization (e.g., catalytically active fragment). The polymerase includes catalytically inactive polymerases, catalytically active polymerases, reverse transcriptases, and other enzymes comprising a nucleotide binding domain. In some embodiments, a polymerase can be isolated from a cell, or generated using recombinant DNA technology or chemical synthesis methods. In some embodiments, a polymerase can be expressed in prokaryote, eukaryote, viral, or phage organisms. In some embodiments, a polymerase can be post-translationally modified proteins or fragments thereof. A polymerase can be derived from a prokaryote, eukaryote, virus or phage. A polymerase comprises DNA-directed DNA polymerase and RNA-directed DNA polymerase. [00105] As used herein, the term “strand displacing” refers to the ability of a polymerase to locally separate strands of double-stranded nucleic acids and synthesize a new strand in a template-based manner. Strand displacing polymerases displace a complementary strand from a template strand and catalyze new strand synthesis. Strand displacing polymerases include mesophilic and thermophilic polymerases. Strand displacing polymerases include wild type enzymes, and variants including exonuclease minus mutants, mutant versions, chimeric enzymes and truncated enzymes. Examples of strand displacing polymerases include, without limitation, phi29 DNA polymerase, large fragment of Bst DNA polymerase, large fragment of Bsu DNA polymerase (exo-), Bea DNA polymerase (exo-), KI enow fragment of E. coli DNA polymerase, T5 polymerase, M-MuLV reverse transcriptase, HIV viral reverse transcriptase, Deep Vent DNA polymerase and KOD DNA polymerase. The phi29 DNA polymerase can be wild type phi29 DNA polymerase (e.g., MagniPhi® from Expedeon®), or variant EquiPhi29® DNA polymerase (e.g., from Thermo Fisher Scientific®), or chimeric QualiPhi® DNA polymerase (e.g., from 4basebio®).

[00106] The terms “nucleic acid”, "polynucleotide" and "oligonucleotide" and other related terms used herein are used interchangeably and refer to polymers of nucleotides and are not limited to any particular length. Nucleic acids include recombinant and chemically- synthesized forms. Nucleic acids can be isolated. Nucleic acids include DNA molecules (e.g., cDNA or genomic DNA), RNA molecules (e.g., mRNA), analogs of the DNA or RNA generated using nucleotide analogs (e.g., peptide nucleic acids (PNA) and non-naturally occurring nucleotide analogs), and chimeric forms containing DNA and RNA. Nucleic acids can be single-stranded or double-stranded. Nucleic acids comprise polymers of nucleotides, where the nucleotides include natural or non-natural bases and/or sugars. Nucleic acids comprise naturally-occurring internucleosidic linkages, for example and without limitation, phosphodiester linkages. Nucleic acids can lack a phosphate group. Nucleic acids can comprise non-natural internucleoside linkages, including phosphorothioate, phosphorothiolate, or peptide nucleic acid (PNA) linkages. In some embodiments, nucleic acids comprise a one type of polynucleotides or a mixture of two or more different types of polynucleotides.

[00107] The term “operably linked” and “operably joined” or related terms as used herein refers to juxtaposition of components. The juxtapositioned components can be linked together covalently. For example, two nucleic acid components can be enzymatically ligated together where the linkage that joins together the two components comprises phosphodiester linkage. A first and second nucleic acid component can be linked together, where the first nucleic acid component can confer a function on a second nucleic acid component. For example, linkage between a primer binding sequence and a sequence of interest forms a nucleic acid library molecule having a portion that can bind to a primer. In another example, a transgene (e.g., a nucleic acid encoding a polypeptide or a nucleic acid sequence of interest) can be ligated to a vector where the linkage permits expression or functioning of the transgene sequence contained in the vector. In some embodiments, a transgene is operably linked to a host cell regulatory sequence (e.g., a promoter sequence) that affects expression of the transgene. In some embodiments, the vector comprises at least one host cell regulatory sequence, including a promoter sequence, enhancer, transcription and/or translation initiation sequence, transcription and/or translation termination sequence, polypeptide secretion signal sequences, and the like. In some embodiments, the host cell regulatory sequence controls expression of the level, timing and/or location of the transgene.

[00108] The terms “linked”, “joined”, “attached”, “appended” and variants thereof comprise any type of fusion, bond, adherence or association between any combination of compounds or molecules that is of sufficient stability to withstand use in the particular procedure. The procedure can include but are not limited to: nucleotide binding; nucleotide incorporation; de-blocking (e.g., removal of chain-terminating moiety); washing; removing; flowing; detecting; imaging and/or identifying. Such linkage can comprise, for example, covalent, ionic, hydrogen, dipole-dipole, hydrophilic, hydrophobic, or affinity bonding, bonds or associations involving van der Waals forces, mechanical bonding, and the like. In some embodiments, such linkage occurs intramolecularly, for example linking together the ends of a single-stranded or double-stranded linear nucleic acid molecule to form a circular molecule. In some embodiments,, such linkage can occur between a combination of different molecules, or between a molecule and a non-molecule, including but not limited to: linkage between a nucleic acid molecule and a solid surface; linkage between a protein and a detectable reporter moiety; linkage between a nucleotide and detectable reporter moiety; and the like. Some examples of linkages can be found, for example, in Hermanson, G., “Bioconjugate Techniques”, Second Edition (2008); Aslam, M., Dent, A., “Bioconjugation: Protein Coupling Techniques for the Biomedical Sciences”, London: Macmillan (1998); Aslam, M., Dent, A., “Bioconjugation: Protein Coupling Techniques for the Biomedical Sciences”, London: Macmillan (1998).

[00109] The term “primer” and related terms used herein refer to an oligonucleotide that is capable of hybridizing with a DNA and/or RNA polynucleotide template to form a duplex molecule. Primers comprise natural nucleotides and/or nucleotide analogs. Primers can be recombinant nucleic acid molecules. Primers may have any length, but typically range from 4-50 nucleotides. A typical primer comprises a 5’ end and 3’ end. The 3’ end of the primer can include a 3’ OH moiety which serves as a nucleotide polymerization initiation site in a polymerase-catalyzed primer extension reaction. Alternatively, the 3’ end of the primer can lack a 3’ OH moiety, or can include a terminal 3’ blocking group that inhibits nucleotide polymerization in a polymerase-catalyzed reaction. Any one nucleotide, or more than one nucleotide, along the length of the primer can be labeled with a detectable reporter moiety. A primer can be in solution (e.g., a soluble primer) or can be immobilized to a support (e.g., a capture primer).

[00110] The term “template nucleic acid”, “template polynucleotide”, “target nucleic acid” “target polynucleotide”, “template strand” and other variations refer to a nucleic acid strand that serves as the basis nucleic acid molecule for any of the methods describe herein e.g. sequencing or amplification methods. The template nucleic acid can be single-stranded or double-stranded, or the template nucleic acid can have single-stranded or double-stranded portions. The template nucleic acid can be obtained from a naturally-occurring source, recombinant form, or chemically synthesized to include any type of nucleic acid analog. The template nucleic acid can be linear, circular, or other forms. The template nucleic acids can include an insert portion having an insert sequence. The template nucleic acids can also include at least one adaptor sequence. The insert portion can be isolated in any form, including chromosomal, genomic, organellar (e.g., mitochondrial, chloroplast or ribosomal), recombinant molecules, cloned, amplified, cDNA, RNA such as precursor mRNA or mRNA, oligonucleotides, whole genomic DNA, obtained from fresh frozen paraffin embedded tissue, needle biopsies, circulating tumor cells, cell free circulating DNA, or any type of nucleic acid library. The insert portion can be isolated from any source including from organisms such as prokaryotes, eukaryotes (e.g., humans, plants and animals), fungus, viruses, cells, tissues, normal or diseased cells or tissues, body fluids including blood, urine, serum, lymph, tumor, saliva, anal and vaginal secretions, amniotic samples, perspiration, semen, environmental samples, culture samples, or synthesized nucleic acid molecules prepared using recombinant molecular biology or chemical synthesis methods. The insert portion can be isolated from any organ, including head, neck, brain, breast, ovary, cervix, colon, rectum, endometrium, gallbladder, intestines, bladder, prostate, testicles, liver, lung, kidney, esophagus, pancreas, thyroid, pituitary, thymus, skin, heart, larynx, or other organs. The template nucleic acid can be subjected to nucleic acid analysis, including sequencing and composition analysis. [00111] The term “adaptor” and related terms refer to oligonucleotides that can be operably linked to a target polynucleotide, where the adaptor confers a function to the cojoined adaptor-target molecule. Adaptors comprise DNA, RNA, chimeric DNA/RNA, or analogs thereof. Adaptors can include at least one ribonucleoside residue. Adaptors can be single-stranded, double-stranded, or have single-stranded and/or double-stranded portions. Adaptors can be configured to be linear, stem-looped, hairpin, or Y-shaped forms. Adaptors can be any length, including 4-100 nucleotides or longer. Adaptors can have blunt ends, overhang ends, or a combination of both. Overhang ends can include 5’ overhang and/or 3’ overhang ends. The 5’ end of a single-stranded adaptor, or one strand of a double-stranded adaptor, can have a 5’ phosphate group or lack a 5’ phosphate group. Adaptors can include a 5’ tail that does not hybridize to a target polynucleotide (e.g., tailed adaptor), or adaptors can be non-tailed. An adaptor can include a sequence that is complementary to at least a portion of a primer, such as an amplification primer, a sequencing primer, or a capture primer (e.g., soluble or immobilized capture primers). Adaptors can include a random sequence or degenerate sequence. Adaptors can include at least one inosine residue. Adaptors can include at least one phosphorothioate, phosphorothiolate and/or phosphoramidate linkage. Adaptors can include a barcode sequence which can be used to distinguish polynucleotides (e.g., insert sequences) from different sample sources in a multiplex assay. Adaptors can include a unique identification sequence (e.g., unique molecular index, UMI; or a unique molecular tag) that can be used to uniquely identify a nucleic acid molecule to which the adaptor is appended. In some embodiments, a unique identification sequence can be used to increase error correction and accuracy, reduce the rate of false-positive variant calls and/or increase sensitivity of variant detection. Adaptors can include at least one restriction enzyme recognition sequence, including any one or any combination of two or more selected from a group consisting of type I, type II, type III, type IV, type Hs or type IIB.

[00112] In some embodiments, primer sequences, such as any of the amplification primer sequences, sequencing primer sequences, capture primer sequences, target capture sequences, circularization anchor sequences, sample barcode sequences, spatial barcode sequences, or anchor region sequences can be about 3-50 nucleotides in length, or about 5-40 nucleotides in length, or about 5-25 nucleotides in length.

[00113] The term “universal sequence” and related terms refer to a sequence in a nucleic acid molecule that is common among two or more polynucleotide molecules. For example, an adaptor having a universal sequence can be operably joined to a plurality of polynucleotides so that the population of co-joined molecules carry the same universal adaptor sequence. Examples of universal adaptor sequences include an amplification primer sequence, a sequencing primer sequence or a capture primer sequence (e.g., soluble or immobilized capture primers).

[00114] When used in reference to nucleic acid molecules, the terms “hybridize” or “hybridizing” or “hybridization” or other related terms refer to hydrogen bonding between two different nucleic acids to form a duplex nucleic acid. Hybridization also includes hydrogen bonding between two different regions of a single nucleic acid molecule to form a self-hybridizing molecule having a duplex region. Hybridization can comprise Watson-Crick or Hoogstein binding to form a duplex double-stranded nucleic acid, or a double-stranded region within a nucleic acid molecule. The double-stranded nucleic acid, or the two different regions of a single nucleic acid, may be wholly complementary, or partially complementary. Complementary nucleic acid strands need not hybridize with each other across their entire length. The complementary base pairing can be the standard A-T or C-G base pairing, or can be other forms of base-pairing interactions. Duplex nucleic acids can include mismatched base-paired nucleotides.

[00115] When used in reference to nucleic acids, the terms “extend”, “extending”, “extension” and other variants, refers to incorporation of one or more nucleotides into a nucleic acid molecule. Nucleotide incorporation comprises polymerization of one or more nucleotides into the terminal 3’ OH end of a nucleic acid strand, resulting in extension of the nucleic acid strand. Nucleotide incorporation can be conducted with natural nucleotides and/or nucleotide analogs. Typically, but not necessarily, nucleotide incorporation occurs in a template-dependent fashion. Any suitable method of extending a nucleic acid molecule may be used, including primer extension catalyzed by a DNA polymerase or RNA polymerase. [00116] The term “nucleotides” and related terms refers to a molecule comprising an aromatic base, a five carbon sugar (e.g., a ribose or a deoxyribose), and at least one phosphate group. Canonical or non-canonical nucleotides are consistent with use of the term. The phosphate in some embodiments comprises a monophosphate, a diphosphate, or a triphosphate, or a corresponding phosphate analog. The term “nucleoside” refers to a molecule comprising an aromatic base and a sugar. Nucleotides and nucleosides can be nonlabeled or labeled with a detectable reporter moiety.

[00117] Nucleotides (and nucleosides) typically comprise a hetero cyclic base including substituted or unsubstituted nitrogen-containing parent heteroaromatic ring which are commonly found in nucleic acids, including naturally-occurring, substituted, modified, or engineered variants, or analogs of the same. The base of a nucleotide (or nucleoside) is capable of forming Watson-Crick and/or Hoogstein hydrogen bonds with an appropriate complementary base. Exemplary bases include, but are not limited to, purines and pyrimidines such as: 2-aminopurine, 2,6-diaminopurine, adenine (A), ethenoadenine, N⁶-A²- isopentenyladenine (6iA), N⁶-A²-isopentenyl-2-methylthioadenine (2ms6iA), N⁶- methyladenine, guanine (G), isoguanine, N²-dimethylguanine (dmG), 7-methylguanine (7mG), 2-thiopyrimidine, 6-thioguanine (6sG), hypoxanthine and O⁶-methylguanine; 7- deaza-purines such as 7-deazaadenine (7-deaza-A) and 7-deazaguanine (7-deaza-G); pyrimidines such as cytosine (C), 5-propynylcytosine, isocytosine, thymine (T), 4- thiothymine (4sT), 5,6-dihydrothymine, O⁴-methylthymine, uracil (U), 4-thiouracil (4sU) and 5,6-dihydrouracil (dihydrouracil; D); indoles such as nitroindole and 4-methylindole; pyrroles such as nitropyrrole; nebularine; inosines (I); hydroxymethylcytosines; 5-methycytosines; base (Y); as well as methylated, glycosylated, and acylated base moieties; and the like. Additional exemplary bases can be found in Fasman, 1989, in “Practical Handbook of Biochemistry and Molecular Biology”, pp. 385-394, CRC Press, Boca Raton, Fla.

[00118] Nucleotides (and nucleosides) typically comprise a sugar moiety, such as a carbocyclic moiety (Ferraro and Gotor 2000 Chem. Rev. 100: 4319-48), an acyclic moieties (Martinez, et al., 1999 Nucleic Acids Research 27: 1271-1274; Martinez, et al., 1997 Bioorganic & Medicinal Chemistry Letters vol. 7: 3013-3016), and other sugar moieties (Joeng, et al., 1993 J. Med. Chem. 36: 2627-2638; Kim, et al., 1993 J. Med. Chem. 36: 30-7; Eschenmosser 1999 Science 284:2118-2124; and U.S. Pat. No. 5,558,991). The sugar moiety comprises: ribosyl; 2'-deoxyribosyl; 3 '-deoxyribosyl; 2', 3 '-dideoxyribosyl; 2', 3'- didehydrodideoxyribosyl; 2'-alkoxyribosyl; 2'-azidoribosyl; 2'-aminoribosyl; 2'-fluororibosyl; 2'-mercaptoriboxyl; 2'-alkylthioribosyl; 3 '-alkoxyribosyl; 3 '-azidoribosyl; 3 '-aminoribosyl; 3 '-fluororibosyl; 3'-mercaptoriboxyl; 3 '-alkylthioribosyl carbocyclic; acyclic or other modified sugars.

[00119] In some embodiments, nucleotides comprise a chain of one, two or three phosphorus atoms where the chain is typically attached to the 5’ carbon of the sugar moiety via an ester or phosphoramide linkage. In some embodiments, the nucleotide is an analog having a phosphorus chain in which the phosphorus atoms are linked together with intervening O, S, NH, methylene or ethylene. In some embodiments, the phosphorus atoms in the chain include substituted side groups including O, S or BH3. In some embodiments, the chain includes phosphate groups substituted with analogs including phosphoramidate, phosphorothioate, phosphordithioate, and O-methylphosphoramidite groups.

[00120] The term “reporter moiety”, “reporter moieties” or related terms refer to a compound that generates, or causes to generate, a detectable signal. A reporter moiety is sometimes called a “label”. Any suitable reporter moiety may be used, including luminescent, photoluminescent, electroluminescent, bioluminescent, chemiluminescent, fluorescent, phosphorescent, chromophore, radioisotope, electrochemical, mass spectrometry, Raman, hapten, affinity tag, atom, or an enzyme. A reporter moiety generates a detectable signal resulting from a chemical or physical change (e.g., heat, light, electrical, pH, salt concentration, enzymatic activity, or proximity events). A proximity event includes two reporter moieties approaching each other, or associating with each other, or binding each other. It is well known to one skilled in the art to select reporter moieties so that each absorbs excitation radiation and/or emits fluorescence at a wavelength distinguishable from the other reporter moieties to permit monitoring the presence of different reporter moieties in the same reaction or in different reactions. Two or more different reporter moieties can be selected having spectrally distinct emission profiles, or having minimal overlapping spectral emission profiles. Reporter moieties can be linked (e.g., operably linked) to nucleotides, nucleosides, nucleic acids, enzymes (e.g., polymerases or reverse transcriptases), or support (e.g., surfaces).

[00121] A reporter moiety (or label) generally comprises a fluorescent label or a fluorophore. Exemplary fluorescent moieties which may serve as fluorescent labels or fluorophores include, but are not limited to fluorescein and fluorescein derivatives such as carboxyfluorescein, tetrachlorofluorescein, hexachlorofluorescein, carboxynapthofluorescein, fluorescein isothiocyanate, NHS-fluorescein, iodoacetamidofluorescein, fluorescein maleimide, SAMSA-fluorescein, fluorescein thiosemicarbazide, carbohydrazinomethylthioacetyl-amino fluorescein, rhodamine and rhodamine derivatives such as TRITC, TMR, lissamine rhodamine, Texas Red, rhodamine B, rhodamine 6G, rhodamine 10, NHS-rhodamine, TMR-iodoacetamide, lissamine rhodamine B sulfonyl chloride, lissamine rhodamine B sulfonyl hydrazine, Texas Red sulfonyl chloride, Texas Red hydrazide, coumarin and coumarin derivatives such as AMCA, AMCA-NHS, AMCA-sulfo- NHS, AMCA-HPDP, DCIA, AMCE-hydrazide, BODIPY and derivatives such as BODIPY FL C3-SE, BODIPY 530/550 C3, BODIPY 530/550 C3-SE, BODIPY 530/550 C3 hydrazide, BODIPY 493/503 C3 hydrazide, BODIPY FL C3 hydrazide, BODIPY FL IA, BODIPY 530/551 IA, Br-BODIPY 493/503, Cascade Blue and derivatives such as Cascade Blue acetyl azide, Cascade Blue cadaverine, Cascade Blue ethylenediamine, Cascade Blue hydrazide, Lucifer Yellow and derivatives such as Lucifer Yellow iodoacetamide, Lucifer Yellow CH, cyanine and derivatives such as indolium based cyanine dyes, benzo-indolium based cyanine dyes, pyridium based cyanine dyes, thiozolium based cyanine dyes, quinolinium based cyanine dyes, imidazolium based cyanine dyes, Cy 3, Cy5, lanthanide chelates and derivatives such as BCPDA, TBP, TMT, BHHCT, BCOT, Europium chelates, Terbium chelates, Alexa Fluor® dyes, DyLight® dyes, Atto™ dyes, LightCycler® Red dyes, CAL Flour dyes, JOE and derivatives thereof, Oregon Green™ dyes, WellRED dyes, IRD dyes, phycoerythrin and phycobilin dyes, Malachite green, stilbene, DEG dyes, NR dyes, nearinfrared dyes and others known in the art such as those described in Haugland, Molecular Probes Handbook, (Eugene, Oreg.) 6th Edition; Lakowicz, Principles of Fluorescence Spectroscopy, 2nd Ed., Plenum Press New York (1999), or Hermanson, Bioconjugate Techniques, 2nd Edition, or derivatives thereof, or any combination thereof. Cyanine dyes may exist in either sulfonated or non-sulfonated forms, and consist of two indolenin, benzo- indolium, pyridium, thiozolium, and/or quinolinium groups separated by a polymethine bridge between two nitrogen atoms. Commercially available cyanine fluorophores include, for example, Cy3, (which may comprise l-[6-(2,5-dioxopyrrolidin-l-yloxy)-6-oxohexyl]-2- (3-{ l-[6-(2,5-dioxopyrrolidin-l-yloxy)-6-oxohexyl]-3,3-dimethyl-l,3-dihydro-2H-indol-2- ylidenejprop- 1 -en- 1 -yl)-3 ,3 -dimethyl-3H-indolium or 1 - [6-(2, 5-dioxopyrrolidin- 1 -yloxy)-6- oxohexyl]-2-(3-{ l-[6-(2,5-dioxopyrrolidin-l-yloxy)-6-oxohexyl]-3,3-dimethyl-5-sulfo-l,3- dihydro-2H-indol-2-ylidene}prop-l-en-l-yl)-3,3-dimethyl-3H-indolium-5-sulfonate), Cy5 (which may comprise l-(6-((2,5-dioxopyrrolidin-l-yl)oxy)-6-oxohexyl)-2-((lE,3E)-5-((E)-l- (6-((2,5-dioxopyrrolidin-l-yl)oxy)-6-oxohexyl)-3,3-dimethyl-5-indolin-2-ylidene)penta-l,3- dien- 1 -yl)-3 ,3 -dimethyl-3H-indol- 1 -ium or 1 -(6-((2, 5-dioxopyrrolidin- 1 -yl)oxy)-6- oxohexyl)-2-((lE,3E)-5-((E)-l-(6-((2,5-dioxopyrrolidin-l-yl)oxy)-6-oxohexyl)-3,3-dimethyl- 5-sulfoindolin-2-ylidene)penta-l,3-dien-l-yl)-3,3-dimethyl-3H-indol-l-ium-5-sulfonate), and Cy7 (which may comprise l-(5-carboxypentyl)-2-[(lE,3E,5E,7Z)-7-(l-ethyl-l,3-dihydro-2H- indol-2-ylidene)hepta-l,3,5-trien-l-yl]-3H-indolium or l-(5-carboxypentyl)-2- [(lE,3E,5E,7Z)-7-(l-ethyl-5-sulfo-l,3-dihydro-2H-indol-2-ylidene)hepta-l,3,5-trien-l-yl]- 3H-indolium-5-sulfonate), where “Cy” stands for 'cyanine', and the first digit identifies the number of carbon atoms between two indolenine groups. Cy2 which is an oxazole derivative rather than indolenin, and the benzo-derivatized Cy3.5, Cy5.5 and Cy7.5 are exceptions to this rule. Additional suitable dyes are described, for example, in U.S. 2024/0240249A1, the contents of which are incorporated by reference in their entirety herein.

[00122] In some embodiments, the reporter moiety can be a FRET pair, such that multiple classifications can be performed under a single excitation and imaging step. As used herein, FRET may comprise excitation exchange (Forster) transfers, or electron-exchange (Dexter) transfers.

[00123] When used in reference to nucleic acids, the terms “amplify”, “amplifying”, “amplification”, and other related terms include producing multiple copies of an original polynucleotide template molecule, where the copies comprise a sequence that is complementary to the template sequence, or the copies comprise a sequence that is the same as the template sequence. In some embodiments, the copies comprise a sequence that is substantially identical to a template sequence, or is substantially identical to a sequence that is complementary to the template sequence.

[00124] The term “support” as used herein refers to a substrate that is designed for deposition of biological molecules or biological samples for assays and/or analyses. Examples of biological molecules to be deposited onto a support include nucleic acids (e.g., DNA, RNA), polypeptides, saccharides, lipids, a single cell or multiple cells. Examples of biological samples include but are not limited to saliva, phlegm, mucus, blood, plasma, serum, urine, stool, sweat, tears and fluids from tissues or organs.

[00125] A “capture primer” or “surface capture primer” and the like refers to an oligonucleotide immobilized to a support that is complementary to a portion of, and capable of hybridizing with a given oligonucleotide, such as the library molecules and/or template molecules described herein. A “pinning primer” or “surface pinning primer” and the like refers to an oligonucleotide immobilized to a support that is complementary to a second portion of, and capable of hybridizing with the given oligonucleotide, thereby “pinning” an additional portion of the nucleotide to the support. [00126] In some embodiments, the support is solid, semi-solid, or a combination of both. In some embodiments, the support is porous, semi-porous, non-porous, or any combination of porosity. In some embodiments, the support can be substantially planar, concave, convex, or any combination thereof. In some embodiments, the support can be cylindrical, for example comprising a capillary or interior surface of a capillary.

[00127] In some embodiments, the surface of the support can be substantially smooth. In some embodiments, the support can be regularly or irregularly textured, including bumps, etched, pores, three-dimensional scaffolds, or any combination thereof.

[00128] In some embodiments, the support comprises a bead having any shape, including spherical, hemi-spherical, cylindrical, barrel-shaped, toroidal, disc-shaped, rod-like, conical, triangular, cubical, polygonal, tubular or wire-like.

[00129] The support can be fabricated from any material, including but not limited to glass, fused-silica, silicon, a polymer (e.g., polystyrene (PS), macroporous polystyrene (MPPS), polymethylmethacrylate (PMMA), polycarbonate (PC), polypropylene (PP), polyethylene (PE), high density polyethylene (HDPE), cyclic olefin polymers (COP), cyclic olefin copolymers (COC), polyethylene terephthalate (PET)), or any combination thereof. Various compositions of both glass and plastic substrates are contemplated.

[00130] The support can have a plurality (e.g., two or more) of nucleic acid template molecules immobilized thereon. The plurality of immobilized nucleic acid template molecules have the same sequence or have different sequences. In some embodiments, individual template molecules in the plurality of nucleic acid template molecules are immobilized to a different site on the support. In some embodiments, two or more individual template molecules in the plurality of nucleic acid template molecules are immobilized to a site on the support.

[00131] The term “array” refers to a support comprising a plurality of sites located at predetermined locations on the support to form an array of sites. The sites can be discrete and separated by interstitial regions. In some embodiments, the pre-determined sites on the support can be arranged in one dimension in a row or a column, or arranged in two dimensions in rows and columns. In some embodiments, the plurality of pre-determined sites is arranged on the support in an organized fashion. In some embodiments, the plurality of pre-determined sites is arranged in any organized pattern, including rectilinear, hexagonal patterns, grid patterns, patterns having reflective symmetry, patterns having rotational symmetry, or the like. The pitch between different pairs of sites can be that same or can vary. In some embodiments, the support comprises at least 10² sites, at least 10³ sites, at least 10⁴ sites, at least IO⁵ sites, at least 10⁶ sites, at least 10⁷ sites, at least 10⁸ sites, at least 10⁹ sites, at least IO¹⁰ sites, at least IO¹¹ sites, at least 10¹² sites, at least 10¹³ sites, at least 10¹⁴ sites, at least IO¹⁵ sites, or more, where the sites are located at pre-determined locations on the support. In some embodiments, a plurality of pre-determined sites on the support (e.g., 10² - 10¹⁵ sites or more) are immobilized with nucleic acid template molecules to form a nucleic acid template array. In some embodiments, the support comprises about 10² sites and about 10¹⁵ sites, between about 10⁵ sites and about 10¹⁵ sites, between about IO¹⁰ sites and about

10¹⁵ sites, between about 10³ sites and about 10¹⁴ sites, between about 10⁴ sites and about

10¹³ sites, between about 10⁵ sites and about 10¹² sites, between about 10⁶ and about 10¹¹ sites, between about 10⁷ sites and about IO¹⁰ sites, or between about 10⁸ sites and about IO¹⁰ sites, or any range therebetween, on the support. In some embodiments, the nucleic acid template molecules that are immobilized at a plurality of pre-determined sites by hybridization to immobilized surface capture primers, or the nucleic acid template molecules are covalently attached to the surface capture primer. In some embodiments, the nucleic acid template molecules that are immobilized at a plurality of pre-determined sites, for example immobilized at 10² - 10¹⁵ sites or more. In some embodiments, the immobilized nucleic acid template molecules are clonally-amplified to generate immobilized nucleic acid clusters (also referred to as “polonies”) at the plurality of pre-determined sites. In some embodiments, individual immobilized nucleic acid clusters comprise linear clusters, or comprise singlestranded or double-stranded concatemer template molecules.

[00132] In some embodiments, a support comprising a plurality of sites located at random locations on the support is referred to herein as a support having randomly located sites thereon. The location of the randomly located sites on the support are not pre-determined. The plurality of randomly-located sites is arranged on the support in a disordered and/or unpredictable fashion. In some embodiments, the support comprises at least 10² sites, at least 10³ sites, at least 10⁴ sites, at least 10⁵ sites, at least 10⁶ sites, at least 10⁷ sites, at least 10⁸ sites, at least 10⁹ sites, at least IO¹⁰ sites, at least 10¹¹ sites, at least 10¹² sites, at least 10¹³ sites, at least 10¹⁴ sites, at least 10¹⁵ sites, or more, where the sites are randomly located on the support. In some embodiments, a plurality of randomly located sites on the support (e.g., 10² - 10¹⁵ sites or more) are immobilized with nucleic acid template molecules to form a support immobilized with nucleic acid template molecules. In some embodiments, the support comprises about 10² sites and about 10¹⁵ sites, between about 10⁵ sites and about 10¹⁵ sites, between about IO¹⁰ sites and about 10¹⁵ sites, between about 10³ sites and about 10¹⁴ sites, between about 10⁴ sites and about 10¹³ sites, between about 10⁵ sites and about 10¹² sites, between about 10⁶ and about 10¹¹ sites, between about 10⁷ sites and about IO¹⁰ sites, or between about 10⁸ sites and about IO¹⁰ sites, or any range therebetween, on the support. In some embodiments, the nucleic acid template molecules that are immobilized at a plurality of randomly located sites by hybridization to immobilized surface capture primers, or the nucleic acid template molecules are covalently attached to the surface capture primer. In some embodiments, the nucleic acid template molecules that are immobilized at a plurality of randomly located sites, for example immobilized at 10² - 10¹⁵ sites or more. In some embodiments, the immobilized nucleic acid template molecules are clonally-amplified to generate immobilized nucleic acid clusters at the plurality of randomly located sites. In some embodiments, individual immobilized nucleic acid clusters comprise linear clusters, or comprise single-stranded or double-stranded concatemer template molecules.

[00133] In some embodiments, the support comprises a plurality of surface capture primer immobilized to the support (“immobilized surface capture primers”). In some embodiment, the plurality of immobilized surface capture primers on the support are in fluid communication with each other to permit flowing a solution of reagents (e.g., template molecules, soluble primers, enzymes, nucleotides, divalent cations, buffers, and the like) onto the support so that the plurality of immobilized surface capture primers on the support can be essentially simultaneously reacted with the reagents in a massively parallel manner. In some embodiments, the fluid communication of the plurality of immobilized surface capture primers can be used to conduct nucleic acid amplification reactions (e.g., RCA, MDA, PCR and bridge amplification) essentially simultaneously on the plurality of immobilized surface capture primers.

[00134] In some embodiment, the plurality of immobilized nucleic acid clusters on the support are in fluid communication with each other to permit flowing a solution of reagents (e.g., enzymes, nucleotides, divalent cations, and the like) onto the support so that the plurality of immobilized nucleic acid clusters on the support can be essentially simultaneously reacted with the reagents in a massively parallel manner. In some embodiments, the fluid communication of the plurality of immobilized nucleic acid clusters can be used to conduct nucleotide binding assays and/or conduct nucleotide polymerization reactions (e.g., primer extension or sequencing) essentially simultaneously on the plurality of immobilized nucleic acid clusters, and optionally to conduct detection and imaging for massively parallel sequencing.

[00135] When used in reference to immobilized enzymes, the term “immobilized” and related terms refer to enzymes (e.g., polymerases) that are attached to a support through covalent bond or non-covalent interaction, or attached to a coating on the support, or buried within a matrix formed by a coating on the support.

[00136] When used in reference to immobilized nucleic acids, the term “immobilized” and related terms refer to nucleic acid molecules that are attached to a support through covalent bond or non-covalent interaction, or attached to a coating on the support, or buried within a matrix formed by a coating on the support, where the nucleic acid molecules include surface capture primers, template molecules and extension products of capture primers. Extension products of capture primers includes nucleic acid concatemers (e.g., nucleic acid clusters). [00137] In some embodiments, one or more nucleic acid template molecules are immobilized on the support, for example immobilized at the sites on the support, thereby generating immobilized nucleic acid template molecules. In some embodiments, the one or more nucleic acid template molecules are clonally-amplified. In some embodiments, the one or more nucleic acid template molecules are concatemer template molecules. In some embodiments, the one or more nucleic acid template molecules are clonally-amplified off the support (e.g., in-solution) and then deposited onto the support and immobilized on the support. In some embodiments, the clonal amplification reaction of the one or more nucleic acid template molecules is conducted on the support resulting in immobilization on the support. In some embodiments, the one or more nucleic acid template molecules are clonally- amplified (e.g., in solution or on the support) using a nucleic acid amplification reaction. Nucleic acid amplification reactions include, for example and without limitation, any one or any combination of: polymerase chain reaction (PCR), multiple displacement amplification (MDA), transcription-mediated amplification (TMA), nucleic acid sequence-based amplification (NASBA), strand displacement amplification (SDA), real-time SDA, bridge amplification, isothermal bridge amplification, rolling circle amplification (RCA), circle-to- circle amplification, helicase-dependent amplification, recombinase-dependent amplification, and/or single-stranded binding (SSB) protein-dependent amplification.

[00138] As used herein, the term “binding complex” refers to a complex formed by binding together a nucleic acid duplex, a polymerase, and a free nucleotide or a nucleotide moiety of a multivalent molecule, where the nucleic acid duplex comprises a nucleic acid template molecule hybridized to a nucleic acid primer. In the binding complex, the free nucleotide or nucleotide moiety may or may not be bound to the 3’ end of the nucleic acid primer at a position that is opposite a complementary nucleotide in the nucleic acid template molecule. A “ternary complex” is an example of a binding complex which is formed by binding together a nucleic acid duplex, a polymerase, and a free nucleotide or nucleotide moiety of a multivalent molecule, where the free nucleotide or nucleotide moiety is bound to the 3’ end of the nucleic acid primer (as part of the nucleic acid duplex) at a position that is opposite a complementary nucleotide in the nucleic acid template molecule.

[00139] The term “persistence time” and related terms refers to the length of time that a binding complex, which is formed between the target nucleic acid, a primer, a polymerase, a conjugated or unconjugated nucleotide, remains stable without any binding component dissociates from the binding complex. The persistence time is indicative of the stability of the binding complex and strength of the binding interactions. Persistence time can be measured by observing the onset and/or duration of a binding complex, such as by observing a signal from a labeled component of the binding complex. For example, a labeled nucleotide or a labeled reagent comprising one or more nucleotides may be present in a binding complex, thus allowing the signal from the label to be detected during the persistence time of the binding complex. One exemplary label is a fluorescent label.

Methods for Generating Compact DNA Nanoballs

[00140] The present disclosure provides methods for generating a plurality of compact DNA nanoballs immobilized to a support, comprising step (a): providing a support comprising (i) a plurality of surface capture primers immobilized to the support, wherein individual surface capture primers comprise a 3’ extendible end, (ii) a plurality of surface pinning primers immobilized to the support wherein individual surface pinning primers comprise a 3’ non-extendible end, and (iii) a plurality of covalently closed circular polynucleotide molecules (also referred to herein as “covalently closed circular library molecules” and the like), wherein individual covalently closed circular polynucleotide molecules are hybridized to a surface capture primer thereby forming a plurality of immobilized circular molecule-capture primer duplexes (e.g., FIGS. 15-20).

[00141] In some embodiments, in step (a), the support comprises glass, plastic and/or a polymer material. In some embodiments, in step (a), the support can be passivated with at least one hydrophilic polymer coating. In some embodiments, the plurality of surface capture primers and the plurality of surface pinning primers can be covalently joined to the at least one hydrophilic polymer coating. In some embodiments, in step (a), the at least one hydrophilic polymer coating can have a water contact angle of no more than 45 degrees. [00142] In some embodiments, in step (a), the support comprises a plurality of immobilized surface primers including a mixture of capture primers and pinning primers which are immobilized to the support or immobilized to the coating on the support. [00143] In some embodiments, in step (a), the plurality of surface capture primers can be immobilized to the support at random locations. In some embodiments, in step (a), the plurality of surface capture primers can be immobilized to the support at pre-determined locations. For example, the plurality of surface capture primers can be immobilized to the support in a pattern.

[00144] In some embodiments, in step (a), the plurality of immobilized surface capture primers include or lack a nucleotide having a scissile moiety that can be cleaved.

[00145] In some embodiments, in step (a), the plurality of surface pinning primers can be immobilized to the support at random locations. In some embodiments, in step (a), the plurality of surface pinning primers can be immobilized to the support at pre-determined locations. For example, the plurality of surface pinning primers can be immobilized to the support in a pattern.

[00146] In some embodiments, in step (a), the support comprises a plurality of surface capture primers immobilized thereon at a density of about 10² - 10¹⁵ surface capture primers per mm², e.g., between about 10² sites and about 10¹⁵ sites, between about 10⁵ sites and about 10¹⁵ sites, between about 10¹⁰ sites and about 10¹⁵ sites, between about 10³ sites and about

10¹⁴ sites, between about 10⁴ sites and about 10¹³ sites, between about 10⁵ sites and about 10¹² sites, between about 10⁶ and about 10¹¹ sites, between about 10⁷ sites and about 10¹⁰ sites, or between about 10⁸ sites and about 10¹⁰ sites, or any range therebetween.

[00147] In some embodiments, in step (a), the support comprises a plurality of surface pinning primers immobilized thereon at a density of about 10² - 10¹⁵ surface pinning primers per mm², e.g., between about 10² sites and about 10¹⁵ sites, between about 10⁵ sites and about

10¹⁵ sites, between about 10¹⁰ sites and about 10¹⁵ sites, between about 10³ sites and about

[00148] In some embodiments, in step (a), the support comprises a mixture of capture and pinning primers immobilized thereon at a density of about 10² - 10¹⁵ pinning primers per mm², e.g., between about 10² sites and about 10¹⁵ sites, between about 10⁵ sites and about

10¹⁵ sites, between about 10¹⁰ sites and about 10¹⁵ sites, between about 10³ sites and about 10¹⁴ sites, between about 10⁴ sites and about 10¹³ sites, between about 10⁵ sites and about 10¹² sites, between about 10⁶ and about 10¹¹ sites, between about 10⁷ sites and about 10¹⁰ sites, or between about 10⁸ sites and about 10¹⁰ sites, or any range therebetween. [00149] In some embodiments, in step (a), the support comprises a mixture of capture and pinning primers immobilized thereon at a density of about 10² - 10¹⁵ capture primers per mm², e.g., between about 10² sites and about 10¹⁵ sites, between about 10⁵ sites and about 10¹⁵ sites, between about IO¹⁰ sites and about 10¹⁵ sites, between about 10³ sites and about 10¹⁴ sites, between about 10⁴ sites and about 10¹³ sites, between about 10⁵ sites and about 10¹² sites, between about 10⁶ and about 10¹¹ sites, between about 10⁷ sites and about IO¹⁰ sites, or between about 10⁸ sites and about 10¹⁰ sites, or any range therebetween.

[00150] In some embodiments, in step (a), the support lacks partitions or barriers that separate regions of the support. In some embodiments, in step (a), the support comprises partitions or barriers that separate regions of the support.

[00151] In some embodiments, in step (a), the plurality of covalently closed circular polynucleotide molecules comprise RNA, cDNA or DNA. In some embodiments, in step (a), individual covalently closed circular polynucleotide molecules in the plurality comprise a sequence-of-interest (110) that is 200 - 5000 (e.g., between about 200 and about 3000, between about 500 and about 2000, between about 1000 and about 2500, or any range therebetween) nucleotides in length. In some embodiments, in step (a), individual covalently closed circular polynucleotide molecules in the plurality comprise a sequence-of-interest (110) and lack a universal adaptor sequence. For example individual covalently closed circular polynucleotide molecules comprise RNA, cDNA or DNA which are not appended to a universal adaptor sequence (e.g., FIG. 20).

[00152] In some embodiments, in step (a), individual covalently closed circular polynucleotide molecules in the plurality comprise a covalently closed circular nucleic acid library molecule which comprises a sequence of interest (110) and any one or any combination of two or more universal sequences including: (i) a surface pinning primer binding site sequence (120) (or a complementary sequence thereof), which can be universal; (ii) a surface capture primer binding site sequence (130) (or a complementary sequence thereof), which can be universal; (iii) at least one universal sequence for binding a first sequencing primer (e.g., a forward sequencing primer binding site sequence, (140)) (or a complementary sequence thereof); (iv) at least one universal sequence for binding a second sequencing primer (e.g., a reverse sequencing primer binding site sequence, (150)) (or a complementary sequence thereof); (v) at least one universal sequence for binding a soluble amplification primer (or a complementary sequence thereof); and/or (vi) a universal sequence for binding a compaction oligonucleotide (or a complementary sequence thereof) (e.g., FIGS. 15-19, 25, 26A-26C, 27A-27C). In some embodiments, the covalently closed circular nucleic acid library molecule comprise two or more universal adaptor sequences arranged in any order relative to the sequence of interest (110).

[00153] In some embodiments, the methods for generating a plurality of compact DNA nanoballs immobilized to a support, comprises step (b): contacting the plurality of immobilized circular molecule-capture primer duplexes with a plurality of soluble amplification primers under a condition suitable for hybridizing at least one soluble amplification primer to individual immobilized circular molecule-capture primer duplexes (e.g., FIGS. 15-20). In some embodiments, the circular molecule-capture primer duplexes bind to a plurality of soluble amplification primers, i.e. are multiply primed circular molecule-capture primer duplexes.

[00154] In some embodiments, in step (b), individual immobilized circular moleculecapture primer duplexes comprise a covalently closed circular polynucleotide molecule hybridized to (i) an immobilized capture primer and (ii) hybridized to 1, 2, 3, 4, 5, 6, 7, 8, 9 or 10 soluble amplification primers (e.g., FIGS. 15-20). In some embodiments, two or more soluble amplification primers can hybridize to the covalently closed circular polynucleotide molecule so that the two or more soluble amplification primers abut each other to form a nick between the two or more soluble amplification primers (e.g., FIG. 18). In some embodiments, two or more soluble amplification primers can hybridize to the covalently closed circular polynucleotide molecule so that the two or more soluble amplification primers are separated from each other to form a gap of at least one nucleotide distance between the two or more soluble amplification primers (e.g., FIG. 18).

[00155] In some embodiments, in step (b), individual immobilized circular moleculecapture primer duplexes comprise a covalently closed circular polynucleotide molecule hybridized to an immobilized capture primer and at least one soluble amplification primer, wherein the at least one soluble amplification primer is hybridized to any one or any combination of two or more of: (i) the sequence of interest (110); (ii) the surface capture primer binding site sequence (130) (or a complementary sequence thereof), which can be a universal sequence; (iii) the surface pinning primer binding site sequence (120) (or a complementary sequence thereof), which can be a universal sequence; (iv) the universal sequence for binding a first sequencing primer (e.g., a forward sequencing primer binding site sequence, (140)); (v) the universal sequence for binding a second sequencing primer (e.g., a reverse sequencing primer binding site sequence, (150)); and/or (vi) the universal sequence for binding a compaction oligonucleotide (or a complementary sequence thereof) (e.g., FIGS. 15-19). [00156] In some embodiments, in step (b), individual soluble amplification primers can bind to a sequence in individual covalently closed circular polynucleotide molecules, wherein the soluble amplification primer can bind to any one or any combination of two or more of (i) at least a portion of the sequence of interest (110); (ii) at least a portion of the surface pinning primer binding site sequence (120) (or a complementary sequence thereof), which can be a universal sequence; (iii) at least a portion of the surface capture primer binding site sequence (130) (or a complementary sequence thereof), which can be a universal sequence; (iv) at least a portion of the universal sequence for binding a first sequencing primer (e.g., a forward sequencing primer binding site sequence, (140)); (v) at least a portion of the universal sequence for binding a second sequencing primer (e.g., a reverse sequencing primer binding site sequence, (150)); and/or (vi) at least a portion of the universal sequence for binding a compaction oligonucleotide (or a complementary sequence thereof) (e.g., FIGS. 15- 19).

[00157] In some embodiments, in step (b), the plurality of soluble amplification primers comprise at least one nucleotide analog and/or modified nucleotide linkages that inhibit nuclease digestion including for example phosphorothioate, 2’-O-methyl RNA, inverted dT, and/or 2’ 3’ dideoxy-dT.

[00158] In some embodiments, the methods for generating a plurality of compact DNA nanoballs immobilized to a support, comprises step (c): conducting rolling circle amplification reaction on the plurality of immobilized circular molecule-capture primer duplexes, in the presence of a plurality of compaction oligonucleotides, thereby generating a plurality of compact DNA nanoballs immobilized to the support. In some embodiments, individual compact DNA nanoballs comprise (i) a concatemer template molecule generated by RCA-extension of an immobilized capture primer and (ii) at least one concatemer template molecule generated by RCA-extension of a soluble amplification primer (e.g., FIGS. 15-20). In some embodiments, at least a portion of individual compact DNA nanoballs is hybridized to an immobilized pinning primer (e.g., FIG. 21).

[00159] In some embodiments, in step (c), the rolling circle amplification reaction generates a plurality of compact DNA nanoballs immobilized to the support at a density of about 10² - 10¹⁵ compact DNA nanoballs per mm². In some embodiments, the rolling circle amplification reaction generates a plurality of compact DNA nanoballs immobilized to the support at a density of about 10² - 10³ compact DNA nanoballs per mm², or about 10³ - 10⁴ compact DNA nanoballs per mm², or about 10⁴ - 10⁵ compact DNA nanoballs per mm², or about 10⁵ - 10⁶ compact DNA nanoballs per mm², or about 10⁶ - 10⁷ compact DNA nanoballs per mm², or about 10⁷ - 10⁸ compact DNA nanoballs per mm², or about 10⁸ - 10⁹ compact DNA nanoballs per mm², or about 10⁹ - IO¹⁰ compact DNA nanoballs per mm², or about IO¹⁰ - 10¹¹ compact DNA nanoballs per mm², or about 10¹¹ - 10¹² compact DNA nanoballs per mm², or about 10¹² - 10¹³ compact DNA nanoballs per mm², or about 10¹³ - 10¹⁴ compact DNA nanoballs per mm², or about 10¹⁴ - 10¹⁵ compact DNA nanoballs per mm², or any range therebetween.

[00160] In some embodiments, in step (c), the rolling circle amplification reaction generates a plurality of compact DNA nanoballs immobilized to the support that are in fluid communication with each other to permit flowing a solution of reagents onto the support so that the plurality of immobilized compact DNA nanoballs on the support react with the solution of reagents in a massively parallel manner.

[00161] In some embodiments, in step (c), the rolling circle amplification reaction comprises contacting the plurality of the immobilized circular molecule-capture primer duplexes of step (b) with a plurality of strand displacing polymerases, a plurality of nucleotides, and a plurality of compaction oligonucleotides. In some embodiments, the plurality of nucleotides comprise at least one nucleotide having a scissile moiety that can be cleaved to generate an abasic site in the immobilized compact DNA nanoball. In some embodiments, the at least one nucleotide having a scissile moiety comprises uridine, 8-oxo- 7,8-dihydrogunine or deoxyinosine.

[00162] In some embodiments, in step (c), the plurality of compaction oligonucleotides comprise at least a first and second compaction oligonucleotide. In some embodiments, the first compaction oligonucleotide comprises a first portion that hybridizes to a first portion of a concatemer template molecule generated by RCA-extension of an immobilized capture primer, and a second portion that hybridizes to a second portion of the same concatemer template molecule to pull together distal portions of the concatemer template molecule causing compaction of the concatemer molecule generated by RCA-extension of an immobilized capture primer. In some embodiments, the second compaction oligonucleotide comprises a first portion that hybridizes to a first portion of a concatemer template molecule generated by RCA-extension of a soluble amplification primer, and a second portion that hybridizes to a second portion of the same concatemer template molecule to pull together distal portions of the concatemer template molecule causing compaction of the concatemer template molecule generated by RCA-extension of a soluble amplification primer. In some embodiments, compaction of the concatemer template molecule generated by RCA-extension of an immobilized capture primer and compaction of the concatemer template molecule generated by RCA-extension of a soluble amplification primer generates a compact DNA nanoball. In some embodiments, the first and the second compaction oligonucleotides comprise the same sequence or different sequences.

[00163] In some embodiments, in step (c), individual compaction oligonucleotides in the plurality comprise nucleic acids and can have any shape including a linear, a branched, a star or a dendrimer shape (e.g., a bottle brush shape) (e.g., FIGS. 30-35C). In some embodiments, a compaction oligonucleotide can fold by forming intra-molecule base pairing having duplex portions via Watson-Crick base pairing, Hoogstein base pairing and/or a G-quadruplex structure. In some embodiments, the compaction oligonucleotides comprise nucleic acids that can fold into any shape having at least one hairpin, at least one stem-loop and/or at least one star shape. In some embodiments, individual compaction oligonucleotides comprise at least two binding regions that hybridize to at least a first and second portion of the same concatemer template molecule (e.g., FIGS. 30-35C). In some embodiments, individual compaction oligonucleotides comprise three binding regions that hybridize to a first, second and third portion of the same concatemer template molecule (e.g., FIGS. 31A-31C, 32A-32B, 35C). In some embodiments, individual compaction oligonucleotides comprise four binding regions that hybridize to a first, second, third and fourth portion of the same concatemer template molecule (e.g., FIG. 34).

[00164] In some embodiments, in step (c), the first portion of the first compaction oligonucleotide can hybridize to a first portion of a concatemer template molecule generated by RCA-extension of an immobilized capture primer. In some embodiments, the first portion of a concatemer template molecule generated by RCA-extension of an immobilized capture primer comprises: (i) at least a portion of the sequence of interest (110); (ii) at least a portion of the surface pinning primer binding site sequence (120) (or a complementary sequence thereof), which can be a universal sequence; (iii) at least a portion of the surface capture primer binding site sequence (130) (or a complementary sequence thereof), which can be a universal sequence; (iv) at least a portion of the universal sequence for binding a first sequencing primer (e.g., the forward sequencing primer binding site sequence, (140)); or (v) at least a portion of the universal sequence for binding a second sequencing primer (e.g., a reverse sequencing primer binding site sequence, (150)).

[00165] In some embodiments, in step (c), the second portion of the first compaction oligonucleotide can hybridize to a second portion of a concatemer template molecule generated by RCA-extension of an immobilized capture primer. In some embodiments, the second portion of a concatemer template molecule generated by RCA-extension of an immobilized capture primer comprises: (i) at least a portion of the sequence of interest (110); (ii) at least a portion of the surface pinning primer binding site sequence (120) (or a complementary sequence thereof), which can be a universal sequence; (iii) at least a portion of the surface capture primer binding site sequence (130) (or a complementary sequence thereof), which can be a universal sequence; (iv) at least a portion of the universal sequence for binding a first sequencing primer (e.g., the forward sequencing primer binding site sequence, (140)); or (v) at least a portion of the universal sequence for binding a second sequencing primer (e.g., a reverse sequencing primer binding site sequence, (150)).

[00166] In some embodiments, in step (c), the first portion of the second compaction oligonucleotide can hybridize to a first portion of a concatemer template molecule generated by RCA-extension of a soluble amplification primer. In some embodiments, the first portion of a concatemer template molecule generated by RCA-extension of an immobilized capture primer comprises: (i) at least a portion of the sequence of interest (110); (ii) at least a portion of the surface pinning primer binding site sequence (120) (or a complementary sequence thereof), which can be a universal sequence; (iii) at least a portion of the surface capture primer binding site sequence (130) (or a complementary sequence thereof), which can be a universal sequence; (iv) at least a portion of the universal sequence for binding a first sequencing primer (e.g., the forward sequencing primer binding site sequence, (140)); or (v) at least a portion of the universal sequence for binding a second sequencing primer (e.g., a reverse sequencing primer binding site sequence, (150)).

[00167] In some embodiments, in step (c), the second portion of the second compaction oligonucleotide can hybridize to a second portion of a concatemer template molecule generated by RCA-extension of a soluble amplification primer. In some embodiments, the second portion of a concatemer template molecule generated by RCA-extension of an immobilized capture primer comprises: (i) at least a portion of the sequence of interest (110); (ii) at least a portion of the surface pinning primer binding site sequence (120) (or a complementary sequence thereof), which can be a universal sequence; (iii) at least a portion of the surface capture primer binding site sequence (130) (or a complementary sequence thereof), which can be a universal sequence; (iv) at least a portion of the universal sequence for binding a first sequencing primer (e.g., the forward sequencing primer binding site sequence, (140)); or (v) at least a portion of the universal sequence for binding a second sequencing primer (e.g., a reverse sequencing primer binding site sequence, (150)).

[00168] In some embodiments, in step (c), the rolling circle amplification reaction further comprises at least one nucleic acid condenser agent. In some embodiments, the at least one nucleic acid condenser agent comprising a chemical compound which condenses DNA and/or RNA. In some embodiments, the at least one condenser agent comprises any one or any combination of two or more of a polyamine (e.g., MW approximately 600), spermine, spermidine, cadaverine, putrescene, 1,3-diaminopropane (1,3-DAP), polypeptide (e.g., poly(lysine), poly(arginine) or peptide octamers of alternating lysines and serines), manganese chloride, sodium ions, potassium ions, dextran sulfate (e.g., about 150 kDa or about 500 kDa), poly-L-lysine, ethylene glycol, polyethylene glycol (e.g., 2-10 kDa PEG) and/or polyethyleneimine (PEI). In some embodiments, the PEG comprises thiol reactive PEG, methoxy-PEG-maleimide or diamine PEG. In some embodiments, in step (c), the rolling circle amplification reaction lacks a nucleic acid condenser agent.

[00169] In some embodiments, in step (c), plurality of compact DNA nanoballs are immobilized to the support at a high density. In some embodiments, at least some of the immobilized compact DNA nanoballs comprise nearest neighbor compact DNA nanoballs that touch each other and/or overlap each other when viewed from any angle of the support including above, below or side views of the support (e.g., FIG. 13 A(ii)).

[00170] In some embodiments, the methods for generating a plurality of compact DNA nanoballs immobilized to a support, comprises step (d): removing the plurality of covalently closed circular polynucleotide molecules and retaining the plurality of compact DNA nanoballs immobilized to the support.

[00171] In some embodiments, in step (d), the removing comprises washing away the plurality of covalently closed circular polynucleotide molecules and retaining the plurality of compact DNA nanoballs immobilized to the support.

[00172] In some embodiments, the methods for generating a plurality of compact DNA nanoballs immobilized to a support, comprises step (e): sequencing the plurality of the immobilized compact DNA nanoballs.

[00173] In some embodiments, the sequencing of step (e) comprises sequencing the plurality of immobilized compact DNA nanoballs in a massively parallel manner.

[00174] In some embodiments, in step (e), the plurality of compact DNA nanoballs immobilized to the support are in fluid communication with each other to permit flowing a solution of reagents onto the support so that the plurality of immobilized compact DNA nanoballs on the support react with the solution of reagents in a massively parallel manner. [00175] In some embodiments, the sequencing of step (e) comprises sequencing at least a portion of individual immobilized compact DNA nanoballs. [00176] In some embodiments, the rolling circle amplification of step (c) can generate a plurality compact DNA nanoball each comprising (i) a concatemer template molecule generated by RCA-extension of an immobilized capture primer and (ii) at least one concatemer template molecule generated by RCA-extension of a soluble amplification primer.

[00177] In some embodiments, the concatemer template molecule generated by RCA- extension of an immobilized capture primer comprises a concatemer template molecule which can be sequenced in step (e). In some embodiments, the sequencing of step (e) comprises sequencing at least a portion of the concatemer template molecule generated by RCA-extension of an immobilized capture primer.

[00178] In some embodiments, the concatemer template molecule generated by RCA- extension of a soluble amplification primer comprises a concatemer template molecule which can be sequenced in step (e). In some embodiments, the sequencing of step (e) comprises sequencing at least a portion of the concatemer template molecule generated by RCA- extension of a soluble amplification primer.

[00179] In some embodiments, the sequencing of step (e) comprises conducting a plurality of cycles of sequencing reactions on the plurality of compact DNA nanoballs. In some embodiments, the sequencing of step (e) comprises sequencing the plurality of compact DNA nanoballs in a massively parallel sequencing workflow, wherein in any given sequencing cycle individual compact DNA nanoballs give increased signal intensity compared to conventional concatemer template molecules that are generated by RCA-extension of an immobilized capture primer in the absence of soluble amplification primers. In some embodiments, the increased signal intensity emitted by individual compact DNA nanoballs improves the sequencing quality score of individual bases undergoing sequencing. In some embodiments, the increased signal intensity emitted by individual compact DNA nanoballs generates a sequencing quality of Q30, Q40 or Q50 across the length of the library insert regions (110). In some embodiments, the increased signal intensity emitted by individual compact DNA nanoballs generates a sequencing quality of Q30, Q40 or Q50 across the length of the library insert regions (110) on both concatemer template molecule strands in a pairwise sequencing workflow.

[00180] In some embodiments, the sequence of step (e) comprises contacting individual compact DNA nanoballs with a plurality of sequencing primers, a plurality of sequencing polymerases and a plurality of nucleotide reagents. In some embodiments, the plurality of nucleotide reagents comprises nucleotides, nucleotide analogs and/or multivalent molecules. [00181] In some embodiments, the sequencing of step (e) comprises conducting a two- stage sequencing reaction using a plurality of nucleotide reagents, including a plurality of detectably labeled multivalent molecules and a plurality of nucleotide analogs. In some embodiments, in step (e), the sequencing comprises contacting individual compact DNA nanoballs with a plurality of sequencing primers, a plurality of sequencing polymerases and a plurality of detectably labeled multivalent molecules. In some embodiments, individual detectably labeled multivalent molecules comprise a core attached to multiple polymer arms, and wherein individual polymer arms comprises at least one nucleotide moiety (e.g., FIGS. 1- 4).

[00182] In some embodiments, in step (e), the sequencing comprises: (i) binding a concatemer template molecule generated by RCA-extension of an immobilized capture primer with a plurality of sequencing primers, a plurality of sequencing polymerases, and a plurality of detectably labeled multivalent molecules, and (ii) binding a concatemer template molecule generated by RCA-extension of a soluble amplification primer with a plurality of sequencing primers, a plurality of sequencing polymerases, and a plurality of detectably labeled multivalent molecules, thereby generating a compact DNA nanoball immobilized to the support that emits a detectable signal.

[00183] In some embodiments, in step (e), individual detectably labeled multivalent molecules comprise (a) a core; and (b) a plurality of nucleotide arms which comprise (i) a core attachment moiety, (ii) a spacer, (iii) a linker, and (iv) a nucleotide moiety (e.g., FIGS. 2-5). In some embodiments, the core is attached to the plurality of nucleotide arms via their core attachment moiety. In some embodiments, the core attachment moiety is attached to the spacer. In some embodiments, the spacer is attached to the linker. In some embodiments, the linker is attached to the nucleotide moiety.

[00184] In some embodiments, in step (e), individual detectably labeled multivalent molecules comprise (a) a core; and (b) a plurality of nucleotide arms which comprise (i) a core attachment moiety, (ii) a spacer and (iii) a nucleotide moiety (e.g., FIGS. 2-5). In some embodiments, the core is attached to the plurality of nucleotide arms via their core attachment moiety. In some embodiments, the core attachment moiety is attached to the spacer. In some embodiments, the spacer is attached to the nucleotide moiety.

[00185] In some embodiments, in step (e), the linker of a detectably labeled multivalent molecule comprises an aliphatic chain having 2-6 subunits or an oligo ethylene glycol chain having 2-6 subunits (e.g., FIG. 6). [00186] In some embodiments, in step (e), in a detectably labeled multivalent molecule, the plurality of nucleotide arms attached to a given core have the same type of nucleotide moiety. In some embodiments, the nucleotide moiety comprises dATP, dGTP, dCTP, dTTP or dUTP.

[00187] In some embodiments, in step (e), the plurality of multivalent molecules comprise one type of a multivalent molecule. In some embodiments, individual multivalent molecule in the plurality has the same type of nucleotide moiety selected from a group consisting of dATP, dGTP, dCTP, dTTP and dUTP.

[00188] In some embodiments, in step (e), the plurality of multivalent molecules comprise a mixture of any combination of two or more types of multivalent molecules, individual types of multivalent molecules having nucleotide moieties selected from the group consisting of dATP, dGTP, dCTP, dTTP and/or dUTP.

[00189] In some embodiments, in step (e), individual detectably labeled multivalent molecules in the plurality comprise a core attached to a fluorophore, a polymer arm attached to a fluorophore and/or a nucleotide moiety attached to a fluorophore.

[00190] In some embodiments, in step (e), the sequencing further comprises contacting individual compact DNA nanoballs with a plurality of non-catalytic divalent cations that inhibit polymerase-catalyzed nucleotide incorporation. In some embodiments, the non- catalytic divalent cations comprise strontium, calcium or barium.

[00191] In some embodiments, in step (e), the sequencing comprises: (i) binding a first sequencing primer, a first sequencing polymerase, and a first multivalent molecule to a first portion of a concatemer template molecule of a compact DNA nanoball thereby forming a first binding complex, wherein a first nucleotide moiety of the first multivalent molecule binds to the first sequencing polymerase; and (ii) binding a second sequencing primer, a second sequencing polymerase, and the first multivalent molecule to a second portion of the same concatemer thereby forming a second binding complex, wherein a second nucleotide moiety of the first multivalent molecule binds to the second sequencing polymerase. In some embodiments, the first and the second binding complexes which include the same multivalent molecule form an avidity complex.

[00192] In some embodiments, in step (e), the sequencing comprises: (i) contacting a first plurality of sequencing polymerases and a first plurality of sequencing primers with different portions of a concatemer template molecule of a compact DNA nanoball to form at least first and second polymerase complexes on the same concatemer template molecule; (ii) contacting a plurality of detectably labeled multivalent molecules to the at least first and second polymerase complexes on the same concatemer template molecule, under conditions suitable to bind a single multivalent molecule from the plurality to the first and second polymerase complexes, wherein at least a first nucleotide moiety of the single multivalent molecule is bound to the first polymerase complex which includes a first sequencing primer hybridized to a first portion of the concatemer template molecule thereby forming a first binding complex, and wherein at least a second nucleotide moiety of the single multivalent molecule is bound to the second polymerase complex which includes a second sequencing primer hybridized to a second portion of the same concatemer template molecule thereby forming a second binding complex, wherein the contacting is conducted under a condition suitable to inhibit polymerase-catalyzed incorporation of the bound first and second nucleotide moieties in the first and second binding complexes, and wherein the first and second binding complexes which are bound to the same multivalent molecule forms an avidity complex; (iii) detecting the first and second binding complexes on the same concatemer template molecule; and (iv) identifying the first nucleotide moiety in the first binding complex thereby determining the sequence of the first portion of the concatemer template molecule, and identifying the second nucleotide moiety in the second binding complex thereby determining the sequence of the second portion of the concatemer template molecule.

[00193] In some embodiments, in step (e), the sequencing comprises contacting individual compact DNA nanoballs with a plurality of sequencing primers, a plurality of sequencing polymerases and a plurality of nucleotides or a plurality of nucleotide analogs.

[00194] In some embodiments, in step (e), the sequencing comprises contacting individual compact DNA nanoballs with a plurality of detectably labeled nucleotides comprising: (i) binding a concatemer template molecule generated by RCA-extension of an immobilized capture primer with a plurality of sequencing primers, a plurality of sequencing polymerases, and a plurality of detectably labeled nucleotides, and (ii) binding a concatemer template molecule generated by RCA-extension of a soluble amplification primer with a plurality of sequencing primers, a plurality of sequencing polymerases, and a plurality of detectably labeled nucleotides, thereby generating a compact DNA nanoball immobilized to the support that emits a detectable signal.

[00195] In some embodiments, in step (e), individual detectably labeled nucleotides in the plurality comprise an aromatic base, a five carbon sugar, and 1-10 phosphate groups.

[00196] In some embodiments, in step (e), the plurality of detectably labeled nucleotides comprises one type of nucleotide selected from the group consisting of dATP, dGTP, dCTP, dTTP and dUTP. [00197] In some embodiments, in step (e), the plurality of detectably labeled nucleotides comprises a mixture of any combination of two or more types of nucleotides selected from the group consisting of dATP, dGTP, dCTP, dTTP and dUTP.

[00198] In some embodiments, in step (e), at least one detectably labeled nucleotide in the plurality is labeled with a fluorophore. In some embodiments, in step (e), at least one nucleotide in the plurality lacks a fluorophore label.

[00199] In some embodiments, in step (e), at least one of the detectably labeled nucleotides in the plurality comprises a removable chain terminating moiety attached to the 3’ carbon position of the sugar group. In some embodiments, the removable chain terminating moiety comprises an alkyl group, an alkenyl group, an alkynyl group, an allyl group, an aryl group, a benzyl group, an azide group, an azido group, an O-azidomethyl group, an amine group, an amide group, a keto group, an isocyanate group, a phosphate group, a thio group, a disulfide group, a carbonate group, a urea group, an acetal group or a silyl group. In some embodiments, the removable chain terminating moiety is cleavable with a chemical compound to generate an extendible 3 ’OH moiety on the sugar group.

[00200] In some embodiments, in step (e), the sequencing further comprises contacting individual compact DNA nanoballs with a plurality of catalytic divalent cations that promote polymerase-catalyzed nucleotide incorporation. In some embodiments, the catalytic divalent cations comprise magnesium or manganese.

Capture Primers and Pinning Primers

[00201] In some embodiments of the methods disclosed herein, the plurality of surface capture primers immobilized to the support (immobilized capture primers) comprises single stranded oligonucleotides comprising DNA, RNA or a combination of DNA and RNA. The surface capture primers can be immobilized to the support or immobilized to a coating on the support (e.g., FIGS. 15-20). The immobilized capture primers can be embedded and attached (coupled) to the coating on the support. The immobilized capture primers can be covalently attached to the coating on the support. In some embodiments, the 5’ end of the immobilized capture primers are immobilized to the support or immobilized to a coating on the support. Alternatively, an interior portion or the 3’ end of the immobilized capture primers can be immobilized to the support or immobilized to a coating on the support. In some embodiments the support comprises a plurality of immobilized capture primers having the same sequence (e.g., a universal capture primer sequence). In some embodiments, individual immobilized capture primers comprise a sequence that can hybridize to at least a portion of individual covalently closed circular polynucleotide molecules. The immobilized capture primers can be any length, for example 4-50 nucleotides, or 50-100 nucleotides, or 100-150 nucleotides, or any range therebetween, or longer lengths. In some embodiments, the 3’ terminal end of the immobilized capture primers comprise an extendible 3’ OH moiety. In some embodiments, the 3’ terminal end of the immobilized capture primers comprise a 3’ non-extendible moiety. In some embodiments, the non-extendible moiety at the 3 terminal end of individual capture primers can be converted to a 3’ extendible end.

[00202] In some embodiments, the plurality of immobilized capture primers comprise at least one phosphorothioate diester bond at their 5’ ends which can render the capture primers resistant to exonuclease degradation. In some embodiments, the plurality of immobilized capture primers comprise 2-5 or more consecutive phosphorothioate diester bonds at their 5’ ends. In some embodiments, the plurality of immobilized capture primers comprise at least one ribonucleotide and/or at least one 2’-O-methyl or 2’ -O-m ethoxy ethyl (MOE) nucleotide which can render the capture primers resistant to exonuclease degradation.

[00203] In some embodiments, the immobilized capture primers comprise at least one locked nucleic acid (LNA) which comprises a methylene bridge bond between a 2’ oxygen and 4’ carbon of the pentose ring. Immobilized capture primers that include at least one LNA can be resistant to nuclease digestion and can exhibit increased melting temperature when hybridized to a portion of the covalently closed circular polynucleotide molecules.

[00204] In some embodiments, the immobilized capture primers include or lack a nucleotide having a scissile moiety that can be cleaved to generate an abasic site in the capture primer. Exemplary nucleotides having a scissile moiety include uridine, 8-oxo-7,8- dihydrogunine and deoxyinosine.

[00205] In some embodiments, the plurality of surface pinning primers of comprise single stranded oligonucleotides comprising DNA, RNA or a combination of DNA and RNA. The pinning primers can be immobilized to the support or immobilized to a coating on the support (e.g., FIGS. 15-20) (immobilized pinning primers). The immobilized pinning primers can be embedded and attached (coupled) to the coating on the support. The immobilized pinning primers can be covalently attached to the coating on the support. In some embodiments, the 5’ end of the immobilized pinning primers are immobilized to the support or immobilized to a coating on the support. Alternatively, an interior portion or the 3’ end of the immobilized pinning primers can be immobilized to the support or immobilized to a coating on the support. The immobilized pinning primers can be any length, for example 4-50 nucleotides, or 50-100 nucleotides, or 100-150 nucleotides, or any range therebetween, or longer lengths. [00206] In some embodiments the support comprises a plurality of immobilized pinning primers having the same sequence (e.g., a universal pinning primer sequence). In some embodiments, individual immobilized pinning primers comprise a sequence that can hybridize to at least a portion of individual concatemer template molecules in a compact DNA nanoball generated by conducting a rolling circle amplification reaction on the immobilized circular molecule-capture primer duplexes of step (c). In some embodiments, individual compact DNA nanoballs generated in step (c) comprise: (i) a concatemer template molecule generated by RCA-extension of an immobilized capture primer and (ii) at least one concatemer template molecule generated by RCA-extension of a soluble amplification primer. In some embodiments, at least a portion of individual compact DNA nanoballs is hybridized to an immobilize pinning primer.

[00207] In some embodiments, the 3’ terminal ends of the immobilized pinning primers comprise a 3’ non-extendible moiety. In some embodiments, the 3’ terminal end of the immobilized pinning primers comprise a moiety that blocks polymerase-catalyzed primer extension (e.g., non-extendible terminal 3’ end), such as for example a phosphate group, a dideoxycytidine group, an inverted dT, or an amino group. In some embodiments, the immobilized pinning primers are not extendible in a primer extension reaction. In some embodiments, the immobilized pinning primers lack a nucleotide having a scissile moiety. In some embodiments, the 3’ terminal ends of the immobilized pinning primers comprise an extendible 3’ OH moiety.

[00208] In some embodiments, the plurality of immobilized pinning primers comprise at least one phosphorothioate diester bond at their 5’ ends which can render the pinning primers resistant to exonuclease degradation. In some embodiments, the plurality of immobilized pinning primers comprise 2-5 or more consecutive phosphorothioate diester bonds at their 5’ ends. In some embodiments, the plurality of immobilized pinning primers comprise at least one ribonucleotide and/or at least one 2’-O-methyl or 2’ -O-m ethoxy ethyl (MOE) nucleotide which can render the pinning primers resistant to exonuclease degradation.

[00209] In some embodiments, the immobilized pinning primers comprise at least one locked nucleic acid (LNA) which comprises a methylene bridge bond between a 2’ oxygen and 4’ carbon of the pentose ring. Immobilized pinning primers that include at least one LNA can be resistant to nuclease digestions and can exhibit increased melting temperature when hybridized to a portion of individual concatemer template molecules in a compact DNA nanoball. Sources of Polynucleotides

[00210] In some embodiments of the methods disclosed herein, the covalently closed circular polynucleotide molecules comprise polynucleotide molecules that include at least one universal adaptor sequence or lack universal adaptor sequences. In some embodiments, a polynucleotide molecule that includes at least one universal adaptor sequence comprises a nucleic acid library molecule which includes a sequence of interest (110) appended to at least one universal adaptor sequence. In some embodiments, a polynucleotide molecule that lacks a universal adaptor sequence comprises a sequence of interest (110). In some embodiments, the polynucleotide molecules can be linear polynucleotide molecules prepared from any source and circularized to generate the covalently closed circular polynucleotide molecules. [00211] In some embodiments, the sequence of interest (110) of a covalently closed circularized polynucleotide molecule can be any length, for example about 50-250, or about 250-500, or about 500-750, or about 750-1000, or about 1000-1500, or about 1500-2000, or about 2000-5000 nucleotides, , or any range therebetween, or more than 5000 nucleotides in length.

[00212] In some embodiments, the sequence of interest (110) of the covalently closed circularized polynucleotide molecules comprise RNA, cDNA or DNA.

[00213] In some embodiments, the sequence of interest (110) of the covalently closed circularized polynucleotide molecules can be extracted from any source, can be prepared by chemical synthesis methods, or can be prepared using recombinant nucleic acid technology including but not limited to any combination of vector cloning, transgenic host cell preparation, host cell culturing and/or PCR amplification.

[00214] In some embodiments, the sequence of interest (110) of the covalently closed circularized polynucleotide molecules can be extracted from any organism including viruses, prokaryotes, archaeal organisms, fungus or eukaryotes (e.g., humans, plants and animals). [00215] In some embodiments, the sequence of interest (110) of the covalently closed circularized polynucleotide molecules can be isolated in any form, including without limitation chromosomal, genomic, organellar (e.g., mitochondrial, chloroplast or ribosomal), recombinant molecules, cloned, amplified, cDNA, RNA such as precursor mRNA (e.g., unspliced RNA or partially spliced RNA), mRNA, or whole genomic DNA.

[00216] In some embodiments, the sequence of interest (110) of the covalently closed circularized polynucleotide molecules can be obtained from fresh frozen paraffin embedded tissue, needle biopsies, circulating tumor cells, cell free circulating DNA, or any type of nucleic acid library.

[00217] In some embodiments, the sequence of interest (110) of the covalently closed circularized polynucleotide molecules can be obtained from cells, tissues, normal or diseased cells or tissues, body fluids including blood, urine, serum, lymph, tumor, saliva, anal and vaginal secretions, amniotic samples, perspiration, smears, semen, environmental samples or culture samples.

[00218] In some embodiments, the sequence of interest (110) of the covalently closed circularized polynucleotide molecules can be isolated from any organ, including head, neck, brain, breast, ovary, cervix, colon, rectum, endometrium, gallbladder, intestines, bladder, prostate, testicles, liver, lung, kidney, esophagus, pancreas, thyroid, pituitary, thymus, skin, heart, larynx, or other organs.

[00219] In some embodiments, the sequence of interest (110) of a covalently closed circularized polynucleotide molecule can be obtained from any type of cells and from any organism including prokaryotes, archaebacteria, eubacteria or eukaryotes (such as animals, plants, fungi, protista). In some embodiments, the polynucleotides can be obtained from any type of cells and from any organism including human, simian, ape, canine, feline, bovine, equine, murine, porcine, caprine, lupine, ranine, piscine, plant, insect or bacteria.

[00220] In some embodiments, the sequence of interest (110) of a covalently closed circularized polynucleotide molecule can be obtained from any type of cells including skin, heart, lung, kidney, breath, bone marrow, stool, semen, vaginal fluid, interstitial fluids derived from tumorous tissue, breast, pancreas, cerebral spinal fluid, tissue, throat swab, biopsy, smears, placental fluid, amniotic fluid, liver, muscle, smooth muscle, bladder, gall bladder, colon, intestine, brain, cavity fluids, sputum, pus, micropiota, meconium, breast milk, prostate, esophagus, thyroid, serum, saliva, urine, gastric and digestive fluid, tears, ocular fluids, sweat, mucus, earwax, oil, glandular secretions, spinal fluid, hair, fingernails, skin cells, plasma, nasal swab, nasopharyngeal sample, oropharyngeal sample, bronchoalveolar lavage fluid, tracheal aspirate, bronchial wash, spinal fluid, cerebrospinal fluid, pericardial fluid, cord blood, emphatic fluids, and/or other excretions or body tissues. [00221] In some embodiments, the sequence of interest (110) of a covalently closed circularized polynucleotide molecule can be obtained from any type of cells including white blood cells, red blood cells, platelets, epithelial cells, endothelial cells, neurons, glial cells, astrocytes, fibroblasts, skeletal muscle cells, smooth muscle cells, gametes, or cells from the heart, lungs, brain, liver, kidney, spleen, pancreas, thymus, bladder, stomach, colon, or small intestine.

[00222] In some embodiments, the polynucleotides can be obtained from any type of cells including cells belonging to a subset of cells, such as immune cells. In some embodiments, the immune cells are T cells, cytotoxic (killer) T cells, helper T cells, alpha beta T cells, gamma delta T cells, T cell progenitors, B cells, B-cell progenitors, lymphoid stem cells, myeloid progenitor cells, lymphocytes, granulocytes, Natural Killer cells, plasma cells, memory cells, neutrophils, eosinophils, basophils, mast cells, monocytes, dendritic cells, macrophages, undifferentiated human stem cells, or human stem cells that have been induced to differentiate.

[00223] In some embodiments, the sequence of interest (110) of a covalently closed circularized polynucleotide molecule can be obtained from any type of cells including healthy cells, diseased cells including cancerous cells, or pathogenic cells that are infected with a pathogen.

[00224] In some embodiments, the sequence of interest (110) of a covalently closed circularized polynucleotide molecule can be obtained from any type of cells including rare cells, for example circulating tumor cells (CTCs), circulating epithelial cells, circulating endothelial cells, circulating endometrial cells, bone marrow cells, progenitor cells, foam cells, mesenchymal cells, or trophoblasts.

[00225] In some embodiments, the sequence of interest (110) of a covalently closed circularized polynucleotide molecule can be obtained by any method including needle biopsy (e.g., fine needle biopsy or fine needle aspirate) or micro-forceps.

[00226] In some embodiments, the sequence of interest (110) of a covalently closed circularized polynucleotide molecule can be obtained from any type of plant cells including any plant part, including a fruit, a tuber, a leaf, a stem, a root, a seed, a branch, a pubescent, a nodule, a leaf axil, a flower, a pollen, a stamen, a pistil, a petal, a peduncle, a stalk, a stigma, a style, a bract, a trunk, a carpel, a sepal, an anther, an ovule, a pedicel, a needle, a cone, a rhizome, a stolon, a shoot, a pericarp, an endosperm, a placenta, a berry, a stamen or a leaf sheath.

[00227] In some embodiments, the sequence of interest (110) of a covalently closed circularized polynucleotide molecule can encode a polypeptide, or do not encode a polypeptide. In some embodiments, the polynucleotides comprises a mixture of nucleic acid molecules that encode a polypeptide and nucleic acid molecules that do not encode a polypeptide. [00228] In some embodiments, the sequence of interest (110) of a covalently closed circularized polynucleotide molecule comprises mRNA, poly A RNA, or RNA lacking a poly A tail.

[00229] In some embodiments, the sequence of interest (110) of a covalently closed circularized polynucleotide molecule comprises tRNA, rRNA, small nuclear RNA (snRNA), small nucleolar RNA (snoRNA), microRNA (miRNA), small interfering RNA (siRNA), piwi-interacting RNA (piRNA) or antisense RNA.

[00230] In some embodiments, the sequence of interest (110) of a covalently closed circularized polynucleotide molecule comprises pre-sliced RNA, RNA splice variants, and mature-spliced RNA comprising only exons. In some embodiments, the polynucleotides comprise an exon sequence, an intron sequence, an exon-intron junction sequence, or a mixture of exon sequence and intron sequences.

[00231] In some embodiments, the sequence of interest (110) of a covalently closed circularized polynucleotide molecule comprises at least one region of RNA including a 5’ untranslated region, a 5’ cap region, a region having a start codon, a coding region, a region having a stop codon, and/or a 5’ untranslated region. In some embodiments, the 5' cap site of an RNA comprises an N7-methylated guanosine residue joined to the 5'-most residue of the RNA via a 5 '-5' triphosphate linkage. In some embodiments, the 5' cap region of a RNA includes the 5' cap structure and the first 50 nucleotides adjacent to the 5’ cap site.

Circularization of Polynucleotides

[00232] In some embodiments, the plurality of covalently closed circular polynucleotide molecules can be generated by circularizing linear polynucleotide molecules. There are several methods for generating a plurality of covalently closed circular polynucleotide molecules from a plurality of linear polynucleotide molecules. Exemplary methods of preparing covalently closed circular polynucleotide molecules, and generating concatemer template molecules therefrom, are described in WO2022266470, WO2023168444, WO2023168443, W02024040058, W02024011145 and W02024059550, the contents of each of which are incorporated by reference in their entireties herein.

[00233] In some embodiments, the covalently closed circular polynucleotide molecules comprise polynucleotide molecules that include at least one universal adaptor sequence or lack universal adaptor sequences. In some embodiments, a polynucleotide molecule that includes at least one universal adaptor sequence comprises a nucleic acid library molecule which includes a sequence of interest (110) appended to at least one universal adaptor sequence. In some embodiments, a polynucleotide molecule that lacks a universal adaptor sequence comprises a sequence of interest (110).

[00234] In some embodiments, the ends of single-stranded linear polynucleotide molecules can undergo intramolecular ligation using a single-stranded ligase (e.g., CircLigase from Epicentre™ or Lucigen™) thereby generating a plurality of covalently closed circular polynucleotide molecules.

[00235] In some embodiments, covalently closed circular polynucleotide molecules (e.g., circularized DNA molecules) can be generated using a protelomerase instead of a nucleic acid ligase. Protelomerase enzymes identifies an enzyme recognition sequence within a polynucleotide molecule, cleaves the enzyme recognition sequence to generate an end having a 5’ and 3’ exposed cleavage ends, rejoins 5’ and 3’ cleavage ends of a single exposed end at the enzyme recognition site to form a single linear molecule from the cleaved 5’ and 3’ ends. When this reaction is performed on both ends of a double-stranded polynucleotide molecule having the enzyme recognition sequence at each end, the result is a covalently closed circular polynucleotide molecule. An adaptor carrying the enzyme recognition sequence can be joined to both ends of the double-stranded DNA polynucleotide molecule via ligation or PCR using tailed PCR primers. A number of enzymes or enzyme combinations are compatible with this reaction, including a protelomerase. One exemplary type of protelomerase is TelN protelomerase, such as that from E. coli phage Nl.

[00236] In some embodiments, a population of double-stranded linear polynucleotide molecules can be circularized to generate covalently closed circular polynucleotide molecules. In some embodiments, the 5’ ends of linear polynucleotide molecules can be phosphorylated for subsequent enzymatic ligation. For example, a population of linear polynucleotide molecules can be contacted with an enzyme that catalyzes 5’ phosphorylation of the ends of the linear molecules, such as for example T4 polynucleotide kinase. In some embodiments, the population of linear polynucleotide molecules having blunt ends can be contacted with a ligase enzyme for intramolecular ligation, where the ligase enzyme comprises T3 or T4 DNA ligase. In some embodiments, the population of linear polynucleotide molecules having overhang ends (e.g., sticky ends) can be contacted with a T7 DNA ligase to generate covalently closed circular polynucleotide molecules. In some embodiments, the linear polynucleotide molecules can be reacted with the T4 polynucleotide kinase enzyme and the ligase enzyme either sequentially or simultaneously to generate covalently closed circular polynucleotide molecules. The non-circular molecules can be degraded using at least one exonuclease enzyme, such as for example T7 exonuclease and/or exonuclease I (e.g., thermolabile exonuclease I).

Circularizing Polynucleotides using Padlock Probes

[00237] In some embodiments, the covalently closed circular polynucleotide molecules can be generated using padlock probes. For a description of padlock probes see, for example, Szemes, M. et al. Nucleic Acids Research, Volume 33, Issue 8, 1 April 2005, Page e70, the contents of which are incorporated by reference in their entirety herein.

[00238] In some embodiments, a padlock probe workflow can be used to generate single stranded covalently closed circular molecules (e.g., FIG. 25). Typically, the arrangement of the sequence of interest (insert sequence) and adaptors in a padlock probe differs from a standard linear library molecule. In some embodiments, a padlock probe comprises a singlestranded linear oligonucleotide having a 5’ portion, an optional internal linker portion, and a 3’ portion. The 5’ and 3’ portions each comprise a portion that can hybridize to a target sequence of interest. The 5’ and 3’ portions are separately complementary to a target sequence of interest (e.g., a contiguous target sequence of interest), while the internal linker portion is designed to have little or no complementarity to the target sequence (e.g., FIG. 25). The 5’ and 3’ ends of the padlock probe can hybridize to adjacent positions on the target nucleic acid molecule to form an open circularized molecule with a nick between the hybridized 5’ and 3’ ends. The nick can be ligated to generate a covalently close circular molecule. Alternatively, the 5’ and 3’ ends of the padlock probe can hybridize to adjacent positions on the target nucleic acid molecule to form an open circularized molecule with a gap between the hybridized 5’ and 3’ ends. The gap can be subject to a polymerase-mediated filled-in reaction to form a nick, and the nick can be ligated to generate a covalently close circular molecule. In some embodiments, the padlock probe comprises: a surface pinning primer binding site sequence (120) (e.g., batch-specific surface pinning primer binding site sequence); a left sample index sequence (160); a forward sequencing primer binding site sequence (140) (e.g., batch-specific forward sequencing primer binding site sequence); a sequence of interest (110); a reverse sequencing primer binding site sequence (150) (e.g., batch-specific reverse sequencing primer binding site sequence); a right sample index sequence (170); a surface capture primer binding site sequence (130) (e.g., batch-specific surface capture primer binding site sequence); and an optional unique identification sequence (e g., UMI) (see, e g., FIG. 25). Circularizing Polynucleotides using Single-Stranded Splint Strands

[00239] In some embodiments, in the methods for generating a plurality of compact DNA nanoballs immobilized to a support, the covalently closed circular polynucleotide molecules of step (a) can be generated using single stranded splint strands. In some embodiments, a population of the single stranded linear polynucleotide molecules can be circularized to generate single stranded covalently closed circular polynucleotide molecules using single stranded splint strands (e.g., FIGS. 26A-26C). In some embodiments, individual single stranded linear polynucleotide molecules comprise a linear library molecule which includes a sequence of interest (an insert sequence, (110)) flanked at both ends with at least one universal adaptor sequence. For example, the single stranded linear library molecules comprises: a sequence of interest (110) and any one or any combination of two or more universal sequences including: (i) a surface pinning primer binding site sequence (120) (or a complementary sequence thereof), which can be a universal sequence; (ii) a surface capture primer binding site sequence (130) (or a complementary sequence thereof), which can be a universal sequence; (iii) at least one universal sequence for binding a first sequencing primer (e.g., the forward sequencing primer binding site sequence, (140)) (or a complementary sequence thereof); (iv) at least one universal sequence for binding a second sequencing primer (e.g., a reverse sequencing primer binding site sequence, (150)) (or a complementary sequence thereof); (v) at least one universal sequence for binding a soluble amplification primer (or a complementary sequence thereof); (vi) a universal sequence for binding a compaction oligonucleotide (or a complementary sequence thereof); and/or at least one sample index sequence ((160) and/or (170)) which can be used for distinguishing sequences of interest obtained from different sample sources in a multiplex assay (e.g., see FIG. 26A). [00240] A population of double stranded linear library molecules can be denatured to generate single stranded linear library molecules. The single stranded linear library molecules (100) can be hybridized to single stranded splint strands (200) to generate library-splint complexes (300) with a nick (e.g., FIG. 26A). The single stranded splint strands (200) comprise a first and second region. In some embodiments, the first region (210) hybridizes with the surface pinning primer binding site sequence (120) (or a complementary sequence thereof) on one end of the linear single stranded library molecule (e.g., see FIG. 26A). In some embodiments, the second region (220) hybridizes with a surface capture primer binding site sequence (130) (or a complementary sequence thereof) on the other end of the same linear single stranded library molecule (e.g., see FIG. 26A). [00241] In some embodiments, the single stranded library molecule (100) hybridizes to a single stranded splint strand to generate a library-splint complex (300) having one nick (e.g., see FIG. 26A). The library-splint complexes (300) can be reacted with T4 polynucleotide kinase and a ligase either sequentially or simultaneously, to (i) phosphorylate the 5’ end of the library molecule, the 5’ end of the splint strand, and to (ii) close the nick by enzymatic ligation, thereby generating a single stranded covalently closed circular library molecule (400) which is hybridized to the single stranded splint strand (e.g., see FIG. 26B). The ligase can comprise a T7 DNA ligase, a T3 ligase, a T4 ligase or a Taq ligase.

[00242] The non-circular molecules and the single stranded splint strands (200) can be degraded using at least one exonuclease enzyme, such as, for example and without limitation, a T7 exonuclease and/or an exonuclease I e.g., a thermolabile exonuclease I).

[00243] The remaining single stranded covalently closed circular library molecules (400) can be distributed onto a support having a plurality of immobilized capture primers and optionally pinning primers, and can be subjected to a rolling circle amplification reaction to generate concatemer template molecules. In some embodiments, the concatemer template molecules are generated by RCA-extension of an immobilized capture primer (e.g., see FIGS. 15-19).

[00244] The remaining single-stranded covalently closed circular library molecules (400) can be hybridized to at least one soluble amplification primer and subjected to a rolling circle amplification (RCA) reaction to generate a concatemer template molecule generated by RCA-extension of a soluble amplification primer (e.g., see FIGS. 15-19).

[00245] In some embodiments, a compact DNA nanoball comprises (i) a concatemer template molecule generated by RCA-extension of an immobilized capture primer and (ii) at least one concatemer template molecule generated by RCA-extension of a soluble amplification primer.

[00246] In some embodiments, an immobilized surface pinning primer can hybridize to at least one portion of the concatemer template molecule generated by RCA-extension of an immobilized capture primer or can hybridize to at least a portion of the concatemer template molecule generated by RCA-extension of a soluble amplification primer (e.g., FIG. 21).

[00247] In some embodiments, in any of the methods described herein, the surface pinning primer binding site sequence (120) in the library molecules comprise the sequence 5’- CATGTAATGCACGTACTTTCAGGGT -3’ (SEQ ID NO: 55). [00248] In some embodiments, in any of the methods described herein, the surface pinning primer binding site sequence (120) in the library molecules comprise the sequence 5’- AATGATACGGCGACCACCGA-3’ (SEQ ID NO: 28).

[00249] In some embodiments, in any of the methods described herein, the forward sequencing primer binding site sequence (140) in the library molecules comprises the sequence

[00250] 5’-CGTGCTGGATTGGCTCACCAGACACCTTCCGACAT -3’ (SEQ ID NO: 161).

[00251] In some embodiments, in any of the methods described herein, the forward sequencing primer binding site sequence (140) in the library molecules comprises the sequence

[00252] 5’- ACACTCTTTCCCTACACGACGCTCTTCCGATCT -3’ (SEQ ID NO: 150).

[00253] In some embodiments, in any of the methods described herein, the forward sequencing primer binding site sequence (140) in the library molecules comprise the sequence

[00254] 5’ - TCGTCGGCAGCGTCAGATGTGTATAAGAGACAG -3’ (SEQ ID NO:

174).

[00255] In some embodiments, in any of the methods described herein, the reverse sequencing primer binding site sequence (150) in the library molecules comprise the sequence

5’- ATGTCGGAAGGTGTGCAGGCTACCGCTTGTCAACT -3’ (SEQ ID NO: 156). [00256] In some embodiments, in any of the methods described herein, the reverse sequencing primer binding site sequence (150) in the library molecules comprise the sequence

5’- AGATCGGAAGAGCACACGTCTGAACTCCAGTCAC -3’ (SEQ ID NO: 152). [00257] In some embodiments, in any of the methods described herein, the reverse sequencing primer binding site sequence (150) in the library molecules comprise the sequence

5’- CTGTCTCTTATACACATCTCCGAGCCCACGAGAC -3’ (SEQ ID NO: 163).

[00258] In some embodiments, in any of the methods described herein, the surface capture primer binding site sequence (130) in the library molecules comprise the sequence 5’- AGTCGTCGCAGCCTCACCTGATC -3’ (SEQ ID NO: 109). [00259] In some embodiments, in any of the methods described herein, the surface capture primer binding site sequence (130) in the library molecules comprise the sequence 5’- TCGTATGCCGTCTTCTGCTTG -3’ (SEQ ID NO: 173).

Circularizing Polynucleotides using Double-Stranded Splint Adaptors

[00260] In some embodiments, in the methods for generating a plurality of compact DNA nanoballs immobilized to a support, the covalently closed circular polynucleotide molecules of step (a) can be generated using double stranded splint adaptors. In some embodiments, a population of the single-stranded linear polynucleotide molecules can be circularized to generate single-stranded covalently closed circular polynucleotide molecules using doublestranded splint adaptors (e.g., FIGS. 27A-27C). In some embodiments, individual single stranded linear polynucleotide molecules comprise a linear library molecule which includes a sequence of interest (an insert sequence, (110)) flanked at both ends with at least one universal adaptor sequence. For example, the single stranded linear library molecules comprises: a sequence of interest (110) and any one or any combination of two or more universal sequences including: (i) a surface pinning primer binding site sequence (120) (or a complementary sequence thereof), which can be a universal sequence; (ii) a surface capture primer binding site sequence (130) (or a complementary sequence thereof), which can be a universal sequence; (iii) at least one universal sequence for binding a first sequencing primer (e.g., the forward sequencing primer binding site sequence, (1 0)) (or a complementary sequence thereof); (iv) at least one universal sequence for binding a second sequencing primer (e.g., a reverse sequencing primer binding site sequence, (150)) (or a complementary sequence thereof); (v) at least one universal sequence for binding a soluble amplification primer (or a complementary sequence thereof); (vi) a universal sequence for binding a compaction oligonucleotide (or a complementary sequence thereof); and/or at least one sample index sequence ((160) and/or (170)) which can be used for distinguishing sequences of interest obtained from different sample sources in a multiplex assay (e.g., see FIGS. 27A- 27C).

[00261] A population of double stranded linear library molecules can be denatured to generate single stranded linear library molecules. The single stranded linear library molecules can be hybridized to double stranded splint adaptors (500) to generate library-splint complexes (800) comprising circular library molecules with two nicks (e.g., FIG. 27A). [00262] The double-stranded splint adaptors (500) comprises a first splint strand (long splint strand (600)) and a second splint strand (short splint strand (700)), where the first and second splint strands are hybridized together to form the double-stranded splint adaptor (500) having a double-stranded region and two flanking single-stranded regions (e.g., see FIG. 27A).

[00263] In some embodiments, the first splint strand (600) comprises: (i) a left sequence (620) that hybridizes to a surface pinning primer binding sequence (120) of the linear library molecule; (ii) an internal portion (610) that hybridizes to the second splint strand; and (iii) a right sequence (630) that hybridizes to a surface capture primer binding sequence (130) of the linear library molecule (e.g., see FIG. 27 A).

[00264] The second splint strand (700) introduces one or more additional adaptor sequences into the covalently closed circularized library molecule (900). The second splint strand (700) carries the additional adaptor sequence(s), such as for example an additional universal sequence for binding a capture primer on the support, an additional universal sequencing for binding a pinning primer on the support and/or an additional sample index sequence. In some embodiments, the second splint strand (700) comprises three sub-regions for example arranged in a 3’ to 5’ direction: a first sub-region, a second sub-region and a third sub-region (e.g., FIG. 27A).

[00265] In some embodiments, the first sub-region comprises an additional universal sequence for binding a capture primer on the support, an additional universal sequencing for binding a pinning primer on the support or an additional sample index sequence. In some embodiments, the second sub-region comprises an additional universal sequence for binding a capture primer on the support, an additional universal sequencing for binding a pinning primer on the support or an additional sample index sequence. In some embodiments, the third sub-region comprises an additional universal sequence for binding a capture primer on the support, an additional universal sequencing for binding a pinning primer on the support or an additional sample index sequence.

[00266] In some embodiments, the second splint strand (700) comprises an additional universal sequence for binding a capture primer on the support which differs from the universal sequence for binding a capture primer (130) in the library molecule (100). In some embodiments, the second splint strand (700) comprises an additional universal sequence for binding a pinning primer on the support which differs from the universal surface pinning primer binding site sequence (120) in the library molecule (100).

[00267] In some embodiments, the internal portion (610) of the first splint strand (600) comprises a sequence that can hybridize to the second splint strand (700). The insert sequence of interest (110) does not hybridize to the first or second splint strands. [00268] A single-stranded library molecule (100) can hybridize to a double stranded splint adaptor (500) to generate a library-splint complex (800) having two nicks (FIG. 27A). The first nick is located between the 5’ end of the library molecule and the 3’ end of the second splint strand. The second nick is located between the 3’ end of the library molecule and the 5’ end of the second splint strand.

[00269] The library-splint complexes can be reacted with T4 polynucleotide kinase and a ligase (e.g., T7 DNA ligase) either sequentially or simultaneously, to (i) phosphorylate the 5’ end of the library molecule, the 5’ end of the first splint strand, and the 5’ end of the second splint strand, and to (ii) close the first and second nicks by enzymatic ligation, thereby generating a single stranded covalently closed circular library molecule (900) which is hybridized to the first splint strand (600) (FIG. 27B). The ligase can comprise a T7 DNA ligase, a T3 ligase, a T4 ligase or a Taq ligase.

[00270] The non-circular molecules and the first splint strands can be degraded using at least one exonuclease enzyme, such as for example a T7 exonuclease and/or an exonuclease I (e.g., therm olabile exonuclease I).

[00271] The remaining single stranded covalently closed circular library molecules (900) can be distributed onto a support having a plurality of immobilized capture primers and pinning primers, and can be subjected to a rolling circle amplification reaction to generate concatemer template molecules. In some embodiments, the concatemer template molecules can be generated by RCA-extension of an immobilized capture primer (e.g., see FIGS. 15- 19).

[00272] The remaining single stranded covalently closed circular library molecules (900) can be hybridized to at least one soluble amplification primer and subjected to a rolling circle amplification (RCA) reaction to generate a concatemer template molecule generated by RCA-extension of a soluble amplification primer (e.g., see FIGS. 15-19).

[00273] In some embodiments, a compact DNA nanoball comprises (i) a concatemer template molecule generated by RCA-extension of an immobilized capture primer and (ii) at least one concatemer template molecule generated by RCA-extension of a soluble amplification primer.

[00274] In some embodiments, an immobilized pinning primer can hybridize to at least one portion of the concatemer template molecule generated by RCA-extension of an immobilized capture primer or can hybridize to at least a portion of the concatemer template molecule generated by RCA-extension of a soluble amplification primer (e.g., FIG. 21). [00275] In some embodiments, in any of the methods for forming a plurality of librarysplint complexes (800) described herein, the library molecule includes a surface pinning primer binding site sequence, (120)) which binds the first region of the first splint strand (620), where the surface pinning primer binding site sequence (120) comprises the sequence 5’- AATGATACGGCGACCACCGA-3’ (SEQ ID NO: 28).

[00276] In some embodiments, in any of the methods for forming a plurality of librarysplint complexes (800) described herein, the library molecule includes a surface pinning primer binding site sequence, (120)) which binds the first region of the first splint strand (620), where the surface pinning primer binding site sequence (120) comprises the sequence 5’- CATGTAATGCACGTACTTTCAGGGT -3’ (SEQ ID NO: 55).

[00277] In some embodiments, in any of the methods for forming a plurality of librarysplint complexes (800) described herein, the library molecule includes a forward sequencing primer binding site sequence, (140)) where the forward sequencing primer binding site sequence comprises the sequence 5’- ACACTCTTTCCCTACACGACGCTCTTCCGATCT - 3’ (SEQ ID NO: 150).

[00278] In some embodiments, in any of the methods for forming a plurality of librarysplint complexes (800) described herein, the library molecule includes a forward sequencing primer binding site sequence, (1 0)) where the forward sequencing primer binding site sequence comprises the sequence 5’- TCGTCGGCAGCGTCAGATGTGTATAAGAGACAG -3’ (SEQ ID NO: 174).

[00279] In some embodiments, in any of the methods for forming a plurality of librarysplint complexes (800) described herein, the library molecule includes a forward sequencing primer binding site sequence, (140)) where the forward sequencing primer binding site sequence comprises the sequence 5’- CGTGCTGGATTGGCTCACCAGACACCTTCCGACAT -3’ (SEQ ID NO: 161).

[00280] In some embodiments, in any of the methods for forming a plurality of librarysplint complexes (800) described herein, the library molecule includes a forward sequencing primer binding site sequence, (140)) where the forward sequencing primer binding site sequence comprises the sequence 5’ - GCTCACAGAACGACATGGCTACGATCCGACTT - 3’ (SEQ ID NO: 166).

[00281] In some embodiments, in any of the methods for forming a plurality of librarysplint complexes (800) described herein, the library molecule includes a forward sequencing primer binding site sequence, (140)) where the forward sequencing primer binding site sequence comprises the sequence 5’ - GAACGACATGGCTACGATCCGACTT -3’ (SEQ ID NO: 164).

[00282] In some embodiments, in any of the methods for forming a plurality of librarysplint complexes (800) described herein, the library molecule includes a reverse sequencing primer binding site sequence, (150)) where the reverse sequencing primer binding site sequence comprises the sequence 5’- AGATCGGAAGAGCACACGTCTGAACTCCAGTCAC -3’ (SEQ ID NO: 152).

[00283] In some embodiments, in any of the methods for forming a plurality of librarysplint complexes (800) described herein, the library molecule includes a reverse sequencing primer binding site sequence, (150)) where the reverse sequencing primer binding site sequence comprises the sequence 5’- CTGTCTCTTATACACATCTCCGAGCCCACGAGAC -3’ (SEQ ID NO: 163).

[00284] In some embodiments, in any of the methods for forming a plurality of librarysplint complexes (800) described herein, the library molecule includes a reverse sequencing primer binding site sequence, (150)) where the reverse sequencing primer binding site sequence comprises the sequence 5’- ATGTCGGAAGGTGTGCAGGCTACCGCTTGTCAACT -3’ (SEQ ID NO: 156).

[00285] In some embodiments, in any of the methods for forming a plurality of librarysplint complexes (800) described herein, the library molecule includes a reverse sequencing primer binding site sequence, (150)) where the reverse sequencing primer binding site sequence comprises the sequence 5’ - AAGTCGGAGGCCAAGCGGTCTTAGGAAGACAA -3’ (SEQ ID NO: 148).

[00286] In some embodiments, in any of the methods for forming a plurality of librarysplint complexes (800) described herein, the library molecule includes a surface capture primer binding site sequence, (130)) which binds the second region (630) of the first splint strand (600), where the surface capture primer binding site sequence comprises the sequences’- TCGTATGCCGTCTTCTGCTTG -3’ (SEQ ID NO: 173).

[00287] In some embodiments, in any of the methods for forming a plurality of librarysplint complexes (800) described herein, the library molecule includes a surface capture primer binding site sequence, (130)) which binds the second region (630) of the first splint strand (600), where the surface capture primer binding site sequence comprises the sequence 5’- AGTCGTCGCAGCCTCACCTGATC -3’ (SEQ ID NO: 109). [00288] In some embodiments, in any of the methods for forming a plurality of librarysplint complexes (800) described herein, the first sub-region of the second splint strand (700) comprises the sequence 5’- CATGTAATGCACGTACTTTCAGGGT-3’ (SEQ ID NO: 55).

[00289] In some embodiments, the second sub-region of the second splint strand (700) comprises the sequence 5’-AGTCGTCGCAGCCTCACCTGATC-3’ (SEQ ID NO: 109).

[00290] In some embodiments, the second splint strand (700) comprises a first and second sub-region comprising the sequence 5’- AGTCGTCGCAGCCTCACCTGATCCATGTAATGCACGTACTTTCAGGGT-3’ (SEQ ID NO: 155).

[00291] In some embodiments, in any of the methods for forming a plurality of librarysplint complexes (800) described herein, the first region (620) of the first splint strand (600) includes a first universal adaptor sequence which comprises a universal binding sequence (or a complementary sequence thereof) for a first surface primer (e.g., a pinning primer binding site sequence or a capture primer binding site sequence), where the first region (620) comprises the sequence 5’-TCGGTGGTCGCCGTATCATT-3’ (SEQ ID NO: 171). For example, the first region (620) of the first splint strand (600) can hybridize to a P5 surface primer or a complementary sequence of the P5 surface primer. For example, the P5 surface primer comprises the sequence

5’- AATGATACGGCGACCACCGA-3’ (short P5; SEQ ID NO: 28), or the P5 surface primer comprises the sequence 5’- AATGATACGGCGACCACCGAGATC-3’ (long P5; SEQ ID NO: 149).

[00292] In some embodiments, the second region (630) of the first splint strand (600) includes a second universal adaptor sequence which comprises a universal binding sequence (or a complementary sequence thereof) for a second surface primer (e.g., a pinning primer binding site sequence or a capture primer binding site sequence), where the second region (630) comprises the sequence 5’- CAAGCAGAAGACGGCATACGA -3’ (SEQ ID NO: 157). For example, the second region (630) of the first splint strand (600) can hybridize to a P7 surface primer or a complementary sequence of the P7 surface primer. For example, the P7 surface primer comprises the sequence 5’- CAAGCAGAAGACGGCATACGA -3’ (short P7; SEQ ID NO: 157), or the P7 surface primer comprises the sequence 5’- CAAGCAGAAGACGGCATACGAGAT-3’ (long P7; SEQ ID NO: 79).

[00293] In some embodiments, the first splint strand (600) includes an internal region (610) which comprises a fourth sub-region having the sequence

[00294] 5’-ACCCTGAAAGTACGTGCATTACATG-3’ (SEQ ID NO: 151). [00295] In some embodiments, the first splint strand (600) includes an internal region (610) which comprises a fifth sub-region having the sequence

[00296] 5’- GATCAGGTGAGGCTGCGACGACT -3’ (SEQ ID NO: 112).

[00297] In some embodiments, the first splint strand (600) comprises a first region (620), an internal region (610) having a fourth and fifth sub-region, and a second region (630), having the sequence 5’- TCGGTGGTCGCCGTATCATTACCCTGAAAGTACGTGCATTACATGGATCAGGTGA GGCTGCGACGACTCAAGCAGAAGACGGCATACGA-3’ (SEQ ID NO: 172).

Soluble Amplification Primers

[00298] In some embodiments, in any of the methods disclosed herein, the plurality of soluble amplification primers comprises single stranded oligonucleotides comprising DNA, RNA or a combination of DNA and RNA. In some embodiments, the plurality of soluble amplification primers are not immobilized to the support or immobilized to a coating on the support. The soluble amplification primers can be any length, for example 4-50 nucleotides, or 50-100 nucleotides, or 100-150 nucleotides, or any range therebetween, ,or longer lengths. In some embodiments, the 3’ terminal end of the soluble amplification primers comprises an extendible 3’ OH moiety. In some embodiments, the 3’ terminal end of the soluble amplification primers comprises a 3’ non-extendible moiety. In some embodiments, the nonextendible moiety at the 3 -terminal end of individual soluble amplification primers can be converted to a 3’ extendible end.

[00299] In some embodiments the plurality of soluble amplification primers comprises the same sequence (e.g., a universal soluble amplification primer sequence). In some embodiments, the plurality of soluble amplification primers can bind to at least a portion of the covalently closed circular polynucleotide molecules. In some embodiments, the plurality of soluble amplification primers can bind to any one or any combination of two or more of: (i) at least a portion of the sequence of interest (110); (ii) at least a portion of the universal sequence for binding a pinning primer (e.g., a surface pinning primer binding site sequence, (120)) (or a complementary sequence thereof); (iii) at least a portion of the universal sequence for binding a capture primer (e.g., a surface capture primer binding site sequence, (130)) (or a complementary sequence thereof); (iv) at least a portion of the universal sequence for binding a first sequencing primer (e.g., a forward sequencing primer binding site sequence, (1 0)); (v) at least a portion of the universal sequence for binding a second sequencing primer (e.g., a reverse sequencing primer binding site sequence, (150)); and/or (vi) at least a portion of the universal sequence for binding a compaction oligonucleotide (or a complementary sequence thereof).

[00300] In some embodiments the plurality of soluble amplification primers comprise at least a first and second sub-population of soluble amplification primers, wherein the soluble amplification primers in the first and second sub-population have different sequences. In some embodiments, the first and second sub-populations of soluble amplification primers can bind to different portions of the covalently closed circular polynucleotide molecules.

[00301] For example, the soluble amplification primers in the first sub-population can bind to any one or any combination of two or more of: (i) at least a portion of the sequence of interest (110); (ii) at least a portion of the universal sequence for binding a pinning primer (e.g., a surface pinning primer binding site sequence, (120)) (or a complementary sequence thereof); (iii) at least a portion of the universal sequence for binding a capture primer (e.g., a surface capture primer binding site sequence, (130)) (or a complementary sequence thereof); (iv) at least a portion of the universal sequence for binding a first sequencing primer (e.g., a forward sequencing primer binding site sequence, (140)); (v) at least a portion of the universal sequence for binding a second sequencing primer (e.g., a reverse sequencing primer binding site sequence, (150)); and/or (vi) at least a portion of the universal sequence for binding a compaction oligonucleotide (or a complementary sequence thereof).

[00302] For example, the soluble amplification primers in the second sub-population can bind to a different portion of the covalently closed circular polynucleotide molecules including any one or any combination of two or more of: (i) at least a portion of the sequence of interest (110); (ii) at least a portion of the universal sequence for binding a pinning primer (e.g., a surface pinning primer binding site sequence, (120)) (or a complementary sequence thereof); (iii) at least a portion of the universal sequence for binding a capture primer (e.g., a capture primer binding site sequence, (130)) (or a complementary sequence thereof); (iv) at least a portion of the universal sequence for binding a first sequencing primer (e.g., a forward sequencing primer binding site sequence, (1 0)); (v) at least a portion of the universal sequence for binding a second sequencing primer (e.g., a reverse sequencing primer binding site sequence, (150)); and/or (vi) at least a portion of the universal sequence for binding a compaction oligonucleotide (or a complementary sequence thereof).

[00303] In some embodiments, the plurality of soluble amplification primers comprises at least one phosphorothioate diester bond at their 5’ ends which can render the soluble amplification primers resistant to exonuclease degradation. In some embodiments, the plurality of soluble amplification primers comprises at least one or 2-5 or more consecutive phosphorothioate diester bonds at their 5’ ends. In some embodiments, the plurality of soluble amplification primers comprises at least one ribonucleotide and/or at least one 2’-O- methyl or 2’-O-methoxyethyl (MOE) nucleotide which can render the soluble amplification primers resistant to exonuclease degradation.

[00304] In some embodiments, the soluble amplification primers comprise at least one locked nucleic acid (LNA) which comprises a methylene bridge bond between a 2’ oxygen and 4’ carbon of the pentose ring. The soluble amplification primers that include at least one LNA can be resistant to nuclease digestions and can exhibit increased melting temperature when hybridized to a portion of the covalently closed circular polynucleotide molecules.

Rolling Circle Amplification with Uracil

[00305] In some embodiments, the rolling circle amplification (RCA) reaction of can be conducted with a plurality of strand displacing polymerases, a plurality of nucleotides, and a plurality of compaction oligonucleotides. The RCA reaction can generate a plurality of immobilized compact DNA nanoballs, wherein individual compact DNA nanoballs comprise (i) a concatemer template molecule generated by RCA-extension of an immobilized capture primer and (ii) at least one concatemer template molecule generated by RCA-extension of a soluble amplification primer. Individual covalently closed circular library molecules can be subjected to rolling circle amplification, using an immobilized capture primer and at least one soluble amplification primer, to generate multiple concatemer template molecules which increases the copy number of polynucleotide units of individual polonies. In some embodiments, each polynucleotide unit comprises a sequence of interest and at least one sequencing primer binding site. Individual polonies comprising increased copy number of polynucleotide units can increase the number of binding complexes formed on a given polony during sequencing. In some embodiments, a binding complex comprises a portion of a concatemer template molecule hybridized to a sequencing primer thereby forming a nucleic acid duplex, a sequencing polymerase, and a detectably labeled multivalent molecule or a detectably labeled free nucleotide. The increased number of binding complexes on a given polony can increase signal intensity during forward and reverse sequencing runs in a pairwise sequencing workflow (e.g., FIGS. 22A and 22B). The increased signal intensity can generate sequencing quality scores above Q30 across the length of the library insert regions (110) in pairwise sequencing runs. For example, in a forward sequencing run, the sequencing quality scores remain above Q40 at bases 100-150. FIG. 23A shows the sequencing quality scores using one soluble amplification primer, and FIG. 23B shows the sequencing quality scores using three soluble amplification primers. In a reverse sequencing run, the sequencing quality scores remain above Q35 at bases 100-150. FIG. 24A shows the sequencing quality scores using one soluble amplification primer, and FIG. 24B show the sequencing quality scores using three soluble amplification primers.

[00306] In some embodiments, in the rolling circle amplification reactions disclosed herein, the plurality of nucleotides comprises a nucleotide mixture containing dATP, dCTP, dGTP, dTTP and a nucleotide having a scissile moiety to generate immobilized compact DNA nanoballs which includes at least one nucleotide having a scissile moiety. The scissile moieties in the immobilized compact DNA nanoballs can be converted into abasic sites. In some embodiments, the nucleotide having the scissile moiety comprises uridine, 8-oxo-7,8- dihydroguanine (e.g., 8oxoG) or deoxyinosine. The uridine can be converted to an abasic site using uracil DNA glycosylase (UDG), the 8oxoG can be converted to an abasic site using FPG glycosylase, and the deoxyinosine can be converted to an abasic site using AlkA glycosylase.

[00307] In some embodiments, the nucleotide mixture can include an amount of dUTP so that a target percent of the thymidine in the resulting compact DNA nanoballs are replaced with dUTP. For example, when 30% of dTTP in the compact DNA nanoballs are to be replaced with dUTP (e.g., 30% is the target percent) then the nucleotide mixture can contain 7.5% dUTP (e.g., 30/4 = 7.5%), 17.5% dTTP, and 25% each for dATP, dCTP and dGTP. The target percent of dTTP to be replaced by dUTP can be about 0.1-1%, or about 1-5%, or about 5-10%, or about 10-20%, or about 20-30% , or about 30-45%, or about 45-50%, or any range therebetween, or a higher percent of the dTTP in the immobilized compact DNA nanoballs and are replaced with nucleotides having a scissile moiety.

[00308] In some embodiments, the nucleotide mixture can include an amount of deoxyinosine so that a target percent of the guanosine in the resulting compact DNA nanoballs are replaced with deoxyinosine. For example, when 30% of dGTP in the compact DNA nanoballs are to be replaced with deoxyinosine (e.g., 30% is the target percent) then the nucleotide mixture can contain 7.5% deoxyinosine (e.g., 30/4 = 7.5%), 17.5% dGTP, and 25% each for dATP, dCTP and dTTP. The target percent of dGTP to be replaced by deoxyinosine can be about 0.1-1%, or about 1-5%, or about 5-10%, or about 10-20%, or about 20-30% , or about 30-45%, or about 45-50%, or any range therebetween, or a higher percent of the dGTP in the immobilized compact DNA nanoballs and are replaced with nucleotides having a scissile moiety. [00309] In some embodiments, the nucleotide mixture can include an amount of 8oxoG so that a target percent of the guanosine in the resulting compact DNA nanoballs are replaced with 8oxoG. For example, when 30% of dGTP in the compact DNA nanoballs are to be replaced with 8oxoG (e.g., 30% is the target percent) then the nucleotide mixture can contain 7.5% 8oxoG (e.g., 30/4 = 7.5%), 17.5% dGTP, and 25% each for dATP, dCTP and dTTP. The target percent of dGTP to be replaced by 8oxoG can be about 0.1-1%, or about 1-5%, or about 5-10%, or about 10-20%, or about 20-30% , or about 30-45%, or about 45-50%, or any range therebetween, or a higher percent of the dGTP in the immobilized compact DNA nanoballs and are replaced with nucleotides having a scissile moiety.

[00310] In some embodiments, the rolling circle amplification reaction generates immobilized compact DNA nanoballs with incorporated nucleotides having a scissile moiety that are distributed at random positions along individual concatemer template molecules within a given compact DNA nanoball. In some embodiments, the nucleotides having a scissile moiety are distributed at different positions in the different concatemer template molecules within a given compact DNA nanoball.

Compaction Oligonucleotides

[00311] In some embodiments, the rolling circle amplification (RCA) reaction can be conducted with compaction oligonucleotides to generate single stranded concatemer template molecules having multiple copies of a polynucleotide unit arranged in tandem, where each polynucleotide unit comprises a sequence-of-interest and at least one binding site for a compaction oligonucleotide.

[00312] In some embodiments, the rolling circle amplification (RCA) reaction can be conducted with a plurality of strand displacing polymerases, a plurality of nucleotides, and a plurality of compaction oligonucleotides. The rolling circle amplification reaction can generate a plurality of immobilized compact DNA nanoballs, wherein individual compact DNA nanoballs comprise (i) a concatemer template molecule generated by RCA-extension of an immobilized capture primer and (ii) at least one concatemer template molecule generated by RCA-extension of a soluble amplification primer.

[00313] In some embodiments, inclusion of compaction oligonucleotides during rolling circle amplification can promote formation of compact DNA nanoballs having tighter size and shape compared to concatemer template molecules generated in the absence of the compaction oligonucleotides. The compact and stable characteristics of the compact DNA nanoballs can improve sequencing accuracy by increasing signal intensity and they retain their shape and size and resist unraveling during multiple sequencing cycles.

[00314] In some embodiments, individual compaction oligonucleotides in the plurality comprise at least one oligonucleotide comprising DNA, RNA, or a combination of DNA and RNA. The compaction oligonucleotides can be any length, including 20-150 nucleotides, or 30-100 nucleotides, or 40-80 nucleotides in length, or any range therebetween.

[00315] In some embodiments, individual compaction oligonucleotides in the plurality comprise one or more oligonucleotides and can have any shape including for example linear, branched, star, comb, dendrimer or other shape. In some embodiments, compaction oligonucleotides can include two, three, four or more regions that bind a concatemer template molecule (e.g., FIGS. 30-35C). The different binding regions of the compaction oligonucleotides are designed to hybridize to distal portions of the same concatemer template molecule and pull together the distal portions causing compaction of the concatemer to form a compact DNA nanoball.

[00316] In some embodiments, the compaction oligonucleotides comprise a 5’ region and a 3’ region, and optionally an intervening region between the 5’ and the 3’ regions. The intervening region can be any length, for example about 2-20 nucleotides in length. In some embodiments, the intervening region comprises a homopolymer having consecutive identical bases (e.g., AAA, GGG, CCC, TTT or UUU). In some embodiments, the intervening region comprises a non-homopolymer sequence.

[00317] The 5’ region of the compaction oligonucleotides can be wholly complementary or partially complementary along its length to a first portion of a concatemer template molecule. The 3’ region of the compaction oligonucleotides can be wholly complementary or partially complementary along its length to a second portion of the same concatemer template molecule. In some embodiments, the terminal 3’ end of the compaction oligonucleotides is not extendible in a polymerase-catalyzed extension reaction.

[00318] In some embodiments, the 5’ and the 3’ regions of individual compaction oligonucleotides can hybridize to different portions of the same concatemer template molecule generated by RCA-extension of an immobilized capture primer. In some embodiments, the 5’ and the 3’ regions of individual compaction oligonucleotides can hybridize to different portions of the same concatemer template molecule generated by RCA- extension of a soluble amplification primer.

[00319] In some embodiments, the 5’ and the 3’ regions of individual compaction oligonucleotides can hybridize to a portion of a concatemer template molecule generated by RCA-extension of an immobilized capture primer and a portion of a concatemer template molecule generated by RCA-extension of a soluble amplification primer. Individual compaction oligonucleotides can pull together a portion of a concatemer template molecule generated by RCA-extension of an immobilized capture primer and a portion of a concatemer template molecule generated by RCA-extension of a soluble amplification primer, thereby causing compaction of different concatemer template molecules generated from the same covalently closed circular library molecule (e.g., FIGS. 16-20). Inclusion of compaction oligonucleotides during RCA can promote formation of compact DNA nanoballs having tighter size and shape compared to concatemers generated in the absence of the compaction oligonucleotides.

[00320] In some embodiments, individual compaction oligonucleotides comprise at least a first and a second binding region (e.g., FIGS. 30-35C). In some embodiments, a first binding region of individual compaction oligonucleotides can hybridize to a portion of a concatemer template molecule generated by RCA-extension of an immobilized capture primer, and a second binding region of the same individual compaction oligonucleotides can hybridize to a portion of a concatemer template molecule generated by RCA-extension of a soluble amplification primer. The first and second binding regions of individual compaction oligonucleotides can pull together a portion of a concatemer template molecule generated by RCA-extension of an immobilized capture primer and a portion of a concatemer template molecule generated by RCA-extension of a soluble amplification primer, thereby causing compaction of different concatemer template molecules generated from the same covalently closed circular library molecule (e.g., FIGS. 16-20). Inclusion of compaction oligonucleotides during RCA can promote formation of compact DNA nanoballs having tighter size and shape compared to concatemers generated in the absence of the compaction oligonucleotides.

[00321] The 5’ and the 3’ regions of the compaction oligonucleotide can hybridize to binding sites in the concatemer template molecule to pull together distal portions of the concatemer template molecule causing compaction of the concatemer template molecule to form a compact DNA nanoball. For example, the 5’ region of the compaction oligonucleotide is designed to hybridize to a first portion of the concatemer template molecule, and the 3’ region of the compaction oligonucleotide is designed to hybridized to a second portion of the same concatemer template molecule. Inclusion of compaction oligonucleotides during RCA can promote formation of compact DNA nanoballs having tighter size and shape compared to concatemers generated in the absence of the compaction oligonucleotides. The compact and stable characteristics of the compact DNA nanoballs improves sequencing accuracy by increasing signal intensity and they retain their shape and size during multiple sequencing cycles.

[00322] Inclusion of compaction oligonucleotides in any rolling circle amplification reaction described herein can improve FWHM (full width half maximum) of a spot image of the compact DNA nanoball. The spot image can be represented as a Gaussian spot and the size can be measured as a FWHM. A smaller spot size as indicated by a smaller FWHM typically correlates with an improved image of the spot. In some embodiments, the FWHM of a nanoball spot can be about 10 um or smaller.

[00323] In some embodiments, the compaction oligonucleotides can include at least one region having consecutive guanines. For example, the compaction oligonucleotides can include at least one region having 2, 3, 4, 5, 6 or more consecutive guanines. In some embodiments, the compaction oligonucleotides comprise four consecutive guanines which can form a guanine tetrad structure (e.g., FIG. 14A). The guanine tetrad structure can be stabilized via Hoogsteen hydrogen bonding. The guanine tetrad structure can be stabilized by a central cation including potassium, sodium, lithium, rubidium or cesium. At least one compaction oligonucleotide can form a guanine tetrad (e.g., FIG. 14A) and hybridize to the universal binding sequences in a concatemer which can cause the concatemer to fold to form an intramolecular G-quadruplex structure (e.g., FIG. 14B). The concatemers can self-collapse to form compact DNA nanoballs. Formation of the guanine tetrads and G-quadruplexes in the nanostructures may increase the stability of the compact DNA nanoballs to retain their compact size and shape which can withstand changes in pH, temperature and/or repeated flows of reagents.

[00324] In some embodiments, individual compaction oligonucleotides in the plurality comprise nucleic acids and can have any shape including a linear, branched, star or dendrimer shape e.g., bottle brush shape) (FIGS. 30-35C). In some embodiments, a compaction oligonucleotide can fold by forming intra-molecule base pairing having duplex portions via Watson-Crick base pairing, Hoogstein base pairing and/or a G-quadruplex structure. In some embodiments, the compaction oligonucleotides comprise nucleic acids that can fold into any shape having at least one hairpin, at least one stem-loop and/or at least one star shape. In some embodiments, individual compaction oligonucleotides comprise at least two binding regions that hybridize to at least a first and a second portion of the same concatemer template molecule. In some embodiments, individual compaction oligonucleotides comprise three binding regions that hybridize to a first, second and third portion of the same concatemer template molecule. In some embodiments, individual compaction oligonucleotides comprise four binding regions that hybridize to a first, a second, a third and a fourth portion of the same concatemer template molecule. In some embodiments, individual compaction oligonucleotides comprise at least two binding sites, and each binding site hybridizes to a different concatemer template molecule.

Linear Compaction Oligonucleotides with Two Binding Regions

[00325] In some embodiments, individual compaction oligonucleotides comprise a linear nucleic acid having a first binding region and a second binding region, and optionally an intervening linker between the first and second binding regions (e.g., FIG. 30). In some embodiments, the first binding region of a compaction oligonucleotide hybridizes to a first portion of a concatemer template molecule. In some embodiments, the second binding region of the same compaction oligonucleotide hybridizes to a second portion of the same concatemer template molecule. In some embodiments, the first binding region of the compaction oligonucleotide hybridizes to at least a portion of a first universal binding sequence in the concatemer template molecule. In some embodiments, the second binding region of the compaction oligonucleotide hybridizes to at least a portion of a second universal binding sequence in the concatemer template molecule. In some embodiments, the first and second binding regions of the compaction oligonucleotide comprise the same sequence or different sequences. In some embodiments, the second binding region of the compaction oligonucleotide comprises a reverse sequence of the first binding region of the compaction oligonucleotide. In some embodiments, the orientation of the first binding region of the compaction oligonucleotide is a 5’ to 3’ orientation or a 3’ to 5’ orientation. In some embodiments, the orientation of the second binding region of the compaction oligonucleotide is a 5’ to 3’ orientation or a 3’ to 5’ orientation (FIG. 30). In FIG. 30, the 5’ to 3’ orientation of a binding region of a compaction oligonucleotide, or the 3’ to 5’ orientation of a binding region of a compaction oligonucleotide, refers to the orientation of the sugar-phosphate backbone of the binding region.

[00326] In some embodiments, a compaction oligonucleotide comprises a first binding region arranged in a 5’ to 3’ orientation and a second binding region arranged in a 5’ to 3’ orientation (FIG. 30 part (i)). In some embodiments, a compaction oligonucleotide comprises a first binding region arranged in a 3’ to 5’ orientation and a second binding region arranged in a 3’ to 5’ orientation (FIG. 30 part (ii)). In some embodiments, a compaction oligonucleotide comprises a first binding region arranged in a 3’ to 5’ orientation and a second binding region arranged in a 5’ to 3’ orientation (FIG. 30 part (iii)). In some embodiments, a compaction oligonucleotide comprises a first binding region arranged in a 5’ to 3’ orientation and a second binding region arranged in a 3’ to 5’ orientation (FIG. 30 part (iv)).

[00327] In some embodiments, the intervening linker of a compaction oligonucleotide is designed to be flexible. In some embodiments, the intervening linker of a compaction oligonucleotide is designed to be rigid. In some embodiments, the intervening linker of a compaction oligonucleotide comprises any one or any combination of nucleotides, nucleotide analogs and/or a non-nucleotide linker. In some embodiments, the intervening linker of a compaction oligonucleotide exhibits little or no hybridization to any portion of the concatemer template molecule.

Linear Compaction Oligonucleotides with Three Binding Regions

[00328] In some embodiments, the compaction oligonucleotides comprise a linear nucleic acid having a first binding region, a second binding region, a third binding region, and optionally two intervening linkers disposed between the binding regions. In some embodiments, the first intervening linker is located between the first and second binding regions. In some embodiments, the second intervening linker is located between the second and third binding regions (e.g., FIGS. 31A-31C). In some embodiments, the first binding region of the compaction oligonucleotide hybridizes to a first portion of a concatemer template molecule. In some embodiments, the second binding region of the compaction oligonucleotide hybridizes to a second portion of the same concatemer template molecule. In some embodiments, the third binding region of the compaction oligonucleotide hybridizes to a third portion of the same concatemer template molecule.

[00329] In some embodiments, a compaction oligonucleotide comprises a first binding region arranged in a 5’ to 3’ orientation, a second binding region arranged in a 5’ to 3’ orientation, and a third binding region arranged in a 5’ to 3’ orientation (FIG. 31 A part (i)). In some embodiments, a compaction oligonucleotide comprises a first binding region arranged in a 5’ to 3’ orientation, a second binding region arranged in a 5’ to 3’ orientation, and a third binding region arranged in a 3’ to 5’ orientation (FIG. 31A part (ii)). In some embodiments, a compaction oligonucleotide comprises a first binding region arranged in a 5’ to 3’ orientation, a second binding region arranged in a 3’ to 5’ orientation, and a third binding region arranged in a 3’ to 5’ orientation (FIG. 31A part (iii)). [00330] In some embodiments, a compaction oligonucleotide comprises a first binding region arranged in a 5’ to 3’ orientation, a second binding region arranged in a 3’ to 5’ orientation, and a third binding region arranged in a 5’ to 3’ orientation (FIG. 3 IB part (iv)). In some embodiments, a compaction oligonucleotide comprises a first binding region arranged in a 3’ to 5’ orientation, a second binding region arranged in a 5’ to 3’ orientation, and a third binding region arranged in a 5’ to 3’ orientation (FIG. 3 IB part (v)). In some embodiments, a compaction oligonucleotide comprises a first binding region arranged in a 3’ to 5’ orientation, a second binding region arranged in a 3’ to 5’ orientation, and a third binding region arranged in a 5’ to 3’ orientation (FIG. 3 IB part (vi)).

[00331] In some embodiments, a compaction oligonucleotide comprises a first binding region arranged in a 3’ to 5’ orientation, a second binding region arranged in a 5’ to 3’ orientation, and a third binding region arranged in a 5’ to 3’ orientation (FIG. 31C part (vii)). In some embodiments, a compaction oligonucleotide comprises a first binding region arranged in a 3’ to 5’ orientation, a second binding region arranged in a 3’ to 5’ orientation, and a third binding region arranged in a 5’ to 3’ orientation (FIG. 31C part (viii)). In some embodiments, a compaction oligonucleotide comprises a first binding region arranged in a 3’ to 5’ orientation, a second binding region arranged in a 5’ to 3’ orientation, and a third binding region arranged in a 3’ to 5’ orientation (FIG. 31C part (ix)).

[00332] In FIGS. 31 A-31C, the 5’ to 3’ orientation of a binding region of a compaction oligonucleotide, or the 3’ to 5’ orientation of a binding region of a compaction oligonucleotide, refers to the orientation of the sugar-phosphate backbone of the binding region.

[00333] In some embodiments, the first binding region of the compaction oligonucleotide hybridizes to at least a portion of a first universal binding sequence in the concatemer template molecule. In some embodiments, the second binding region of the compaction oligonucleotide hybridizes to at least a portion of a second universal binding sequence in the same concatemer template molecule. In some embodiments, the third binding region of the compaction oligonucleotide hybridizes to at least a portion of a third universal binding sequence in the same concatemer template molecule.

[00334] In some embodiments, the first binding region, the second binding region, and the third binding region of the compaction oligonucleotide comprise the same sequence or different sequences. In some embodiments, the second and the third binding regions of the compaction oligonucleotide have the same sequence, and the first binding region has a different sequence. In some embodiments, the first and the second binding regions of the compaction oligonucleotide have the same sequence, and the third binding region has a different sequence. In some embodiments, the first and the third binding regions of the compaction oligonucleotide have the same sequence, and the second binding region has a different sequence.

[00335] In some embodiments, the third binding region of the compaction oligonucleotide comprises a reverse sequence of the first binding region of the compaction oligonucleotide. In some embodiments, the second binding region of the compaction oligonucleotide comprises a sequence that is a reverse of the first binding region.

[00336] In some embodiments, the intervening linker of a compaction oligonucleotide is designed to be flexible. In some embodiments, the intervening linker of a compaction oligonucleotide is designed to be rigid. In some embodiments, the intervening linker of a compaction oligonucleotide comprises any one or any combination of nucleotides, nucleotide analogs and/or non-nucleotide linker. In some embodiments, the intervening linker of a compaction oligonucleotide exhibits little or no hybridization to any portion of the concatemer template molecule.

Star Structure Compaction Oligonucleotides with Three or More Binding Regions [00337] In some embodiments, the compaction oligonucleotides comprise a star shape nucleic acid having three or more binding arms linked together by an inner intervening linker (e.g., FIGS. 32A, 32B, 33 and 34).

[00338] In some embodiments, the inner intervening linker comprises a star-shaped polymer comprising a multifunctional core and three of more identical polymer arms radiating outwards from the core (e.g., a homostar). In some embodiments, the polymer arms comprise polyethylene oxide (PEO). In some embodiments, the polymer arms comprise polyethylene glyocol (PEG) or polyethylene oxide (PEO). In some embodiments, the polymer polyethylene glyocol (PEG) arms or the polyethylene oxide (PEO) arms having a molecular weight of about 100-200 Da, 200-300 Da, 300-400 Da, 400-500 Da or IK Da. [00339] In some embodiments, a compaction oligonucleotide comprises: (1) an inner intervening linker and a first binding region arranged in a 5’ to 3’ orientation where the 3’ end of the first binding region is directed away from the inner intervening linker; (2) an inner intervening linker and a second binding region arranged in a 5’ to 3’ orientation where the 3’ end of the second binding region is directed away from the inner intervening linker; and (3) an inner intervening linker and a third binding region arranged in a 5’ to 3’ orientation where the 3’ end of the third binding region is directed away from the inner intervening linker (FIG. 32 A part (i)).

[00340] In some embodiments, a compaction oligonucleotide comprises: (1) an inner intervening linker and a first binding region arranged in a 3’ to 5’ orientation where the 5’ end of the first binding region is directed away from the inner intervening linker; (2) an inner intervening linker and a second binding region arranged in a 3’ to 5’ orientation where the 5’ end of the second binding region is directed away from the inner intervening linker; and (3) an inner intervening linker and a third binding region arranged in a 3’ to 5’ orientation where the 5’ end of the third binding region is directed away from the inner intervening linker (FIG. 32 A part (ii)).

[00341] In some embodiments, a compaction oligonucleotide comprises: (1) an inner intervening linker and a first binding region arranged in a 5’ to 3’ orientation where the 3’ end of the first binding region is directed away from the inner intervening linker; (2) an inner intervening linker and a second binding region arranged in a 5’ to 3’ orientation where the 3’ end of the second binding region is directed away from the inner intervening linker; and (3) an inner intervening linker and a third binding region arranged in a 3’ to 5’ orientation where the 5’ end of the third binding region is directed away from the inner intervening linker (FIG. 32B part (iii)).

[00342] In some embodiments, a compaction oligonucleotide comprises: (1) an inner intervening linker and a first binding region arranged in a 5’ to 3’ orientation where the 3’ end of the first binding region is directed away from the inner intervening linker; (2) an inner intervening linker and a second binding region arranged in a 3’ to 5’ orientation where the 5’ end of the second binding region is directed away from the inner intervening linker; and (3) an inner intervening linker and a third binding region arranged in a 3’ to 5’ orientation where the 5’ end of the third binding region is directed away from the inner intervening linker (FIG. 32B part (iv)).

[00343] In FIGS. 32A-32B, the 5’ to 3’ orientation of a binding region of a compaction oligonucleotide, or the 3’ to 5’ orientation of a binding region of a compaction oligonucleotide, refers to the orientation of the sugar-phosphate backbone of the binding region.

[00344] In some embodiments, the first binding region of the compaction oligonucleotide hybridizes to at least a portion of a first universal binding sequence in the concatemer template molecule. In some embodiments, the internal region of the compaction oligonucleotide hybridizes to at least a portion of a second universal binding sequence in the concatemer template molecule. In some embodiments, the third binding region of the compaction oligonucleotide hybridizes to at least a portion of a third universal binding sequence in the concatemer template molecule. In some embodiments, the first binding region, the internal region, and the second binding region of the compaction oligonucleotide comprise the same sequence or different sequences. In some embodiments, the internal and the second binding regions of the compaction oligonucleotide have the same sequence, and the first binding region has a different sequence. In some embodiments, the first binding and the internal regions of the compaction oligonucleotide have the same sequence, and the second binding region has a different sequence. In some embodiments, the first binding and the second binding regions of the compaction oligonucleotide have the same sequence, and the internal region has a different sequence. In some embodiments, the second binding region of the compaction oligonucleotide comprises a reverse sequence of the first binding region of the compaction oligonucleotide. In some embodiments, the internal region of the compaction oligonucleotide comprises a sequence that is a reverse of the first binding region.

[00345] In some embodiments, the intervening linker of a compaction oligonucleotide is designed to be flexible or rigid. In some embodiments, the intervening linker of a compaction oligonucleotide comprises any one or any combination of nucleotides, nucleotide analogs and/or non-nucleotide linker. In some embodiments, the intervening linker of a compaction oligonucleotide exhibits little or no hybridization to any portion of the concatemer template molecule.

[00346] In some embodiments, a compaction oligonucleotide comprises three binding arms where each binding arm comprises: an inner intervening linker, a first binding region, an intervening linker, and a second binding region. In some embodiments, the first binding regions and second binding regions are both arranged in a 5’ to 3’ orientation. In some embodiments, the 3’ end of the second binding region is directed away from the intervening linker (e.g., FIG. 33). In some embodiments, the 3’ end of the first binding region is directed away from the inner intervening linker (e.g., FIG. 33). In some embodiments, each binding arm comprises, from 5’ to 3’, an inner intervening linker, a first binding region, an intervening linker, and a second binding region. In FIG. 33, the 5’ to 3’ orientation of a binding region of a compaction oligonucleotide, or the 3’ to 5’ orientation of a binding region of a compaction oligonucleotide, refers to the orientation of the sugar-phosphate backbone of the binding region.

[00347] In some embodiments, a compaction oligonucleotide comprises four binding regions, and optionally four intervening linkers. In some embodiments, a compaction oligonucleotide comprises: (1) an inner intervening linker and a first binding region arranged in a 5’ to 3’ orientation where the 3’ end of the first binding region is directed away from the inner intervening linker; (2) an inner intervening linker and a second binding region arranged in a 5’ to 3’ orientation where the 3’ end of the second binding region is directed away from the inner intervening linker; (3) an inner intervening linker and a third binding region arranged in a 5’ to 3’ orientation where the 3’ end of the third binding region is directed away from the inner intervening linker; and (4) an inner intervening linker and a fourth binding region arranged in a 5’ to 3’ orientation where the 3’ end of the fourth binding region is directed away from the inner intervening linker (FIG. 34 part (i)).

[00348] In some embodiments, a compaction oligonucleotide comprises: (1) an inner intervening linker and a first binding region arranged in a 3’ to 5’ orientation where the 5’ end of the first binding region is directed away from the inner intervening linker; (2) an inner intervening linker and a second binding region arranged in a 3’ to 5’ orientation where the 5’ end of the second binding region is directed away from the inner intervening linker; (3) an inner intervening linker and a third binding region arranged in a 3’ to 5’ orientation where the 5’ end of the third binding region is directed away from the inner intervening linker; and (4) an inner intervening linker and a fourth binding region arranged in a 3’ to 5’ orientation where the 5’ end of the fourth binding region is directed away from the inner intervening linker (FIG. 34 part (ii)).

[00349] In FIG. 34, the 5’ to 3’ orientation of a binding region of a compaction oligonucleotide, or the 3’ to 5’ orientation of a binding region of a compaction oligonucleotide, refers to the orientation of the sugar-phosphate backbone of the binding region.

Comb Structure Compaction Oligonucleotides with a Plurality of Binding Regions [00350] In some embodiments, the compaction oligonucleotide comprises at least three binding arms. In some embodiments, the compaction oligonucleotide comprises a plurality of binding arms having the same sequence. In some embodiments, individual binding arms comprise a first binding region arranged in a 5’ to 3’ orientation where the 3’ end of the first binding region is directed away from the linker moiety. In some embodiments, individual binding arms are joined to the linker moiety by an inner intervening linker (e.g., FIG. 35A). [00351] In some embodiments, the compaction oligonucleotide comprises at least three binding arms. In some embodiments, the compaction oligonucleotide comprises a plurality of binding arms having one of two different sequences. In some embodiments, individual binding arms comprise a first binding region arranged in a 5’ to 3’ orientation where the 3’ end of the first binding region is directed away from the linker moiety. In some embodiments, individual binding arms comprise a second binding region arranged in a 5’ to 3’ orientation where the 3’ end of the second binding region is directed away from the linker moiety. In some embodiments, individual binding arms are joined to the linker moiety by an inner intervening linker (e.g., FIG. 35B).

[00352] In some embodiments, the compaction oligonucleotide comprises at least three binding arms. In some embodiments, the compaction oligonucleotide comprises a plurality of binding arms having one of three different sequences. In some embodiments, individual binding arms comprise a first binding region arranged in a 5’ to 3’ orientation where the 3’ end of the first binding region is directed away from the linker moiety. In some embodiments, individual binding arms comprise a second binding region arranged in a 5’ to 3’ orientation where the 3’ end of the second binding region is directed away from the linker moiety. In some embodiments, individual binding arms comprise a third binding region arranged in a 5’ to 3’ orientation where the 3’ end of the third binding region is directed away from the linker moiety. In some embodiments, individual binding arms are joined to the linker moiety by an inner intervening linker (e.g., FIG. 35C).

[00353] In FIGS. 35A-35C, the 5’ to 3’ orientation of a binding region of a compaction oligonucleotide, or the 3’ to 5’ orientation of a binding region of a compaction oligonucleotide, refers to the orientation of the sugar-phosphate backbone of the binding region.

Intervening Regions of Compaction Oligonucleotides

[00354] In some embodiments, the intervening linker of any of the compaction oligonucleotides described herein can be a polynucleotide linker. In some embodiments, the intervening linker comprises nucleotides, nucleotide analogs, or a combination thereof. The intervening linker can be any length, for example about 2-20 nucleotides in length. The intervening linker can comprise a homopolymer having consecutive identical bases (e.g., AAA, GGG, CCC, TTT or UUU). Alternatively, or in addition, the intervening linker can comprise a non-homopolymer sequence. In some embodiments, the intervening linker comprises at least one inosine. In some embodiments, the intervening linker comprises a homopolymer having consecutive identical bases (e.g., inosine).

[00355] In some embodiments, the intervening linker comprises a spacer. In some embodiments, the spacer comprises a non-nucleotide linker. In some embodiments, the spacer comprises an 18-carbon spacer (e.g., comprising a hexa-ethyleneglycol spacer), multiple C3 spacer phosphoramidites, or a spacer 9 (triethylene glycol chain that is 9 atoms long, and includes 6 carbons and 3 oxygens), which comprises a trimethylene glycol spacer. In some embodiments, the spacer comprises a polyethylene glycol spacer, including a PEG2, PEG3 or PEG4 spacer.

[00356] In some embodiments, the intervening linker comprises at least one nonnucleotide linker and at least one PEG spacer in any arrangement. For example, the intervening linker comprises 5 ’-right arm-([PEG-spacer]-[C18-spacer])_n-left arm-3’ where “n” is 1-10. In another example, the intervening linker comprises 5’-right arm-([C18-spacer]- [PEG-spacer])_n-left arm-3’ where “n” is 1-10.

Sequences of Binding Regions of Compaction Oligonucleotides

[00357] Any of the binding regions of a compaction oligonucleotide can be wholly complementary or partially complementary along their length to a portion of a concatemer template molecule. In some embodiments, the binding regions of a compaction oligonucleotide are designed to hybridize to a universal binding sequencing in a concatemer template molecule.

[00358] In some embodiments, the compaction oligonucleotide comprises two or more binding regions, and all of the binding regions have the same sequence. In some embodiments, the compaction oligonucleotide comprises two binding regions having different sequences. In some embodiments, the compaction oligonucleotide comprises three or more binding regions and at least two of the binding regions have different sequences. [00359] In some embodiments, the compaction oligonucleotide comprises two or more binding regions and all of the binding regions have the same sequence. In some embodiments, the compaction oligonucleotide comprises two binding regions having different sequences. In some embodiments, the compaction oligonucleotide comprises three or more binding regions and at least two of the binding regions have different sequences. [00360] The first binding region of the compaction oligonucleotide can have the same sequence as the second binding region. The first binding region of the compaction oligonucleotide can have a sequence that is different from the second binding region.

[00361] In some embodiments, the first binding region of a compaction oligonucleotide comprises a sequence according to any of SEQ ID NOs: 1, 4, 7, 10, 13, 16, 19, 22, 25, 28, 31, 34, 37, 40, 43, 46, 49, 52, 55, 58, 61, 64, 67, 70, 73, 76, 79, 82, 85, 88, 91, 94, 97, 100, 103, 106, 109, 112, 115, 118, 121, 124, 127, 130, 133, 136, 139, 142, or 145 (see Table 6). [00362] In some embodiments, the second, third, fourth, fifth or any subsequent binding region of the compaction oligonucleotide comprises a sequence that is a reverse sequence of the first binding region (e.g., the reverse sequence according to any of one of SEQ ID NOs: 2, 5, 8, 11, 14, 17, 20, 23, 26, 29, 32, 35, 38, 41, 44, 47, 50, 53, 56, 59, 62, 65, 68, 71, 74, 77, 80, 83, 86, 89, 92, 95, 98, 101, 104, 107, 110, 113, 116, 119, 122, 125, 128, 131, 134, 137, 140, 143, or 146 (see Table 6). The sequence of the second, third, fourth, fifth or any subsequent binding region comprises the same sequence of the first binding region oriented in the opposite order.

[00363] In some embodiments, the first binding region of a compaction oligonucleotide comprises a sequence according to any of SEQ ID NOs: 2, 5, 8, 11, 14, 17, 20, 23, 26, 29, 32, 35, 38, 41, 44, 47, 50, 53, 56, 59, 62, 65, 68, 71, 74, 77, 80, 83, 86, 89, 92, 95, 98, 101, 104, 107, 110, 113, 116, 119, 122, 125, 128, 131, 134, 137, 140, 143, or 146 (see Table 6).

[00364] In some embodiments, the second, the third, the fourth, the fifth or any subsequent binding region of the compaction oligonucleotide comprises a sequence that is a reverse sequence of the first binding region, where the second, third, fourth, fifth or any subsequence binding region comprises any of one of SEQ ID NOs: 1, 4, 7, 10, 13, 16, 19, 22, 25, 28, 31, 34, 37, 40, 43, 46, 49, 52, 55, 58, 61, 64, 67, 70, 73, 76, 79, 82, 85, 88, 91, 94, 97, 100, 103, 106, 109, 112, 115, 118, 121, 124, 127, 130, 133, 136, 139, 142, or 145 (see Table 6).

[00365] In some embodiments, first binding region of the compaction oligonucleotide can have a sequence that is a reverse sequence of the second binding region (e.g., the reverse sequence according to any of one of SEQ ID NOs: 2, 5, 8, 11, 14, 17, 20, 23, 26, 29, 32, 35, 38, 41, 44, 47, 50, 53, 56, 59, 62, 65, 68, 71, 74, 77, 80, 83, 86, 89, 92, 95, 98, 101, 104, 107, 110, 113, 116, 119, 122, 125, 128, 131, 134, 137, 140, 143, or 146 (see Table 6).

[00366] In some embodiments, the second binding region of a compaction oligonucleotide comprises a sequence according to any of SEQ ID NOs: 1, 4, 7, 10, 13, 16, 19, 22, 25, 28, 31, 34, 37, 40, 43, 46, 49, 52, 55, 58, 61, 64, 67, 70, 73, 76, 79, 82, 85, 88, 91, 94, 97, 100, 103, 106, 109, 112, 115, 118, 121, 124, 127, 130, 133, 136, 139, 142, or 145 (see Table 6).

[00367] In some embodiments, the third binding region of a compaction oligonucleotide comprises a sequence according to any of SEQ ID NOs: 1, 4, 7, 10, 13, 16, 19, 22, 25, 28, 31, 34, 37, 40, 43, 46, 49, 52, 55, 58, 61, 64, 67, 70, 73, 76, 79, 82, 85, 88, 91, 94, 97, 100, 103, 106, 109, 112, 115, 118, 121, 124, 127, 130, 133, 136, 139, 142, or 145 (see Table 6).

[00368] In some embodiments, the fourth binding region of a compaction oligonucleotide comprises a sequence according to any of SEQ ID NOs: 1, 4, 7, 10, 13, 16, 19, 22, 25, 28, 31, 34, 37, 40, 43, 46, 49, 52, 55, 58, 61, 64, 67, 70, 73, 76, 79, 82, 85, 88, 91, 94, 97, 100, 103, 106, 109, 112, 115, 118, 121, 124, 127, 130, 133, 136, 139, 142, or 145 (see Table 6). [00369] In some embodiments, the fifth binding region of a compaction oligonucleotide comprises a sequence according to any of SEQ ID NOs: 1, 4, 7, 10, 13, 16, 19, 22, 25, 28, 31, 34, 37, 40, 43, 46, 49, 52, 55, 58, 61, 64, 67, 70, 73, 76, 79, 82, 85, 88, 91, 94, 97, 100, 103, 106, 109, 112, 115, 118, 121, 124, 127, 130, 133, 136, 139, 142, or 145 (see Table 6). [00370] In some embodiments, the subsequent binding region(s) of a compaction oligonucleotide comprise a sequence according to any of SEQ ID NOs: 1, 4, 7, 10, 13, 16, 19, 22, 25, 28, 31, 34, 37, 40, 43, 46, 49, 52, 55, 58, 61, 64, 67, 70, 73, 76, 79, 82, 85, 88, 91, 94, 97, 100, 103, 106, 109, 112, 115, 118, 121, 124, 127, 130, 133, 136, 139, 142, or 145 (see Table 6).

[00371] In some embodiments, the compaction oligonucleotides comprise a full-length sequence according to any one of SEQ ID NOs: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60, 63, 66, 69, 72, 75, 78, 81, 84, 87, 90, 93, 96, 99, 102, 105, 108, 111, 114, 117, 120, 123, 126, 129, 132, 135, 138, 141, 144, or 147 (see Table 6).

[00372] In some embodiments, the terminal 3’ end of any of the compaction oligonucleotides can include at least one additional base comprising one or more 2’-O-methyl RNA bases (e.g., designated mUmUmU) or the terminal 3’ end lacks additional 2’-O-methyl RNA bases.

[00373] In some embodiments, the compaction oligonucleotides comprise one or more modified bases or linkages at their 5’ or 3’ ends to confer certain functionalities. In some embodiments, the compaction oligonucleotides comprise at least one phosphorothioate linkages at their 5’ and/or 3’ ends to confer exonuclease resistance. In some embodiments, at least one nucleotide at or near the 3’ end comprises a 2’ fluoro base which confers exonuclease resistance. In some embodiments, the 3’ end of the compaction oligonucleotides comprise at least one 2’-O-methyl RNA base which blocks polymerase-catalyzed extension. For example, the 3’ end of the compaction oligonucleotide comprises at least one base comprising 2’-O-methyl RNA base (e.g., designated mUmUmU). In some embodiments, the compaction oligonucleotides comprise a 3’ inverted dT at their 3’ ends which blocks polymerase-catalyzed extension. In some embodiments, the compaction oligonucleotides comprise 3’ phosphorylation which blocks polymerase-catalyzed extension. In some embodiments, the compaction oligonucleotides comprise at least one locked nucleic acid (LNA) which increases the thermal stability of duplexes formed by hybridizing a compaction oligonucleotide to a concatemer template molecule. [00374] The compaction oligonucleotides can include at least one region (e.g., hybridization/binding region) having consecutive guanines. For example, the compaction oligonucleotides can include at least one region having 2, 3, 4, 5, 6 or more consecutive guanines. In some embodiments, the compaction oligonucleotides comprise four consecutive guanines which can form a guanine tetrad structure (e.g., FIG. 14A). The guanine tetrad structure can be stabilized via Hoogsteen hydrogen bonding. The guanine tetrad structure can be stabilized by a central cation including potassium, sodium, lithium, rubidium, or cesium. [00375] At least one compaction oligonucleotide can form a guanine tetrad (e.g., FIG.

14 A) and hybridize to the universal binding sequences in a concatemer which can cause the concatemer to fold to form an intramolecular G-quadruplex structure (e.g., FIG. 14B). The concatemers can self-collapse to form compact nanostructures. Formation of the guanine tetrads and G-quadruplexes in the nanostructures may increase the stability of the nanostructures to retain their compact size and shape which can withstand changes in pH, temperature and/or repeated flows of reagents.

[00376] In some embodiments, the plurality of compaction oligonucleotides comprises the same sequence. In some embodiments, the plurality of compaction oligonucleotides comprise a sequence according to any one of SEQ ID NOs: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60, 63, 66, 69, 72, 75, 78, 81, 84, 87, 90, 93, 96, 99, 102, 105, 108, 111, 114, 117, 120, 123, 126, 129, 132, 135, 138, 141, 144, or 147 (see Table 6). In some embodiments, the plurality of compaction oligonucleotides comprise a sequence according to any one of SEQ ID NOs: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60, 63, 66, 69, 72, 75, 78, 81, 84, 87, 90, 93, 96, 99, 102, 105, 108, 111, 114, 117, 120, 123, 126, 129, 132, 135, 138, 141, 144, or 147 (see Table 6), where the 3’ end of the compaction oligonucleotide also includes three bases comprising 2’-O-methyl RNA base (e.g., designated mUmUmU).

[00377] In some embodiments, the plurality of compaction oligonucleotides comprises a mixture of two or more different populations of compaction oligonucleotides having different sequences. In some embodiments, the plurality of compaction oligonucleotides comprises a mixture of 2, 3, 4, 5, 6, 7, 8, 9 or 10 different populations of compaction oligonucleotides wherein the compaction oligonucleotides in the different populations have different sequences. In some embodiments, in the mixture of different compaction oligonucleotides, any given population of compaction oligonucleotides comprise a sequence according to any one of SEQ ID NOs: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60, 63, 66, 69, 72, 75, 78, 81, 84, 87, 90, 93, 96, 99, 102, 105, 108, 111, 114, 117, 120, 123, 126, 129, 132, 135, 138, 141, 144, or 147 (see Table 6).

Quality Scores

[00378] In some embodiments, the sequencing comprises sequencing the plurality of compact DNA nanoballs in a massively parallel sequencing workflow using detectably labeled nucleotide reagents to yield increased signal intensity at any given sequencing cycle. For example, the compact DNA nanoballs exhibit increased signal intensity in long sequencing runs up to and beyond 300 sequencing cycles (e.g., FIGS. 22A and 22B). The compact DNA nanoballs also exhibit increased signal intensity in pairwise sequencing runs where the forward and reverse sequencing runs include more than 300 sequencing cycles. The increased signal intensity results in quality scores that exceed Q30 for both forward and reverse strands in a pairwise sequencing run (e.g., FIGS. 23A-23B and 24A-24B) where the insert region is about 300-350 bases in length. By contrast, DNA concatemer template molecules generated by using immobilized capture and pinning primers but lacking soluble amplification primers during RCA generate lower signal intensity and quality scores for forward and reverse strands in a pairwise sequencing run.

[00379] In some embodiments, any of the disclosed nucleic acids sequencing methods and systems can be employed and provide an average base-calling accuracy of at least 80%, at least 85%, at least 90%, at least 92%, at least 94%, at least 96%, at least 98%, at least 99%, at least 99.5%, at least 99.8%, or at least 99.9% correct over the course of a sequencing run.

[00380] In some embodiments, any of the disclosed nucleic acids sequencing methods and systems can be employed and provide an average base-calling accuracy of at least 80%, at least 85%, at least 90%, at least 92%, at least 94%, at least 96%, at least 98%, at least 99%, at least 99.5%, at least 99.8%, or at least 99.9% correct per every 1,000 bases, 10,0000 bases, 25,000 bases, 50,000 bases, 75,000 bases, or 100,000 bases called.

[00381] In some embodiments, the quality or accuracy of a sequencing run may be assessed by calculating a Phred quality score (also referred to as a quality score or “Q- score”), which indicates the probability that a given base is called incorrectly by the sequencing system. For example, in some embodiments base calling accuracy for a specific sequencing chemistry and/or sequencing system may be assessed for a large empirical data set derived from performing sequencing runs on a library of known nucleic acid sequences. The Q-score may then be calculated according to the equation: Q = -10 logioP. In some embodiments, P is the base calling error probability. A Q-score of 30, for example, indicates a probability of making a base calling error of 1 in every 1000 bases called (or a base calling accuracy of 99.9%).

[00382] In some embodiments, any of the disclosed nucleic acid sequencing methods and systems can be employed to provide a more accurate base readout. In some embodiments, for example, the disclosed nucleic acid sequencing methods and systems may provide a Q-score for base-calling accuracy over a sequencing run that ranges from about 20 to about 50. In some embodiments, the average Q-score for the run may be at least 20, at least 25, at least 30, at least 35, at least 40, at least 45, or at least 50.

[00383] In some embodiments, any of the disclosed nucleic acid sequencing methods and systems can be employed and provide a Q-score of greater than 20 for at least 50%, at least 60%, at least 70%, at least 80%, at least 85%, at least 90%, at least 95%, at least 98%, or at least 99% of the nucleotide bases identified. In some embodiments, the disclosed nucleic acid sequencing methods and systems may provide a Q-score of greater than 25 for at least 50%, at least 60%, at least 70%, at least 80%, at least 85%, at least 90%, at least 95%, at least 98%, or at least 99% of the nucleotide bases identified. In some embodiments, the disclosed nucleic acid sequencing methods and systems may provide a Q-score of greater than 30 for at least 50%, at least 60%, at least 70%, at least 80%, at least 85%, at least 90%, at least 95%, at least 98%, or at least 99% of the nucleotide bases identified. In some embodiments, the disclosed nucleic acid sequencing methods and systems may provide a Q-score of greater than 35 for at least 50%, at least 60%, at least 70%, at least 80%, at least 85%, at least 90%, at least 95%, at least 98%, or at least 99% of the nucleotide bases identified. In some embodiments, the disclosed nucleic acid sequencing methods and systems may provide a Q-score of greater than 40 for at least 50%, at least 60%, at least 70%, at least 80%, at least 85%, at least 90%, at least 95%, at least 98%, or at least 99% of the nucleotide bases identified. In some embodiments, the disclosed nucleic acid sequencing methods and systems may provide a Q- score of greater than 45 for at least 50%, at least 60%, at least 70%, at least 80%, at least 85%, at least 90%, at least 95%, at least 98%, or at least 99% of the nucleotide bases identified. In some embodiments, the disclosed compositions, methods, and systems for nucleic acid sequencing may provide a Q-score of greater than 50 for at least 50%, at least 60%, at least 70%, at least 80%, at least 85%, at least 90%, at least 95%, at least 98%, or at least 99% of the nucleotide bases identified. Batch Sequencing

[00384] For massively parallel sequencing, the limit of optical resolution impedes the ability to perform highly multiplex sequencing. Batch-specific sequencing enables sequencing a desired subset (e.g., a batch) of the template molecules immobilized to the same flow cell using selected batch-specific sequencing primers to reduce over-crowding signals and images which are generated during sequencing. The use of batch-specific sequencing primers produces optical images that are intense and resolvable. The batch-specific sequencing methods described herein have many uses. For example, the number of spots that are imaged and associated with sequencing can be counted. The counted spots can be used as a measure for target nucleic acid levels in a sample.

[00385] In some aspects, the present disclosure provides compositions, apparatus and methods for conducting separate sequencing batches on a support having concatemer template molecules immobilized thereon, where the separate sequencing batches can be conducted using any massively parallel sequencing technology. In some embodiments, a plurality of sub-populations of concatemer template molecules are immobilized to the support including at least a first and second sub-population. In some embodiments, the first subpopulation of template molecules undergo first sequencing reactions (e.g., first batch sequencing) and a region of the support is imaged to detect the first sequencing reactions, wherein the second sub-population of template molecules do not undergo sequencing reactions. In some embodiments, the second sub-population of template molecules undergo second sequencing reactions (e.g., second batch sequencing) and the same region of the support is imaged to detect the second sequencing reactions, wherein the first sub-population of concatemer template molecules do not undergo sequencing reactions. Thus, the first and second sub-populations of concatemer template molecules undergo batch sequencing.

[00386] In some embodiments, the plurality of sub-populations of nucleic acid concatemer template molecules are immobilized to the support at a high density where at least some of the concatemer template molecules in the first and second sub-populations comprise nearest neighbor template molecules that touch each other and/or overlap each other when viewed from any angle of the support including above, below or side views of the support. For example, the plurality of sub-populations of template molecules are immobilized to the support at a density of about 10² - 10¹⁵ template molecules per mm², e.g., between about 10² - 10¹⁵ template molecules per mm², between about 10⁵ - 10¹⁵ template molecules per mm², between about 10¹⁰ - 10¹⁵ template molecules per mm², between about 10³ - 10¹⁴ template molecules per mm², between about 10⁴ - 10¹³ template molecules per mm², between about IO⁵ - 10¹² template molecules per mm², between about 10⁶ - 10¹¹ template molecules per mm², between about 10⁷ - IO¹⁰ template molecules per mm², or between about 10⁸ - IO¹⁰ template molecules per mm², or any range therebetween.

[00387] In some embodiments, the support comprises a plurality of concatemer template molecules immobilized at pre-determined positions on the support (e.g., a patterned support). In some embodiments, the support comprises a plurality of template molecules immobilized at random and non-pre-determined positions on the support. In some embodiments, the support comprises a mixture of at least two sub-populations of template molecules immobilized at random and non-pre-determined positions on the support.

[00388] In some embodiments, the support lacks any contours (e.g., wells, protrusions, and the like) arranged in a pre-determined pattern. In some embodiments, the support lacks contours which include features as sites for attachment of the template molecules. In some embodiments, the support lacks interstitial regions arranged in a pre-determined pattern where the interstitial regions are sites designed to have no attached surface capture primers and/or template molecules. In some embodiments, the support lacks features that can be prepared using photo-chemical, photo-lithography, or micron-scale or nano-scale printing. [00389] In some embodiments, individual template molecules in a given sub-population of template molecules comprise a sequence of interest, a batch barcode sequence that corresponds to the sequence of interest, and a batch sequencing primer binding site sequence that corresponds to the sequence of interest. In some embodiments, a pre-determined batch barcode sequence can be linked to a given sequence of interest, thus the pre-determined batch barcode sequence corresponds to a given sequence of interest. In some embodiments, a predetermined batch sequencing primer binding site sequence can be linked to a given sequence of interest, thus the pre-determined batch sequencing primer binding site sequence corresponds to a given sequence of interest. In some embodiments, template molecules within a given sub-population have the same or different sequences of interest. In some embodiments, template molecules within a given sub-population have the same batch barcode sequence. In some embodiments, template molecules within a given sub-population have the same sequencing primer binding site sequence. Thus, the different sub-populations of template molecules can undergo batch sequencing using a batch-specific sequencing primer. [00390] In some embodiments, the sequence of interest region need not undergo sequencing. Instead, the batch barcode can be sequenced by conducting a small number of sequencing cycles to reveal the batch barcode which corresponds to its sequence of interest. In some embodiments, the batch barcode and the sequence of interest can be sequenced. [00391] In some embodiments, individual template molecules in a given sub-population of template molecules further comprise a sample index sequence that can be used to distinguish sequences of interest obtained from different sample sources in a multiplex assay. In some embodiments, template molecules within a given sub-population have the same or different sample index sequences.

[00392] In some embodiments, the sequence of interest region need not undergo sequencing. Instead, the batch barcode and the sample index can be sequenced by conducting a small number of sequencing cycles to reveal the batch barcode which corresponds to its sequence of interest and to reveal the sample index which corresponds to the sample source of the sequence of interest. In some embodiments, the template molecules lack a sample index and the batch barcode can serve as a sample index.

[00393] In some embodiments, the same portion of individual template molecules can be re-sequenced (e.g., reiterative sequencing) from the same start position to generate overlapping sequencing reads that can be aligned to a reference sequence. For example, the same portion of individual template molecules can be sequenced at least two, three, four, five, up to 50 times, up to 100 times, or more than 100 times. The start sequencing site can be any location of the template molecule and is dictated by the sequencing primers which are designed to anneal to a selected position within the template molecule. In some embodiments, the batch barcodes (or the batch barcodes and the sample indexes) can be reiteratively sequenced by repeatedly conducting a short number of sequencing cycles of the batch barcode region (or the batch barcode and the sample index regions) of a given template molecule. The reiterative sequencing reads increase the redundancy of sequencing information for individual bases in the template molecule. Reiteratively sequencing one strand of the template molecule provides enough base coverage so that pairwise sequencing of the complementary strand is not necessary.

[00394] In some embodiments, after sequencing the first and/or the second subpopulations of template molecules, the support can be re-seeded at least once with additional sub-populations of template molecules (e.g., a third sub-population) which can undergo additional batch sequencing. In some embodiments, an ongoing batch sequencing run can be stopped prior to completion (e.g., interrupted) to permit re-seeding the support with an additional sub-population of concatemer template molecules (e.g., the third sub-population) and then the interrupted batch sequencing can be resumed. Thus, the support can be re-seeded any time and/or before a previous sequencing batch is completed. [00395] In some embodiments, the support comprises a plurality of template molecules immobilized at an initial low density where most of the nearest neighbor template molecules do not touch each other and/or do not overlap each other. In some embodiments, the initial low density support comprises a plurality of concatemer template molecules having interstitial space between the concatemer template molecules.

[00396] In some embodiments, the same support can undergo a first re-seeding with additional template molecules immobilized to the support, so that the first re-seeded density has some nearest template molecules (e.g., 10 - 30% of the first immobilized re-seeded template molecules) that touch each other and/or overlap each other. In some embodiments, the resulting first re-seeded support comprises a plurality of concatemer template molecules having a reduced number of interstitial space (and/or having a reduced size of interstitial space) between the concatemer template molecules compared to the initial low density support.

[00397] In some embodiments, the same support can undergo a second re-seeding with additional template molecules immobilized to the support, so that the second re-seeded density has an increase in nearest neighbor template molecules (e.g., 25 - 50% or more of the first immobilized re-seeded template molecules) that touch each other and/or overlap each other. In some embodiments, the resulting second re-seeded support comprises a plurality of concatemer template molecules having a further reduced number of interstitial space (and/or having a further reduced size of interstitial space) between the concatemer template molecules compared to the first re-seeded density support. In some embodiments, the support can undergo multiple re-seeding workflows to generate increasing nearest neighbor template molecules that touch each other and/or overlap each other.

[00398] In some embodiments, individual template molecules comprise concatemer template molecules. In some embodiments, a concatemer template molecule can be generated by conducting a rolling circle amplification of a circularized nucleic acid library molecule. In some embodiments, a concatemer template molecule comprises a single-stranded nucleic acid strand carrying numerous tandem copies of a polynucleotide unit. In some embodiments, individual polynucleotide units comprise a sequence of interest region and at least one batch sequencing primer binding site. In some embodiments, individual polynucleotide units further comprise at least one batch barcode sequence. In some embodiments, individual polynucleotide units further comprise at least one sample index sequence. Individual polynucleotide units can bind a sequencing primer, a sequencing polymerase and a detectably-labeled nucleotide reagent (e.g., detectably labeled multivalent molecules or nucleotide analogs), to form a detectable sequencing complex. In some embodiments, individual concatemer template molecules can collapse into a compact DNA nanoball. In some embodiments, individual compact DNA nanoballs carry numerous tandem copies of a polynucleotide unit along their lengths. During batch sequencing, individual compact DNA nanoballs carry numerous detectable sequencing complexes. Thus, the compact nature of the compact DNA nanoballs increases the local concentration of detectably-labeled nucleotide reagents that are used during batch sequencing which increases the signal intensity emitted from a compact DNA nanoball to give a discrete detectable signal which can be imaged as a fluorescent spot. In some embodiments, a spot corresponds to a concatemer and each concatemer corresponds to a sequence of interest. Multiple spots can be detected and imaged simultaneously on a support having a high density of concatemer template molecules immobilized thereon.

[00399] In some embodiments, the methods described herein employ batch sequencing on high density immobilized concatemer template molecules which offers an advantage of maximizing space on a support (e.g., flow cell). Furthermore, the same seeded support can be re-used by re-seeding the support with additional concatemer template molecules and conducting additional sequencing reactions on the re-seeded concatemer template molecules. [00400] Batch sequencing can be conducted using concatemer template molecules arranged in a pre-determined manner on the support (e.g., a patterned support). Alternatively, batch sequencing can be conducted using concatemer template molecules arranged in a random manner on the support, which obviates the need to fabricate a support having organized and pre-determined features for attaching concatemer template molecules (e.g., fabrication via lithography is not needed).

[00401] By conducting short sequencing reads of the batch barcode regions of the concatemer template molecules, batch sequencing also may significantly reduce sequencing run times, reagent use, and reagent costs.

[00402] As a further advantage, when short sequencing reads of the batch barcode regions are conducted in a reiterative manner, it is not necessary to assemble the sequencing reads or to obtain a full length sequence of the sequence of interest which reduces the need for long assembly computations. Also, the redundant sequencing information obtained from the short sequencing reads can obviate the need to sequence the complementary strand of the template molecules, e.g., concatemer template molecule, thus pairwise sequencing is not necessary. [00403] Batch sequencing can also offer the flexibility of re-seeding the support any time between sequencing different batches, or an ongoing sequencing batch can be interrupted to permit re-seeding and then the ongoing batch sequencing can be resumed. The ability to reseed the support at any time increases throughput and efficiency.

[00404] Conducting batch sequencing with immobilized concatemer template molecules offers advantages over one-copy template molecules (e.g., one-copy template molecule generated via bridge amplification). For example, concatemer template molecules carry multiple sequencing primer binding sites along the same concatemer template molecule. The multiple sequencing primer binding sites can be used to generate multiple sequencing reads for increased sequencing depth. Together, reiteratively sequencing one strand of the concatemer template molecules increases sequencing base coverage and sequencing depth compared to sequencing a one-copy template molecule.

[00405] Batch sequencing has many uses including but not limited to detecting specific nucleic acids of interest, mutant nucleic acid sequences, splice variants, and their abundance levels thereof.

[00406] In some aspects, the present disclosure provides methods for sequencing comprising step (a): providing a support comprising a plurality of template molecules (e.g., concatemer template molecules) immobilized to the support. In some embodiments, the plurality of template molecules comprises a plurality of sub-populations of template molecules including at least a first and a second sub-population of template molecules. In some embodiments, the first sub-population of template molecules comprises a first batch sequencing primer binding site and at least one first sequence-of-interest. In some embodiments, the second sub-population of template molecules comprises a second batch sequencing primer binding site and at least one second sequence-of-interest. In some embodiments, template molecules within the first sub-population have the same first batch sequencing primer binding site, and have the same sequence of interest or different sequences of interest. In some embodiments, the sequence of the first batch sequencing primer binding site sequence corresponds to the first sequence of interest, or the first batch sequencing primer binding site sequence corresponds to one of the first sequences of interest in the first sub-population. In some embodiments, a pre-determined first batch sequencing primer binding site sequence can be linked to a given sequence of interest in the first sub-population, thus the pre-determined first batch sequencing primer binding site sequence corresponds to a given sequence of interest in the first sub-population. In some embodiments, a predetermined first batch sequencing primer binding site sequence can be linked to different sequences of interest in a first sub-population. [00407] In some embodiments, the sequences of interest in the first sub-population are about 50-250 bases in length, or about 250-500 bases in length, or about 500-800 bases in length, or about 800-1200 bases in length, or about 1200-2000 bases in length, or up to 2000 bases in length, or any range therebetween.

[00408] In some embodiments, template molecules within the second sub-population have the same second batch sequencing primer binding site, and have the same sequence of interest or different sequences of interest. In some embodiments, the sequence of the second batch sequencing primer binding site sequence corresponds to the second sequence of interest, or the sequence of the second batch sequencing primer binding site sequence corresponds to one of the second sequences of interest in the second sub-population. In some embodiments, a pre-determined second batch sequencing primer binding site sequence can be linked to a given sequence of interest in the second sub-population, thus the pre-determined second batch sequencing primer binding site sequence corresponds to a given sequence of interest in the second sub-population. In some embodiments, a pre-determined second batch sequencing primer binding site sequence can be linked to different sequences of interest in a second sub-population.

[00409] In some embodiments, the sequences of interest in the second sub-population are about 50-250 bases in length, or about 250-500 bases in length, or about 500-800 bases in length, or about 800-1200 bases in length, or about 1200-2000 bases in length, or any range therebetween, or up to 2000 bases in length.

[00410] In some embodiments, the first and the second batch sequencing primer binding sites have different sequences.

[00411] In some embodiments, the plurality of template molecules can be immobilized to the support at random and non-pre-determined positions on the support, or at pre-determined positions on the support (e.g., a patterned support).

[00412] In some embodiments, in the methods for sequencing of step (a), the support comprises a plurality of concatemer template molecules immobilized thereon at a density of about 10² - 10¹⁵ template molecules per mm² (immobilized concatemer template molecules). In some embodiments, the concatemer template molecules comprise a mixture of at least two sub-populations of template molecules including at least a first and second sub-population of template molecules. In some embodiments, the plurality of sub-populations of template molecules are immobilized to the support at a high density. In some embodiments, at least some of the concatemer template molecules in the first and the second sub-populations comprise nearest neighbor template molecules that touch each other and/or overlap each other when viewed from any angle of the support including above, below or side views of the support. In some embodiments, the support comprises up to 500 million template molecules immobilized thereon, or up to 1 billion template molecules immobilized thereon, or up to 2 billion template molecules immobilized thereon, or up to 3 billion template molecules immobilized thereon, or up to 4 billion template molecules immobilized thereon, or up to 5 billion template molecules immobilized thereon, or up to 6 billion template molecules immobilized thereon. In some embodiments, the support comprises up to 7 billion template molecules immobilized thereon, or up to 8 billion template molecules immobilized thereon, or up to 9 billion template molecules immobilized thereon, or up to 10 billion template molecules immobilized thereon, or up to 20 billion template molecules immobilized thereon. In some embodiments, the support comprises between about 500 million and about 20 billion template molecules immobilized thereon, between about 1 billion and about 10 billion template molecules immobilized thereon, between about 2 billion and about 9 billion template molecules immobilized thereon, between about 3 billion and about 8 billion template molecules immobilized thereon, between about 4 billion and about 7 billion template molecules immobilized thereon, or between about 5 billion and about 6 billion template molecules immobilized thereon, or any range therebetween.

[00413] In some embodiments, in the methods for sequencing of step (a), the support comprises features that are located in a random and non-pre-determined manner, where the features are sites for attachment of the template molecules.

[00414] In some embodiments, the support is passivated with at least one polymer layer comprising a plurality of surface capture primers covalently tethered to the at least one polymer layer.

[00415] In some embodiments, the support is passivated with multiple polymer layers. In some embodiments, at least one of the polymer layers comprise oligonucleotide primers including capture primers, pinning primers, or a mixture of capture and pinning primers. In some embodiments, the plurality of oligonucleotide primers comprise one type of capture primer (e.g., having that same batch capture primer sequence) or a mixture of 2-500 different types of capture primers (e.g., having 2-500 different batch capture primer sequences). In some embodiments, the plurality of oligonucleotide primers comprise one type of pinning primer (e.g., having that same batch pinning primer sequence) or a mixture of 2-500 different types of pinning primers (e.g., having 2-500 different batch pinning primer sequences). In some embodiments, the plurality of oligonucleotide types comprises between 2 and 500, between 10 and 400, between 20 and 300, between 50 and 200, between 100 and 500, between 200 and 400, between 2 and 250, between 10 and 150, between 20 and 200, or between 20 and 100 or between 5 and 50 different capture primers and/or pinning primers, or any range therebetween.

[00416] In some embodiments, the plurality of surface capture primers comprise a plurality of sub-populations of surface capture primers including at least a first and second sub-population of surface capture primers. In some embodiments, the surface capture primers in the at least first and second sub-population have different sequences. In some embodiments, the surface capture primers in the at least first and second sub-population can hybridize to and capture different circularized library molecules carrying different surface capture primer binding site sequences.

[00417] In some embodiments, the plurality of surface capture primers are randomly distributed throughout and embedded within the at least one polymer layer.

[00418] In some embodiments, the support lacks any contours (e.g., wells, protrusions, and the like) arranged in a pre-determined pattern where the contours have features that are sites for attachment of the template molecules. In some embodiments, the support lacks interstitial regions arranged in a pre-determined pattern where the interstitial regions are sites designed to have no attached template molecules.

[00419] In some embodiments, in the methods for sequencing of step (a), the support lacks partitions and/or barriers that would create separate regions of the support. Thus, the concatemer template molecules immobilized to the support are in fluid communication with each other in a massively parallel manner with no barriers to physically separate different batches of template molecules.

[00420] In some embodiments, the plurality of surface capture primers are located at predetermined positions on the at least one polymer layer and/or the plurality of surface capture primers are embedded within the at least one polymer layer at pre-determined locations.

[00421] In some embodiments, the support includes contours (e.g., wells, protrusions, and the like) arranged in a pre-determined pattern where the contours have features that are sites for attachment of the template molecules. In some embodiments, the support includes interstitial regions arranged in a pre-determined pattern where the interstitial regions are sites designed to have no attached template molecules.

[00422] In some embodiments, in the methods for sequencing of step (a), individual template molecules in the first sub-population further comprise a first batch barcode sequence which corresponds to the first sequence of interest, or the first batch barcode sequence corresponds to one of the first sequences of interest in the first sub-population. In some embodiments, a pre-determined first batch barcode sequence can be linked to a given sequence of interest in the first sub-population, thus the pre-determined first batch barcode sequence corresponds to a given sequence of interest in the first sub-population. In some embodiments, a pre-determined first batch barcode sequence can be linked to different sequences of interest in a first sub-population.

[00423] In some embodiments, individual template molecules in the second subpopulation further comprise a second batch barcode sequence which corresponds to the second sequence of interest, or the second batch barcode sequence corresponds to one of the second sequences of interest in the second sub-population. In some embodiments, a predetermined second batch barcode sequence can be linked to a given sequence of interest in the second sub-population, thus the pre-determined second batch barcode sequence corresponds to a given sequence of interest in the second sub-population. In some embodiments, a pre-determined second batch barcode sequence can be linked to different sequences of interest in a second sub-population.

[00424] In some embodiments, in the methods for sequencing of step (a), individual template molecules in the first sub-population further comprises at least one sample index sequence that can be used in a multiplex assay to distinguish the first sequences of interest obtained from different sample sources. In some embodiments, individual template molecules in the second sub-population further comprises at least one sample index sequence that can be used in a multiplex assay to distinguish the second sequences of interest obtained from different sample sources.

[00425] In some embodiments, the first batch barcode and/or the first batch sample index can include a short random sequence (e.g., NNN) that is 3-20 in length. In some embodiments, the first batch sample index sequence can include a short random sequence (e.g., NNN) that is 3-20 in length. In some embodiments, both the first batch barcode sequence and the first batch sample index sequence both include a short random sequence (e.g., NNN) that is 3-20 in length. In some embodiments, sequencing the short random sequence can provide nucleotide diversity and color balance. In some embodiments, sequencing and imaging the short random sequence can be used for polony mapping, location, and template registration because the short random sequence provides sufficient nucleotide diversity and color balance.

[00426] In some embodiments, in the first sub-population of library molecules the short random sequence (e.g., NNN) has an overall base composition of about 25% or about 20- 30% of all four nucleotide bases (e.g., A, G, C and T/U) to provide nucleotide diversity at each sequencing cycle during sequencing the short random sequence (e.g., NNN).

[00427] In some embodiments, in the first sub-population of library molecules the proportion of adenine (A) at any given position in the short random sequence is about 20- 30%, about 15-35%, or about 10-40%. In some embodiments, in the first sub-population of library molecules the proportion of guanine (G) at any given position in the short random sequence is about 20-30%, about 15-35%, or about 10-40%. In some embodiments, in the first sub-population of library molecules the proportion of cytosine (C) at any given position in the short random sequence is about 20-30%, about 15-35%, or about 10-40%. In some embodiments, in the first sub-population of library molecules the proportion of thymine (T) or uracil (U) at any given position in the short random sequence is about 20-30%, about 15- 35%, or about 10-40%.

[00428] In some embodiments, in the first sub-population of library molecules the proportion of adenine (A) and thymine (T), or the proportion of adenine (A) and uracil (U), at any given position in the short random sequence is about 10-65%. In some embodiments, in the first sub-population of library molecules the proportion of guanine (G) and cytosine (C) at any given position in the short random sequence is about 10-65%.

[00429] In some embodiments, the second batch barcode and/or the second batch sample index can include a short random sequence (e.g., NNN) that is 3-20 in length. In some embodiments, the second batch sample index can include a short random sequence (e.g., NNN) that is 3-20 in length. In some embodiments, both the second batch barcode sequence and the second batch sample index sequence both include a short random sequence (e.g., NNN) that is 3-20 in length. In some embodiments, sequencing the short random sequence can provide nucleotide diversity and color balance. In some embodiments, sequencing and imaging the short random sequence can be used for polony mapping and location and template registration because the short random sequence provides sufficient nucleotide diversity and color balance.

[00430] In some embodiments, in the second sub-population of library molecules the short random sequence (e.g., NNN) has an overall base composition of about 25% or about 20- 30% of all four nucleotide bases (e.g., A, G, C and T/U) to provide nucleotide diversity at each sequencing cycle during sequencing the short random sequence (e.g., NNN).

[00431] In some embodiments, in the second sub-population of library molecules the proportion of adenine (A) at any given position in the short random sequence is about 20- 30%, about 15-35%, or about 10-40%. In some embodiments, in the second sub-population of library molecules the proportion of guanine (G) at any given position in the short random sequence is about 20-30%, about 15-35%, or about 10-40%. In some embodiments, in the second sub-population of library molecules the proportion of cytosine (C) at any given position in the short random sequence is about 20-30%, about 15-35%, or about 10-40%. In some embodiments, in the second sub-population of library molecules the proportion of thymine (T) or uracil (U) at any given position in the short random sequence is about 20- 30%, about 15-35%, or about 10-40%.

[00432] In some embodiments, in the second sub-population of library molecules the proportion of adenine (A) and thymine (T), or the proportion of adenine (A) and uracil (U), at any given position in the short random sequence is about 10-65%. In some embodiments, in the second sub-population of library molecules the proportion of guanine (G) and cytosine (C) at any given position in the short random sequence is about 10-65%.

[00433] In some embodiments, in the methods for sequencing of step (a), the plurality of template molecules comprises concatemer template molecules. In some embodiments, the concatemer template molecules comprise at least first and second sub-populations of concatemer template molecules. In some embodiments, the concatemer template molecules can be generated by conducting rolling circle amplification (RCA) using circularized library molecules and amplification primers. In some embodiments, a concatemer template molecule comprises numerous tandem copies of a polynucleotide unit, where each polynucleotide unit comprises a sequence of interest and at least one sequencing primer binding site. In some embodiments, concatemer template molecules immobilized to a support can be generated using circularized library molecules and conducting rolling circle amplification. In some embodiments, the circularized library molecules can be generated using padlock probes, single-stranded splint strands, or double-stranded adaptors. In some embodiments, the circularized library molecules comprise a mixture of any combination of circularized padlock probes, linear library molecules circularized using single-stranded splint strands, and/or linear library molecules circularized using double-stranded adaptors. Methods for generating circularized library molecules are described herein. Methods for generating circularized library molecules are described in WO2023168444, WO2023168443, W02024011145, W02024059550, WO2025024465, the contents of each of which are incorporated by reference in their entirety herein.

[00434] In some embodiments, individual concatemers in the first sub-population comprise a plurality of tandem polynucleotide units. In some embodiments, individual polynucleotide units comprise a first sequence of interest and a first batch sequencing primer binding site sequence which corresponds to the first sequence of interest. In some embodiments, individual polynucleotide units further comprise a first batch barcode sequence which corresponds to the first sequence of interest. In some embodiments, individual polynucleotide units further comprise at least one sample index sequence that can be used in a multiplex assay to distinguish sequences of interest obtained from different sample sources. In some embodiments, concatemer template molecules in the first sub-population have the same first batch sequencing primer binding site, and have the same sequence of interest or different sequences of interest.

[00435] In some embodiments, individual concatemers in the second sub-population comprise a plurality of tandem polynucleotide units. In some embodiments, individual polynucleotide units comprise a second sequence of interest and a second batch sequencing primer binding site sequence which corresponds to the second sequence of interest. In some embodiments, individual polynucleotide units further comprise a second batch barcode sequence which corresponds to the second sequence of interest. In some embodiments, individual polynucleotide units further comprise at least one sample index sequence that can be used in a multiplex assay to distinguish sequences of interest obtained from different sample sources. In some embodiments, concatemer template molecules in the second subpopulation have the same second batch sequencing primer binding site, and have the same sequence of interest or different sequences of interest.

[00436] In some embodiments, in the methods for sequencing of step (a), the plurality of concatemer template molecules can be generated by conducting a rolling circle amplification reaction in the presence of a plurality of compaction oligonucleotides. Exemplary compaction oligonucleotides are described in W02024040058, the contents of which are incorporated by reference herein in their entirety. In some embodiments, individual compaction oligonucleotides can hybridize to two different locations on the same concatemer template molecule to pull together distal portions of the template molecule, thereby causing compaction of the concatemer template molecule to form a compact DNA nanoball. In some embodiments, individual immobilized concatemer template molecules collapse into a compact polony or nucleic acid (e.g., DNA) nanoball having a compact size and shape compared to a non-collapsed concatemer template molecule.

[00437] In some embodiments, the methods for sequencing further comprise step (b): sequencing the first sub-population of template molecules using a plurality of first batch sequencing primers, thereby generating a plurality of first batch sequencing read products. In some embodiments, the sequencing of step (b) comprises imaging a region of the support to detect the sequencing reactions of the first sub-population of template molecules.

[00438] In some embodiments, the sequencing of step (b) comprises conducting any massively parallel nucleic acid sequencing method that employs a plurality of sequencing polymerases and a plurality of nucleotide reagents. In some embodiments, the plurality of nucleotide reagents comprises nucleotides, nucleotide analogs and/or multivalent molecules. Exemplary methods are described in WO2022266470, US20240191278A1 and WO2024159166, the contents of which are incorporated by reference in their entirety herein. [00439] In some embodiments, the sequencing of step (b) comprises conducting a two- stage sequencing method. In some embodiments, the first stage comprises contacting the first sub-population of template molecules with a plurality of first batch sequencing primers, a first plurality of sequencing polymerase and a plurality of detectably labeled multivalent molecules. In some embodiments, the first stage comprises binding detectably labeled multivalent molecules to polymerase complexes to form multivalent-polymerase complexes, and detecting the multivalent-polymerase complexes. In some embodiments, individual multivalent molecules comprise a core attached to multiple nucleotide arms and each nucleotide arm is attached to a nucleotide (e.g., a nucleotide moiety) (e.g., FIGS. 1-5). In some embodiments, the multivalent molecules can be labeled with at least one detectable moiety that emits a signal. In some embodiments, the multivalent molecules can be labeled with at least one fluor ophore.

[00440] In some embodiments, individual polymerase complexes comprise a first sequencing polymerase bound to a nucleic acid duplex where the nucleic acid duplex comprises a template molecule hybridized to a sequencing primer. In some embodiments, the detectably labeled multivalent molecules bind to the polymerase complexes to form a plurality of multivalent-polymerase complexes. In some embodiments, the detectably labeled multivalent molecules are bound to the polymerase complexes in the presence of a trapping reagent. In some embodiments, the trapping reagent can be formulated to promote binding of the detectably labeled multivalent molecules to the polymerase complexes. In some embodiments, the trapping reagent can be formulated to inhibit incorporation of the nucleotide moiety of the multivalent molecules. In some embodiments, the trapping reagent comprises a plurality of multivalent molecules. In some embodiments, the trapping reagent comprises a first plurality of sequencing polymerases. In some embodiments, the at least one non-catalytic cation inhibits polymerase-catalyzed nucleotide incorporation. [00441] In some embodiments, the multivalent-polymerase complexes can be exposed to excitation illumination to induce fluorescent signals from the multivalent-polymerase complexes. In some embodiments, prior to conducting the second sequencing stage, the detectably labeled multivalent molecules can be dissociated from the polymerase complexes and removed (e.g., washing). In some embodiments, prior to conducting the sequencing second stage, the first plurality of sequencing polymerases can be dissociated from the first sub-population of template molecules wherein the first sub-population of template molecules can remain immobilized to the support and the first batch sequencing primers can be retained and can remain hybridized to the first sub-population of template molecules.

[00442] In some embodiments, the second stage of the two-stage sequencing method comprises contacting the first sub-population of template molecules and the retained first batch sequencing primers with a second plurality of sequencing polymerases and a plurality of nucleotides (e.g., non-conjugated free nucleotides). In some embodiments, the second stage comprises binding the plurality of nucleotides to the polymerase complexes to form nucleotide-polymerase complexes, and promoting nucleotide incorporation. In some embodiments, the second stage of the two-stage sequencing method comprises nucleotide incorporation and extension of the first batch sequencing primer.

[00443] In some embodiments, the plurality of nucleotides comprises fluorophore-labeled nucleotides, or the nucleotides are non-labeled. In some embodiments, when the nucleotides are fluorophore-labeled, then detecting and imaging of the incorporated nucleotides can be performed. In some embodiments, when the nucleotides are non-labeled, detecting and imaging of the incorporated nucleotides can be omitted.

[00444] In some embodiments, the nucleotides comprises chain terminating nucleotides where individual nucleotides comprise a chain terminating moiety attached to the 3’ sugar position. In some embodiments, the nucleotides are not chain terminating nucleotides. In some embodiments, when the nucleotides comprise chain terminating nucleotides, then the chain terminating moieties can be cleaved from the incorporated chain terminating nucleotides to generate an extendible 3 ’OH group.

[00445] In some embodiments, nucleotide incorporation can be conducted in the presence of a stepping reagent. In some embodiments, the stepping reagent comprises a plurality of nucleotides (e.g., non-conjugated free nucleotides), a second plurality of sequencing polymerases and at least one catalytic cation promotes polymerase-catalyzed nucleotide incorporation. In some embodiments, in the stepping reagent, the plurality of nucleotides comprises chain terminating nucleotides where individual nucleotides comprise a chain terminating moiety attached to the 3’ sugar position. In some embodiments, in the stepping reagent, the plurality of nucleotides are not chain terminating nucleotides.

[00446] In some embodiments, the sequencing of step (b) comprises conducting a two- stage sequencing method including repeating the first stage and second stage at least once thereby generating a plurality of first batch sequencing read products. In some embodiments, when conducting a two-stage sequencing method, one sequencing cycle comprises completion of a first and a second stage. In some embodiments, the sequencing of step (b) comprises conducting 4-25 sequencing cycles, or 25-50 sequencing cycles, or 50-75 sequencing cycles, or 75-100 sequencing cycles, or 100-200 sequencing cycles, or 200-500 sequencing cycles, or 500-750 sequencing cycles, or 750-1000 sequencing cycles, or any range therebetween. In some embodiments, the sequencing of step (b) comprises sequencing at least a portion of the first batch barcode and/or sequencing at least a portion of the first sample index. In some embodiments, the sequencing of step (b) comprises sequencing at least a portion of the first sequence of interest.

[00447] In some embodiments, prior to sequencing the second sub-population of template molecules, the plurality of first batch sequencing read products can be removed from the first sub-population of template molecules and the first sub-population of template molecules can be retained on the support using a de-hybridization reagent. In some embodiments, the dehybridization reagent comprises an SSC buffer (e.g., saline-sodium citrate) buffer, with or without formamide.

[00448] In some embodiments, the de-hybridization step can be conducted at a temperature that promotes nucleic acid denaturation such as for example 50 - 90 °C. In some embodiments, the first batch sequencing read products are not removed from the first subpopulation of template molecules.

[00449] In some embodiments, the sequencing reactions of the first sub-population of template molecules is stopped before initiating the sequencing reactions of the second subpopulation of template molecules.

[00450] In some embodiments, the method for sequencing further comprises step (bl): conducting short read sequencing by performing up to 1000 sequencing cycles of the first sub-population of template molecules to generate a plurality of first batch sequencing read products that comprise up to 1000 bases in length. In some embodiments, step (bl) comprises conducting 5-25 sequencing cycles, or 25-50 sequencing cycles, or 50-75 sequencing cycles, or 75-100 sequencing cycles, or 100-200 sequencing cycles, or 200-500 sequencing cycles, or 500-750 sequencing cycles, or 750-1000 sequencing cycles, or any range therebetween. In some embodiments, the first batch sequencing read products comprise a first batch barcode sequence. In some embodiments, the first batch sequencing read products comprise a first batch barcode sequence and a sample index sequence. In some embodiments, the first batch sequencing read products comprise a first batch barcode sequence and at least a portion of a first sequence of interest. In some embodiments, the first batch sequencing read products comprise a first batch barcode sequence, a sample index sequence, and at least a portion of a first sequence of interest. In some embodiments, the short read sequencing comprises hybridizing sequencing primers to sequencing primer binding sites on concatemer template molecules and conducting up to 1000 cycles of polymerase-catalyzed sequencing reactions using nucleotide reagents. In some embodiments, 500 million - 1 billion copies of the first sub-population of concatemer template molecules can be sequenced. In some embodiments, up to 1 billion, or up to 2 billion, or up to 3 billion, or up to 4 billion, or up to 5 billion copies of the first sub-population of concatemer template molecules can be sequenced. In some embodiments, up to 6 billion, or up to 7 billion, or up to 8 billion, or up to 9 billion, or up to 10 billion of the first sub-population of concatemer template molecules can be sequenced. In some embodiments, between about 500 million and about 10 billion, between about 1 billion and about 9 billion, between about 2 billion and about 8 billion, between about 3 billion and about 7 billion, between about 4 billion and about 6 billion, or any range therebetween of the first sub-population of concatemer template molecules can be sequenced.

[00451] In some embodiments, the sequencing of step (bl) comprises conducting any massively parallel nucleic acid sequencing method that employs a plurality of sequencing polymerases and a plurality of nucleotide reagents. In some embodiments, the plurality of nucleotide reagents comprise nucleotides, nucleotide analogs and/or multivalent molecules. In some embodiments, the reiterative sequencing of step (bl) comprises conducting a two- stage sequencing method described herein.

[00452] In some embodiments, the methods for sequencing further comprises step (b2): stopping/blocking the short read sequencing of step (bl). In some embodiments, the stopping/blocking comprises incorporating a chain terminating nucleotide to the 3’ terminal end of the first batch sequencing read products to inhibit further sequencing reactions. Exemplary chain terminating nucleotides include dideoxynucleotide or a nucleotide having a 2’ or 3’ chain terminating moiety.

[00453] In some embodiments, the methods for sequencing further comprise step (b3): removing the plurality of first batch sequencing read products from the template molecules of the first sub-population, and retaining the template molecules of the first sub-population. In some embodiments, the first batch sequencing read products can be removed from the template molecules by denaturation using heat and/or a de-hybridization reagent.

[00454] In some embodiments, the methods for sequencing further comprise step (b4): reiteratively sequencing the template molecules of the first sub-population by repeating steps (bl) - (b3) at least once. In some embodiments, the reiterative sequencing can be conducted 1-10 times, or 10-25 times, or 25-50 times, any range therebetween, or more than 50 times. For example, the reiterative sequencing can be conducted up to 100 times.

[00455] In some embodiments, the sequences of all of the first batch sequencing read products can be determined and aligned with a first reference sequence to confirm the presence of the first sequence of interest. The first reference sequence can be the first batch barcode and/or the first sequence of interest.

[00456] In some embodiments, hybridizing the sequencing primers to the concatemer template molecules of step (bl) can be conducted with a hybridization reagent comprising an SSC buffer (e.g., 2X saline-sodium citrate) buffer with formamide (e.g., 10-20% formamide).

[00457] In some embodiments, in step (b3) the plurality of plurality of first batch sequencing read products can be removed from the template molecules and the plurality of template molecules can be retained using a de-hybridization reagent comprising an SSC buffer (e.g., saline-sodium citrate) buffer, with or without formamide, at a temperature that promotes nucleic acid denaturation such as for example 50 - 90 °C.

[00458] In some embodiments, the methods for sequencing further comprise step (c): sequencing the second sub-population of template molecules using a plurality of second batch sequencing primers thereby generating a plurality of second batch sequencing read products and imaging the same region of the support to detect the sequencing reactions of the second sub-population of template molecules.

[00459] In some embodiments, the sequencing reactions of the first sub-population of template molecules is stopped before initiating the sequencing reactions of the second subpopulation of template molecules.

[00460] In some embodiments, the sequencing of step (c) comprises conducting any massively parallel nucleic acid sequencing method that employs a plurality of sequencing polymerases and a plurality of nucleotide reagents. In some embodiments, the plurality of nucleotide reagents comprise nucleotides, nucleotide analogs and/or multivalent molecules. Exemplary sequencing methods are described in WO2022266470, the contents of which are incorporated by reference in their entirety herein. [00461] In some embodiments, the sequencing of step (c) comprises conducting a two- stage sequencing method. In some embodiments, the first stage generally comprises contacting the second sub-population of template molecules with a plurality of second batch sequencing primers, a first plurality of sequencing polymerase and a plurality of detectably labeled multivalent molecules. In some embodiments, the first stage comprises binding detectably labeled multivalent molecules to polymerase complexes to form multivalent- polymerase complexes, and detecting the multivalent-polymerase complexes. In some embodiments, individual multivalent molecules comprise a core attached to multiple nucleotide arms and individual nucleotide arms are attached to a nucleotide (e.g., a nucleotide moiety) (e.g., FIGS. 1-5). In some embodiments, the multivalent molecules can be labeled with at least one detectable moiety that emits a signal. In some embodiments, the multivalent molecules can be labeled with at least one fluorophore.

[00462] In some embodiments, individual polymerase complexes comprise a first sequencing polymerase bound to a nucleic acid duplex where the nucleic acid duplex comprises a template molecule hybridized to a sequencing primer. In some embodiments, the detectably labeled multivalent molecules bind to the polymerase complexes to form a plurality of multivalent-polymerase complexes. In some embodiments, the detectably labeled multivalent molecules are bound to the polymerase complexes in the presence of a trapping reagent. In some embodiments, the trapping reagent can be formulated to promote binding of the detectably labeled multivalent molecules to the polymerase complexes. In some embodiments, the trapping reagent can be formulated to inhibit incorporation of the nucleotide moiety of the multivalent molecules. In some embodiments, the trapping reagent comprises a plurality of multivalent molecules, a first plurality of sequencing polymerases and at least one non-catalytic cation inhibits polymerase-catalyzed nucleotide incorporation. [00463] In some embodiments, the multivalent-polymerase complexes can be exposed to excitation illumination to induce fluorescent signals from the multivalent-polymerase complexes. In some embodiments, the fluorescent signals from the multivalent-polymerase complexes can be imaged in the presence of an imaging reagent. In some embodiments, the imaging reagent can be formulated to reduce photo damage of the fluorescently-labeled multivalent-polymerase complexes upon exposure to the excitation illumination. In some embodiments, prior to conducting the second sequencing stage, the detectably labeled multivalent molecules can be dissociated from the polymerase complexes and removed (e.g., washing). In some embodiments, prior to conducting the second sequencing stage, the first plurality of sequencing polymerases can be dissociated from the second sub-population of template molecules. In some embodiments, the second sub-population of template molecules can remain immobilized to the support and the second batch sequencing primers can be retained and remain hybridized to the second sub-population of template molecules.

[00464] In some embodiments, the second stage of the two-stage sequencing method generally comprises contacting the second sub-population of template molecules and the retained second batch sequencing primers with a second plurality of sequencing polymerases and a plurality of nucleotides (e.g., non-conjugated, free nucleotides). In some embodiments, the second stage comprises binding the plurality of nucleotides to the polymerase complexes to form nucleotide-polymerase complexes, and promoting nucleotide incorporation. In some embodiments, the second stage of the two-stage sequencing method comprises nucleotide incorporation and extension of the second batch sequencing primer.

[00465] In some embodiments, the plurality of nucleotides comprises fluorophore-labeled nucleotides, or the nucleotides are non-labeled. In some embodiments, when the nucleotides are fluorophore-labeled, then detecting and imaging of the incorporated nucleotides can be performed. In some embodiments, when the nucleotides are non-labeled, detecting and imaging of the incorporated nucleotides can be omitted.

[00466] In some embodiments, the nucleotides comprise chain terminating nucleotides where individual nucleotides comprise a chain terminating moiety attached to the 3’ sugar position. In some embodiments, the nucleotides are not chain terminating nucleotides. In some embodiments, when the nucleotides comprise chain terminating nucleotides, then the chain terminating moieties can be cleaved from the incorporated chain terminating nucleotides, e.g., to generate an extendible 3 ’OH group.

[00467] In some embodiments, nucleotide incorporation can be conducted in the presence of a stepping reagent. In some embodiments, the stepping reagent can be formulated to promote polymerase-catalyzed nucleotide incorporation. In some embodiments, the stepping reagent comprises a plurality of nucleotides (e.g., non-conjugated, free nucleotides), a second plurality of sequencing polymerases, and at least one catalytic cation promotes polymerase- catalyzed nucleotide incorporation. In some embodiments, the plurality of nucleotides in the stepping reagent comprises chain terminating nucleotides where individual nucleotides comprise a chain terminating moiety attached to the 3’ sugar position. In some embodiments, in the stepping reagent, the plurality of nucleotides are not chain terminating nucleotides.

[00468] In some embodiments, the sequencing of step (c) comprises conducting a two- stage sequencing method including repeating the first stage and second stage at least once thereby generating a plurality of second batch sequencing read products. In some

I l l embodiments, when conducting a two-stage sequencing method, one sequencing cycle comprises completion of a first and a second stage. In some embodiments, the sequencing of step (c) comprises conducting 5-25 sequencing cycles, or 25-50 sequencing cycles, or 50-75 sequencing cycles, or 75-100 sequencing cycles, or 100-200 sequencing cycles, or 200-500 sequencing cycles, or 500-750 sequencing cycles, or 750-1000 sequencing cycles, or any range therebetween. In some embodiments, the sequencing of step (c) comprises sequencing at least a portion of the second batch barcode and/or sequencing at least a portion of the second sample index. In some embodiments, the sequencing of step (c) comprises sequencing at least a portion of the second sequence of interest.

[00469] In some embodiments, prior to sequencing a subsequent sub-population of template molecules (e.g., after sequencing the second sub-population of template molecules), the plurality of second batch sequencing read products can be removed from the second subpopulation of template molecules and the second sub-population of template molecules can be retained on the support using a de-hybridization reagent. In some embodiments, the dehybridization reagent comprises an SSC buffer (e.g., saline-sodium citrate) buffer, with or without formamide, at a temperature that promotes nucleic acid denaturation such as for example 50 - 90 °C. In some embodiments, the second batch sequencing read products are not removed from the second sub-population of template molecules.

[00470] In some embodiments, the sequencing reactions of the second sub-population of template molecules is stopped before initiating the sequencing reactions of the subsequent sub-population of template molecules.

[00471] In some embodiments, the methods for sequencing further comprise step (cl): conducting short read sequencing by performing up to 1000 sequencing cycles of the second sub-population of template molecules to generate a plurality of second batch sequencing read products that comprise up to 1000 bases in length. In some embodiments, step (cl) comprises conducting 5-25 sequencing cycles, or 25-50 sequencing cycles, or 50-75 sequencing cycles, or 75-100 sequencing cycles, or 100-200 sequencing cycles, or 200-500 sequencing cycles, or 500-750 sequencing cycles, or 750-1000 sequencing cycles, or any range therebetween. In some embodiments, the second batch sequencing read products comprise a second batch barcode sequence. In some embodiments, the second batch sequencing read products comprise a second batch barcode sequence and a sample index sequence. In some embodiments, the second batch sequencing read products comprise a second batch barcode sequence and at least a portion of a second sequence of interest. In some embodiments, the second batch sequencing read products comprise a second batch barcode sequence, a sample index sequence, and at least a portion of a second sequence of interest. In some embodiments, the short read sequencing comprises hybridizing sequencing primers to sequencing primer binding sites on concatemer template molecules and conducting up to 1000 cycles of polymerase-catalyzed sequencing reactions using nucleotide reagents. In some embodiments, 500 million - 1 billion copies of the second sub-population of concatemer template molecules can be sequenced. In some embodiments, up to 1 billion, or up to 2 billion, or up to 3 billion, or up to 4 billion, or up to 5 billion copies of the second sub-population of concatemer template molecules can be sequenced. In some embodiments, up to 6 billion, or up to 7 billion, or up to 8 billion, or up to 9 billion, or up to 10 billion copies of the second subpopulation of concatemer template molecules can be sequenced. In some embodiments, between about 500 million and about 10 billion, between about 1 billion and about 9 billion, between about 2 billion and about 8 billion, between about 3 billion and about 7 billion, between about 4 billion and about 6 billion, or any range therebetween of the second subpopulation of concatemer template molecules can be sequenced.

[00472] In some embodiments, the sequencing of step (cl) comprises conducting any massively parallel nucleic acid sequencing method that employs a plurality of sequencing polymerases and a plurality of nucleotide reagents. In some embodiments, the plurality of nucleotide reagents comprises nucleotides, nucleotide analogs and/or multivalent molecules. In some embodiments, the reiterative sequencing of step (cl) comprises conducting a two- stage sequencing method described herein.

[00473] In some embodiments, the methods for sequencing further comprise step (c2): stopping and/or blocking the short read sequencing of step (cl). In some embodiments, the stopping and/or blocking comprises incorporating a chain terminating nucleotide to the 3’ terminal end of the first batch sequencing read products to inhibit further sequencing reactions. Exemplary chain terminating nucleotides include dideoxynucleotide or a nucleotide having a 2’ or 3’ chain terminating moiety.

[00474] In some embodiments, the methods for sequencing further comprise step (c3): removing the plurality of second batch sequencing read products from the template molecules of the second sub-population, and retaining the template molecules of the second subpopulation. In some embodiments, the second batch sequencing read products can be removed from the template molecules by denaturation using heat and/or a de-hybridization reagent.

[00475] In some embodiments, the methods for sequencing further comprise step (c4): reiteratively sequencing the template molecules of the second sub-population by repeating steps (cl) - (c3) at least once. In some embodiments, the reiterative sequencing can be conducted 1-10 times, or 10-25 times, or 25-50 times, any range therebetween, or more than 50 times.

[00476] In some embodiments, the sequences of all of the second batch sequencing read products can be determined and aligned with a second reference sequence to confirm the presence of the second sequence of interest. The second reference sequence can be the second batch barcode and/or the second sequence of interest.

[00477] In some embodiments, hybridizing the sequencing primers to the concatemer template molecules of step (cl) can be conducted with a hybridization reagent comprising an SSC buffer (e.g., 2X saline-sodium citrate) buffer with formamide (e.g., 10-20% formamide). [00478] In some embodiments, in step (c3) the plurality of plurality of second batch sequencing read products can be removed from the template molecules and the plurality of template molecules can be retained using a de-hybridization reagent comprising an SSC buffer (e.g., saline-sodium citrate) buffer, with or without formamide, at a temperature that promotes nucleic acid denaturation such as for example 50 - 90 °C.

Re-Seeding a Support with Interrupted Sequencing

[00479] In some aspects, the present disclosure provides methods for re-seeding a support comprising step (a): providing a support comprising a plurality of surface capture primers immobilized to the support. In some embodiments, the plurality of capture primers have the same sequence. In some embodiments, the plurality of capture primers comprise at least two sub-populations of capture primers including at least a first sub-population of capture primers having a first sequence and a second sub-population of capture primers having a second sequence. In some embodiments, the plurality of surface capture primers comprise singlestranded oligonucleotides. In some embodiments, the plurality of surface capture primers can be used to generate concatemer template molecules immobilized to the support. In some embodiments, the density of the plurality of surface capture primers is about 10² - 10¹⁵ per urn², e.g. between about 10¹⁰ and about 10¹⁵ surface capture primers per mm², between about

10⁵ and about 10¹⁵ surface capture primers per mm², between about 10³ and about 10¹⁴ surface capture primers per mm², between about 10⁴ and about 10¹³ surface capture primers per mm², between about 10⁵ and about 10¹² surface capture primers per mm², between about

10⁶ and about 10¹¹ surface capture primers per mm², between about 10⁷ and about 10¹⁰ surface capture primers per mm², or between about 10⁸ and about 10¹⁰ surface capture primers per mm², or any range therebetween. [00480] In some embodiments, the plurality of surface capture primers can be immobilized to the support at random and non-pre-determined positions. In some embodiments, the plurality of surface capture primers can be immobilized to the support at pre-determined positions (e.g., a patterned support).

[00481] In some embodiments, the support is passivated with at least one polymer layer comprising a plurality of surface capture primers covalently tethered to the at least one polymer layer. In some embodiments, the plurality of surface capture primers are randomly distributed throughout and embedded within the at least one polymer layer.

[00482] In some embodiments, the support lacks any contours (e.g., wells, protrusions, and the like) arranged in a pre-determined pattern where the contours have features that are sites for attachment (e.g., immobilization) of the template molecules.

[00483] In some embodiments, the support lacks partitions/barriers that would create separate regions of the support.

[00484] In some embodiments, the plurality of surface capture primers are located at predetermined positions on the at least one polymer layer and/or the plurality of surface capture primers are embedded within the at least one polymer layer at pre-determined locations. [00485] In some embodiments, the support includes contours (e.g., wells, protrusions, and the like) arranged in a pre-determined pattern where the contours have features that are sites for attachment of the template molecules. In some embodiments, the support includes interstitial regions arranged in a pre-determined pattern where the interstitial regions are sites designed to have no attached template molecules.

[00486] In some embodiments, the methods for re-seeding a support further comprise step (b): distributing on the support a first plurality of circularized nucleic acid library molecules under a condition suitable for hybridizing individual circularized library molecules to individual surface capture primers to generate a first plurality of primed circularized library molecules and conducting a rolling circle amplification reaction in a template-dependent manner using individual circularized library molecules in the first plurality, thereby generating a first plurality of nucleic acid concatemer template molecules immobilized to the support. In some embodiments, a subset of the surface capture primers hybridize individual circularized library molecules to generate the first plurality of concatemer template molecules. In some embodiments, the number of surface capture primers immobilized to the support exceeds the number of first plurality of circularized nucleic acid library molecules distributed onto the support. In some embodiments, the support comprises up to 500 million of a first plurality of concatemer template molecules immobilized thereon, or up to 1 billion a first plurality of concatemer template molecules immobilized thereon, or up to 2 billion a first plurality of concatemer template molecules immobilized thereon, or up to 3 billion a first plurality of concatemer template molecules immobilized thereon, or up to 4 billion a first plurality of concatemer template molecules immobilized thereon, or up to 5 billion a first plurality of concatemer template molecules immobilized thereon, or up to 6 billion a first plurality of concatemer template molecules immobilized thereon. In some embodiments, between about 500 million and about 6 billion, between about 1 billion and about 5 billion, between about 2 billion and about 6 billion, between about 1 billion and about 4 billion, between about 2 billion and about 4 billion, or any range therebetween of the first plurality of concatemer template molecules are immobilized to the support. In some embodiments, individual concatemer template molecules in the first plurality comprise a plurality of tandem copies of a polynucleotide unit. In some embodiments, individual polynucleotide units comprise a sequence of interest and a batch seeding sequencing primer binding site sequence. In some embodiments, the first plurality of circularized library molecules can be generated using padlock probes, single-stranded splint strands, or double-stranded adaptors. In some embodiments, the first plurality of circularized library molecules comprises a mixture of any combination of circularized padlock probes, linear library molecules circularized using single-stranded splint strands, and/or linear library molecules circularized using doublestranded adaptors. Methods for generating circularized library molecules are described herein.

[00487] In some embodiments, in the methods for re-seeding a support of step (b), individual circularized library molecules in the first plurality comprise a sequence of interest, a seeding batch sequencing primer binding site sequence which corresponds to the sequence of interest, and a surface capture primer binding site. In some embodiments, a pre-determined first seeding batch sequencing primer binding site sequence can be linked to a given sequence of interest in the first plurality of circularized library molecules, thus the pre-determined first seeding batch sequencing primer binding site sequence corresponds to a given sequence of interest in the first plurality of circularized library molecules. In some embodiments, a predetermined first seeding batch sequencing primer binding site sequence can be linked to different sequences of interest in a first plurality of circularized library molecules.

[00488] In some embodiments, individual circularized library molecules in the first plurality further comprise a seeding batch barcode sequence which corresponds to the sequence of interest. In some embodiments, a pre-determined first seeding batch barcode sequence can be linked to a given sequence of interest in the first plurality of circularized library molecules, thus the pre-determined first seeding batch barcode sequence corresponds to a given sequence of interest in the first plurality of circularized library molecules. In some embodiments, a pre-determined first seeding batch barcode sequence can be linked to different sequences of interest in a first plurality of circularized library molecules.

[00489] In some embodiments, individual circularized library molecules in the first plurality comprise a sequence of interest, the same seeding batch sequencing primer binding site sequence which corresponds to the sequence of interest, and individual circularized library molecules further comprise a surface capture primer binding site, and a first seeding batch barcode sequence which corresponds to the sequence of interest.

[00490] In some embodiments, the sequences of interest in the first plurality of circularized nucleic acid library molecules are about 50-250 bases in length, or about 250-500 bases in length, or about 500-800 bases in length, or about 800-1200 bases in length, or about 1200-2000 bases in length, or any range therebetween, or up to 2000 bases in length.

[00491] In some embodiments, the concentration of the first plurality of circularized nucleic acid library molecules that are distributed onto the support can be about 1-5 pM, or about 5-10 pM, or about 10-50 pM, or any range therebetween,.

[00492] In some embodiments, in the methods for re-seeding a support of step (b), the first plurality of circularized nucleic acid library molecules comprise a plurality of subpopulations of circularized library molecules including at least a first and a second subpopulation of circularized library molecules.

[00493] In some embodiments, individual circularized library molecules in the first subpopulation comprise the same first sub-population seeding batch sequencing primer binding site sequence and have the same sequence of interest or different sequences of interest. In some embodiments, the first sub-population seeding batch sequencing primer binding site sequence corresponds to the first sequence of interest. Alternatively, in some embodiments, the first sub-population seeding batch sequencing primer binding site sequence corresponds to one of the sequences of interest in the first sub-population. In some embodiments, a predetermined first sub-population seeding batch sequencing primer binding site sequence can be linked to a given sequence of interest in the first sub-population of circularized library molecules, thus the pre-determined first sub-population seeding batch sequencing primer binding site sequence corresponds to a given sequence of interest in the first sub-population of circularized library molecules. In some embodiments, a pre-determined first subpopulation seeding batch sequencing primer binding site sequence can be linked to different sequences of interest in a first sub-population of circularized library molecules. [00494] In some embodiments, individual circularized library molecules in the first subpopulation further comprise a first sub-population seeding batch barcode sequence which corresponds to the first sequence of interest. Alternatively, in some embodiments, the first sub-population seeding batch barcode sequence corresponds to one of the sequences of interest in the first sub-population. In some embodiments, a pre-determined first subpopulation seeding batch barcode sequence can be linked to a given sequence of interest in the first sub-population of circularized library molecules, thus the pre-determined first subpopulation seeding batch barcode sequence corresponds to a given sequence of interest in the first sub-population of circularized library molecules. In some embodiments, a predetermined first sub-population seeding batch barcode sequence can be linked to different sequences of interest in a first sub-population of circularized library molecules.

[00495] In some embodiments, individual circularized library molecules in the first subpopulation further comprise a sample index sequence that can be used in a multiplex assay to distinguish sequences of interest obtained from different sample sources. In some embodiments, individual circularized library molecules in the first sub-population further comprise a surface capture primer binding site. In some embodiments, individual circularized library molecules in the first sub-population further comprise a surface pinning primer binding site. In some embodiments, individual circularized library molecules in the first subpopulation further comprise a compaction oligonucleotide binding site.

[00496] In some embodiments, the sequences of interest in the first sub-population of circularized nucleic acid library molecules are about 50-250 bases in length, or about 250-500 bases in length, or about 500-800 bases in length, or about 800-1200 bases in length, or about 1200-2000 bases in length, any range therebetween, or up to 2000 bases in length.

[00497] In some embodiments, in the methods for re-seeding a support of step (b), the method comprises conducting a rolling circle amplification reaction, in a template-dependent manner using individual circularized library molecules in the first sub-population, thereby generating a first sub-population concatemer template molecules immobilized to the support. In some embodiments, a subset of the surface capture primers hybridize to individual circularized library molecules to generate the plurality of first sub-population concatemer template molecules.

[00498] In some embodiments, the first sub-population concatemer template molecules can be immobilized to the support at random and non-predetermined positions on the support, or at pre-determined positions on the support (e.g., a patterned support). [00499] In some embodiments, in the methods for re-seeding a support of step (b), individual circularized library molecules in the second sub-population comprise the same second sub-population seeding batch sequencing primer binding site sequence and have the same sequence of interest or different sequences of interest. In some embodiments, the second sub-population seeding batch sequencing primer binding site sequence corresponds to the second sequence of interest, or the second sub-population seeding batch sequencing primer binding site sequence corresponds to one of the sequences of interest in the second sub-population. In some embodiments, a pre-determined second sub-population seeding batch sequencing primer binding site sequence can be linked to a given sequence of interest in the second sub-population of circularized library molecules, thus the pre-determined second sub-population seeding batch sequencing primer binding site sequence corresponds to a given sequence of interest in the second sub-population of circularized library molecules. In some embodiments, a pre-determined second sub-population seeding batch sequencing primer binding site sequence can be linked to different sequences of interest in a second subpopulation of circularized library molecules.

[00500] In some embodiments, individual circularized library molecules in the second subpopulation further comprise a second sub-population seeding batch barcode sequence which corresponds to the second sequence of interest. Alternatively, in some embodiments, the second sub-population seeding batch barcode sequence corresponds to one of the sequences of interest in the second sub-population. In some embodiments, a pre-determined second subpopulation seeding batch barcode sequence can be linked to a given sequence of interest in the second sub-population of circularized library molecules, thus the pre-determined second subs-population seeding batch barcode sequence corresponds to a given sequence of interest in the second sub-population of circularized library molecules. In some embodiments, a predetermined second sub-population seeding batch barcode sequence can be linked to different sequences of interest in a second sub-population of circularized library molecules.

[00501] In some embodiments, individual circularized library molecules in the second subpopulation further comprise a sample index sequence that can be used in a multiplex assay to distinguish sequences of interest obtained from different sample sources. In some embodiments, individual circularized library molecules in the second sub-population further comprise a surface capture primer binding site. In some embodiments, individual circularized library molecules in the second sub-population further comprise a surface pinning primer binding site. In some embodiments, individual circularized library molecules in the second sub-population further comprise a compaction oligonucleotide binding site. [00502] In some embodiments, the sequences of interest in the second sub-population of circularized nucleic acid library molecules are about 50-250 bases in length, or about 250-500 bases in length, or about 500-800 bases in length, or about 800-1200 bases in length, or 1200- 2000 bases in length, or any range therebetween, or up to 2000 bases in length.

[00503] In some embodiments, the first sub-population seeding batch sequencing primer binding site sequence and second sub-population seeding batch sequencing primer binding site sequence have different sequences.

[00504] In some embodiments, in the methods for re-seeding a support of step (b), the method comprises conducting a rolling circle amplification reaction, in a template-dependent manner using individual circularized library molecules in the second sub-population, thereby generating a plurality of second sub-population concatemer template molecules immobilized to the support. In some embodiments, a subset of the surface capture primers hybridize to individual circularized library molecules to generate the plurality of second sub-population concatemer template molecules.

[00505] In some embodiments, the second sub-population concatemer template molecules can be immobilized to the support at random and non-predetermined positions on the support, or at pre-determined positions on the support (e.g., a patterned support).

[00506] In some embodiments, in the methods for re-seeding a support of step (b), the rolling circle amplification reaction comprises contacting the primed circularized library molecules with a plurality of a strand displacing polymerase, and a plurality of nucleotides which include dATP, dCTP, dGTP, and/or dTTP.

[00507] In some embodiments, the plurality of nucleotide further comprises a plurality of a nucleotide having a scissile moiety (e.g., uracil).

[00508] In some embodiments, the rolling circle amplification reaction of step (b) can be conducted in the presence of a plurality of compaction oligonucleotides. In some embodiments, the rolling circle amplification reaction of step (b) can be conducted in the absence of a plurality of compaction oligonucleotides. In some embodiments, individual compaction oligonucleotides can hybridize to two different locations on the same the template molecule to pull together distal portions of the template molecule causing compaction of the template molecule to form a compact DNA nanoball.

[00509] In some embodiments, the methods for re-seeding a support further comprise step (c): sequencing at least a subset of the first plurality of concatemer template molecules thereby generating a first plurality of sequencing read products. In some embodiments, the sequencing of step (c) comprises imaging a region of the support to detect the sequencing reactions of the first plurality of concatemer template molecules.

[00510] In some embodiments, the concatemer template molecules in the first plurality are sequenced. For example, at least 30-50%, or at least 50-70%, or at least 70-90%, or any range therebetween, of the concatemer template molecules in the first plurality are sequenced. In some embodiments, 500 million - 1 billion copies of the first plurality of concatemer template molecules can be sequenced. In some embodiments, up to 1 billion, or up to 2 billion, or up to 3 billion, or up to 4 billion, or up to 5 billion copies of the first plurality of concatemer template molecules can be sequenced. In some embodiments, up to 6 billion, or up to 7 billion, or up to 8 billion, or up to 9 billion, or up to 10 billion copies of the first plurality of concatemer template molecules can be sequenced. In some embodiments, between about 500 million and about 10 billion concatemer template molecules, between about 1 billion and about 9 billion concatemer template molecules, between about 2 billion and about 8 billion concatemer template molecules, between about 3 billion and about 7 billion concatemer template molecules, between about 4 billion and about 5 billion concatemer template molecules, or any range therebetween of concatemer template molecules of the first plurality of concatemer template molecules can be sequenced.

[00511] In some embodiments, the full length of the concatemer template molecules in the first plurality are sequenced. In some embodiments, a partial length of the concatemer template molecules in the first plurality are sequenced.

[00512] In some embodiments, the sequencing of step (c) comprises hybridizing sequencing primers to sequencing primers binding sites on the first plurality of concatemer template molecules and conducting up to 1000 cycles of polymerase-catalyzed sequencing reactions using nucleotide reagents. In some embodiments, the concatemer template molecules in the first plurality can be subjected to 5-25 sequencing cycles, or 25-50 sequencing cycles, or 50-75 sequencing cycles, or 75-100 sequencing cycles, or 100-200 sequencing cycles, or 200-500 sequencing cycles, or 500-750 sequencing cycles, or 750-1000 sequencing cycles, or any range therebetween.

[00513] In some embodiments, a partial length of the concatemer template molecules in the first plurality are reiteratively sequenced.

[00514] In some embodiments, in the methods for re-seeding a support of step (c), a first sub-population of the concatemer template molecules in the first plurality are sequenced using the first batch sequencing primer binding sites in the first sub-population of concatemer template molecules. [00515] In some embodiments, the full length of the concatemer template molecules in the first sub-population are sequenced. In some embodiments, a partial length of the concatemer template molecules in the first sub-population are sequenced.

[00516] In some embodiments, the sequencing of step (c) comprises hybridizing sequencing primers to sequencing primers binding sites on the first sub-population of the first plurality of concatemer template molecules and conducting up to 1000 cycles of polymerase- catalyzed sequencing reactions using nucleotide reagents. In some embodiments, the concatemer template molecules in the first sub-population can be subjected to 5-25 sequencing cycles, or 25-50 sequencing cycles, or 50-75 sequencing cycles, or 75-100 sequencing cycles, or 100-200 sequencing cycles, or 200-500 sequencing cycles, or 500-750 sequencing cycles, or 750-1000 sequencing cycles, or any range therebetween.

[00517] In some embodiments, a partial length of the concatemer template molecules in the first sub-population are reiteratively sequenced.

[00518] In some embodiments, the sequencing of step (c) comprises conducting any massively parallel nucleic acid sequencing method that employs a plurality of sequencing polymerases and a plurality of nucleotide reagents. In some embodiments, the plurality of nucleotide reagents comprises nucleotides, nucleotide analogs and/or multivalent molecules. [00519] In some embodiments, the sequencing of step (c) comprises conducting a two- stage sequencing method. In some embodiments, the first stage generally comprises contacting the first sub-population of template molecules in the first plurality with a plurality of first batch sequencing primers, a first plurality of sequencing polymerase and a plurality of detectably labeled multivalent molecules. In some embodiments, the first stage comprises binding detectably labeled multivalent molecules to polymerase complexes to form multivalent-polymerase complexes, and detecting the multivalent-polymerase complexes. In some embodiments, individual multivalent molecules comprise a core attached to multiple nucleotide arms, wherein individual nucleotide arms are attached to a nucleotide (e.g., a nucleotide moiety) (e.g., FIGS. 1-5). In some embodiments, the multivalent molecules can be labeled with at least one detectable moiety that emits a signal. In some embodiments, the multivalent molecules can be labeled with at least one fluorophore.

[00520] In some embodiments, individual polymerase complexes comprise a first sequencing polymerase bound to a nucleic acid duplex where the nucleic acid duplex comprises a nucleic acid template molecule hybridized to a sequencing primer. In some embodiments, the detectably labeled multivalent molecules bind to the polymerase complexes to form a plurality of multivalent-polymerase complexes. In some embodiments, the detectably labeled multivalent molecules are bound to the polymerase complexes in the presence of a trapping reagent. In some embodiments, the trapping reagent can be formulated to promote binding of the detectably labeled multivalent molecules to the polymerase complexes. In some embodiments, the trapping reagent can be formulated to inhibit incorporation of the nucleotide moiety of the multivalent molecules. In some embodiments, the trapping reagent comprises a plurality of multivalent molecules, a first plurality of sequencing polymerases, and at least one non-catalytic cation inhibits polymerase-catalyzed nucleotide incorporation.

[00521] In some embodiments, the multivalent-polymerase complexes can be exposed to excitation illumination to induce fluorescent signals from the multivalent-polymerase complexes. In some embodiments, prior to conducting the second sequencing stage, the detectably labeled multivalent molecules can be dissociated from the polymerase complexes and removed (e.g., washing). In some embodiments, prior to conducting the second sequencing stage, the first plurality of sequencing polymerases can be dissociated from the first sub-population of template molecules in the first plurality, wherein the first subpopulation of template molecules in the first plurality can remain immobilized to the support and the first batch sequencing primers can be retained and can remain hybridized to the first sub-population of template molecules in the first plurality.

[00522] In some embodiments, the second stage of the two-stage sequencing method comprises contacting the first sub-population of template molecules in the first plurality and the retained first batch sequencing primers with a second plurality of sequencing polymerases and a plurality of nucleotides (e.g., non-conjugated free nucleotides). In some embodiments, the second stage comprises binding the plurality of nucleotides to the polymerase complexes to form nucleotide-polymerase complexes, and promoting nucleotide incorporation. In some embodiments, the second stage of the two-stage sequencing method comprises nucleotide incorporation and extension of the first batch sequencing primer.

[00523] In some embodiments, the plurality of nucleotides comprises fluorophore-labeled nucleotides, or the nucleotides are non-labeled. In some embodiments, when the nucleotides are fluorophore-labeled, then detecting and imaging of the incorporated nucleotides can be performed. In some embodiments, when the nucleotides are non-labeled, detecting and imaging of the incorporated nucleotides can be omitted.

[00524] In some embodiments, the nucleotides comprise chain terminating nucleotides where individual nucleotides comprise a chain terminating moiety attached to the 3’ sugar position. In some embodiments, the nucleotides are not chain terminating nucleotides. In some embodiments, when the nucleotides comprise chain terminating nucleotides, the chain terminating moieties can be cleaved from the incorporated chain terminating nucleotides to generate an extendible 3 ’OH group.

[00525] In some embodiments, nucleotide incorporation can be conducted in the presence of a stepping reagent. In some embodiments, the stepping reagent can be formulated to promote polymerase-catalyzed nucleotide incorporation. In some embodiments, the stepping reagent comprises a plurality of nucleotides (e.g., non-conjugated free nucleotides), a second plurality of sequencing polymerases, and at least one catalytic cation promotes polymerase- catalyzed nucleotide incorporation. In some embodiments, in the stepping reagent, the plurality of nucleotides comprises chain terminating nucleotides. In some embodiments, individual nucleotides comprise a chain terminating moiety attached to the 3’ sugar position. In some embodiments, in the stepping reagent, the plurality of nucleotides are not chain terminating nucleotides.

[00526] In some embodiments, the sequencing of step (c) comprises conducting a two- stage sequencing method including repeating the first stage and the second stage at least once thereby generating a plurality of first batch sequencing read products. In some embodiments, when conducting a two-stage sequencing method, one sequencing cycle comprises completion of a first and a second stage. In some embodiments, the sequencing of step (c) comprises conducting 5-25 sequencing cycles, or 25-50 sequencing cycles, or 50-75 sequencing cycles, or 75-100 sequencing cycles, or 100-200 sequencing cycles, or 200-500 sequencing cycles, or 500-750 sequencing cycles, or 750-1000 sequencing cycles, or any range therebetween.

[00527] In some embodiments, in the methods for re-seeding a support of step (c), a second sub-population of the concatemer template molecules in the first plurality are sequenced using the second batch sequencing primer binding sites in the second subpopulation of concatemer template molecules.

[00528] In some embodiments, the full length of the concatemer template molecules in the second sub-population are sequenced. In some embodiments, a partial length of the concatemer template molecules in the second sub-population are sequenced.

[00529] In some embodiments, the sequencing of step (c) comprises hybridizing sequencing primers to sequencing primers binding sites on the second sub-population of the first plurality of concatemer template molecules and conducting up to 1000 cycles of polymerase-catalyzed sequencing reactions using nucleotide reagents. In some embodiments, the concatemer template molecules in the second sub-population plurality can be subjected to 5-25 sequencing cycles, or 25-50 sequencing cycles, or 50-75 sequencing cycles, or 75-100 sequencing cycles, or 100-200 sequencing cycles, or 200-500 sequencing cycles, or 500-750 sequencing cycles, or 750-1000 sequencing cycles, or any range therebetween.

[00530] In some embodiments, a partial length of the concatemer template molecules in the second sub-population are reiteratively sequenced.

[00531] In some embodiments, the sequencing of step (c) comprises conducting any massively parallel nucleic acid sequencing method that employs a plurality of sequencing polymerases and a plurality of nucleotide reagents. In some embodiments, the plurality of nucleotide reagents comprises nucleotides, nucleotide analogs and/or multivalent molecules. [00532] In some embodiments, the sequencing of step (c) comprises conducting a two- stage sequencing method. In some embodiments, the first stage comprises contacting the second sub-population of template molecules in the first plurality with a plurality of second batch sequencing primers, a first plurality of sequencing polymerase and a plurality of detectably labeled multivalent molecules. In some embodiments, the first stage comprises binding detectably labeled multivalent molecules to polymerase complexes to form multivalent-polymerase complexes, and detecting the multivalent-polymerase complexes. In some embodiments, individual multivalent molecules comprise a core attached to multiple nucleotide arms, individual nucleotide arms attached to a nucleotide (e.g., a nucleotide moiety) (e.g., FIGS. 1-5). In some embodiments, the multivalent molecules can be labeled with at least one detectable moiety that emits a signal. In some embodiments, the multivalent molecules can be labeled with at least one fluorophore.

[00533] In some embodiments, individual polymerase complexes comprise a first sequencing polymerase bound to a nucleic acid duplex where the nucleic acid duplex comprises a nucleic acid template molecule hybridized to a sequencing primer. In some embodiments, the detectably labeled multivalent molecules bind to the polymerase complexes to form a plurality of multivalent-polymerase complexes. In some embodiments, the detectably labeled multivalent molecules are bound to the polymerase complexes in the presence of a trapping reagent. In some embodiments, the trapping reagent can be formulated to promote binding of the detectably labeled multivalent molecules to the polymerase complexes. In some embodiments, the trapping reagent can be formulated to inhibit incorporation of the nucleotide moiety of the multivalent molecules. In some embodiments, the trapping reagent comprises a plurality of multivalent molecules, a first plurality of sequencing polymerases, and at least one non-catalytic cation inhibits polymerase-catalyzed nucleotide incorporation. [00534] In some embodiments, the multivalent-polymerase complexes can be exposed to excitation illumination to induce fluorescent signals from the multivalent-polymerase complexes. In some embodiments, prior to conducting the second sequencing stage, the detectably labeled multivalent molecules can be dissociated from the polymerase complexes and removed (e.g., washing). In some embodiments, prior to conducting the second sequencing stage, the first plurality of sequencing polymerases can be dissociated from the second sub-population of the first plurality of template molecules. In some embodiments, the second sub-population of the first plurality of template molecules can remain immobilized to the support and the second batch sequencing primers can be retained and can remain hybridized to the second sub-population of the first plurality of template molecules.

[00535] In some embodiments, the second stage of the two-stage sequencing method generally comprises contacting the second sub-population of template molecules in the first plurality and the retained second batch sequencing primers with a second plurality of sequencing polymerases and a plurality of nucleotides (e.g., non-conjugated free nucleotides). In some embodiments, the second stage comprises binding the plurality of nucleotides to the polymerase complexes to form nucleotide-polymerase complexes, and promoting nucleotide incorporation. In some embodiments, the second stage of the two-stage sequencing method comprises nucleotide incorporation and extension of the second batch sequencing primer. [00536] In some embodiments, the plurality of nucleotides comprise fluorophore-labeled nucleotides, or the nucleotides are non-labeled. In some embodiments, when the nucleotides are fluorophore-labeled, detecting and imaging of the incorporated nucleotides can be performed. In some embodiments, when the nucleotides are non-labeled, detecting and imaging of the incorporated nucleotides can be omitted.

[00537] In some embodiments, the nucleotides comprises chain terminating nucleotides where individual nucleotides comprise a chain terminating moiety attached to the 3’ sugar position. In some embodiments, the nucleotides are not chain terminating nucleotides. In some embodiments, when the nucleotides comprise chain terminating nucleotides, the chain terminating moieties can be cleaved from the incorporated chain terminating nucleotides to generate an extendible 3 ’OH group.

[00538] In some embodiments, nucleotide incorporation can be conducted in the presence of a stepping reagent. In some embodiments, the stepping reagent can be formulated to promote polymerase-catalyzed nucleotide incorporation. In some embodiments, the stepping reagent comprises a plurality of nucleotides (e.g., non-conjugated free nucleotides), a second plurality of sequencing polymerases, and at least one catalytic cation promotes polymerase- catalyzed nucleotide incorporation. In some embodiments, in the stepping reagent, the plurality of nucleotides comprises chain terminating nucleotides where individual nucleotides comprise a chain terminating moiety attached to the 3’ sugar position. In some embodiments, the plurality of nucleotides in the stepping reagent are not chain terminating nucleotides. [00539] In some embodiments, the sequencing of step (c) comprises conducting a two- stage sequencing method including repeating the first stage and the second stage at least once thereby generating a plurality of second batch sequencing read products. In some embodiments, when conducting a two-stage sequencing method, one sequencing cycle comprises completion of a first and a second stage. In some embodiments, the sequencing of step (c) comprises conducting 5-25 sequencing cycles, or 25-50 sequencing cycles, or 50-75 sequencing cycles, or 75-100 sequencing cycles, or 100-200 sequencing cycles, or 200-500 sequencing cycles, or 500-750 sequencing cycles, or 750-1000 sequencing cycles, or any range therebetween.

[00540] In some embodiments, the methods for re-seeding a support further comprise step (d): distributing on the support a second plurality of circularized nucleic acid library molecules under a condition suitable for hybridizing individual circularized library molecules to individual surface capture primers and conducting a second rolling circle amplification reaction, in a template-dependent manner using individual circularized library molecules in the second plurality as templates, thereby generating a second plurality of concatemer template molecules immobilized to the support. In some embodiments, the support comprises up to 500 million copies of a second plurality of concatemer template molecules immobilized thereon, or up to 1 billion copies of a second plurality of concatemer template molecules immobilized thereon, or up to 2 billion copies of a second plurality of concatemer template molecules immobilized thereon, or up to 3 billion copies of a second plurality of concatemer template molecules immobilized thereon, or up to 4 billion copies of a second plurality of concatemer template molecules immobilized thereon, or up to 5 billion copies of a second plurality of concatemer template molecules immobilized thereon, or up to 6 billion copies of a second plurality of concatemer template molecules immobilized thereon. In some embodiments, between about 500 million and about 6 billion, between about 1 billion and about 5 billion, between about 2 billion and about 6 billion, between about 1 billion and about 4 billion, between about 2 billion and about 4 billion, or any range therebetween of the second plurality of concatemer template molecules are immobilized to the support. In some embodiments, individual concatemer template molecules in the second plurality comprise a plurality of tandem copies of a polynucleotide unit. In some embodiments, individual polynucleotide units comprise a sequence of interest and a batch seeding sequencing primer binding site sequence. In some embodiments, the first plurality of concatemer template molecules of step (c) can be completely sequenced or the sequencing can be interrupted at any time prior to distributing the second plurality of circularized nucleic acid library molecules onto the support of step (d). In some embodiments, the second plurality of circularized library molecules can be generated using padlock probes, single-stranded splint strands, or double-stranded adaptors. In some embodiments, the second plurality of circularized library molecules comprises a mixture of any combination of circularized padlock probes, linear library molecules circularized using single-stranded splint strands, and/or linear library molecules circularized using double-stranded adaptors. Methods for generating circularized library molecules are described herein.

[00541] In some embodiments, in the methods for re-seeding the support of step (d), individual circularized library molecules in the second plurality comprise a sequence of interest, a seeding batch sequencing primer binding site sequence which corresponds to the sequence of interest, and a surface capture primer binding site. In some embodiments, a predetermined second seeding batch sequencing primer binding site sequence can be linked to a given sequence of interest in the second plurality of circularized library molecules (or can be linked to different sequences of interest in a second plurality of circularized library molecules), thus the pre-determined second seeding batch sequencing primer binding site sequence corresponds to a given sequence of interest in the second plurality of circularized library molecules. In some embodiments, a pre-determined second seeding batch sequencing primer binding site sequence can be linked to different sequences of interest in a second plurality of circularized library molecules.

[00542] In some embodiments, individual circularized library molecules in the second plurality further comprise a seeding batch barcode sequence which corresponds to the sequence of interest.

[00543] In some embodiments, a pre-determined second seeding batch barcode sequence can be linked to a given sequence of interest in the second plurality of circularized library molecules, thus the pre-determined second seeding batch barcode sequence corresponds to a given sequence of interest in the second plurality of circularized library molecules. In some embodiments, a pre-determined second seeding batch barcode sequence can be linked to different sequences of interest in a second plurality of circularized library molecules.

[00544] In some embodiments, individual circularized library molecules in the second plurality comprise a sequence of interest, the same seeding batch sequencing primer binding site sequence which corresponds to the sequence of interest, and individual circularized library molecules further comprise a surface capture primer binding site, and a second seeding batch barcode sequence which corresponds to the sequence of interest.

[00545] In some embodiments, the sequences of interest in the second plurality of circularized nucleic acid library molecules are about 50-250 bases in length, or about 250-500 bases in length, or about 500-800 bases in length, or about 800-1200 bases in length, or about 1200-2000 bases in length, or up to 2000 bases in length, or any range therebetween.

[00546] In some embodiments, the concentration of the second plurality of circularized nucleic acid library molecules that are distributed onto the support can be about 1-5 pM, or about 5-10 pM, or about 10-50 pM, or any range therebetween.

[00547] In some embodiments, in the methods for re-seeding a support of step (d), the second plurality of circularized nucleic acid library molecules comprises a plurality of subpopulations of circularized library molecules including at least a third and a fourth subpopulation of circularized library molecules.

[00548] In some embodiments, individual circularized library molecules in the third subpopulation comprise the same third sub-population seeding batch sequencing primer binding site sequence and have the same sequence of interest. In some embodiments, individual circularized library molecules in the third sub-population comprise the same third subpopulation seeding batch sequencing primer binding site sequence and have different sequences of interest. In some embodiments, the third sub-population seeding batch sequencing primer binding site sequence corresponds to the third sequence of interest, or the third sub-population seeding batch sequencing primer binding site sequence corresponds to one of the sequences of interest in the third sub-population. In some embodiments, a predetermined third sub-population seeding batch sequencing primer binding site sequence can be linked to a given sequence of interest in the third sub-population of circularized library molecules, thus the pre-determined third sub-population seeding batch sequencing primer binding site sequence corresponds to a given sequence of interest in the third sub-population of circularized library molecules. In some embodiments, a pre-determined third subpopulation seeding batch sequencing primer binding site sequence can be linked to different sequences of interest in a third sub-population of circularized library molecules.

[00549] In some embodiments, individual circularized library molecules in the third subpopulation further comprise a third sub-population seeding batch barcode sequence which corresponds to the third sequence of interest, or the third sub-population seeding batch barcode sequence corresponds to one of the sequences of interest in the third sub-population. In some embodiments, a pre-determined third sub-population seeding batch barcode sequence can be linked to a given sequence of interest in the third sub-population of circularized library molecules, thus the pre-determined third sub-population seeding batch barcode sequence corresponds to a given sequence of interest in the third sub-population of circularized library molecules. In some embodiments, a pre-determined third sub-population seeding batch barcode sequence can be linked to different sequences of interest in a third sub-population of circularized library molecules.

[00550] In some embodiments, individual circularized library molecules in the third subpopulation further comprise a sample index sequence that can be used in a multiplex assay to distinguish sequences of interest obtained from different sample sources. In some embodiments, individual circularized library molecules in the third sub-population further comprise a surface capture primer binding site. In some embodiments, individual circularized library molecules in the third sub-population further comprise a surface pinning primer binding site. In some embodiments, individual circularized library molecules in the third subpopulation further comprise a compaction oligonucleotide binding site.

[00551] In some embodiments, the sequences of interest in the third sub-population of circularized nucleic acid library molecules are about 50-250 bases in length, or about 250-500 bases in length, or about 500-800 bases in length, or about 800-1200 bases in length, or about 1200-2000 bases in length, or up to 2000 bases in length, or any range therebetween.

[00552] In some embodiments, in the methods for re-seeding a support of step (d), the method comprises conducting a rolling circle amplification reaction, in a template-dependent manner using individual circularized library molecules in the third sub-population, thereby generating a plurality of third sub-population concatemer template molecules immobilized to the support, wherein a subset of the surface capture primers hybridize to individual circularized library molecules to generate the plurality of third sub-population concatemer template molecules.

[00553] In some embodiments, the third sub-population concatemer template molecules can be immobilized to the support at random and non-predetermined positions, or at predetermined positions (e.g., a patterned support).

[00554] In some embodiments, in the methods for re-seeding a support of step (d), individual circularized library molecules in the fourth sub-population comprise the same fourth sub-population seeding batch sequencing primer binding site sequence and have the same sequence of interest or different sequences of interest. In some embodiments, the fourth sub-population seeding batch sequencing primer binding site sequence corresponds to the fourth sequence of interest, or the fourth sub-population seeding batch sequencing primer binding site sequence corresponds to one of the sequences of interest in the fourth subpopulation. In some embodiments, a pre-determined fourth sub-population seeding batch sequencing primer binding site sequence can be linked to a given sequence of interest in the fourth sub-population of circularized library molecules, thus the pre-determined fourth subpopulation seeding batch sequencing primer binding site sequence corresponds to a given sequence of interest in the fourth sub-population of circularized library molecules. In some embodiments, a pre-determined fourth sub-population seeding batch sequencing primer binding site sequence can be linked to different sequences of interest in a fourth subpopulation of circularized library molecules.

[00555] In some embodiments, individual circularized library molecules in the fourth subpopulation further comprise a fourth sub-population seeding batch barcode sequence which corresponds to the fourth sequence of interest, or the fourth sub-population seeding batch barcode sequence corresponds to one of the sequences of interest in the fourth subpopulation. In some embodiments, a pre-determined fourth sub-population seeding batch barcode sequence can be linked to a given sequence of interest in the fourth sub-population of circularized library molecules, thus the pre-determined fourth subs-population seeding batch barcode sequence corresponds to a given sequence of interest in the fourth sub-population of circularized library molecules. In some embodiments, a pre-determined fourth sub-population seeding batch barcode sequence can be linked to different sequences of interest in a fourth sub-population of circularized library molecules.

[00556] In some embodiments, individual circularized library molecules in the fourth subpopulation further comprise a sample index sequence that can be used in a multiplex assay to distinguish sequences of interest obtained from different sample sources. In some embodiments, individual circularized library molecules in the fourth sub-population further comprise a surface capture primer binding site. In some embodiments, individual circularized library molecules in the fourth sub-population further comprise a surface pinning primer binding site. In some embodiments, individual circularized library molecules in the fourth sub-population further comprise a compaction oligonucleotide binding site.

[00557] In some embodiments, the sequences of interest in the fourth sub-population of circularized nucleic acid library molecules are about 50-250 bases in length, or about 250-500 bases in length, or about 500-800 bases in length, or about 800-1200 bases in length, or about 1200-2000 bases in length, or up to 2000 bases in length, or any range therebetween. [00558] In some embodiments, the third sub-population seeding batch sequencing primer binding site sequence and fourth sub-population seeding batch sequencing primer binding site sequence have different sequences.

[00559] In some embodiments, in the methods for re-seeding a support of step (d), the method comprises conducting a rolling circle amplification reaction in a template-dependent manner using individual circularized library molecules in the fourth sub-population, thereby generating a fourth sub-population concatemer template molecules immobilized to the support. In some embodiments, a subset of the surface capture primers hybridize to individual circularized library molecules to generate the fourth sub-population concatemer template molecules.

[00560] In some embodiments, the fourth sub-population concatemer template molecules can be immobilized to the support at random and non-predetermined positions, or at predetermined positions (e.g., a patterned support).

[00561] In some embodiments, in the methods for re-seeding a support of step (d), the rolling circle amplification reaction comprises contacting the primed circularized library molecules with a plurality of a strand displacing polymerase, and a plurality of nucleotides which include dATP, dCTP, dGTP, and/or dTTP.

[00562] In some embodiments, the plurality of nucleotide further comprises a plurality of a nucleotide having a scissile moiety (e.g., uracil).

[00563] In some embodiments, the rolling circle amplification reaction of step (d) can be conducted in the presence, or in the absence, of a plurality of compaction oligonucleotides. In some embodiments, individual compaction oligonucleotides can hybridize to two different locations on the same the template molecule to pull together distal portions of the template molecule causing compaction of the template molecule to form a compact DNA nanoball.

[00564] In some embodiments, the methods for re-seeding a support further comprise step (e): sequencing at least a subset of the second plurality of immobilized concatemer template molecules thereby generating a second plurality of sequencing read products. In some embodiments, the sequencing of step (e) comprises imaging a region of the support to detect the sequencing reactions of the second plurality of template molecules. In some embodiments, the same region of the support is sequenced in steps (c) and (e). In some embodiments, different regions of the support are sequenced in steps (c) and (e).

[00565] In some embodiments, the concatemer template molecules in the second plurality are sequenced. For example, at least 30-50%, or at least 50-70%, or at least 70-90% of the concatemer template molecules in the second plurality are sequenced. In some embodiments, 500 million - 1 billion copies of the second plurality of concatemer template molecules can be sequenced. In some embodiments, up to 1 billion, or up to 2 billion, or up to 3 billion, or up to 4 billion, or up to 5 billion copies of the second plurality of concatemer template molecules can be sequenced. In some embodiments, up to 6 billion, or up to 7 billion, or up to 8 billion, or up to 9 billion, or up to 10 billion copies of the second plurality of concatemer template molecules can be sequenced. In some embodiments, between about 500 million and about 10 billion concatemer template molecules, between about 1 billion and about 9 billion concatemer template molecules, between about 2 billion and about 8 billion concatemer template molecules, between about 3 billion and about 7 billion concatemer template molecules, between about 4 billion and about 5 billion concatemer template molecules, or any range therebetween of concatemer template molecules of the second plurality of concatemer template molecules can be sequenced.

[00566] In some embodiments, the full length of the concatemer template molecules in the second plurality are sequenced. In some embodiments, a partial length of the concatemer template molecules in the second plurality are sequenced.

[00567] In some embodiments, the sequencing of step (e) comprises hybridizing sequencing primers to sequencing primers binding sites on the second plurality of concatemer template molecules and conducting up to 1000 cycles of polymerase-catalyzed sequencing reactions using nucleotide reagents. In some embodiments, the concatemer template molecules in the second plurality can be subjected to 5-25 sequencing cycles, or 25-50 sequencing cycles, or 50-75 sequencing cycles, or 75-100 sequencing cycles, or 100-200 sequencing cycles, or 200-500 sequencing cycles, or 500-750 sequencing cycles, or 750-1000 sequencing cycles, or any range therebetween.

[00568] In some embodiments, a partial length of the concatemer template molecules in the second plurality are reiteratively sequenced.

[00569] In some embodiments, in the methods for re-seeding a support of step (e), the third sub-population of the immobilized concatemer template molecules in the second plurality are sequenced using the third batch sequencing primer binding sites in the third subpopulation of immobilized concatemer template molecules.

[00570] In some embodiments, the full length of the concatemer template molecules in the third sub-population are sequenced. In some embodiments, a partial length of the concatemer template molecules in the third sub-population are sequenced.

[00571] In some embodiments, the sequencing of step (e) comprises hybridizing sequencing primers to sequencing primers binding sites on the third sub-population of the second plurality of concatemer template molecules and conducting up to 1000 cycles of polymerase-catalyzed sequencing reactions using nucleotide reagents. In some embodiments, the concatemer template molecules in the third sub-population can be subjected to 5-25 sequencing cycles, or 25-50 sequencing cycles, or 50-75 sequencing cycles, or 75-100 sequencing cycles, or 100-200 sequencing cycles, or 200-500 sequencing cycles, or 500-750 sequencing cycles, or 750-1000 sequencing cycles, or any range therebetween.

[00572] In some embodiments, a partial length of the concatemer template molecules in the third sub-population are reiteratively sequenced.

[00573] In some embodiments, the sequencing of step (e) comprises conducting any massively parallel nucleic acid sequencing method that employs a plurality of sequencing polymerases and a plurality of nucleotide reagents. In some embodiments, the plurality of nucleotide reagents comprises nucleotides, nucleotide analogs and/or multivalent molecules. [00574] In some embodiments, the sequencing of step (e) comprises conducting a two- stage sequencing method. In some embodiments, the first stage generally comprises contacting the third sub-population of template molecules in the second plurality with a plurality of third batch sequencing primers, a first plurality of sequencing polymerase and a plurality of detectably labeled multivalent molecules. In some embodiments, the first stage comprises binding detectably labeled multivalent molecules to polymerase complexes to form multivalent-polymerase complexes, and detecting the multivalent-polymerase complexes. In some embodiments, individual multivalent molecules comprise a core attached to multiple nucleotide arms and each nucleotide arm is attached to a nucleotide (e.g., a nucleotide moiety) (e.g., FIGS. 1-5). In some embodiments, the multivalent molecules can be labeled with at least one detectable moiety that emits a signal. In some embodiments, the multivalent molecules can be labeled with at least one fluorophore.

[00575] In some embodiments, individual polymerase complexes comprise a first sequencing polymerase bound to a nucleic acid duplex where the nucleic acid duplex comprises a nucleic acid template molecule hybridized to a sequencing primer. In some embodiments, the detectably labeled multivalent molecules bind to the polymerase complexes to form a plurality of multivalent-polymerase complexes. In some embodiments, the detectably labeled multivalent molecules are bound to the polymerase complexes in the presence of a trapping reagent. In some embodiments, the trapping reagent can be formulated to promote binding of the detectably labeled multivalent molecules to the polymerase complexes. In some embodiments, the trapping reagent can be formulated to inhibit incorporation of the nucleotide moiety of the multivalent molecules. In some embodiments, the trapping reagent comprises a plurality of multivalent molecules, a first plurality of sequencing polymerases, and at least one non-catalytic cation inhibits polymerase-catalyzed nucleotide incorporation.

[00576] In some embodiments, the multivalent-polymerase complexes can be exposed to excitation illumination to induce fluorescent signals from the multivalent-polymerase complexes. In some embodiments, prior to conducting the second sequencing stage, the detectably labeled multivalent molecules can be dissociated from the polymerase complexes and removed (e.g., washing). In some embodiments, prior to conducting the second sequencing stage, the first plurality of sequencing polymerases can be dissociated from the third sub-population of template molecules in the second plurality. In some embodiments, the third sub-population of template molecules in the second plurality can remain immobilized to the support and the third batch sequencing primers can be retained and can remain hybridized to the third sub-population of template molecules in the second plurality.

[00577] In some embodiments, the second stage of the two-stage sequencing method comprises contacting the third sub-population of template molecules in the second plurality and the retained third batch sequencing primers with a second plurality of sequencing polymerases and a plurality of nucleotides (e.g., non-conjugated free nucleotides). In some embodiments, the second stage comprises binding the plurality of nucleotides to the polymerase complexes to form nucleotide-polymerase complexes, and promoting nucleotide incorporation. In some embodiments, the second stage of the two-stage sequencing method comprises nucleotide incorporation and extension of the third batch sequencing primer.

[00578] In some embodiments, the plurality of nucleotides comprises fluorophore-labeled nucleotides, or the nucleotides are non-labeled. In some embodiments, when the nucleotides are fluorophore-labeled, detecting and imaging of the incorporated nucleotides can be performed. In some embodiments, when the nucleotides are non-labeled, detecting and imaging of the incorporated nucleotides can be omitted.

[00579] In some embodiments, the nucleotides comprise chain terminating nucleotides where individual nucleotides comprise a chain terminating moiety attached to the 3’ sugar position. In some embodiments, the nucleotides are not chain terminating nucleotides. In some embodiments, when the nucleotides comprise chain terminating nucleotides, the chain terminating moieties can be cleaved from the incorporated chain terminating nucleotides to generate an extendible 3 ’OH group.

[00580] In some embodiments, nucleotide incorporation can be conducted in the presence of a stepping reagent. In some embodiments, the stepping reagent can be formulated to promote polymerase-catalyzed nucleotide incorporation. In some embodiments, the stepping reagent comprises a plurality of nucleotides (e.g., non-conjugated free nucleotides), a second plurality of sequencing polymerases, and at least one catalytic cation promotes polymerase- catalyzed nucleotide incorporation. In some embodiments, in the stepping reagent, the plurality of nucleotides comprises chain terminating nucleotides where individual nucleotides comprise a chain terminating moiety attached to the 3’ sugar position. In some embodiments, in the stepping reagent, the plurality of nucleotides are not chain terminating nucleotides. [00581] In some embodiments, the sequencing of step (e) comprises conducting a two- stage sequencing method including repeating the first stage and second stage at least once thereby generating a plurality of third batch sequencing read products. In some embodiments, when conducting a two-stage sequencing method, one sequencing cycle comprises completion of a first and a second stage. In some embodiments, the sequencing of step (e) comprises conducting 5-25 sequencing cycles, or 25-50 sequencing cycles, or 50-75 sequencing cycles, or 75-100 sequencing cycles, or 100-200 sequencing cycles, or 200-500 sequencing cycles, or 500-750 sequencing cycles, or 750-1000 sequencing cycles, or any range therebetween.

[00582] In some embodiments, in the methods for re-seeding a support of step (e), the fourth sub-population of the concatemer template molecules in the second plurality are sequenced using the fourth batch sequencing primer binding sites in the fourth sub-population of concatemer template molecules.

[00583] In some embodiments, the full length of the concatemer template molecules in the fourth sub-population are sequenced. In some embodiments, a partial length of the concatemer template molecules in the fourth sub-population are sequenced.

[00584] In some embodiments, the sequencing of step (e) comprises hybridizing sequencing primers to sequencing primers binding sites on the fourth sub-population of the second plurality of concatemer template molecules and conducting up to 1000 cycles of polymerase-catalyzed sequencing reactions using nucleotide reagents. In some embodiments, the concatemer template molecules in the fourth sub-population can be subjected to 5-25 sequencing cycles, or 25-50 sequencing cycles, or 50-75 sequencing cycles, or 75-100 sequencing cycles, or 100-200 sequencing cycles, or 200-500 sequencing cycles, or 500-750 sequencing cycles, or 750-1000 sequencing cycles, or any range therebetween.

[00585] In some embodiments, a partial length of the concatemer template molecules in the fourth sub-population are reiteratively sequenced. [00586] In some embodiments, the sequencing of step (e) comprises conducting any massively parallel nucleic acid sequencing method that employs a plurality of sequencing polymerases and a plurality of nucleotide reagents. In some embodiments, the plurality of nucleotide reagents comprises nucleotides, nucleotide analogs and/or multivalent molecules. [00587] In some embodiments, the sequencing of step (e) comprises conducting a two- stage sequencing method. In some embodiments, the first stage comprises contacting the fourth sub-population of template molecules in the second plurality with a plurality of fourth batch sequencing primers, a first plurality of sequencing polymerase and a plurality of detectably labeled multivalent molecules. In some embodiments, the first stage comprises binding detectably labeled multivalent molecules to polymerase complexes to form multivalent-polymerase complexes, and detecting the multivalent-polymerase complexes. In some embodiments, individual multivalent molecules comprise a core attached to multiple nucleotide arms, individual nucleotide arms attached to a nucleotide (e.g., a nucleotide moiety) (e.g., FIGS. 1-5). In some embodiments, the multivalent molecules can be labeled with at least one detectable moiety that emits a signal. In some embodiments, the multivalent molecules can be labeled with at least one fluorophore.

[00588] In some embodiments, individual polymerase complexes comprise a first sequencing polymerase bound to a nucleic acid duplex where the nucleic acid duplex comprises a nucleic acid template molecule hybridized to a sequencing primer. In some embodiments, the detectably labeled multivalent molecules bind to the polymerase complexes to form a plurality of multivalent-polymerase complexes. In some embodiments, the detectably labeled multivalent molecules are bound to the polymerase complexes in the presence of a trapping reagent. In some embodiments, the trapping reagent can be formulated to promote binding of the detectably labeled multivalent molecules to the polymerase complexes. In some embodiments, the trapping reagent can be formulated to inhibit incorporation of the nucleotide moiety of the multivalent molecules. In some embodiments, the trapping reagent comprises a plurality of multivalent molecules, a first plurality of sequencing polymerases, and at least one non-catalytic cation inhibits polymerase-catalyzed nucleotide incorporation.

[00589] In some embodiments, the multivalent-polymerase complexes can be exposed to excitation illumination to induce fluorescent signals from the multivalent-polymerase complexes. In some embodiments, prior to conducting the second sequencing stage, the detectably labeled multivalent molecules can be dissociated from the polymerase complexes and removed (e.g., washing). In some embodiments, prior to conducting the second sequencing stage, the first plurality of sequencing polymerases can be dissociated from the fourth sub-population of template molecules in the second plurality. In some embodiments, the fourth sub-population of template molecules in the second plurality can remain immobilized to the support and the fourth batch sequencing primers can be retained and can remain hybridized to the fourth sub-population of template molecules in the second plurality. [00590] In some embodiments, the second stage of the two-stage sequencing method comprises contacting the fourth sub-population of template molecules in the second plurality and the retained fourth batch sequencing primers with a second plurality of sequencing polymerases and a plurality of nucleotides (e.g., non-conjugated free nucleotides). In some embodiments, the second stage comprises binding the plurality of nucleotides to the polymerase complexes to form nucleotide-polymerase complexes, and promoting nucleotide incorporation. In some embodiments, the second stage of the two-stage sequencing method comprises nucleotide incorporation and extension of the fourth batch sequencing primer. [00591] In some embodiments, the plurality of nucleotides comprises fluorophore-labeled nucleotides, or the nucleotides are non-labeled. In some embodiments, when the nucleotides are fluorophore-labeled, detecting and imaging of the incorporated nucleotides can be performed. In some embodiments, when the nucleotides are non-labeled, detecting and imaging of the incorporated nucleotides can be omitted.

[00592] In some embodiments, the nucleotides comprise chain terminating nucleotides where individual nucleotides comprise a chain terminating moiety attached to the 3’ sugar position. In some embodiments, the nucleotides are not chain terminating nucleotides. In some embodiments, when the nucleotides comprise chain terminating nucleotides, the chain terminating moieties can be cleaved from the incorporated chain terminating nucleotides to generate an extendible 3 ’OH group.

[00593] In some embodiments, nucleotide incorporation can be conducted in the presence of a stepping reagent. In some embodiments, the stepping reagent can be formulated to promote polymerase-catalyzed nucleotide incorporation. In some embodiments, the stepping reagent comprises a plurality of nucleotides (e.g., non-conjugated free nucleotides), a second plurality of sequencing polymerases, and at least one catalytic cation promotes polymerase- catalyzed nucleotide incorporation. In some embodiments, in the stepping reagent, the plurality of nucleotides comprises chain terminating nucleotides. In some embodiments, individual nucleotides comprise a chain terminating moiety attached to the 3’ sugar position. In some embodiments, in the stepping reagent, the plurality of nucleotides are not chain terminating nucleotides. [00594] In some embodiments, the sequencing of step (e) comprises conducting a two- stage sequencing method including repeating the first stage and second stage at least once thereby generating a plurality of fourth batch sequencing read products. In some embodiments, when conducting a two-stage sequencing method, one sequencing cycle comprises completion of a first and a second stage. In some embodiments, the sequencing of step (e) comprises conducting 5-25 sequencing cycles, or 25-50 sequencing cycles, or 50-75 sequencing cycles, or 75-100 sequencing cycles, or 100-200 sequencing cycles, or 200-500 sequencing cycles, or 500-750 sequencing cycles, or 750-1000 sequencing cycles, or any range therebetween.

[00595] In some embodiments, the methods for re-seeding a support further comprise reiteratively sequencing the first sub-population of the first plurality of concatemer template molecules, which comprises step (cl): conducting short read sequencing by performing up to 1000 sequencing cycles of the first sub-population of concatemer template molecules to generate a plurality of first sub-population batch sequencing read products that comprise up to 1000 bases in length. In some embodiments, step (cl) comprises conducting 5-25 sequencing cycles, or 25-50 sequencing cycles, or 50-75 sequencing cycles, or 75-100 sequencing cycles, or 100-200 sequencing cycles, or 200-500 sequencing cycles, or 500-750 sequencing cycles, or 750-1000 sequencing cycles, or any range therebetween.

[00596] In some embodiments, the first sub-population batch sequencing read products comprise a first sub-population seeding batch barcode sequence.

[00597] In some embodiments, the first sub-population batch sequencing read products comprise a first sub-population seeding batch barcode sequence and a sample index sequence.

[00598] In some embodiments, the first sub-population batch sequencing read products comprise a first sub-population seeding batch barcode sequence and at least a portion of a first sequence of interest.

[00599] In some embodiments, the first sub-population batch sequencing read products comprise a first sub-population seeding batch barcode sequence, a sample index sequence, and at least a portion of a first sequence of interest.

[00600] In some embodiments, in step (cl), the short read sequencing comprises hybridizing sequencing primers to sequencing primer binding sites on the first sub-population of concatemer template molecules and conducting up to 1000 cycles of polymerase-catalyzed sequencing reactions using nucleotide reagents. In some embodiments, 500 million - 1 billion copies of the first sub-population of concatemer template molecules can be sequenced. In some embodiments, up to 1 billion, or up to 2 billion, or up to 3 billion, or up to 4 billion, or up to 5 billion copies of the first sub-population of concatemer template molecules can be sequenced. In some embodiments, up to 6 billion, or up to 7 billion, or up to 8 billion, or up to 9 billion, or up to 10 billion copies of the first sub-population of concatemer template molecules can be sequenced. In some embodiments, between about 500 million and about 10 billion concatemer template molecules, between about 1 billion and about 9 billion concatemer template molecules, between about 2 billion and about 8 billion concatemer template molecules, between about 3 billion and about 7 billion concatemer template molecules, between about 4 billion and about 5 billion concatemer template molecules, or any range therebetween of the first sub-population of concatemer template molecules can be sequenced.

[00601] In some embodiments, the sequencing of step (cl) comprises conducting any massively parallel nucleic acid sequencing method that employs a plurality of sequencing polymerases and a plurality of nucleotide reagents. In some embodiments, the plurality of nucleotide reagents comprises nucleotides, nucleotide analogs and/or multivalent molecules. In some embodiments, the reiterative sequencing of step (cl) comprises conducting a two- stage sequencing method described herein.

[00602] In some embodiments, the methods for re-seeding a support further comprise step (c2): stopping and/or blocking the short read sequencing of step (cl). In some embodiments, the stopping and/or blocking comprises incorporating a chain terminating nucleotide to the 3’ terminal end of the first sub-population batch sequencing read products to inhibit further sequencing reactions. Exemplary chain terminating nucleotides include dideoxynucleotide or a nucleotide having a 2’ or 3’ chain terminating moiety.

[00603] In some embodiments, the methods for re-seeding a support further comprise step (c3): removing the plurality of first sub-population batch sequencing read products and retaining the concatemer template molecules of the first sub -population. In some embodiments, step (c3) is optional. In some embodiments, the first sub-population batch sequencing read products can be removed from the concatemer template molecules by denaturation using heat and/or a de-hybridization reagent.

[00604] In some embodiments, the methods for re-seeding a support further comprise step (c4): reiteratively sequencing the concatemer template molecules of the first sub-population by repeating steps (cl) - (c3) at least once. In some embodiments, the reiterative sequencing can be conducted 1-10 times, or 10-25 times, or 25-50 times, or more than 50 times. [00605] In some embodiments, the sequences of the first sub-population batch sequencing read products can be determined and aligned with a first reference sequence to confirm the presence of the first sequence of interest. The first reference sequence can be the first subpopulation seeding batch barcode and/or the first sequence of interest.

[00606] In some embodiments, the methods for re-seeding a support further comprise reiteratively sequencing the second sub-population of concatemer template molecules in a manner similar to steps (cl) - (c4) as described above for the first sub-population of concatemer template molecules.

[00607] In some embodiments, hybridizing the sequencing primers to the concatemer template molecules of any of steps (cl) can be conducted with a hybridization reagent comprising an SSC buffer (e.g., 2X saline-sodium citrate) buffer with formamide (e.g., 10- 20% formamide).

[00608] In some embodiments, in step (c3) the plurality of first sub-population batch sequencing read products can be removed from the template molecules and the plurality of template molecules can be retained using a de-hybridization reagent comprising an SSC buffer (e.g., saline-sodium citrate) buffer, with or without formamide, at a temperature that promotes nucleic acid denaturation such as for example 50 - 90 °C.

[00609] In some embodiments, in step (c3) the plurality of first sub-population batch sequencing read products can be removed from the template molecules and the plurality of template molecules can be retained using a de-hybridization reagent. In some embodiments, the de-hybridization of step (c3) can be conducted at a temperature that promotes nucleic acid denaturation such as for example 50 - 90 °C.

[00610] In some embodiments, the methods for re-seeding a support further comprise reiteratively sequencing the second sub-population of concatemer template molecules, which comprises step (el): conducting short read sequencing by performing up to 1000 sequencing cycles of the third sub-population of the second plurality of concatemer template molecules to generate a plurality of second sub-population batch sequencing read products that comprise up to 1000 bases in length. In some embodiments, step (el) comprises conducting 5-25 sequencing cycles, or 25-50 sequencing cycles, or 50-75 sequencing cycles, or 75-100 sequencing cycles, or 100-200 sequencing cycles, or 200-500 sequencing cycles, or 500-750 sequencing cycles, or 750-1000 sequencing cycles, or any range therebetween.

[00611] In some embodiments, the third sub-population batch sequencing read products comprise a third sub-population seeding batch barcode sequence. [00612] In some embodiments, the third sub-population batch sequencing read products comprise a third sub-population seeding batch barcode sequence and a sample index sequence.

[00613] In some embodiments, the third sub-population batch sequencing read products comprise a third sub-population seeding batch barcode sequence and at least a portion of a second sequence of interest.

[00614] In some embodiments, the third sub-population batch sequencing read products comprise a third sub-population seeding batch barcode sequence, a sample index sequence, and at least a portion of a second sequence of interest.

[00615] In some embodiments, in step (el), the short read sequencing comprises hybridizing sequencing primers to sequencing primer binding sites on the third subpopulation of concatemer template molecules and conducting up to 1000 cycles of polymerase-catalyzed sequencing reactions using nucleotide reagents. In some embodiments, 500 million - 1 billion copies of the third sub-population of concatemer template molecules can be sequenced. In some embodiments, up to 1 billion, or up to 2 billion, or up to 3 billion, or up to 4 billion, or up to 5 billion copies of the third sub-population of concatemer template molecules can be sequenced. In some embodiments, up to 6 billion, or up to 7 billion, or up to 8 billion, or up to 9 billion, or up to 10 billion copies of the third sub-population of concatemer template molecules can be sequenced. In some embodiments, between about 500 million and about 10 billion concatemer template molecules, between about 1 billion and about 9 billion concatemer template molecules, between about 2 billion and about 8 billion concatemer template molecules, between about 3 billion and about 7 billion concatemer template molecules, between about 4 billion and about 5 billion concatemer template molecules, or any range therebetween of the third sub-population of concatemer template molecules can be sequenced.

[00616] In some embodiments, the sequencing of step (el) comprises conducting any massively parallel nucleic acid sequencing method that employs a plurality of sequencing polymerases and a plurality of nucleotide reagents. In some embodiments, the plurality of nucleotide reagents comprise nucleotides, nucleotide analogs and/or multivalent molecules. In some embodiments, the reiterative sequencing of step (el) comprises conducting a two- stage sequencing method described herein.

[00617] In some embodiments, the methods for re-seeding a support further comprise step (e2): stopping and/or blocking the short read sequencing of step (el). In some embodiments, the stopping and/or blocking comprises incorporating a chain terminating nucleotide to the 3’ terminal end of the second sub-population batch sequencing read products to inhibit further sequencing reactions. Exemplary chain terminating nucleotides include dideoxynucleotide or a nucleotide having a 2’ or a 3’ chain terminating moiety.

[00618] In some embodiments, the methods for re-seeding a support further comprise step (e3): removing the plurality of second sub-population batch sequencing read products and retaining the concatemer template molecules of the second sub-population. In some embodiments, step (e3) is optional. In some embodiments, the third sub-population batch sequencing read products can be removed from the concatemer template molecules by denaturation using heat and/or a de-hybridization reagent.

[00619] In some embodiments, the methods for re-seeding a support further comprise step (e4): reiteratively sequencing the concatemer template molecules of the third sub-population by repeating steps (el) - (e3) at least once. In some embodiments, the reiterative sequencing can be conducted 1-10 times, or 10-25 times, or 25-50 times, or more than 50 times.

[00620] In some embodiments, the sequences of the third sub-population batch sequencing read products can be determined and aligned with a second reference sequence to confirm the presence of the second sequence of interest. The second reference sequence can be the third sub-population seeding batch barcode and/or the second sequence of interest.

[00621] In some embodiments, the methods for re-seeding a support further comprise reiteratively sequencing the fourth sub-population of concatemer template molecules in a manner similar to steps (el) - (e4) as described above for the third sub-population of concatemer template molecules.

[00622] In some embodiments, hybridizing the sequencing primers to the concatemer template molecules of any of steps (el) can be conducted with a hybridization reagent comprising an SSC buffer (e.g., 2X saline-sodium citrate) buffer with formamide (e.g., 10- 20% formamide).

[00623] In some embodiments, in step (e3) the plurality of third sub-population batch sequencing read products can be removed from the template molecules and the plurality of template molecules can be retained using a de-hybridization reagent comprising an SSC buffer (e.g., saline-sodium citrate) buffer, with or without formamide, at a temperature that promotes nucleic acid denaturation such as for example 50 - 90 °C.

[00624] In some embodiments, in step (e3) the plurality of third sub-population batch sequencing read products can be removed from the template molecules and the plurality of template molecules can be retained using a de-hybridization reagent. In some embodiments, the de-hybridization of step (e3) can be conducted at a temperature that promotes nucleic acid denaturation such as for example 50 - 90 °C.

The Support

[00625] In some aspects, the present disclosure provides a support for use in conducting any of the methods described herein including methods for generating compact DNA nanoballs, batch sequencing, reiterative sequencing and/or re-seeding methods. In some embodiments, the support is solid, semi-solid, or a combination of both. In some embodiments, the support is porous, semi-porous, non-porous, or any combination of porosity. In some embodiments, the support can be substantially planar, concave, convex, or any combination thereof. In some embodiments, the support can be cylindrical, for example comprising a capillary or interior surface of a capillary.

[00626] In some embodiments, the support comprises any material, including but not limited to glass, fused-silica, silicon, a polymer (e.g., polystyrene (PS), macroporous polystyrene (MPPS), polymethylmethacrylate (PMMA), polycarbonate (PC), polypropylene (PP), polyethylene (PE), high density polyethylene (HDPE), cyclic olefin polymers (COP), cyclic olefin copolymers (COC), polyethylene terephthalate (PET)), or any combination thereof. Various compositions of both glass and plastic substrates are contemplated.

[00627] In some embodiments, the surface of the support can be substantially smooth and lack contours and texture. In some embodiments, the support can be regularly or irregularly contoured or textured, including protrusions, bumps, wells, etchings, pores, three- dimensional scaffolds, or any combination thereof. In some embodiments, the support comprises contours arranged in a pre-determined pattern. In some embodiments, the support comprises contours arranged in a repeating pattern. In some embodiments, the support comprises interstitial regions between the contours, where the interstitial regions are arranged in a pre-determined. In some embodiments, the interstitial regions are arranged in a repeating pattern.

[00628] In some embodiments, the contours and interstitial regions can be fabricated using any combination of photo-chemical, photo-lithography, electron beam lithography, micro- or nano-imprint lithography, ink-jet printing, or micron-scale printing and/or nano-scale printing.

[00629] In some embodiments, the contours can be functionalized to promote tethering/immobilizing nucleic acid molecules (e.g., capture primers, pinning primers and/or template molecules) and/or for tethering an enzyme (e.g., a polymerase). In some embodiments, the interstitial regions can be modified to inhibit tethering nucleic acid molecules (e.g., capture primers, pinning primers and/or template molecules) and/or for inhibiting tethering an enzyme (e.g., a polymerase).

[00630] In some embodiments, the support comprises at least one region (e.g., a feature) which can be functionalized to tether/immobilize nucleic acid molecules and/or enzymes. In some embodiments, the features are arranged on the support in a non-predetermined manner (e.g., randomly positioned features; e.g., FIG. 13A(i)). In some embodiments, the features are arranged on the support in a predetermined manner (e.g., patterned features; e.g., FIG. 13B(iii) and (iv)). In some embodiments, the features are arranged on the support in repeating pattern (e.g., FIG. 13B parts (iii) and (iv)).

[00631] In some embodiments, a support comprises a plurality of features located at random and non-predetermined positions on the support. In some embodiments, individual features can attach to a nucleic acid molecule (e.g., capture primer, pinning primer or template molecule). Individual features on the support can be functionalized with a chemical compound to attach to a nucleic acid molecule.

[00632] For example, the features on the support can attach to nucleic acid capture primers (e.g., see FIG. 13A part (i)). In some embodiments, the capture primers can be attached to the support such that some of the nearest neighbor capture primers touch each other and/or overlap each other when viewed from any angle of the support including above, below or side views of the support. The dotted lines that surround the four capture primers represents nearest neighbor capture primers that touch each other (e.g., FIG. 13A part (i)).

[00633] In some embodiments, the capture primers on the support can attach to template molecules having one of four different batch sequences (e.g., see FIG. 13A part (ii)). In some embodiments, the template molecules can attach to the support (via attachment to the capture primers) such that some of the nearest neighbor template molecules touch each other and/or overlap each other when viewed from any angle of the support including above, below or side views of the support. The dotted lines that surround the four template molecules represent nearest neighbor template molecules that touch each other (e.g., FIG. 13A part (ii)).

[00634] In some embodiments, the support comprises a contour and at least one feature on or near the contour for tethering nucleic acid molecules. For example, one or more wells (e.g., a plurality of contours) can be fabricated on the support where the bottom of individual wells include a feature having a chemical modification for tethering one or more nucleic acid molecules. The skilled artisan will recognize that the support can be fabricated with any type of contour(s) and feature(s) that are on or near the contour(s), where the features are designed to tether at least one nucleic acid molecule.

[00635] In some embodiments, the support lacks contours. In some embodiments, the support lacks features arranged in a pre-determined pattern where the features have a chemical functionality for tethering nucleic acid molecules and/or enzymes to the support. In some embodiments, the support comprises features positioned at random non-predetermined locations on the support. In some embodiments, the support lacks interstitial regions arranged in a pre-determined pattern where the interstitial regions are sites designed to inhibit tethering nucleic acid molecules or enzymes.

[00636] In some embodiments, any of the features for tethering nucleic acids and/or enzymes can be positioned on the support using ink-jet printing, or micron-scale or nanoscale printing. In some embodiments, the features can be made in any shape including, for example, circular, square, triangular or rectangular (e.g., FIGS. 13A parts (i) and (iii)). [00637] In some embodiments, at least one surface of the support can be modified with a chemical compound that enables attachment of a polymer coating to the support. For example, the support can be modified with a silane compound. In some embodiments, the silane compound can bind a polymer coating. In some embodiments, at least one surface of the support is passivated with at least one polymer layer (e.g., FIG. 12). In some embodiments, the support is passivated with 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 or more polymer layers. In some embodiments, the coating forms a continuous layer on the support wherein the coating forms no pre-determined pattern.

[00638] In some embodiments, the surface coating may be patterned, such that the chemical modification layers are confined to one or more discrete regions of the support. For example, the coating may be patterned using photolithographic techniques to create an ordered array or random pattern of chemically-modified regions on the support. Alternately, or in combination, the coating may be patterned using, e.g., contact printing and/or ink-jet printing techniques. In some embodiments, the coating is distributed on the support in a predetermined pattern, for example the pre-determined pattern or spots arranged in rows and/or columns or other pre-determined patterns. In some embodiments, the coating having a predetermined pattern comprises at least one interstitial region that lacks a polymer coating. In some embodiments, the passivated layer forms a porous or semi-porous layer.

[00639] In some embodiments, at least one of the polymer layers comprises a hydrophilic polymer layer. In some embodiments, at least one polymer layer comprises polymer molecules having a molecular weight of at least 1000 Daltons. The hydrophilic polymer layer can comprise polyethylene glycol (PEG). The hydrophilic polymer layer can comprise unbranched PEG. The hydrophilic polymer layer can comprise branched PEG having at least 4 branches, for example the branched PEG comprises 4-16 branches. In some embodiments, the hydrophilic polymer layer comprises cross-linking or lacks cross-linking. In some embodiments, the hydrophilic polymer layer comprises cross-linking to form a hydrogel. [00640] In some embodiments, the hydrophilic polymer layer comprises a monolayer having unbranched polymers which can form a brush monolayer. In some embodiments, the brush monolayer can form an extended brush monolayer. In some embodiments, the brush monolayer comprises a plurality of unbranched polymers where one end of a given unbranched polymer is attached to the support and the other end of the same given unbranched polymer is attached to an oligonucleotide primer (e.g., capture primer or pinning primer). In some embodiments, the density of the plurality of oligonucleotide primers attached to the brush monolayer is about 10² - 10¹⁵ per pm², , for example, between about IO¹⁰ and about 10¹⁵ surface oligonucleotide primers per mm², between about 10⁵ and about 10¹⁵ oligonucleotide primers per mm², between about 10³ and about 10¹⁴ oligonucleotide primers per mm², between about 10⁴ and about 10¹³ oligonucleotide primers per mm², between about 10⁵ and about 10¹² oligonucleotide primers per mm², between about 10⁶ and about 10¹¹ oligonucleotide primers per mm², between about 10⁷ and about IO¹⁰ oligonucleotide primers per mm², or between about 10⁸ and about IO¹⁰ oligonucleotide primers per mm², or any range therebetween.

[00641] In some embodiments, the coating layer has a degree of hydrophilicity which can be measured as a water contact angle, where the water contact angle is no more than 45 degrees.

[00642] In some embodiments, any layer of the polymer coating includes a plurality of oligonucleotide primers covalently tethered to the polymer layer. In some embodiments, the plurality of oligonucleotide primers is distributed at a plurality of depths throughout any of the polymer layers. In some embodiments, the density of the plurality of oligonucleotide primers in any of the polymer layers is about 10² - 10¹⁵ per pm², , for example, between about 10¹⁰ and about 10¹⁵ surface oligonucleotide primers per mm², between about 10⁵ and about 10¹⁵ oligonucleotide primers per mm², between about 10³ and about 10¹⁴ oligonucleotide primers per mm², between about 10⁴ and about 10¹³ oligonucleotide primers per mm², between about 10⁵ and about 10¹² oligonucleotide primers per mm², between about 10⁶ and about 10¹¹ oligonucleotide primers per mm², between about 10⁷ and about 10¹⁰ oligonucleotide primers per mm², or between about 10⁸ and about 10¹⁰ oligonucleotide primers per mm², or any range therebetween. In some embodiments, individual oligonucleotide primers comprise nucleic acid molecules comprising DNA, RNA, DNA/RNA chimeric or analogs thereof. In some embodiments, the plurality of oligonucleotide primers is about 10 - 100 nucleotides in length, or any range therebetween. In some embodiments, individual oligonucleotide primers in the plurality comprise 3’ extendible ends or 3’ non-extendible ends. In some embodiments, the 3’ non-extendible ends comprise a 3’ chain terminating moiety. In some embodiments, individual oligonucleotide primers have their 5’ or 3’ ends or an internal region attached to the polymer layer. In some embodiments, the 5’ ends of the plurality of oligonucleotide primers are attached to the polymer layer. In some embodiments, the plurality of oligonucleotide primer is randomly distributed throughout and embedded within at least one of the polymer layers. In some embodiments, the plurality of oligonucleotide primer is distributed in or on at least one of the polymer layers in a random manner or a pre-determined pattern. In some embodiments, the plurality of oligonucleotide primers is distributed in or on at least one of the polymer layers in a non-random pre-determined pattern, for example the pre-determined pattern comprises stripes or spots arranged in rows and/or columns or other pre-determined patterns.

[00643] In some embodiments, the support comprises a first layer comprising a first monolayer having hydrophilic polymer molecules tethered to the support. In some embodiments, at least some of the polymer molecules in the first layer are covalently tethered to oligonucleotide primers. In some embodiments, the tethered oligonucleotide primers in the first monolayer are arranged in a random manner. In some embodiments, the tethered oligonucleotide primers in the first monolayer are arranged in a pre-determined pattern. In some embodiments, the polymer molecules in the first layer are not tethered to oligonucleotide primers.

[00644] In some embodiments, the support further comprises a second layer comprising a second monolayer having hydrophilic polymer molecules tethered to the first monolayer. In some embodiments, at least some of the polymer molecules in the second layer are covalently tethered to oligonucleotide primers. In some embodiments, the tethered oligonucleotide primers in the second monolayer are arranged in a random manner or in a pre-determined pattern. In some embodiments, the polymer molecules in the second layer are not tethered to oligonucleotide primers.

[00645] In some embodiments, the support further comprises a third layer comprising a third monolayer having hydrophilic polymer molecules tethered to the second monolayer. In some embodiments, at least some of the polymer molecules in the third layer are covalently tethered to oligonucleotide primers. In some embodiments, the tethered oligonucleotide primers in the third monolayer are arranged in a random manner or in a pre-determined pattern. In some embodiments, the polymer molecules in the third layer are not tethered to oligonucleotide primers.

[00646] In some embodiments, the support comprises a functionalized polymer layer covalently bound at least to a portion of the support via a chemical group on the support, a primer grafted to the functionalized polymer coating, and a water-soluble protective coating on the primer and the functionalized polymer coating. In some embodiments, the functionalized polymer coating comprises a poly(N-(5-azidoacetamidylpentyl)acrylamide-co- acrylamide (PAZAM).

[00647] In some embodiments, at least one of the polymer layers comprise oligonucleotide primers including capture primers, pinning primers, or a mixture of capture and pinning primers. In some embodiments, the plurality of oligonucleotide primers comprises one type of capture primer (e.g., having that same batch capture primer sequence) or a mixture of 2- 100 different types of capture primers (e.g., having 2-100 different batch capture primer sequences). In some embodiments, the plurality of oligonucleotide primers comprises one type of pinning primer (e.g., having that same batch pinning primer sequence) or a mixture of 2-100 different types of pinning primers (e.g., having 2-100 different batch pinning primer sequences).

[00648] In some embodiments, individual capture primers (e.g., which are tethered to and/or embedded in a polymer layer) can be used in an on-support amplification reaction. In some embodiments, individual capture primers hybridize to a capture primer binding site in a circularized library molecule, and rolling circle amplification can be conducted to generate a concatemer template molecule which is tethered and/or embedded in the polymer layer.

[00649] In some embodiments, individual capture primers (e.g., individual capture primers tethered to and/or embedded in a polymer layer) can be used in an in-solution amplification workflow wherein individual capture primers can hybridize to a capture primer binding site in a nascent concatemer template molecule, and rolling circle amplification can continue on the polymer layer to generate a concatemer template molecule which is tethered and/or embedded in the polymer layer.

[00650] In some embodiments, the density of the capture primers in a polymer layer can be modulated (e.g., increased or decreased) to achieve a desired density of immobilized concatemer template molecules on a support. Generally, a polymer layer having a high density of capture primers will generate concatemer template molecules that are tightly packed and immobilized to the support at a density of about 10⁵ - 10¹⁵ per mm² which cannot be achieved using supports fabricated to include nano-scale features for attachment of template molecules.

[00651] In some embodiments, a single pinning primer (e.g., a single pinning primer tethered to or embedded in a polymer layer) can hybridize to a pinning primer binding site in a concatemer template molecule to generate a concatemer template molecule which is tethered or embedded (e.g., pinned down) in the polymer layer.

[00652] In some embodiments, at least one of the polymer layers comprise a plurality of capture primers and/or pinning primers having a cleavable region that is cleavable with a restriction endonuclease enzyme. For example, the cleavable region comprises a recognition site for a type I, a type II, a type Ils, a type IIB, a type III, or a type IV restriction enzyme. In some embodiments, the plurality of capture primers and/or pinning primers include a cleavable region that is cleavable with an enzyme that generates an abasic site. For example, the cleavable region comprises at least one nucleotide having a scissile moiety including uridine, 8-oxo-7,8-dihydrogunine or deoxyinosine. In some embodiments, the plurality of capture primers and/or pinning primers lack a cleavable region.

[00653] In some embodiments, the support comprises at least one partition/barrier that creates separate regions of the support. For example, the partition/barrier can prevent fluid flow on one portion of the support. The partition/barrier can inhibit nucleic acid and/or enzyme reactions on a portion of the support. In some embodiments, the partition/barrier can be placed on the support. In some embodiments, the partition/barrier is not placed on the support but is positioned to block fluid flow onto the support.

[00654] In some embodiments, the support lacks partitions/barriers that would create separate regions of the support. For example, the support is passivated with at least one polymer coating (“layer”) formed as a continuous layer, and at least one of the polymer layers comprise a plurality of capture primers that are randomly distributed throughout and on the polymer layer. The capture primers can be used to generate immobilized concatemer template molecules. Thus, in some embodiments, the immobilized concatemer template molecules are in fluid communication with each other in a massively parallel manner with no barriers to physically separate different batches of template molecules. Instead, in such embodiments, sub-populations of template molecules carry different batch sequencing primer binding sites which enables batch sequencing. Asynchronous sequencing can be achieved using concatemer template molecules in fluid communication with each other on the same non-partitioned support. Fragmenting Nucleic Acids

[00655] In some aspects, the present disclosure provides methods for use in conducting any of the methods described herein including methods for generating compact DNA nanoballs, batch sequencing, reiterative sequencing and/or re-seeding methods. In some embodiments, the insert region of a nucleic acid library molecule comprises a sequence of interest extracted from any source. The insert region can be prepared using recombinant nucleic acid technology including but not limited to any combination of vector cloning, transgenic host cell preparation, host cell culturing and/or PCR amplification.

[00656] In some embodiments, the insert region can be in fragmented or un-fragmented form, and can be used to prepare linear nucleic acid library molecules. Fragmented forms of the insert region can be obtained by mechanical force, enzymatic or chemical fragmentation methods. The fragmented insert regions can be generated using procedures that yield a population of fragments having overlapping sequences or non-overlapping sequences.

[00657] Mechanical fragmentation typically generates randomly fragmented nucleic acid molecules. Mechanical fragmentation methods include mechanical shearing such as fluid shear, constant shear and pulsatile shear. Mechanical fragmentation methods also include mechanical stress including sonication, nebulization and acoustic cavitation. In some embodiments focused acoustic energy can be used to randomly fragment nucleic acid molecules. A commercially-available apparatus (e.g., Covaris®) can be used to fragment nucleic acid molecules using focused acoustic energy.

[00658] Enzymatic fragmentation procedures can be conducted under conditions suitable to generate randomly or non-randomly fragmented nucleic acid molecules. For example, restriction endonuclease enzyme digestion can be conducted to completion to generate non- randomly fragmented nucleic acid molecule. Alternatively, partial or incomplete restriction enzyme digestion can be conducted to generate randomly-fragmented nucleic acid molecules. Enzymatic fragmentation using restriction endonuclease enzymes includes, without limitation, any one or any combination of two or more restriction enzymes selected from a group consisting of type I, type II, type Ils, type IIB, type III, or type IV restriction enzymes. Enzymatic fragmentation can include digestion of the nucleic acid with a rare-cutting restriction enzyme, comprising Not I, Asc I, Bae I, AspC I, Pac I, Fse I, Sap I, Sfi I or Psr I. Enzymatic fragmentation include use of any combination of a nicking restriction endonuclease, endonuclease and/or exonuclease. Enzymatic fragmentation can be achieved by conducting a nick translation reaction. [00659] In some embodiments, enzymatic fragmentation can be achieved by reacting nucleic acids with an enzyme mixture, for example an enzyme that generates single-stranded nicks and another enzyme that catalyzes double-stranded cleavage. An exemplary enzyme mixture is FRAGMENTASE® (e.g., from New England Biolabs®).

[00660] Fragments of the insert region can be generated with PCR using sequence-specific primers that hybridize to target regions in genomic DNA samples to generate insert regions having known fragment lengths and sequences.

[00661] Targeted genome fragmentation methods using CRISPR/Cas9 can be used to generate fragmented insert regions.

[00662] Fragments of the insert portion can also be generated using a transposase-based tagmentation method using NEXTERA® (from Epicentre®).

[00663] The insert region can be single-stranded or double-stranded. The ends of the double-stranded insert region can be blunt-ended, or have a 5’ overhang or a 3’ overhang end, or any combination thereof. One or both ends of the insert region can be subjected to an enzymatic tailing reaction to generate a non-template poly-A tail by employing a terminal transferase reaction. The ends of the insert region can be compatible for joining to at least one adaptor sequence (e.g., universal adaptor sequence or batch-specific adaptor sequence). [00664] The insert region can be any length, for example the insert region can be about 50- 250, or about 250-500, or about 500-750, or about 750-1000, or about 1000-1500, or about 1500-2000 bases or more base pairs in length, or any range therebetween. In some embodiments, the insert region can be 2000-5000 bases or base pairs in length.

[00665] The fragments containing the insert region can be subjected to a size selection process, or the fragments are not size selected. For example, the fragments can be size selected by gel electrophoresis and gel slice extraction. The fragments can be size selected using a solid phase adherence/immobilization method which typically employs micro paramagnetic beads coated with a chemical functional group that interacts with nucleic acids under certain ionic strength conditions with or without polyethylene glycol or polyalkylene glycol. Commercially-available solid phase adherence beads include SPRI (Solid Phase Reversible Immobilization) beads from Beckman Coulter® (AMPUR XP® paramagnetic beads, catalog No. B23318), MAGNA PURE® magnetic glass particles (Roche Diagnostics®, catalog No. 03003990001), MAGNASIL® paramagnetic beads from Promega® (catalog No. MD1360), MAGTRATION® paramagnetic beads and system from Precision System Science (catalog Nos. Al 120 and A1060), MAG-BIND® from Omega Bio- Tek (catalog No. M1378-01), MAGPREP® silica from Millipore® (catalog No. 101193), SNARE DNA purification systems from Bangs Laboratories® (catalog Nos. BP691, BP692 and BP693), and CHEMAGEN M-PVA beads from Perkin Elmer® (catalog No. CMG-200). [00666] In some embodiments, the fragmented nucleic acids can be subjected to enzymatic reactions for end-repair and/or A-tailing. The fragmented nucleic acids can be contacted with a plurality of enzymes under a condition suitable to generate nucleic acid fragments having blunt-ended 5’ phosphorylated ends. In some embodiments, the plurality of enzymes generates blunt-ended fragment having a non-template A-tail at their 3’ ends. The plurality of enzymes comprise two or more enzymes that can catalyze nucleic acid end-repair, phosphorylation and/or A-tailing. The end-repair enzymes include a DNA polymerase (e.g., T4 DNA polymerase) and Klenow fragment. The 5’ end phosphorylation enzyme comprises T4 polynucleotide kinase. The A-tailing enzyme includes a Taq polymerase (e.g., non-proofreading polymerase) and dATP. In some embodiments, the fragmenting, end-repair, phosphorylation and A-tailing can be conducted in a one-pot reaction using a mixture of enzymes.

Appending Adaptors to Fragmented or Unfragmented Nucleic Acids

[00667] The present disclosure provides methods for use in conducting any of the methods described herein including methods for generating compact DNA nanoballs, batch sequencing, reiterative sequencing and/or re-seeding methods. In some embodiments, individual fragmented (or unfragmented) nucleic acids can be covalently joined to at least one adaptor sequence for library preparation. In general, a nucleic acid fragment is covalently joined at both ends to one or more adaptors to generate a linear library molecule having the arrangement left adaptor-insert-right adaptor. In some embodiments, at least one fragment in the population of fragmented nucleic acids comprises a sequence-of-interest. Individual library molecules in the population of library molecules can have an insert region that is the same or different as other library molecules in the population. In some embodiments, about 1- 10 ng, or about 10-50 ng, or about 50-100 ng, or any range therebetween, of input fragmented nucleic acids can be appended to one or more adaptors to generate a linear library.

[00668] Individual nucleic acid fragments can be appended on one or both ends to at least one adaptor sequence to form a recombinant nucleic acid linear library molecule having the general arrangement left adaptor-insert-right adaptor.

[00669] In some embodiments, the nucleic acid fragments can be appended with any one or any combination of two or more adaptors, and arranged in any order, where the adaptors comprise an adaptor having a binding sequence for a surface pinning primer binding site sequence (120), an adaptor having a surface capture primer binding site sequence (130), an adaptor having a forward sequencing primer binding site sequence (1 0), an adaptor having a reverse sequencing primer binding site sequence (150), a left sample index sequence (160), a right sample index sequence (170), a unique identification sequence (UMI) and/or, an adaptor sequence for binding a compaction oligonucleotide.

[00670] In some embodiments, any of the adaptors comprise universal adaptor sequences or batch-specific adaptor sequences.

[00671] Exemplary linear library molecules are shown in FIGS. 25, 26A, 26C, 27A and 27C. The skilled artisan appreciates that many other embodiments of linear library molecules comprising adaptor sequences with other arrangements are possible.

[00672] The adaptors can be prepared using chemical synthesis procedures using native nucleotides with or without nucleotide analogs or modified nucleotide linkages that confer certain properties, including resistance to enzymatic digestion, or increased thermal stability. Examples of nucleotide analogs and modified nucleotide linkages that inhibit nuclease digestion include phosphorothioate, 2’-O-methyl RNA, inverted dT, and 2’ 3’ dideoxy-dT. Insert regions that include locked nucleic acids (LNA) have increased thermal stability.

[00673] The insert region can be joined at one or both ends to at least one adaptor sequence using a ligase enzyme and/or primer extension reaction to generate a linear library molecule. Covalent linkage between an insert region and the adaptor(s) can be achieved with a DNA or RNA ligase. Exemplary DNA ligases that can ligate double-stranded DNA molecules include T4 DNA ligase and T7 DNA ligase. An adaptor sequence can be appended to an insert sequence by PCR using a tailed primer having 5’ region carrying an adaptor sequence and a 3’ region that is complementary to a portion of the insert sequence. An adaptor sequence can be appended to an insert sequence which is flanked one side or both sides with first and second adaptor sequences by PCR using a tailed primer having 5’ region carrying a third adaptor sequence and a 3’ region that is complementary to a portion of the first or second adaptor sequence.

[00674] In some embodiments, the linear single stranded nucleic acid library molecule (100) further comprises at least one junction adaptor sequence located between any of the adaptor sequences described herein (e.g., see FIGS. 26C and 27C). For example, a first left junction adaptor sequence (121) can be located upstream (e.g., located 5’) of the adaptor sequence for a surface pinning primer binding site sequence (120). In some embodiments, a second left junction adaptor sequence (125) can be located between the adaptor sequence for a surface pinning primer binding site sequence (120) and a left sample index sequence (160). In some embodiments, a third left junction adaptor sequence (165) can be located between a left sample index sequence (160) and a forward sequencing primer binding site sequence (140). In some embodiments, a fourth left junction adaptor sequence (145) can be located between a forward sequencing primer binding site sequence (140) and a sequence-of-interest (e.g., an insert region (110)). In some embodiments, a first right junction adaptor sequence (131) can be located downstream (e.g., located 3’) of a surface capture primer binding site sequence (130). In some embodiments, a second right junction adaptor sequence (135) can be located between the surface capture primer binding site sequence (130) and a right sample index sequence (170). In some embodiments, a third right junction adaptor sequence (175) can be located between a right sample index sequence (170) and a reverse sequencing primer binding site sequence (150). In some embodiments, a fourth right junction adaptor sequence (155) can be located between a reverse sequencing primer binding site sequence (150) and the sequence-of-interest (e.g., an insert (110)).

[00675] Any of the junction adaptor sequences can comprise any sequence and can be 3- 60 nucleotides in length. Any of the junction adaptor sequences comprise a universal sequence, a batch-specific sequence, or a unique sequence. Any of the junction adaptor sequences comprise a random sequence (e.g., NNN) having 3-20 nucleotides. Any of the junction adaptor sequences comprise a binding sequence for an amplification primer, a sequencing primer or a compaction oligonucleotide. Any of the junction adaptor sequences comprise a binding sequence for an immobilized capture primer. Any of the junction adaptor sequences comprise a sample index sequence. Any of the junction adaptor sequences comprise a unique identification sequence (e.g., UMI). Any of the junction adaptor sequences, particularly junction adaptor sequence (145) comprises a Tn5 transposon-end sequence, for example 5’- AG AT GT GT AT A AGAG AC AG -3’ (SEQ ID NO: 153). Any of the junction adaptor sequences, particularly junction adaptor sequence (155) comprises a Tn5 transposon-end sequence, for example 5’- CTGTCTCTTATACACATCT -3’ (SEQ ID NO: 162). The Tn5 transposon-end sequences can be introduced into the linear single stranded library molecule (100) via a transposase-mediated reaction which includes contacting doublestranded input DNA (e.g., genomic DNA) with a Tn-5 type transposase enzyme, and a double-stranded oligonucleotide comprising the Tn transposon-end sequence linked to an adaptor sequence or a sample index sequence under a condition that is suitable to form a transposon synaptic complex. In the double-stranded oligonucleotide, the Tn transposon-end sequence can be located 5’ or 3’ relative to an adaptor sequence or a sample index sequence. [00676] In some embodiments, a linear single stranded library molecule (100) can be generated by employing a ligation reaction and an optional primer extension reaction. The library molecule can be generated by joining the first end of a double-stranded insert region (110) to a first double-stranded adaptor, and joining the second end of the double-stranded insert region (110) to a second double-stranded adaptor. The first and second double-stranded adaptors each comprise two nucleic acid strands that are fully complementary along their lengths.

[00677] In some embodiments, individual double-stranded insert regions (110) can be joined to a first and a second double-stranded adaptor using a DNA ligase enzyme to generate a double-stranded recombinant molecule. In some embodiments the first and second doublestranded adaptors carry the same adaptor sequences. In some embodiments the first and second double-stranded adaptors carry different adaptor sequences.

[00678] In some embodiments, the library molecule can be generated by joining the first end of a double-stranded insert region (110) to a first double-stranded adaptor having a forward sequencing primer binding site sequence (140), and joining the second end of the double-stranded insert region (110) to a second double-stranded adaptor having a reverse sequencing primer binding site sequence (150). In some embodiments, the joining is conducted using a DNA ligase enzyme to generate a double-stranded recombinant molecule. In some embodiments, the first double-stranded adaptor further comprises a left sample index sequence (160) and/or a surface pinning primer binding site sequence (120). In some embodiments, the second double-stranded adaptor further comprises a right sample index sequence (170) and/or a surface capture primer binding site sequence (130).

[00679] In some embodiments, the ligating end of the first and/or the second doublestranded adaptors comprise a blunt end, or an overhang end (e.g., 5’ or 3’ overhang end). [00680] In some embodiments, a linear single stranded library molecule (100) can be generated by employing a ligation reaction and primer extension reaction. The library molecule can be generated by joining the first end of a double-stranded insert region (110) to a first double-stranded Y-shaped adaptor (e.g., a first forked adaptor), and joining the second end of a double-stranded insert region (110) to a second double-stranded Y-shaped adaptor (e.g., a second forked adaptor). The first and second Y-shaped adaptors each comprise two nucleic acid strands, where a portion of the two strands are fully complementary to each other and are annealed together and another portion of the two strands are not complementary to each other and are mismatched. In some embodiments, the ligating end of the first and second Y-shaped adaptors comprise an annealed portion that forms a blunt end or an overhang end (e.g., 5’ or 3’ overhang end).

[00681] In some embodiments the first and second Y-shaped adaptors carry the same adaptor sequences. In some embodiments the first and second Y-shaped adaptors carry different adaptor sequences.

[00682] In some embodiments, the first strand of the annealed portion and/or the mismatched portion of the Y-shaped adaptor can include at least a portion of an adaptor sequence having a forward sequencing primer binding site sequence (140) (or a complementary sequence thereof). In some embodiments, the first strand of the annealed portion and/or the mismatched portion of the Y-shaped adaptor can further include a left sample index sequence (160). In some embodiments, the first strand of the annealed portion and/or the mismatched portion of the Y-shaped adaptor can further include an adaptor sequence having a surface pinning primer binding site sequence (120).

[00683] In some embodiments, the second strand of the annealed portion and/or the mismatched portion of the Y-shaped adaptor can include at least a portion of an adaptor sequence having a reverse sequencing primer binding site sequence (150) (or a complementary sequence thereof). In some embodiments, the second strand of the annealed portion and/or the mismatched portion of the Y-shaped adaptor can further include a right sample index sequence (170). In some embodiments, the second strand of the annealed portion and/or the mismatched portion of the Y-shaped adaptor can further include a surface capture primer binding site sequence (130).

[00684] The double-stranded insert region (110) can be joined to the first and second double-stranded Y-shaped adaptors using a DNA ligase enzyme to generate a doublestranded recombinant molecule.

[00685] In some embodiments, the double-stranded recombinant molecules which are generated by ligating the insert region (110) to double-stranded adaptors or Y-shaped adaptors can be subjected to a denaturing condition to generate single-stranded recombinant molecules, and then a primer extension reaction. At least one additional adaptor sequence can be appended to the recombinant molecules by conducting a primer extension reaction using tailed primers (e.g., tailed PCR primers), by contacting/hybri dizing the single-stranded recombinant molecules with a plurality of first tailed primers and conducting at least one primer extension reaction to generate a first double-stranded tailed extension product.

[00686] In some embodiments, an additional adaptor sequence can be appended to the first double-stranded tailed extension product by conducting a primer extension reaction using tailed primers (e.g., tailed PCR primers), by contacting/hybridizing the first double-stranded tailed extension product with a plurality of second tailed primers and conducting at least one primer extension reaction to generate a second double-stranded tailed extension product.

[00687] In some embodiments, individual first tailed primers comprise a 5’ region carrying an adaptor sequence having a surface capture surface primer binding site sequence (130), and a 3’ region that is complementary to at least a portion of the adaptor sequence having a reverse sequencing primer binding site sequence (150) of the single-stranded recombinant molecules.

[00688] In some embodiments, individual first tailed primers comprise a 5’ region carrying an adaptor sequence having a surface capture primer binding site sequence (130), an internal region comprising a right sample index sequence (170), and a 3’ region that is complementary to at least a portion of the adaptor sequence having a reverse sequencing primer binding site sequence (150) of the single-stranded recombinant molecules.

[00689] In some embodiments, individual second tailed primers comprise a 5’ region carrying an adaptor sequence having a surface pinning primer binding site sequence (120), and a 3’ region that is complementary to at least a portion of the adaptor sequence having a forward sequencing primer binding site sequence (140) of the first double-stranded tailed extension product.

[00690] In some embodiments, individual second tailed primers comprise a 5’ region carrying an adaptor sequence having a surface pinning primer binding site sequence (120), an internal region comprising a left sample index sequence (160), and a 3’ region that is complementary to at least a portion of a forward sequencing primer binding site sequence (140) of the first double-stranded tailed extension product.

[00691] In some embodiments, the first tailed PCR primers can be used to conduct a first primer extension reaction and the second tailed PCR primers can be used conduct a second primer extension to generate library molecules comprising an insert region appended on both sides with at least one adaptor. In some embodiments, the first and second tailed PCR primers can be used to conduct multiple PCR cycles (e.g., about 5-20 PCR cycles) to generate library molecules comprising an insert region appended on both sides with at least one adaptor.

Nucleic Acid Concatemer Template Molecules

[00692] The present disclosure provides methods for use in conducting any of the methods described herein including methods for generating compact DNA nanoballs, batch sequencing, reiterative sequencing and/or re-seeding methods. In some embodiments, the plurality of concatemer template molecules is immobilized to a support. In some embodiments, the plurality of concatemer template molecules comprise single-stranded or double-stranded nucleic acid molecules, or a mixture of single-stranded and double-stranded nucleic acid molecules. In some embodiments, the plurality of concatemer template molecules comprise nucleic acid molecules comprising DNA, RNA, DNA/RNA chimeric or analogs thereof. In some embodiments, the plurality of concatemer template molecules is immobilized to the support at a density of about 10² - 10¹⁵ template molecules per mm², or any of the densities described herein.

[00693] In some embodiments, the plurality of concatemer template molecules comprises at least one nucleotide having a scissile moiety that can be cleaved to generate an abasic site in the template molecule. Exemplary nucleotides having a scissile moiety include uridine, 8- oxo-7, 8-dihydrogunine and deoxyinosine. In some embodiments, the plurality of concatemer template molecules lack a nucleotide having a scissile moiety. In some embodiments, the plurality of concatemer template molecules comprise a mixture of concatemer template molecules that either lack a nucleotide having a scissile moiety or include at least one nucleotide having a scissile moiety. In some embodiments, the plurality of concatemer template molecules lack a scissile moiety.

[00694] In some embodiments, the plurality of concatemer template molecules comprise at least one recognition site for a restriction endonuclease enzyme, including type I, type II, type Ils, type IIB, type III, or type IV restriction enzymes. In some embodiments, the plurality of concatemer template molecules comprise the same restriction enzyme site. In some embodiments, the plurality of concatemer template molecules comprise a mixture of concatemer template molecules having different restriction enzyme sites, or a mixture of concatemer template molecules lacking a restriction enzyme site and concatemer template molecules having a restriction enzyme site. In some embodiments, the plurality of concatemer template molecules lack a recognition site for a restriction endonuclease enzyme. [00695] In some embodiments, individual concatemer template molecules in the plurality of template molecules comprise nucleic acid concatemer template molecules. In some embodiments, the concatemer template molecules can be generated by conducting rolling circle amplification using circularized library molecules and amplification primers. In some embodiments, a concatemer template molecule comprises a single-stranded nucleic acid strand carrying numerous tandem copies of a polynucleotide unit, where each polynucleotide unit comprises a sequence of interest and at least one sequencing primer binding site. In some embodiments, the sequence of interest of one of the concatemer template molecules in the plurality and the sequence of interest of a different concatemer template molecule are the same or different.

[00696] In some embodiments, concatemer template molecules immobilized to a support can be generated using circularized library molecules and conducting rolling circle amplification. In some embodiments, the circularized library molecules can be generated using padlock probes, single-stranded splint strands, or double-stranded adaptors. Methods for generating circularized library molecules are described herein.

[00697] In some embodiments, the at least one sequencing primer binding site sequence comprises a pre-determined batch sequencing primer binding site sequence. In some embodiments, a pre-determined batch sequencing primer binding site sequence can be linked to a given sequence of interest, thus the pre-determined batch sequencing primer binding site sequence corresponds to a given sequence of interest. In some embodiments, in a batchspecific sequencing workflow, a batch sequencing primer can be used to selectively sequence at least a portion of a polynucleotide unit having a cognate batch sequencing primer binding site sequence.

[00698] In some embodiments, the polynucleotide unit of a concatemer template molecule comprises at least one barcode sequence. In some embodiments, a pre-determined batch barcode sequence can be linked to a given sequence of interest, thus the pre-determined batch barcode sequence corresponds to a given sequence of interest. In some embodiments, in a batch-specific sequencing workflow, the batch barcode sequence can be sequenced, and the sequence of interest need not be sequenced. Thus, the batch barcode sequence serves as a surrogate for the sequence of interest that is linked to the batch barcode sequence.

[00699] In some embodiments, a polynucleotide unit comprises at least one sample index sequence that can be used in a multiplex assay to distinguish sequences of interest obtained from different sample sources.

[00700] In some embodiments, a polynucleotide unit comprises a capture primer binding site. In some embodiments, a capture primer serves as an immobilized amplification primer for a circularized library molecule in a rolling circle amplification reaction. In some embodiments, the capture primer binding site of the circularized library molecule can hybridize to a surface capture primer which is immobilized to a support thereby immobilizing the circularized library molecule to the support. In some embodiments, an immobilized concatemer template molecule can be generated by hybridizing a single surface capture primer to a single circularized library molecule and conducting rolling circle amplification to generate an immobilized concatemer template molecule.

[00701] In some embodiments, a polynucleotide unit comprises a surface pinning binding site. In some embodiments, in a concatemer template molecule, the surface pinning binding site can hybridize to a pinning primer which is immobilized to a support thereby pinning a portion of the concatemer template molecule to the support.

[00702] In some embodiments, a polynucleotide unit comprises a compaction oligonucleotide binding site. In some embodiments, in a concatemer template molecule, the compaction oligonucleotide binding site binds a compaction oligonucleotide to cause compaction of the concatemer template molecule into a compact DNA nanoball.

[00703] In some embodiments, the plurality of template molecules comprises a plurality of sub-populations of template molecules including at least a first sub-population and a second sub-population. In some embodiments, the plurality of template molecules comprises 2 - 100 (e.g., about 5-90, about 10-80, about 20-75, about 35-50, about 10-30, or about 5-50, or any range therebetween) or more sub-populations of template molecules. In some embodiments, individual concatemer template molecules in a given sub-population comprise a sequence of interest, a sequencing primer binding site sequence that corresponds to the sequence of interest, and optionally a barcode sequence that corresponds to the sequence of interest. In some embodiments, the concatemer template molecules of a given sub-population have a sequencing primer binding site that differs from the sequencing primer binding site in the other sub-populations. Thus, the different sequencing primer binding sites of the different sub-populations enable batch sequencing of the concatemer template molecules.

[00704] In some embodiments, the plurality of concatemer template molecules further comprise any combination of a sample index sequence, a capture primer binding site, a pinning primer binding site and/or a compaction oligonucleotide binding site.

[00705] In some embodiments, at least one of the concatemer template molecules in the plurality comprises a concatemer template molecule which includes a plurality of tandem copies of a polynucleotide unit, where each polynucleotide unit comprises (i) a sequence of interest; (ii) a sequencing primer binding site sequence which corresponds to the sequence of interest; and (iii) optionally a barcode sequence which corresponds to the sequence of interest. In some embodiments, the polynucleotide unit of the at least one concatemer template molecule further comprises any combination of (iv) a sample index sequence that can be used in a multiplex assay to distinguish sequences of interest obtained from different sample sources; (v) a surface capture primer binding site; (vi) a surface pinning primer binding site; and/or (vii) a compaction oligonucleotide binding site.

[00706] In some embodiments, individual concatemer template molecules in the first subpopulation comprise a first sequence of interest, a first batch sequencing primer binding site sequence that corresponds to the first sequence of interest, and optionally a first batch barcode sequence that corresponds to the first sequence of interest. In some embodiments, concatemer template molecules in the first sub-population have the same sequence of interest or different sequences of interest. In some embodiments, concatemer template molecules in the first sub-population have the same first batch sequencing primer binding site sequence which corresponds to the first sequence of interest or corresponds to one of the first sequence of interest. In some embodiments, concatemer template molecules in the first sub-population have the same first batch barcode sequence or different first batch barcode sequences. In some embodiments, a first barcode sequence corresponds to a first sequence of interest, or corresponds to one of the first sequences of interest.

[00707] In some embodiments, individual concatemer template molecules in the first subpopulation comprise the same first sequence of interest, the same first batch sequencing primer binding site sequence that corresponds to the first sequence of interest, and the same first batch barcode sequence that corresponds to the first sequence of interest.

[00708] In some embodiments, individual concatemer template molecules in the first subpopulation comprise at least two different first sequences of interest, the same first batch sequencing primer binding site sequence that corresponds to the different first sequences of interest, and at least two different first batch barcode sequences where each first batch barcode sequence corresponds to a particular first sequence of interest.

[00709] In some embodiments, individual concatemer template molecules in the first subpopulation comprise at least two different first sequences of interest, the same first batch sequencing primer binding site sequence that corresponds to the different first sequences of interest, and one first batch barcode sequence that corresponds to the different first sequences of interest.

[00710] In some embodiments, the concatemer template molecules in the first subpopulation further comprise a sample index sequence that can be used in a multiplex assay to distinguish sequences of interest obtained from different sample sources. In some embodiments, concatemer template molecules in the first sub-population have the same sample index sequences. In some embodiments, the first sub-population comprises a mixture of concatemer template molecules having different sample index sequences. For example, some of the concatemer template molecules in the first sub-population comprises a first batch first sample index sequence, and some of the concatemer template molecules in the first subpopulation comprises a first batch second sample index sequence.

[00711] In some embodiments, the first sub-population comprising a mixture of concatemer template molecules having different sample index sequences can be generated by conducting separate library preparation workflows to generate: (i) a first set of library molecules comprising a first sequence of interest from a first source, a first batch barcode sequence that corresponds to the first sequence of interest, a first batch sequencing primer binding site sequence that corresponds to the first sequence of interest, and a first sample index that corresponds to the first source of the first sequence of interest, and (ii) a second set of library molecules comprising the first sequence of interest from a second source, a first batch barcode sequence that corresponds to the first sequence of interest, a first batch sequencing primer binding site sequence that corresponds to the first sequence of interest, and a second sample index that corresponds to the second source of the first sequence of interest. The resulting first and second library preparations can be mixed together to generate a mixture of concatemer template molecules in the first sub-population having a mixture of different sample index sequences.

[00712] In some embodiments, the concatemer template molecules in the first subpopulation further comprise at least one binding site for a compaction oligonucleotide (e.g., a universal binding site for a compaction oligonucleotide). In some embodiments, individual compaction oligonucleotides can hybridize to two different locations on the same the concatemer template molecule to pull together distal portions of the concatemer template molecule causing compaction of the template molecule to form a compact DNA nanoball. [00713] In some embodiments, the concatemer template molecules in the first subpopulation further comprise a first batch surface capture primer binding site sequence. In some embodiments, concatemer template molecules in the first sub-population have the same first surface batch capture primer binding site sequence.

[00714] In some embodiments, the concatemer template molecules in the first subpopulation further comprise a first batch surface pinning primer binding site sequence which can hybridize to a first surface pinning primer which is immobilized to a support thereby pinning a portion of the template molecules of the first sub-population to the support. In some embodiments, concatemer template molecules in the first sub-population have the same first batch surface pinning primer binding site sequence. [00715] In some embodiments, individual concatemer template molecules in the first subpopulation of template molecules comprise first sub-population concatemer template molecules. In some embodiments, individual concatemer template molecules in the first subpopulation comprise a single-stranded nucleic acid strand carrying a plurality of tandem copies of a polynucleotide unit, where each polynucleotide unit comprises (i) a first sequence of interest; and (ii) a first batch sequencing primer binding site sequence which corresponds to the first sequence of interest. In some embodiments, the polynucleotide unit of individual concatemer template molecules in the first sub-population further comprise any combination of (iii) a first batch barcode sequence which corresponds to the first sequence of interest; (iv) a sample index sequence that can be used in a multiplex assay to distinguish sequences of interest obtained from different sample sources; (v) a first batch surface capture primer binding site sequence; (vi) a first batch surface pinning primer binding site sequence; and/or (vii) a compaction oligonucleotide binding site.

[00716] In some embodiments, individual concatemer template molecules in the second sub-population comprise a second sequence of interest, a second batch sequencing primer binding site sequence that corresponds to the second sequence of interest, and optionally a second batch barcode sequence that corresponds to the second sequence of interest. In some embodiments, concatemer template molecules in the second sub-population have the same sequence of interest or different sequences of interest. In some embodiments, concatemer template molecules in the second sub-population have the same second batch sequencing primer binding site sequence which corresponds to the second sequence of interest or corresponds to one of the second sequence of interest. In some embodiments, the first and second batch sequencing primer binding sites have different sequences. In some embodiments, concatemer template molecules in the second sub-population have the same second batch barcode sequence or different second batch barcode sequences. In some embodiments, a second barcode sequence corresponds to a second sequence of interest, or corresponds to one of the second sequences of interest.

[00717] In some embodiments, individual concatemer template molecules in the second sub-population comprise the same second sequence of interest, the same second batch sequencing primer binding site sequence that corresponds to the second sequence of interest, and the same second batch barcode sequence that corresponds to the second sequence of interest.

[00718] In some embodiments, individual concatemer template molecules in the second sub-population comprise at least two different second sequences of interest, the same second batch sequencing primer binding site sequence that corresponds to the different second sequences of interest, and at least two different second batch barcode sequences where each second batch barcode sequence corresponds to a particular second sequence of interest. [00719] In some embodiments, individual concatemer template molecules in the second sub-population comprise at least two different second sequences of interest, the same second batch sequencing primer binding site sequence that corresponds to the different second sequences of interest, and one second batch barcode sequence that corresponds to the different second sequences of interest.

[00720] In some embodiments, the concatemer template molecules in the second subpopulation further comprise a sample index sequence that can be used in a multiplex assay to distinguish sequences of interest obtained from different sample sources. In some embodiments, concatemer template molecules in the second sub-population have the same sample index sequences. In some embodiments, the second sub-population comprises a mixture of concatemer template molecules having different sample index sequences. For example, some of the concatemer template molecules in the second sub-population comprises a second batch first sample index sequence, and some of the concatemer template molecules in the second sub-population comprises a second batch second sample index sequence. [00721] In some embodiments, the second sub-population comprising a mixture of concatemer template molecules having different sample index sequences can be generated by conducting separate library preparation workflows to generate: (i) a first set of library molecules comprising a second sequence of interest from a first source, a second batch barcode sequence that corresponds to the second sequence of interest, a second batch sequencing primer binding site sequence that corresponds to the second sequence of interest, and a first sample index that corresponds to the first source of the second sequence of interest, and (ii) a second set of library molecules comprising the second sequence of interest from a second source, a second batch barcode sequence that corresponds to the second sequence of interest, a second batch sequencing primer binding site sequence that corresponds to the second sequence of interest, and a second sample index that corresponds to the second source of the second sequence of interest. The resulting first and second library preparations can be mixed together to generate a mixture of template molecules in the second sub-population having a mixture of different sample index sequences.

[00722] In some embodiments, the concatemer template molecules in the second subpopulation further comprise at least one binding site for a compaction oligonucleotide (e.g., a universal binding site for a compaction oligonucleotide). In some embodiments, individual compaction oligonucleotides can hybridize to two different locations on the same concatemer template molecule to pull together distal portions of the template molecule causing compaction of the template molecule to form a compact DNA nanoball.

[00723] In some embodiments, the concatemer template molecules in the second subpopulation further comprise a second batch capture primer binding site sequence. In some embodiments, concatemer template molecules in the second sub-population have the same second batch capture primer binding site sequence.

[00724] In some embodiments, the concatemer template molecules in the second subpopulation further comprise a second batch surface pinning binding site which can hybridize to a second surface pinning primer which is immobilized to a support thereby pinning a portion of the template molecules of the second sub-population to the support. In some embodiments, concatemer template molecules in the second sub-population have the same second batch surface pinning binding site.

[00725] In some embodiments, individual concatemer template molecules in the second sub-population of template molecules comprise second sub-population concatemer template molecules. In some embodiments, individual concatemer template molecules in the second sub-population comprise a single-stranded nucleic acid strand carrying a plurality of tandem copies of a polynucleotide unit, individual polynucleotide units comprising (i) a second sequence of interest; and (ii) a second batch sequencing primer binding site sequence which corresponds to the second sequence of interest. In some embodiments, the polynucleotide unit of individual concatemer template molecules in the second sub-population further comprise any combination of (iii) a second batch barcode sequence which corresponds to the second sequence of interest; (iv) a sample index sequence that can be used in a multiplex assay to distinguish sequences of interest obtained from different sample sources; (v) a second batch capture primer binding site sequence; (vi) a second batch surface pinning primer binding site sequence; and/or (vii) a compaction oligonucleotide binding site.

[00726] In some embodiments, the plurality of concatemer template molecules is immobilized to a support at a density of about 10² - 10¹⁵ template molecules per mm². In some embodiments, the immobilized concatemer template molecules comprise one population or a mixture of at least two sub-populations of concatemer template molecules including at least a first and second sub-population of template molecules.

[00727] In some embodiments, the plurality of concatemer template molecules is immobilized to the support at a density where at least some of the concatemer template molecules comprise nearest neighbor template molecules that do not touch each other and/or do not overlap each other when viewed from any angle of the support including above, below or side views of the support. In some embodiments, the concatemer template molecules have visible interstitial space between the concatemer template molecules at a given field of view (FOV) of the support.

[00728] In some embodiments, the plurality of concatemer template molecules is immobilized to the support at a high density. In some embodiments, at least some of the concatemer template molecules comprise nearest neighbor template molecules that touch each other and/or overlap each other when viewed from any angle of the support including above, below or side views of the support. In some embodiments, the high density concatemer template molecules have little or no visible interstitial space between the concatemer template molecules at a given field of view (FOV) of the support.

[00729] In some embodiments, the concatemer template molecules immobilized to the support are optically resolvable as discrete spots. In some embodiments, the concatemer template molecules are not optically resolvable as spots. In some embodiments, the concatemer template molecules comprise a mixture of template molecules that are, or are not, optically resolvable as discrete spots.

[00730] In some embodiments, about 20-75%, or about 25-65%, or about 30-55%, or about 35-45% of the concatemer template molecules immobilized to the support are optically resolvable as a discrete spot when viewed from any angle above, below or side view of the support.

[00731] In some embodiments, about 20-75%, or about 25-65%, or about 30-55%, or about 35-45% of the concatemer template molecules immobilized to the support have a nearest neighbor distance of 15-10 nm.

[00732] In some embodiments, about 20-75%, or about 25-65%, or about 30-55%, or about 35-45% of the concatemer template molecules immobilized to the support have a nearest neighbor distance of 10-5 nm.

[00733] In some embodiments, about 20-75%, or about 25-65%, or about 30-55%, or about 35-45% of the concatemer template molecules immobilized to the support have a nearest neighbor distance of 5-1 nm or smaller nearest neighbor distance.

[00734] In some embodiments, interstitial space between concatemer template molecules immobilized to the support is about 15-10 nm, or about 10-5 nm, or about 5-1 nm, or smaller. [00735] In some embodiments, the support comprises a plurality of concatemer template molecules immobilized at random (e.g., random and non-repeating positions) and non-pre- determined positions on the support. In some embodiments, the plurality of concatemer template molecules includes one population of template molecules, or a mixture of at least two sub-populations of concatemer template molecules including at least a first and second sub-population of concatemer template molecules. In some embodiments, the support comprises features on the support that are located in a random and non-pre-determined manner, where the features are sites for attachment of the concatemer template molecules. In some embodiments, the support lacks any contours (e.g., wells, protrusions, and the like) arranged in a pre-determined pattern where the contours have features that are sites for attachment of the template molecules. In some embodiments, the support lacks features arranged in a pre-determined pattern. In some embodiments, the support lacks features arranged in a pre-determined pattern where the feature have a chemical functionality for tethering a nucleic acid template molecule to the support. In some embodiments, the support lacks interstitial regions arranged in a pre-determined pattern where the interstitial regions are sites designed to have no attached template molecules.

[00736] In some embodiments, the support comprises a plurality of concatemer template molecules immobilized at pre-determined positions on the support. For example the concatemer template molecules can be immobilized on the support in a pre-determined pattern comprises stripes or spots arranged in rows and/or columns or other pre-determined patterns (e.g., FIGS. 13B(iii) and 13B(iv). In some embodiments, the pre-determined pattern has a repeating pattern. In some embodiments, the plurality of concatemer template molecules includes one population of concatemer template molecules, or a mixture of at least two sub-populations of concatemer template molecules including at least a first and second sub-population of concatemer template molecules. In some embodiments, the support comprises features on the support that are located in a pre-determined manner, where the features are sites for attachment of the concatemer template molecules. In some embodiments, the support includes contours (e.g., wells, protrusions, and the like) arranged in a pre-determined pattern where the contours have features that are sites for attachment of the template molecules. In some embodiments, the support includes features arranged in a predetermined pattern where the features can be fabricated using photo-chemical, photolithography, electron beam lithography, micro- or nano-imprint lithography, ink-jet printing, or micron-scale or nano-scale printing. In some embodiments, the support includes features arranged in a pre-determined pattern where the feature have a chemical functionality for tethering a nucleic acid template molecule to the support. In some embodiments, the support includes interstitial regions arranged in a pre-determined pattern where the interstitial regions are sites designed to have no attached template molecules. Methods for Sequencing

[00737] The present disclosure provides methods for sequencing any of the template molecules (e.g., concatemer template molecules) described herein, including sequencing compact DNA nanoballs, batch sequencing, reiterative sequencing and/or re-seeding methods. Any of the methods for conducting rolling circle amplification reaction described herein can be used to generate a plurality of concatemer template molecules immobilized to a support, and the concatemer template molecules can be subjected to sequencing reactions using sequencing polymerases and nucleotide reagents which include nucleotides, nucleotide analogs and/or multivalent molecules. In some embodiments, the sequencing reactions employ nucleotide reagents comprising detectably labeled nucleotide analogs. In some embodiments, the sequencing reactions employ a two-stage sequencing reaction comprising binding detectably labeled multivalent molecules, and incorporating nucleotide analogs. In some embodiments, the sequencing reactions employ non-labeled nucleotide analogs. Exemplary methods for sequencing are described in WO2022266470, the contents of which are incorporated by reference herein in their entirety.

Methods for Sequencing using Nucleotide Analogs

[00738] The present disclosure provides methods for sequencing any of the concatemer template molecules described herein, including sequencing compact DNA nanoballs, batch sequencing, reiterative sequencing and/or re-seeding methods, wherein the methods for sequencing comprise step (a): contacting a sequencing polymerase to (i) a concatemer template molecule and (ii) a nucleic acid sequencing primer. In some embodiments, the contacting is conducted under a condition suitable to bind the sequencing polymerase to the concatemer template molecule which is hybridized to the nucleic acid primer. In some embodiments, the concatemer template molecule hybridized to the nucleic acid primer forms the nucleic acid duplex. In some embodiments, the sequencing polymerase comprises a recombinant mutant sequencing polymerase that can bind and incorporate nucleotide analogs. In some embodiments, the sequencing primer comprises a 3’ extendible end. In some embodiments, the concatemer template molecules are immobilized to a support.

[00739] In some embodiments, the sequencing primer comprises a 3’ extendible end or a 3’ non-extendible end. In some embodiments, the plurality of concatemer template molecules comprise amplified template molecules (e.g., clonally amplified template molecules). In some embodiments, the plurality of concatemer template molecules comprise one copy of a target sequence of interest. In some embodiments, the plurality of nucleic acid molecules comprises two or more tandem copies of a target sequence of interest (e.g., concatemers). In some embodiments, the concatemer template molecules in the plurality of nucleic acid concatemer template molecules comprise the same target sequence of interest or different target sequences of interest. In some embodiments, the plurality of concatemer template molecules and/or the plurality of nucleic acid primers are in solution or are immobilized to a support. In some embodiments, when the plurality of concatemer template molecules and/or the plurality of nucleic acid primers are immobilized to a support, the binding with the first sequencing polymerase generates a plurality of immobilized first polymerase complexes. In some embodiments, the plurality of concatemer template molecules and/or nucleic acid primers are immobilized to 10² - 10¹⁵ different sites on a support, for example between about 10² sites and about 10¹⁵ sites, between about 10⁵ sites and about 10¹⁵ sites, between about IO¹⁰ sites and about 10¹⁵ sites, between about 10³ sites and about 10¹⁴ sites, between about 10⁴ sites and about 10¹³ sites, between about 10⁵ sites and about 10¹² sites, between about 10⁶ sites and about 10¹¹ sites, between about 10⁷ sites and about IO¹⁰ sites, or between about 10⁸ sites and about IO¹⁰ sites, or any range therebetween, on the support. In some embodiments, the binding of the plurality of concatemer template molecules and nucleic acid primers with the plurality of first sequencing polymerases generates a plurality of first polymerase complexes immobilized to 10² - 10¹⁵ different sites on the support. In some embodiments, the plurality of first polymerase complexes immobilized on the support are immobilized to pre-determined or to random sites on the support. In some embodiments, the plurality of first polymerase complexes are in fluid communication with each other to permit flowing a solution of reagents (e.g., enzymes including sequencing polymerases, multivalent molecules, nucleotides, and/or divalent cations) onto the support so that the plurality of polymerase complexes on the support are reacted with the solution of reagents in a massively parallel manner.

[00740] In some embodiments, the methods for sequencing further comprise step (b): contacting the sequencing polymerase with a plurality of nucleotides under a condition suitable for binding at least one nucleotide to the sequencing polymerase which is bound to the nucleic acid duplex and suitable for polymerase-catalyzed nucleotide incorporation. In some embodiments, the sequencing polymerase is contacted with the plurality of nucleotides in the presence of at least one catalytic cation, e.g., at least one catalytic cation comprising magnesium and/or manganese. In some embodiments, the plurality of nucleotides comprises at least one nucleotide analog having a chain terminating moiety at the sugar 2’ or 3’ position. In some embodiments, the chain terminating moiety is removable from the sugar 2’ or 3’ position to convert the chain terminating moiety to an OH or H group. In some embodiments, the plurality of nucleotides comprises at least one nucleotide that lacks a chain terminating moiety. In some embodiments, at least on nucleotide is labeled with a detectable reporter moiety (e.g., fluorophore). In some embodiments, step (b) further comprises removing the chain terminating moiety from the incorporated chain terminating nucleotide to generate an extendible 3 ’OH group. In some embodiments, the sequencing of step (b) further comprises repeating at least once the steps of: (i) incorporating a detectably labeled chain terminating nucleotide into the terminal 3’ end of a hybridized first sequencing primer; (ii) detecting and identifying the incorporated chain terminating nucleotide; and (iii) removing the chain terminating moiety and/or the detectable label from the incorporated chain terminating nucleotide to generate an extendible 3 ’OH sugar group on the incorporated chain terminating nucleotide.

[00741] In some embodiments, the methods for sequencing further comprise step (c): incorporating at least one nucleotide into the 3’ end of the extendible primer under a condition suitable for incorporating the at least one nucleotide. In some embodiments, the suitable conditions for nucleotide binding the polymerase and for incorporation the nucleotide can be the same or different. In some embodiments, conditions suitable for incorporating the nucleotide comprise inclusion of at least one catalytic cation comprising magnesium and/or manganese. In some embodiments, the at least one nucleotide binds the sequencing polymerase and incorporates into the 3 ’ end of the extendible primer. In some embodiments, the incorporating the nucleotide into the 3’ end of the primer in step (c) comprises a primer extension reaction. In some embodiments, a sequencing cycle comprises completion of steps (b) - (c).

[00742] In some embodiments, the methods for sequencing further comprise step (d): repeating the incorporating at least one nucleotide into the 3’ end of the extendible primer of steps (b) and (c) at least once. In some embodiments, the plurality of nucleotides comprises a plurality of nucleotides labeled with detectable reporter moiety. The detectable reporter moiety comprises a fluorophore. In some embodiments, the fluorophore is attached to the nucleotide base. In some embodiments, the fluorophore is attached to the nucleotide base with a linker which is cleavable/removable from the base. In some embodiments, at least one of the nucleotides in the plurality is not labeled with a detectable reporter moiety. In some embodiments, a particular detectable reporter moiety (e.g., fluorophore) that is attached to the nucleotide can correspond to the nucleotide base (e.g., dATP, dGTP, dCTP, dTTP or dUTP) to permit detection and identification of the nucleotide base. In some embodiments, the method further comprises detecting the at least one incorporated nucleotide at step (c) and/or step (d). In some embodiments, the method further comprises identifying the at least one incorporated nucleotide at step (c) and/or step (d). In some embodiments, the sequence of the nucleic acid concatemer template molecule can be determined by detecting and identifying the nucleotide that binds the sequencing polymerase, thereby determining the sequence of the concatemer template molecule. In some embodiments, the sequence of the concatemer template molecule can be determined by detecting and identifying the nucleotide that incorporates into the 3’ end of the primer, thereby determining the sequence of the concatemer template molecule.

[00743] In some embodiments, in the methods for sequencing, the plurality of sequencing polymerases that are bound to the nucleic acid duplexes comprise a plurality of polymerase complexes, having at least a first and second polymerase complex. In some embodiments, the first polymerase complex comprises a first sequencing polymerase bound to a first nucleic acid duplex comprising a first nucleic acid template sequence which is hybridized to a first nucleic acid primer. In some embodiments, the second polymerase complex comprises a second sequencing polymerase bound to a second nucleic acid duplex comprising a second nucleic acid template sequence which is hybridized to a second nucleic acid primer. In some embodiments, the first and second nucleic acid template sequences comprise the same or different sequences. In some embodiments, the first and second nucleic acid concatemers are clonally-amplified. In some embodiments, the first and second primers comprise extendible 3’ ends or non-extendible 3’ ends. In some embodiments, the plurality of polymerase complexes is immobilized to a support. In some embodiments, the density of the plurality of polymerase complexes is about 10² - 10¹⁵ polymerase complexes per mm² that are immobilized to the support, for example, between about IO¹⁰ and about 10¹⁵ complexed polymerases per mm², between about 10⁵ and about 10¹⁵ complexed polymerases per mm², between about 10³ and about 10¹⁴ complexed polymerases per mm², between about 10⁴ and about 10¹³ complexed polymerases per mm², between about 10⁵ and about 10¹² complexed polymerases per mm², between about 10⁶ and about 10¹¹ complexed polymerases per mm², between about 10⁷ and about IO¹⁰ complexed polymerases per mm², or between about 10⁸ and about IO¹⁰ complexed polymerases per mm², or any range therebetween. Two-Stage Methods for Nucleic Acid Sequencing

[00744] In some aspects, the present disclosure provides a two-stage method for sequencing any of the concatemer template molecules described herein, including sequencing compact DNA nanoballs, batch sequencing, reiterative sequencing and/or re-seeding methods. In some embodiments, the first stage comprises binding multivalent molecules to polymerase complexes to form multivalent-polymerase complexes, and detecting the multivalent-polymerase complexes. In some embodiments, the second stage comprises nucleotide incorporation and extension of the sequencing primer. In some embodiments, one sequencing cycle comprises completion of a first and second stage. In some embodiments, any of the workflows that employ a two-stage sequencing method comprises conducting 5-25 sequencing cycles, or 25-50 sequencing cycles, or 50-75 sequencing cycles, or 75-100 sequencing cycles, or 100-200 sequencing cycles, or 200-500 sequencing cycles, or 500-750 sequencing cycles, or 750-1000 sequencing cycles, or any range therebetween.

[00745] In some embodiments, the first stage comprises step (a): contacting a plurality of a first sequencing polymerase to (i) a plurality of concatemer template molecules and (ii) a plurality of nucleic acid sequencing primers. In some embodiments, the contacting is conducted under a condition suitable to bind the plurality of first sequencing polymerases to the plurality of concatemer template molecules and the plurality of nucleic acid primers thereby forming a plurality of first polymerase complexes each comprising a first sequencing polymerase bound to a nucleic acid duplex wherein the nucleic acid duplex comprises a concatemer template molecule hybridized to a nucleic acid primer. In some embodiments, the first polymerase comprises a recombinant mutant sequencing polymerase. In some embodiments, the sequencing primer comprises a 3’ extendible end.

[00746] In some embodiments, in the methods for sequencing concatemer template molecules, the sequencing primer comprises a 3’ extendible end or a 3’ non-extendible end. In some embodiments, the plurality of concatemer template molecules comprise amplified template molecules (e.g., clonally amplified template molecules). In some embodiments, the plurality of concatemer template molecules comprise one copy of a target sequence of interest. In some embodiments, the plurality of nucleic acid molecules comprises two or more tandem copies of a target sequence of interest (e.g., concatemers). In some embodiments, the concatemer template molecules in the plurality of concatemer template molecules comprise the same target sequence of interest or different target sequences of interest. In some embodiments, the plurality of concatemer template molecules and/or the plurality of nucleic acid primers are in solution or are immobilized to a support. In some embodiments, when the plurality of concatemer template molecules and/or the plurality of nucleic acid primers are immobilized to a support, the binding with the first sequencing polymerase generates a plurality of immobilized first polymerase complexes. In some embodiments, the plurality of concatemer template molecules and/or nucleic acid primers are immobilized to 10² - 10¹⁵ different sites on a support. In some embodiments, the binding of the plurality of concatemer template molecules and nucleic acid primers with the plurality of first sequencing polymerases generates a plurality of first polymerase complexes immobilized to 10² - 10¹⁵ different sites on the support. In some embodiments, the plurality of first polymerase complexes immobilized on the support are immobilized to pre-determined or to random sites on the support. In some embodiments, the plurality of immobilized first polymerase complexes are in fluid communication with each other to permit flowing a solution of reagents (e.g., enzymes including sequencing polymerases, multivalent molecules, nucleotides, and/or divalent cations) onto the support so that the plurality of immobilized polymerase complexes on the support are reacted with the solution of reagents in a massively parallel manner.

[00747] In some embodiments, the methods for sequencing further comprise step (b): contacting the plurality of first polymerase complexes with a plurality of multivalent molecules to form a plurality of multivalent-polymerase complexes (e.g., binding complexes). In some embodiments, individual multivalent molecules in the plurality of multivalent molecules comprise a core attached to multiple nucleotide arms, individual nucleotide arms attached to a nucleotide (e.g., a nucleotide moiety) (e.g., FIGS. 1-4). In some embodiments, the contacting of step (b) is conducted under a condition suitable for binding complementary nucleotide moieties of the multivalent molecules to at least two of the plurality of first polymerase complexes thereby forming a plurality of multivalent-polymerase complexes. In some embodiments, the condition is suitable for inhibiting polymerase- catalyzed incorporation of the complementary nucleotide moieties into the primers of the plurality of multivalent-polymerase complexes. In some embodiments, the plurality of multivalent molecules comprise at least one multivalent molecule having multiple nucleotide arms (e.g., FIGS. 1-4), individual nucleotide arms attached with a nucleotide analog (e.g., a nucleotide analog unit). In some embodiments, the nucleotide analog includes a chain terminating moiety at the sugar 2’ and/or 3’ position. In some embodiments, the plurality of multivalent molecules comprises at least one multivalent molecule comprising multiple nucleotide arms, individual nucleotide arms attached with a nucleotide moiety that lacks a chain terminating moiety. In some embodiments, at least one of the multivalent molecules in the plurality of multivalent molecules is labeled with a detectable reporter moiety. In some embodiments, the detectable reporter moiety comprises a fluorophore. In some embodiments, the contacting of step (b) is conducted in the presence of at least one non-catalytic cation comprising strontium, barium and/or calcium.

[00748] In some embodiments, the methods for sequencing further comprise step (c): detecting the plurality of multivalent-polymerase complexes. In some embodiments, the detecting includes detecting the multivalent molecules that are bound to the polymerase complexes. In some embodiments, the complementary nucleotide moieties of the multivalent molecules are bound to the primers, but incorporation of the complementary nucleotide moieties is inhibited. In some embodiments, the multivalent molecules are labeled with a detectable reporter moiety to permit detection. In some embodiments, the labeled multivalent molecules comprise a fluorophore attached to the core, linker and/or nucleotide moiety of the multivalent molecules.

[00749] In some embodiments, the methods for sequencing further comprise step (d): identifying the nucleo-base of the complementary nucleotide moieties that are bound to the plurality of first polymerase complexes, thereby determining the sequence of the concatemer template molecule. In some embodiments, the multivalent molecules are labeled with a detectable reporter moiety that corresponds to the particular nucleotide moieties attached to the nucleotide arms to permit identification of the complementary nucleotide moieties (e.g., a nucleotide base adenine, guanine, cytosine, thymine or uracil) that are bound to the plurality of first polymerase complexes.

[00750] In some embodiments, the second stage of the two-stage sequencing method generally comprises nucleotide incorporation. In some embodiments, the methods for sequencing further comprise step (e): dissociating the plurality of multivalent-polymerase complexes and removing the plurality of first sequencing polymerases and their bound multivalent molecules, and retaining the plurality of nucleic acid duplexes.

[00751] In some embodiments, the methods for sequencing further comprises step (f): contacting the plurality of the retained nucleic acid duplexes of step (e) with a plurality of second sequencing polymerases, wherein the contacting is conducted under a condition suitable for binding the plurality of second sequencing polymerases to the plurality of the retained nucleic acid duplexes, thereby forming a plurality of second polymerase complexes. In some embodiments, individual second polymerase complexes comprise a second sequencing polymerase bound to a nucleic acid duplex. In some embodiments, the second sequencing polymerase comprises a recombinant mutant sequencing polymerase. [00752] In some embodiments, the plurality of first sequencing polymerases of step (a) have an amino acid sequence that is 100% identical to the amino acid sequence as the plurality of the second sequencing polymerases of step (f). In some embodiments, the plurality of first sequencing polymerases of step (a) have an amino acid sequence that differs from the amino acid sequence of the plurality of the second sequencing polymerases of step (f).

[00753] In some embodiments, the methods for sequencing further comprise step (g): contacting the plurality of second polymerase complexes with a plurality of nucleotides, wherein the contacting is conducted under a condition suitable for binding complementary nucleotides from the plurality of nucleotides to at least two of the second polymerase complexes thereby forming a plurality of nucleotide-polymerase complexes. In some embodiments, the contacting of step (g) is conducted under a condition that is suitable for promoting polymerase-catalyzed incorporation of the bound complementary nucleotides into the primers of the nucleotide-polymerase complexes thereby forming a plurality of nucleotide-polymerase complexes. In some embodiments, the incorporating the nucleotide into the 3’ end of the primer in step (g) comprises a primer extension reaction. In some embodiments, the contacting of step (g) is conducted in the presence of at least one catalytic cation comprising magnesium and/or manganese. In some embodiments, the plurality of nucleotides comprises native nucleotides (e.g., non-analog nucleotides) or nucleotide analogs. In some embodiments, the plurality of nucleotides comprises a 2’ and/or a 3’ chain terminating moiety which is removable or is not removable. In some embodiments, the plurality of nucleotides comprises a plurality of nucleotides labeled with detectable reporter moiety. The detectable reporter moiety comprises a fluorophore. In some embodiments, the fluorophore is attached to the nucleotide base. In some embodiments, the fluorophore is attached to the nucleotide base with a linker which is cleavable/removable from the base or is not removable from the base. In some embodiments, at least one of the nucleotides in the plurality is not labeled with a detectable reporter moiety. In some embodiments, a particular detectable reporter moiety (e.g., a fluorophore) that is attached to the nucleotide can correspond to the nucleotide base (e.g., dATP, dGTP, dCTP, dTTP or dUTP) to permit detection and identification of the nucleotide base.

[00754] In some embodiments, the methods for sequencing further comprise step (h): when the nucleotides of step (g) are detectably labeled, step (h) comprises detecting the complementary nucleotides which are incorporated into the primers of the nucleotide- polymerase complexes. In some embodiments, the plurality of nucleotides is labeled with a detectable reporter moiety to permit detection. In some embodiments, in the methods for sequencing concatemer template molecules, when the nucleotides of step (g) are non-labeled, the detecting of step (h) is omitted.

[00755] In some embodiments, the methods for sequencing further comprise step (i): when the nucleotides of step (g) are detectably labeled, step (i) comprises identifying the bases of the complementary nucleotides which are incorporated into the primers of the nucleotide-polymerase complexes. In some embodiments, the identification of the incorporated complementary nucleotides in step (i) can be used to confirm the identity of the complementary nucleotides of the multivalent molecules that are bound to the plurality of first polymerase complexes in step (d). In some embodiments, the identifying of step (i) can be used to determine the sequence of the concatemer template molecules. In some embodiments, in the methods for sequencing concatemer template molecules, when the nucleotides of step (g) are non-labeled, the identifying of step (i) is omitted.

[00756] In some embodiments, the methods for sequencing further comprise step (j): removing the chain terminating moiety from the incorporated nucleotide when step (g) is conducted by contacting the plurality of second polymerase complexes with a plurality of nucleotides that comprise at least one nucleotide having a 2’ and/or a 3’ chain terminating moiety.

[00757] In some embodiments, the methods for sequencing further comprise step (k): repeating steps (a) - (j) at least once. In some embodiments, the sequence of the nucleic acid concatemer template molecules can be determined by detecting and identifying the multivalent molecules that bind the sequencing polymerases but do not incorporate into the 3’ end of the primer at steps (c) and (d). In some embodiments, the sequence of the nucleic acid concatemer template molecule can be determined (or confirmed) by detecting and identifying the nucleotide that incorporates into the 3’ end of the primer at steps (h) and (i).

[00758] In some embodiments, in any of the methods for sequencing nucleic acid molecules, the binding of the plurality of first polymerase complexes with the plurality of multivalent molecules forms at least one avidity complex, the method comprising the steps: (a) binding a first nucleic acid primer, a first sequencing polymerase, and a first multivalent molecule to a first portion of a concatemer template molecule thereby forming a first binding complex, wherein a first nucleotide moiety of the first multivalent molecule binds to the first sequencing polymerase; and (b) binding a second nucleic acid primer, a second sequencing polymerase, and the first multivalent molecule to a second portion of the same concatemer template molecule thereby forming a second binding complex. In some embodiments, a second nucleotide moiety of the first multivalent molecule binds to the second sequencing polymerase. In some embodiments, the first and the second binding complexes which include the same multivalent molecule form an avidity complex. In some embodiments, the first sequencing polymerase comprises any wild type or mutant polymerase described herein. In some embodiments, the second sequencing polymerase comprises any wild type or mutant polymerase described herein. The concatemer template molecule comprises tandem repeat sequences of a sequence of interest and at least one universal sequencing primer binding site. The first and second nucleic acid primers can bind to a sequencing primer binding site along the concatemer template molecule. Exemplary multivalent molecules are shown in FIGS. 1- 4

[00759] In some embodiments, in any of the methods for sequencing nucleic acid molecules, wherein the method includes binding the plurality of first polymerase complexes with the plurality of multivalent molecules to form at least one avidity complex, the method comprising the steps: (a) contacting the plurality of sequencing polymerases and the plurality of nucleic acid primers with different portions of a concatemer template molecule to form at least first and second polymerase complexes on the same concatemer template molecule; (b) contacting a plurality of multivalent molecules to the at least first and second polymerase complexes on the same concatemer template molecule, under conditions suitable to bind a single multivalent molecule from the plurality to the first and second polymerase complexes, wherein at least a first nucleotide moiety of the single multivalent molecule is bound to the first polymerase complex which includes a first primer hybridized to a first portion of the concatemer template molecule thereby forming a first binding complex (e.g., first ternary complex), and wherein at least a second nucleotide moiety of the single multivalent molecule is bound to the second polymerase complex which includes a second primer hybridized to a second portion of the concatemer template molecule thereby forming a second binding complex (e.g., second ternary complex), wherein the contacting is conducted under a condition suitable to inhibit polymerase-catalyzed incorporation of the bound first and second nucleotide moieties in the first and second binding complexes, and wherein the first and second binding complexes which are bound to the same multivalent molecule form an avidity complex; and (c) detecting the first and second binding complexes on the same concatemer template molecule, and (d) identifying the first nucleotide moiety in the first binding complex thereby determining the sequence of the first portion of the concatemer template molecule, and identifying the second nucleotide moiety in the second binding complex thereby determining the sequence of the second portion of the concatemer template molecule. In some embodiments, the plurality of sequencing polymerases comprise any wild type or mutant sequencing polymerase described herein. The concatemer template molecule comprises tandem repeat sequences of a sequence of interest and at least one universal sequencing primer binding site. The plurality of nucleic acid primers can bind to a sequencing primer binding site along the concatemer template molecule. Exemplary multivalent molecules are shown in FIGS. 1-4.

Sequencing-by-Binding

[00760] In some aspects, the present disclosure provides methods for sequencing any of the immobilized concatemer template molecules described herein, including sequencing compact DNA nanoballs, batch sequencing, reiterative sequencing and/or re-seeding methods, wherein the sequencing methods comprise a sequencing-by-binding (SBB) procedure which employs non-labeled chain-terminating nucleotides. In some embodiments, the sequencing-by-binding (SBB) method comprises the steps of (a) sequentially contacting a primed template nucleic acid with at least two separate mixtures under ternary complex stabilizing conditions, wherein the at least two separate mixtures each include a polymerase and a nucleotide, whereby the sequentially contacting results in the primed template nucleic acid being contacted, under the ternary complex stabilizing conditions, with nucleotide cognates for first, second and third base type base types in the template; (b) examining the at least two separate mixtures to determine whether a ternary complex formed; and (c) identifying the next correct nucleotide for the primed template nucleic acid molecule, wherein the next correct nucleotide is identified as a cognate of the first, second or third base type if ternary complex is detected in step (b), and wherein the next correct nucleotide is imputed to be a nucleotide cognate of a fourth base type based on the absence of a ternary complex in step (b); (d) adding a next correct nucleotide to the primer of the primed template nucleic acid after step (b), thereby producing an extended primer; and (e) repeating steps (a) through (d) at least once on the primed template nucleic acid that comprises the extended primer. Exemplary sequencing-by-binding methods are described in U.S. Patent Nos. 10,246,744 and 10,731,141 (where the contents of both patents are hereby incorporated by reference in their entireties). In some embodiments, a sequencing cycle comprises completion of steps (a) - (d). Sequencing Polymerases

[00761] In some aspects, the present disclosure provides methods for sequencing any of the template molecules described herein, including sequencing compact DNA nanoballs, batch sequencing, reiterative sequencing and/or re-seeding methods, wherein any of the sequencing methods described herein employ at least one type of sequencing polymerase and a plurality of nucleotides, or employ at least one type of sequencing polymerase and a plurality of nucleotides and a plurality of multivalent molecules. In some embodiments, the sequencing polymerase(s) is/are capable of incorporating a complementary nucleotide opposite a nucleotide in a template molecule. In some embodiments, the sequencing polymerase(s) is/are capable of binding a complementary nucleotide moiety of a multivalent molecule opposite a nucleotide in a template molecule. In some embodiments, the plurality of sequencing polymerases comprises recombinant mutant polymerases.

[00762] Examples of suitable polymerases for use in sequencing with nucleotides and/or multivalent molecules include but are not limited to: Klenow DNA polymerase; Thermus aquaticus DNA polymerase I (Taq polymerase); KlenTaq polymerase; Candidatus altiarchaeales archaeon: Candidatus Hadarchaeum Yellow slonense: Hadesarchaea archaeon: Euryarchaeota archaeon: Thermoplasmata archaeon: Thermococcus polymerases such as Thermococcus liloralis. bacteriophage T7 DNA polymerase; human alpha, delta and epsilon DNA polymerases; bacteriophage polymerases such as T4, RB69 and phi29 bacteriophage DNA polymerases; Pyrococcus furiosus DNA polymerase (Pfu polymerase); Bacillus subtilis DNA polymerase III; E. coli DNA polymerase III alpha and epsilon; 9 degree N polymerase; reverse transcriptases such as HIV type M or O reverse transcriptases; avian myeloblastosis virus reverse transcriptase; Moloney Murine Leukemia Virus (MMLV) reverse transcriptase; or telomerase. Further non-limiting examples of DNA polymerases include those from various Archaea genera, such as, Aeropyrum, Archaeglobus, Desulfurococcus, Pyrobaculum, Pyrococcus, Pyrolobus, Pyrodictium, Staphylothermus, Stetteria, Sulfolobus, Thermococcus, and Vulcanisaeta and the like or variants thereof, including such polymerases as are known in the art such as 9 degrees N®, VENT®, DEEP VENT®, THERMINATOR®, Pfu, KOD, Pfx, Tgo and RB69 polymerases. Exemplary polymerases are described in U.S. Patent No. 11,859,241, the contents of which are incorporated by reference herein in their entirety. Nucleotides

[00763] In some aspects, the present disclosure provides methods for sequencing any of the immobilized concatemer template molecules described herein, including sequencing compact DNA nanoballs, batch sequencing, reiterative sequencing and/or re-seeding methods, wherein any of the sequencing methods described herein employ at least one nucleotide. The nucleotides comprise a base, sugar and at least one phosphate group. In some embodiments, at least one nucleotide in the plurality comprises an aromatic base, a five carbon sugar (e.g., ribose or deoxyribose), and one or more phosphate groups (e.g., 1-10 phosphate groups). The plurality of nucleotides can comprise at least one type of nucleotide selected from the group consisting of dATP, dGTP, dCTP, dTTP and dUTP. The plurality of nucleotides can comprise at a mixture of any combination of two or more types of nucleotides selected from the group consisting of dATP, dGTP, dCTP, dTTP and/or dUTP. In some embodiments, at least one nucleotide in the plurality is not a nucleotide analog. In some embodiments, at least one nucleotide in the plurality comprises a nucleotide analog.

[00764] In some embodiments, at least one nucleotide in the plurality of nucleotides comprise a chain of one, two or three phosphorus atoms where the chain is typically attached to the 5’ carbon of the sugar moiety via an ester or phosphoramide linkage. In some embodiments, at least one nucleotide in the plurality is an analog having a phosphorus chain in which the phosphorus atoms are linked together with intervening O, S, NH, methylene or ethylene. In some embodiments, the phosphorus atoms in the chain include substituted side groups including O, S or BH3. In some embodiments, the chain includes phosphate groups substituted with analogs including phosphoramidate, phosphorothioate, phosphordithioate, and O-methylphosphoramidite groups.

[00765] In some embodiments, at least one nucleotide in the plurality of nucleotides comprises a terminator nucleotide analog having a chain terminating moiety (e.g., blocking moiety) at the sugar 2’ position, at the sugar 3’ position, or at the sugar 2’ and 3’ position. In some embodiments, the chain terminating moiety can inhibit polymerase-catalyzed incorporation of a subsequent nucleotide moiety or free nucleotide in a nascent strand during a primer extension reaction. In some embodiments, the chain terminating moiety is attached to the 3’ sugar position where the sugar comprises a ribose or deoxyribose sugar moiety. In some embodiments, the chain terminating moiety is removable/cleavable from the 3’ sugar position to generate a nucleotide having a 3 ’OH sugar group which is extendible with a subsequent nucleotide in a polymerase-catalyzed nucleotide incorporation reaction. In some embodiments, the chain terminating moiety comprises an alkyl group, an alkenyl group, an alkynyl group, an allyl group, an aryl group, a benzyl group, an azide group, an amine group, an amide group, a keto group, an isocyanate group, a phosphate group, a thio group, a disulfide group, a carbonate group, a urea group, or a silyl group. In some embodiments, the chain terminating moiety is cleavable/removable from the nucleotide, for example by reacting the chain terminating moiety with a chemical agent, pH change, light or heat. In some embodiments, the chain terminating moieties alkyl, alkenyl, alkynyl and allyl are cleavable with tetrakis(triphenylphosphine)palladium(0) (Pd(PPhs)4) with piperidine, or with 2,3- Dichl oro-5, 6-di cyano- 1,4-benzo-quinone (DDQ). In some embodiments, the chain terminating moieties aryl and benzyl are cleavable with H2 Pd/C. In some embodiments, the chain terminating moieties amine, amide, keto, isocyanate, phosphate, thio, disulfide are cleavable with phosphine or with a thiol group including beta-mercaptoethanol or dithiothritol (DTT). In some embodiments, the chain terminating moiety carbonate is cleavable with potassium carbonate (K2CO3) in MeOH, with triethylamine in pyridine, or with Zn in acetic acid (AcOH). In some embodiments, the chain terminating moieties urea and silyl are cleavable with tetrabutylammonium fluoride, pyridine-HF, with ammonium fluoride, or with triethylamine trihydrofluoride. In some embodiments, the chain terminating moiety may be cleavable/removable with nitrous acid. In some embodiments, a chain terminating moiety may be cleavable/removable using a solution comprising nitrite, such as, for example, a combination of nitrite with an acid such as acetic acid, sulfuric acid, or nitric acid. In some further embodiments, said solution may comprise an organic acid.

[00766] In some embodiments, at least one nucleotide in the plurality of nucleotides comprises a terminator nucleotide analog having a chain terminating moiety (e.g., blocking moiety) at the sugar 2’ position, at the sugar 3’ position, or at the sugar 2’ and 3’ position. In some embodiments, the chain terminating moiety comprises an azide, azido or azidomethyl group. In some embodiments, the chain terminating moiety comprises a 3’-O-azido or 3’-O- azidomethyl group. In some embodiments, the chain terminating moieties azide, azido and azidomethyl group are cleavable/removable with a phosphine compound. In some embodiments, the phosphine compound comprises a derivatized tri-alkyl phosphine moiety or a derivatized tri-aryl phosphine moiety. In some embodiments, the phosphine compound comprises Tris(2-carboxyethyl)phosphine (TCEP) or bis-sulfo triphenyl phosphine (BS-TPP) or Tri(hydroxyproyl)phosphine (THPP). In some embodiments, the cleaving agent comprises 4-dimethylaminopyridine (4-DMAP). In some embodiments, the chain terminating moiety comprising one or more of a 3’-O-amino group, a 3’-O-aminomethyl group, a 3’-O- methylamino group, or derivatives thereof may be cleaved with nitrous acid, through a mechanism utilizing nitrous acid, or using a solution comprising nitrous acid. In some embodiments, the chain terminating moiety comprising one or more of a 3’-O-amino group, a 3’-O-aminomethyl group, a 3’-O-methylamino group, or derivatives thereof may be cleaved using a solution comprising nitrite. In some embodiments, for example, nitrite may be combined with or contacted with an acid such as acetic acid, sulfuric acid, or nitric acid. In some further embodiments, for example, nitrite may be combined with or contacted with an organic acid such as, for example, formic acid, acetic acid, propionic acid, butyric acid, isobutyric acid, or the like.

[00767] In some embodiments, the nucleotide comprises a chain terminating moiety which is selected from the group consisting of 3’-deoxy nucleotides, 2’, 3 ’-dideoxynucleotides, 3’- methyl, 3 ’-azido, 3 ’-azidomethyl, 3’-O-azidoalkyl, 3’-O-ethynyl, 3’-O-aminoalkyl, 3’-O- fluoroalkyl, 3 ’-fluoromethyl, 3’-difluoromethyl, 3’-trifluoromethyl, 3 ’-sulfonyl, 3 ’-malonyl, 3’-amino, 3’-O-amino, 3’-sulfhydral, 3 ’-aminomethyl, 3’-ethyl, 3’butyl, 3’-tert butyl, 3’- Fluorenylmethyloxycarbonyl, 3’ tert-Butyloxy carbonyl, 3’-O-alkyl hydroxylamino group, 3’- phosphorothioate, and 3-O-benzyl, or derivatives thereof.

[00768] In some embodiments, the plurality of nucleotides comprises a plurality of nucleotides labeled with detectable reporter moiety. The detectable reporter moiety comprises a fluorophore. In some embodiments, the fluorophore is attached to the nucleotide base. In some embodiments, the fluorophore is attached to the nucleotide base with a linker which is cleavable/removable from the base. In some embodiments, at least one of the nucleotides in the plurality is not labeled with a detectable reporter moiety. In some embodiments, a particular detectable reporter moiety (e.g., fluorophore) that is attached to the nucleotide can correspond to the nucleotide base (e.g., dATP, dGTP, dCTP, dTTP or dUTP) to permit detection and identification of the nucleotide base.

[00769] In some embodiments, the cleavable linker on the nucleotide base comprises a cleavable moiety comprising an alkyl group, alkenyl group, alkynyl group, allyl group, aryl group, benzyl group, azide group, amine group, amide group, keto group, isocyanate group, phosphate group, thio group, disulfide group, carbonate group, urea group, or silyl group. In some embodiments, the cleavable linker on the base is cleavable/removable from the base by reacting the cleavable moiety with a chemical agent, pH change, light or heat. In some embodiments, the cleavable moieties alkyl, alkenyl, alkynyl and allyl are cleavable with tetrakis(triphenylphosphine)palladium(0) (Pd(PPhs)4) with piperidine, or with 2,3-Dichloro- 5,6-dicyano-l,4-benzo-quinone (DDQ). In some embodiments, the cleavable moieties aryl and benzyl are cleavable with H2 Pd/C. In some embodiments, the cleavable moieties amine, amide, keto, isocyanate, phosphate, thio, and disulfide are cleavable with phosphine or with a thiol group, including beta-mercaptoethanol or dithiothritol (DTT). In some embodiments, the cleavable moiety carbonate is cleavable with potassium carbonate (K2CO3) in MeOH, with triethylamine in pyridine, or with Zn in acetic acid (AcOH). In some embodiments, the cleavable moieties urea and silyl are cleavable with tetrabutylammonium fluoride, pyridine- HF, with ammonium fluoride, or with triethylamine trihydrofluoride.

[00770] In some embodiments, the cleavable linker on the nucleotide base comprises cleavable moiety including an azide, azido or azidomethyl group. In some embodiments, the cleavable moieties azide, azido and azidomethyl group are cleavable/removable with a phosphine compound. In some embodiments, the phosphine compound comprises a derivatized tri-alkyl phosphine moiety or a derivatized tri-aryl phosphine moiety. In some embodiments, the phosphine compound comprises Tris(2-carboxyethyl)phosphine (TCEP) or bis-sulfo triphenyl phosphine (BS-TPP) or Tri(hydroxyproyl)phosphine (THPP). In some embodiments, the cleaving agent comprises 4-dimethylaminopyridine (4-DMAP).

[00771] In some embodiments, the chain terminating moiety (e.g., at the sugar 2’ and/or sugar 3’ position) and the cleavable linker on the nucleotide base have the same or different cleavable moieties. In some embodiments, the chain terminating moiety (e.g., at the sugar 2’ and/or sugar 3’ position) and the detectable reporter moiety linked to the base are chemically cleavable/removable with the same chemical agent. In some embodiments, the chain terminating moiety (e.g., at the sugar 2’ and/or sugar 3’ position) and the detectable reporter moiety linked to the base are chemically cleavable/removable with different chemical agents.

Multivalent Molecules

[00772] In some aspects, the present disclosure provides methods for sequencing any of the immobilized concatemer template molecules described herein, including sequencing compact DNA nanoballs, batch sequencing, reiterative sequencing and/or re-seeding methods, wherein the sequencing methods employ at least one multivalent molecule. In some embodiments, the multivalent molecule comprises a plurality of nucleotide arms attached to a core and having any configuration including a starburst, helter skelter, or bottle brush configuration (e.g., FIG. 1). The multivalent molecule comprises: (1) a core; and (2) a plurality of nucleotide arms which comprise (i) a core attachment moiety, (ii) a spacer comprising a PEG moiety, (iii) a linker, and (iv) a nucleotide moiety. In some embodiments, the core is attached to the plurality of nucleotide arms. In some embodiments, the spacer is attached to the linker. In some embodiments, the linker is attached to the nucleotide moiety. In some embodiments, the nucleotide moiety comprises a base, sugar and at least one phosphate group, and the linker is attached to the nucleotide moiety through the base. In some embodiments, the linker comprises an aliphatic chain or an oligo ethylene glycol chain, both linker chains having 2-6 subunits. In some embodiments, the linker also includes an aromatic moiety. An exemplary nucleotide arm is shown in FIG. 5. Exemplary multivalent molecules are shown in FIGS. 1-4. An exemplary spacer is shown in FIG. 6 (top) and exemplary linkers are shown in FIGS. 6 (bottom) and FIG. 7. Exemplary nucleotides attached to a linker are shown in FIGS. 8-10. An exemplary biotinylated nucleotide arm is shown in FIG. 11.

[00773] In some embodiments, a multivalent molecule comprises a core attached to multiple nucleotide arms, and wherein the multiple nucleotide arms have the same type of nucleotide moiety, which is selected from the group consisting of dATP, dGTP, dCTP, dTTP and dUTP.

[00774] In some embodiments, a multivalent molecule comprises a core attached to multiple nucleotide arms, where each arm includes a nucleotide moiety. The nucleotide moiety comprises an aromatic base, a five carbon sugar (e.g., a ribose or a deoxyribose), and one or more phosphate groups (e.g., 1-10 phosphate groups). The plurality of multivalent molecules can comprise one type multivalent molecule having one type of nucleotide moiety selected from the group consisting of dATP, dGTP, dCTP, dTTP and dUTP. The plurality of multivalent molecules can comprise at a mixture of any combination of two or more types of multivalent molecules, where individual multivalent molecules in the mixture comprise nucleotide moieties selected from the group consisting of dATP, dGTP, dCTP, dTTP and/or dUTP.

[00775] In some embodiments, the nucleotide moiety comprises a chain of one, two or three phosphorus atoms where the chain is typically attached to the 5’ carbon of the sugar moiety via an ester or phosphoramide linkage. In some embodiments, at least one nucleotide moiety is a nucleotide analog having a phosphorus chain in which the phosphorus atoms are linked together with intervening O, S, NH, methylene or ethylene. In some embodiments, the phosphorus atoms in the chain include substituted side groups including O, S or BEE. In some embodiments, the chain includes phosphate groups substituted with analogs including phosphoramidate, phosphorothioate, phosphordithioate, and O-methylphosphoramidite groups.

[00776] In some embodiments, the multivalent molecule comprises a core attached to multiple nucleotide arms, and wherein individual nucleotide arms comprise a nucleotide moiety which is a nucleotide analog having a chain terminating moiety (e.g., blocking moiety) at the sugar 2’ position, at the sugar 3’ position, or at the sugar 2’ and 3’ position. In some embodiments, the nucleotide moiety comprises a chain terminating moiety (e.g., blocking moiety) at the sugar 2’ position, at the sugar 3’ position, or at the sugar 2’ and 3’ position. In some embodiments, the chain terminating moiety can inhibit polymerase- catalyzed incorporation of a subsequent nucleotide moiety or free nucleotide in a nascent strand during a primer extension reaction. In some embodiments, the chain terminating moiety is attached to the 3’ sugar position where the sugar comprises a ribose or deoxyribose sugar moiety. In some embodiments, the chain terminating moiety is removable/cleavable from the 3’ sugar position to generate a nucleotide having a 3 ’OH sugar group which is extendible with a subsequent nucleotide in a polymerase-catalyzed nucleotide incorporation reaction. In some embodiments, the chain terminating moiety comprises an alkyl group, alkenyl group, alkynyl group, allyl group, aryl group, benzyl group, azide group, amine group, amide group, keto group, isocyanate group, phosphate group, thio group, disulfide group, carbonate group, urea group, or silyl group. In some embodiments, the chain terminating moiety is cleavable/removable from the nucleotide moiety, for example by reacting the chain terminating moiety with a chemical agent, pH change, light or heat. In some embodiments, the chain terminating moieties alkyl, alkenyl, alkynyl and allyl are cleavable with tetrakis(triphenylphosphine)palladium(0) (Pd(PPli3)4) with piperidine, or with 2,3-Dichloro-5,6-dicyano-l,4-benzo-quinone (DDQ). In some embodiments, the chain terminating moieties aryl and benzyl are cleavable with H2 Pd/C. In some embodiments, the chain terminating moieties amine, amide, keto, isocyanate, phosphate, thio, and disulfide are cleavable with phosphine or with a thiol group including beta-mercaptoethanol or dithiothritol (DTT). In some embodiments, the chain terminating moiety carbonate is cleavable with potassium carbonate (K2CO3) in MeOH, with triethylamine in pyridine, or with Zn in acetic acid (AcOH). In some embodiments, the chain terminating moieties urea and silyl are cleavable with tetrabutylammonium fluoride, pyridine-HF, with ammonium fluoride, or with triethylamine trihydrofluoride.

[00777] In some embodiments, the nucleotide moiety comprises a chain terminating moiety (e.g., a blocking moiety) at the sugar 2’ position, at the sugar 3’ position, or at the sugar 2’ and 3’ position. In some embodiments, the chain terminating moiety comprises an azide, azido or azidomethyl group. In some embodiments, the chain terminating moiety comprises a 3’-O-azido or 3’-O-azidomethyl group. In some embodiments, the chain terminating moieties azide, azido and azidomethyl group are cleavable/removable with a phosphine compound. In some embodiments, the phosphine compound comprises a derivatized tri-alkyl phosphine moiety or a derivatized tri-aryl phosphine moiety. In some embodiments, the phosphine compound comprises Tris(2-carboxyethyl)phosphine (TCEP) or bis-sulfo triphenyl phosphine (BS-TPP) or Tri(hydroxyproyl)phosphine (THPP). In some embodiments, the cleaving agent comprises 4-dimethylaminopyridine (4-DMAP).

[00778] In some embodiments, the nucleotide moiety comprising a chain terminating moiety which is selected from a group consisting of 3’-deoxy nucleotides, 2’,3’- dideoxynucleotides, 3 ’-methyl, 3 ’-azido, 3 ’-azidomethyl, 3’-O-azidoalkyl, 3’-O-ethynyl, 3’- O-aminoalkyl, 3’-O-fluoroalkyl, 3’-fluoromethyl, 3 ’-difluoromethyl, 3 ’-trifluoromethyl, 3’- sulfonyl, 3’-malonyl, 3’-amino, 3’-O-amino, 3’-sulfhydral, 3 ’-aminomethyl, 3’-ethyl, 3’butyl, 3’-tert butyl, 3’- Fluorenylmethyloxycarbonyl, 3’ tert-Butyloxycarbonyl, 3’-O-alkyl hydroxylamino group, 3’-phosphorothioate, and 3-O-benzyl, or derivatives thereof.

[00779] In some embodiments, the multivalent molecule comprises a core attached to multiple nucleotide arms. In some embodiments, the nucleotide arms comprise a spacer, a linker and a nucleotide moiety. In some embodiments, wherein the core, the linker and/or the nucleotide moiety is labeled with a detectable reporter moiety. In some embodiments, the detectable reporter moiety comprises a fluorophore. In some embodiments, a particular detectable reporter moiety (e.g., a fluorophore) that is attached to the multivalent molecule can correspond to the base (e.g., dATP, dGTP, dCTP, dTTP or dUTP) of the nucleotide moiety to permit detection and identification of the nucleotide base.

[00780] In some embodiments, at least one nucleotide arm of a multivalent molecule has a nucleotide moiety that is attached to a detectable reporter moiety. In some embodiments, the detectable reporter moiety is attached to the nucleotide base. In some embodiments, the detectable reporter moiety comprises a fluorophore. In some embodiments, a particular detectable reporter moiety (e.g., fluorophore) that is attached to the multivalent molecule can correspond to the base (e.g., dATP, dGTP, dCTP, dTTP or dUTP) of the nucleotide moiety to permit detection and identification of the nucleotide base.

[00781] In some embodiments, the core of a multivalent molecule comprises an avidin-like or streptavidin-like moiety and the core attachment moiety comprises biotin. In some embodiments, the core comprises a streptavidin-type or an avidin-type moiety which includes an avidin protein, as well as any derivatives, analogs and other non-native forms of avidin that can bind to at least one biotin moiety. Other forms of avidin moieties include native and recombinant avidin and streptavidin as well as derivatized molecules, e.g., nonglycosylated avidin and truncated streptavidins. For example, avidin moiety includes de- glycosylated forms of avidin, bacterial streptavidin produced by Streptomyces (e.g., Streptomyces avidinii), as well as derivatized forms, for example, N- acyl avidins, e.g., N-acetyl, N-phthalyl and N-succinyl avidin, and the commercially- available products EXTRAVIDIN®, CAPTA VIDIN®, NEUTRA VIDIN® and NEUTRALITE AVIDIN®.

[00782] In some embodiments, any of the methods for sequencing any of the immobilized concatemer template molecules described herein can include forming a binding complex. In some embodiments, the binding complex comprises (i) a polymerase, a nucleic acid concatemer template molecule duplexed with a primer, and a nucleotide, or (ii) a polymerase, a nucleic acid concatemer template molecule duplexed with a primer, and a nucleotide moiety of a multivalent molecule. In some embodiments, the binding complex has a persistence time of greater than about 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9 or 1 second. The binding complex has a persistence time of greater than about 0.1-0.25 seconds, or about 0.25-0.5 seconds, or about 0.5-0.75 seconds, or about 0.75-1 second, or about 1-2 seconds, or about 2- 3 seconds, or about 3-4 second, or about 4-5 seconds, and/or wherein the method is or may be carried out at a temperature of at or above 15 °C, at or above 20 °C, at or above 25 °C, at or above 35 °C, at or above 37 °C, at or above 42 °C at or above 55 °C at or above 60 °C, or at or above 72 °C, or at or above 80 °C, or within a range defined by any of the foregoing. The binding complex (e.g., ternary complex) remains stable until subjected to a condition that causes dissociation of interactions between any of the polymerase, the template molecule, the primer and/or the nucleotide moiety or the nucleotide. For example, a dissociating condition comprises contacting the binding complex with any one or any combination of a detergent, EDTA and/or water. In some embodiments, the present disclosure provides said method wherein the binding complex is deposited on, attached to, or hybridized to, a surface showing a contrast to noise ratio in the detecting step of greater than 20. In some embodiments, the present disclosure provides said method wherein the contacting is performed under a condition that stabilizes the binding complex when the nucleotide or nucleotide moiety is complementary to a next base of the template nucleic acid, and destabilizes the binding complex when the nucleotide or nucleotide moiety is not complementary to the next base of the template nucleic acid. Supports with Low Non-Specific Binding Coatings

[00783] In some aspects, the present disclosure provides compositions and methods for use of a support having a plurality of surface primers immobilized thereon, for preparing any of the immobilized concatemers described herein, including generating compact DNA nanoballs, batch sequencing, reiterative sequencing and/or re-seeding methods. In some embodiments, the support is passivated with a low non-specific binding coating (e.g., FIG. 12). The surface coatings described herein can exhibit very low non-specific binding to reagents typically used for nucleic acid capture, amplification and sequencing workflows, such as dyes, nucleotides, enzymes, and nucleic acid primers. The surface coatings can exhibit low background fluorescence signals or high contrast-to-noise (CNR) ratios compared to conventional surface coatings.

[00784] In general, the supports comprise a substrate (or support structure), one or more layers of a covalently or non-covalently attached low-binding, chemical modification layers, e.g., silane layers, polymer films, and one or more covalently or non-covalently attached primer sequences that may be used for tethering single-stranded target nucleic acid(s) to the support surface. In some embodiments, the formulation of the surface, e.g., the chemical composition of one or more layers, the coupling chemistry used to cross-link the one or more layers to the support surface and/or to each other, and the total number of layers, may be varied such that non-specific binding of proteins, nucleic acid molecules, and other hybridization and amplification reaction components to the support surface is minimized or reduced relative to a comparable monolayer. Often, the formulation of the surface may be varied such that non-specific hybridization on the support surface is minimized or reduced relative to a comparable monolayer. The formulation of the surface may be varied such that non-specific amplification on the support surface is minimized or reduced relative to a comparable monolayer. The formulation of the surface may be varied such that specific amplification rates and/or yields on the support surface are maximized. Amplification levels suitable for detection are achieved in no more than 2, 3, 4, 5, 6, 7, 8, 9, 10, 15, 20, 25, 30, or more than 30 amplification cycles in some cases disclosed herein.

[00785] The substrate or support structure that comprises one or more chemically- modified layers, e.g., layers of a low non-specific binding polymer, may be independent or integrated into another structure or assembly. For example, in some embodiments, the substrate or support structure may comprise one or more surfaces within an integrated or assembled microfluidic flow cell. The substrate or support structure may comprise one or more surfaces within a microplate format, e.g., the bottom surface of the wells in a microplate. As noted above, in some preferred embodiments, the substrate or support structure comprises the interior surface (such as the lumen surface) of a capillary. In alternate preferred embodiments, the substrate or support structure comprises the interior surface (such as the lumen surface) of a capillary etched into a planar chip.

[00786] The attachment chemistry used to graft a first chemically-modified layer to a surface will generally be dependent on both the material from which the surface is fabricated and the chemical nature of the layer. In some embodiments, the first layer may be covalently attached to the surface. In some embodiments, the first layer may be non-covalently attached, e.g., adsorbed to the surface through non-covalent interactions such as electrostatic interactions, hydrogen bonding, or van der Waals interactions between the surface and the molecular components of the first layer. In either case, the substrate surface may be treated prior to attachment or deposition of the first layer. Any of a variety of surface preparation techniques known to those of skill in the art may be used to clean or treat the surface. For example, glass or silicon surfaces may be acid-washed using a Piranha solution (a mixture of sulfuric acid (H2SO4) and hydrogen peroxide (H2O2)), base treatment in KOH and NaOH, and/or cleaned using an oxygen plasma treatment method.

[00787] Silane chemistries constitute one non-limiting approach for covalently modifying the silanol groups on glass or silicon surfaces to attach more reactive functional groups (e.g., amines or carboxyl groups), which may then be used in coupling linker molecules (e.g., linear hydrocarbon molecules of various lengths, such as C6, Cl 2, Cl 8 hydrocarbons, or linear polyethylene glycol (PEG) molecules) or layer molecules (e.g., branched PEG molecules or other polymers) to the surface. Examples of suitable silanes that may be used in creating any of the disclosed low binding surfaces include, but are not limited to, (3 -Aminopropyl) trimethoxy silane (APTMS), (3 -Aminopropyl) tri ethoxy silane (APTES), any of a variety of PEG-silanes (e.g., comprising molecular weights of IK, 2K, 5K, 10K, 20K, etc.), amino-PEG silane (i.e., comprising a free amino functional group), maleimide-PEG silane, biotin-PEG silane, and the like.

[00788] Any of a variety of molecules known to those of skill in the art including, but not limited to, amino acids, peptides, nucleotides, oligonucleotides, other monomers or polymers, or combinations thereof may be used in creating the one or more chemically-modified layers on the surface, where the choice of components used may be varied to alter one or more properties of the surface, e.g., the surface density of functional groups and/or tethered oligonucleotide primers, the hydrophilicity /hydrophobicity of the surface, or the three three- dimensional nature (i.e., “thickness”) of the surface. Examples of preferred polymers that may be used to create one or more layers of low non-specific binding material in any of the disclosed surfaces include, but are not limited to, polyethylene glycol (PEG) of various molecular weights and branching structures, streptavidin, polyacrylamide, polyester, dextran, poly-lysine, and poly-lysine copolymers, or any combination thereof. Examples of conjugation chemistries that may be used to graft one or more layers of material (e.g. polymer layers) to the surface and/or to cross-link the layers to each other include, but are not limited to, biotin-streptavidin interactions (or variations thereof), his tag - Ni/NTA conjugation chemistries, methoxy ether conjugation chemistries, carboxylate conjugation chemistries, amine conjugation chemistries, NHS esters, maleimides, thiol, epoxy, azide, hydrazide, alkyne, isocyanate, and silane.

[00789] The low non-specific binding surface coating may be applied uniformly across the substrate. Alternately, the surface coating may be patterned, such that the chemical modification layers are confined to one or more discrete regions of the substrate. For example, the surface may be patterned using photolithographic techniques to create an ordered array or random pattern of chemically-modified regions on the surface. Alternately or in combination, the substrate surface may be patterned using, e.g., contact printing and/or ink-jet printing techniques. In some embodiments, an ordered array or random pattern of chemically-modified regions may comprise at least 1, at least 5, at least 10, at least 20, at least 30, at least 40, at least 50, at least 60, at least 70, at least 80, at least 90, at least 100, at least 200, at least 300, at least 400, at least 500, at least 600, at least 700, at least 800, at least 900, at least 1000, at least 2000, at least 3000, at least 4000, at least 5000, at least 6000, at least 7000, at least 8000, at least 9000, at least 10,000, or more than 10,000 discrete regions. [00790] In order to achieve low nonspecific binding surfaces, hydrophilic polymers may be nonspecifically adsorbed or covalently grafted to the surface. Typically, passivation is performed utilizing polyethylene glycol) (PEG, also known as polyethylene oxide (PEO) or polyoxyethylene) or other hydrophilic polymers with different molecular weights and end groups that are linked to a surface using, for example, silane chemistry. The end groups distal from the surface can include, but are not limited to, biotin, methoxy ether, carboxylate, amine, NHS ester, maleimide, and bis-silane. In some embodiments, two or more layers of a hydrophilic polymer, e.g., a linear polymer, branched polymer, or multi-branched polymer, may be deposited on the surface. In some embodiments, two or more layers may be covalently coupled to each other or internally cross-linked to improve the stability of the resulting surface. In some embodiments, oligonucleotide primers with different base sequences and base modifications (or other biomolecules, e.g., enzymes or antibodies) may be tethered to the resulting surface layer at various surface densities. In some embodiments, for example, both surface functional group density and oligonucleotide concentration may be varied to target a certain primer density range. Additionally, primer density can be controlled by diluting oligonucleotide with other molecules that carry the same functional group. For example, amine-labeled oligonucleotide can be diluted with amine-labeled polyethylene glycol in a reaction with an NHS-ester coated surface to reduce the final primer density. Primers with different lengths of linker between the hybridization region and the surface attachment functional group can also be applied to control surface density. Examples of suitable linkers include poly-T and poly-A strands at the 5’ end of the primer (e.g., 0 to 20 bases), PEG linkers (e.g., 3 to 20 monomer units), and carbon-chain (e.g., C6, C12, C18, etc.). To measure the primer density, fluorescently-labeled primers may be tethered to the surface and a fluorescence reading then compared with that for a dye solution of known concentration.

[00791] In order to scale primer surface density and add additional dimensionality to hydrophilic or amphoteric surfaces, surfaces comprising multi-layer coatings of PEG and other hydrophilic polymers have been developed. By using hydrophilic and amphoteric surface layering approaches that include, but are not limited to, the polymer/co-polymer materials described below, it is possible to increase primer loading density on the surface significantly. Traditional PEG coating approaches use monolayer primer deposition, which have been generally reported for single molecule applications, but do not yield high copy numbers for nucleic acid amplification applications. As described herein “layering” can be accomplished using traditional crosslinking approaches with any compatible polymer or monomer subunits such that a surface comprising two or more highly crosslinked layers can be built sequentially. Examples of suitable polymers include, but are not limited to, streptavidin, poly acrylamide, polyester, dextran, poly-lysine, and copolymers of poly-lysine and PEG. In some embodiments, the different layers may be attached to each other through any of a variety of conjugation reactions including, but not limited to, biotin-streptavidin binding, azide-alkyne click reaction, amine-NHS ester reaction, thiol-maleimide reaction, and ionic interactions between positively charged polymer and negatively charged polymer. In some embodiments, high primer density materials may be constructed in solution and subsequently layered onto the surface in multiple steps.

[00792] As noted, the low non-specific binding coatings of the present disclosure exhibit reduced non-specific binding of proteins, nucleic acids, and other components of the hybridization and/or amplification formulation used for solid-phase nucleic acid amplification. The degree of non-specific binding exhibited by a given support surface may be assessed either qualitatively or quantitatively. For example, in some embodiments, exposure of the surface to fluorescent dyes (e.g., cyanine dyes such as Cy3, or Cy5, etc., fluoresceins, coumarins, rhodamines, etc. or other dyes disclosed herein), fluorescently- labeled nucleotides, fluorescently-labeled oligonucleotides, and/or fluorescently-labeled proteins (e.g. polymerases) under a standardized set of conditions, followed by a specified rinse protocol and fluorescence imaging may be used as a qualitative tool for comparison of non-specific binding on supports comprising different surface formulations. In some embodiments, exposure of the surface to fluorescent dyes, fluorescently-labeled nucleotides, fluorescently-labeled oligonucleotides, and/or fluorescently-labeled proteins (e.g. polymerases) under a standardized set of conditions, followed by a specified rinse protocol and fluorescence imaging may be used as a quantitative tool for comparison of non-specific binding on supports comprising different surface formulations - provided that care has been taken to ensure that the fluorescence imaging is performed under a condition where fluorescence signal is linearly related (or related in a predictable manner) to the number of fluorophores on the support surface (e.g., under a condition where signal saturation and/or self-quenching of the fluorophore is not an issue) and suitable calibration standards are used. In some embodiments, other techniques known to those of skill in the art, for example, radioisotope labeling and counting methods may be used for quantitative assessment of the degree to which non-specific binding is exhibited by the different support surface formulations of the present disclosure.

[00793] Some surfaces disclosed herein exhibit a ratio of specific to nonspecific binding of a fluorophore such as Cy3 of at least 2, at least 3, at least 4, at least 5, at least 6, at least 7, at least 8, at least 9, at least 10, at least 11, at least 12, at least 13, at least 14, at least 15, at least 16, at least 17, at least 18, at least 19, at least 20, at least 25, at least 30, at least 35, at least 40, at least 50, at least 75, at least 100, or greater than 100, or any intermediate value spanned by the range herein. Some surfaces disclosed herein exhibit a ratio of specific to nonspecific fluorescence of a fluorophore such as Cy3 of at least 2, at least 3, at least 4, at least 5, at least 6, at least 7, at least 8, at least 9, at least 10, at least 11, at least 12, at least 13, at least 14, at least 15, at least 16, at least 17, at least 18, at least 19, at least 20, at least 25, at least 30, at least 35, at least 40, at least 50, at least 75, at least 100, or greater than 100, or any intermediate value spanned by the range herein.

[00794] As noted, in some embodiments, the degree of non-specific binding exhibited by the disclosed low-binding supports may be assessed using a standardized protocol for contacting the surface with a labeled protein (e.g., bovine serum albumin (BSA), streptavidin, a DNA polymerase, a reverse transcriptase, a helicase, a single-stranded binding protein (SSB), etc., or any combination thereof), a labeled nucleotide, a labeled oligonucleotide, etc., under a standardized set of incubation and rinse conditions, followed be detection of the amount of label remaining on the surface and comparison of the signal resulting therefrom to an appropriate calibration standard. In some embodiments, the label may comprise a fluorescent label. In some embodiments, the label may comprise a radioisotope. In some embodiments, the label may comprise any other detectable label known to one of skill in the art. In some embodiments, the degree of non-specific binding exhibited by a given support surface formulation may thus be assessed in terms of the number of non-specifically bound protein molecules (or other molecules) per unit area. In some embodiments, the low-binding supports of the present disclosure may exhibit non-specific protein binding (or non-specific binding of other specified molecules, (e.g., cyanine dyes such as Cy3, or Cy5, etc., fluoresceins, coumarins, rhodamines, etc. or other dyes disclosed herein)) of less than 0.001 molecule per pm2, less than 0.01 molecule per pm², less than 0.1 molecule per pm², less than 0.25 molecule per pm², less than 0.5 molecule per pm², less than Imolecule per pm², less than 10 molecules per pm², less than 100 molecules per pm², or less than 1,000 molecules per pm². Those of skill in the art will realize that a given support surface of the present disclosure may exhibit non-specific binding falling anywhere within this range, for example, of less than 86 molecules per pm². For example, some modified surfaces disclosed herein exhibit nonspecific protein binding of less than 0.5 molecule / pm² following contact with a 1 pM solution of Cy3 labeled streptavidin (GE Amersham) in phosphate buffered saline (PBS) buffer for 15 minutes, followed by 3 rinses with deionized water. Some modified surfaces disclosed herein exhibit nonspecific binding of Cy3 dye molecules of less than 0.25 molecules per pm². In independent nonspecific binding assays, 1 pM labeled Cy3 SA (ThermoFisher®), 1 pM Cy5 SA dye (ThermoFisher®), 10 pM Aminoallyl-dUTP - ATTO- 647N (Jena Biosciences®), 10 pM Aminoallyl-dUTP - ATTO-Rhol 1 (Jena Biosciences®), 10 pM Aminoallyl-dUTP - ATTO-Rhol 1 (Jena Biosciences®), 10 pM 7-Propargylamino-7- deaza-dGTP - Cy5 (Jena Biosciences®, and 10 pM 7-Propargylamino-7-deaza-dGTP - Cy3 (Jena Biosciences®) were incubated on the low binding substrates at 37°C for 15 minutes in a 384 well plate format. Each well was rinsed 2-3 x with 50 uL deionized RNase/DNase Free water and 2-3 x with 25 mM ACES buffer pH 7.4. The 384 well plates were imaged on a GE Typhoon instrument using the Cy3, AF555, or Cy5 filter sets (according to dye test performed) as specified by the manufacturer at a PMT gain setting of 800 and resolution of 50-100 m. For higher resolution imaging, images were collected on an Olympus 1X83 microscope (Olympus Corp., Center Valley, PA) with a total internal reflectance fluorescence (TIRF) objective (100X, 1.5 NA, Olympus), a CCD camera (e.g., an Olympus EM-CCD monochrome camera, Olympus XM-10 monochrome camera, or an Olympus DP80 color and monochrome camera), an illumination source (e.g., an Olympus 100W Hg lamp, an Olympus 75W Xe lamp, or an Olympus U-HGLGPS fluorescence light source), and excitation wavelengths of 532 nm or 635 nm. Dichroic mirrors were purchased from Semrock (IDEX Health & Science, LLC, Rochester, New York), e.g., 405, 488, 532, or 633 nm dichroic reflectors/beamsplitters, and band pass filters were chosen as 532 LP or 645 LP concordant with the appropriate excitation wavelength. Some modified surfaces disclosed herein exhibit nonspecific binding of dye molecules of less than 0.25 molecules per pm².

[00795] In some embodiments, the surfaces disclosed herein exhibit a ratio of specific to nonspecific binding of a fluorophore such as Cy3 of at least 2, at least 3, at least 4, at least 5, at least 6, at least 7, at least 8, at least 9, at least 10, at least 11, at least 12, at least 13, at least 14, at least 15, at least 16, at least 17, at least 18, at least 19, at least 20, at least 25, at least 30, at least 35, at least 40, at least 50, at least 75, at least 100, or greater than 100, or any intermediate value spanned by the range herein. In some embodiments, the surfaces disclosed herein exhibit a ratio of specific to nonspecific fluorescence signals for a fluorophore such as Cy3 of at least 2, at least 3, at least 4, at least 5, at least 6, at least 7, at least 8, at least 9, at least 10, at least 11, at least 12, at least 13, at least 14, at least 15, at least 16, at least 17, at least 18, at least 19, at least 20, at least 25, at least 30, at least 35, at least 40, at least 50, at least 75, at least 100, or greater than 100, or any intermediate value spanned by the range herein.

[00796] The low-background surfaces consistent with the disclosure herein may exhibit specific dye attachment (e.g., Cy3 attachment) to non-specific dye adsorption (e.g., Cy3 dye adsorption) ratios of at least 4: 1, at least 5: 1, at least 6: 1, at least 7: 1, at least 8: 1, at least 9: 1, at least 10: 1, at least 15: 1, at least 20: 1, at least 30: 1, at least 40: 1, at least 50: 1, or more than 50 specific dye molecules attached per molecule nonspecifically adsorbed. Similarly, when subjected to an excitation energy, low-background surfaces consistent with the disclosure herein to which fluorophores, e.g., Cy3, have been attached may exhibit ratios of specific fluorescence signal (e.g., arising from Cy3-labeled oligonucleotides attached to the surface) to non-specific adsorbed dye fluorescence signals of at least 4: 1, at least 5: 1, at least 6: 1, at least 7: 1, at least 8: 1, at least 9: 1, at least 10: 1, at least 15: 1, at least 20: 1, at least 30: 1, at least 40: 1, at least 50: 1, or more than 50: 1. [00797] In some embodiments, the degree of hydrophilicity (or “wettability” with aqueous solutions) of the disclosed support surfaces may be assessed, for example, through the measurement of water contact angles in which a small droplet of water is placed on the surface and its angle of contact with the surface is measured using, e.g., an optical tensiometer. In some embodiments, a static contact angle may be determined. In some embodiments, an advancing or receding contact angle may be determined. In some embodiments, the water contact angle for the hydrophilic, low-binding support surfaces disclosed herein may range from about 0 degrees to about 30 degrees. In some embodiments, the water contact angle for the hydrophilic, low-binding support surfaced disclosed herein may no more than 50 degrees, no more than 40 degrees, no more than 30 degrees, no more than 25 degrees, no more than 20 degrees, no more than 18 degrees, no more than 16 degrees, no more than 14 degrees, no more than 12 degrees, no more than 10 degrees, no more than 8 degrees, no more than 6 degrees, no more than 4 degrees, no more than 2 degrees, or no more than 1 degree. In many cases the contact angle is no more than 40 degrees. Those of skill in the art will realize that a given hydrophilic, low-binding support surface of the present disclosure may exhibit a water contact angle having a value of anywhere within this range. [00798] In some embodiments, the hydrophilic surfaces disclosed herein facilitate reduced wash times for bioassays, often due to reduced nonspecific binding of biomolecules to the low-binding surfaces. In some embodiments, adequate wash steps may be performed in less than 60 seconds , less than 50 seconds, less than 40 seconds, less than 30 seconds, less than 20 seconds, less than 15 seconds, or less than 10 seconds. For example, in some embodiments adequate wash steps may be performed in less than 30 seconds.

[00799] The low-binding surfaces of the present disclosure exhibit significant improvement in stability or durability to prolonged exposure to solvents and elevated temperatures, or to repeated cycles of solvent exposure or changes in temperature. For example, in some embodiments, the stability of the disclosed surfaces may be tested by fluorescently labeling a functional group on the surface, or a tethered biomolecule (e.g., an oligonucleotide primer) on the surface, and monitoring fluorescence signal before, during, and after prolonged exposure to solvents and elevated temperatures, or to repeated cycles of solvent exposure or changes in temperature. In some embodiments, the degree of change in the fluorescence used to assess the quality of the surface may be less than 1%, less than 2%, less than 3%, less than 4%, less than 5%, less than 10%, less than 15%, less than 20%, or less than 25% over a time period of 1 minute, 2 minutes, 3 minutes, 4 minutes, 5 minutes, 10 minutes, 20 minutes, 30 minutes, 40 minutes, 50 minutes, 60 minutes, 2 hours, 3 hours, 4 hours, 5 hours, 6 hours, 7 hours, 8 hours, 9 hours, 10 hours, 15 hours, 20 hours, 25 hours, 30 hours, 35 hours, 40 hours, 45 hours, 50 hours, or 100 hours of exposure to solvents and/or elevated temperatures (or any combination of these percentages as measured over these time periods). In some embodiments, the degree of change in the fluorescence over a number of cycles used to assess the quality of the surface may be less than 1%, 2%, 3%, 4%, 5%, 10%, 15%, 20%, or 25%. In some embodiments, the number of cycles may be over 5 cycles, over 10 cycles, over 20 cycles, over 30 cycles, over 40 cycles, over 50 cycles, over 60 cycles, over 70 cycles, over 80 cycles, over 90 cycles, over 100 cycles, over 200 cycles, over 300 cycles, over 400 cycles, over 500 cycles, over 600 cycles, over 700 cycles, over 800 cycles, over 900 cycles, or over 1,000 cycles of repeated exposure to solvent changes and/or changes in temperature (or any combination of these percentages as measured over this range of cycles). [00800] In some embodiments, the surfaces disclosed herein may exhibit a high ratio of specific signal to nonspecific signal or other background. For example, when used for nucleic acid amplification, some surfaces may exhibit an amplification signal that is at least 4, at least 5, at least 6, at least 7, at least 8, at least 9, at least 10, at least 15, at least 20, at least 30, at least 40, at least 50, at least 75, at least 100, or greater than 100 fold greater than a signal of an adjacent unpopulated region of the surface. Similarly, some surfaces exhibit an amplification signal that is at least 4, at least 5, at least 6, at least 7, at least 8, at least 9, at least 10, at least 15, at least 20, at least 30, at least 40, at least 50, at least 75, at least 100, or greater than 100 fold greater than a signal of an adjacent amplified nucleic acid population region of the surface.

[00801] In some embodiments, fluorescence images of the disclosed low background surfaces when used in nucleic acid hybridization or amplification applications to create clusters of hybridized or clonally-amplified nucleic acid molecules (e.g., that have been directly or indirectly labeled with a fluorophore) exhibit contrast-to-noise ratios (CNRs) of at least 10, at least 20, at least 30, at least 40, at least 50, at least 60, at least 70, at least 80, at least 90, at least 100, at least 110, at least 120, at least 130, at least 140, at least 150, at least 160, at least 170, at least 180, at least 190, at least 200, at least 210, at least 220, at least 230, at least 240, at least 250, or greater than 250.

[00802] One or more types of primer (e.g., capture primers) may be attached or tethered to the support surface. In some embodiments, the one or more types of adapters or primers may comprise spacer sequences, adapter sequences for hybridization to adapter-ligated target library nucleic acid sequences, forward amplification primers, reverse amplification primers, sequencing primers, and/or molecular barcoding sequences, or any combination thereof. In some embodiments, 1 primer or adapter sequence may be tethered to at least one layer of the surface. In some embodiments, at least 2, at least 3, at least 4, at least 5, at least 6, at least 7, at least 8, at least 9, at least 10, or more than 10 different primer or adapter sequences may be tethered to at least one layer of the surface.

[00803] In some embodiments, the tethered adapter and/or primer sequences may range in length from about 10 nucleotides to about 100 nucleotides. In some embodiments, the tethered adapter and/or primer sequences may be at least 10, at least 20, at least 30, at least 40, at least 50, at least 60, at least 70, at least 80, at least 90, or at least 100 nucleotides in length. In some embodiments, the tethered adapter and/or primer sequences may be at most 100, at most 90, at most 80, at most 70, at most 60, at most 50, at most 40, at most 30, at most 20, or at most 10 nucleotides in length. Any of the lower and upper values described in this paragraph may be combined to form a range included within the present disclosure, for example, in some embodiments the length of the tethered adapter and/or primer sequences may range from about 20 nucleotides to about 80 nucleotides. Those of skill in the art will recognize that the length of the tethered adapter and/or primer sequences may have any value within this range, e.g., about 24 nucleotides.

[00804] In some embodiments, the resultant surface density of primers on the low binding support surfaces of the present disclosure may range from about 100 primer molecules per pm² to about 100,000 primer molecules per pm². In some embodiments, the resultant surface density of primers on the low binding support surfaces of the present disclosure may range from about 100,000 primer molecules per pm² to about 10¹⁵ primer molecules per pm². In some embodiments, the surface density of primers may be at least 1,000, at least 10,000, at least 100,000, or at least 10¹⁵ primer molecules per pm². In some embodiments, the surface density of primers may be at most 10,000, at most 100,000, at most 1,000,000, or at most 10¹⁵ primer molecules per pm². Any of the lower and upper values described in this paragraph may be combined to form a range included within the present disclosure, for example, in some embodiments the surface density of primers may range from about 10,000 molecules per pm² to about 10¹⁵ molecules per pm². Those of skill in the art will recognize that the surface density of primer molecules may have any value within this range, e.g., about 455,000 molecules per pm². In some embodiments, the surface density of target library nucleic acid sequences initially hybridized to adapter or primer sequences on the support surface may be less than or equal to that indicated for the surface density of tethered primers. In some embodiments, the surface density of clonally-amplified target library nucleic acid sequences hybridized to adapter or primer sequences on the support surface may span the same range as that indicated for the surface density of tethered primers.

[00805] Local densities as listed above do not preclude variation in density across a surface, such that a surface may comprise a region having an oligo density of, for example, 500,000 per pm², while also comprising at least a second region having a substantially different local density.

[00806] The low non-specific binding coating comprise one or more layers of a multilayered surface coating may comprise a branched polymer or may be linear. Examples of suitable branched polymers include, but are not limited to, branched PEG, branched poly(vinyl alcohol) (branched PVA), branched poly(vinyl pyridine), branched poly(vinyl pyrrolidone) (branched PVP), branched ), poly(acrylic acid) (branched PAA), branched polyacrylamide, branched poly(N-isopropylacrylamide) (branched PNIPAM), branched poly(methyl methacrylate) (branched PMA), branched poly(2-hydroxylethyl methacrylate) (branched PHEMA), branched poly(oligo(ethylene glycol) methyl ether methacrylate) (branched POEGMA), branched polyglutamic acid (branched PGA), branched poly-lysine, branched poly-glucoside, and dextran.

[00807] In some embodiments, the branched polymers used to create one or more layers of any of the multi-layered surfaces disclosed herein may comprise at least 4 branches, at least 5 branches, at least 6 branches, at least 7 branches, at least 8 branches, at least 9 branches, at least 10 branches, at least 12 branches, at least 14 branches, at least 16 branches, at least 18 branches, at least 20 branches, at least 22 branches, at least 24 branches, at least 26 branches, at least 28 branches, at least 30 branches, at least 32 branches, at least 34 branches, at least 36 branches, at least 38 branches, or at least 40 branched.

[00808] Linear, branched, or multi-branched polymers used to create one or more layers of any of the multi-layered surfaces disclosed herein may have a molecular weight of at least 500, at least 1,000, at least 2,000, at least 3,000, at least 4,000, at least 5,000, at least 10,000, at least 15,000, at least 20,000, at least 25,000, at least 30,000, at least 35,000, at least 40,000, at least 45,000, or at least 50,000 daltons.

[00809] In some embodiments, e.g., wherein at least one layer of a multi-layered surface comprises a branched polymer, the number of covalent bonds between a branched polymer molecule of the layer being deposited and molecules of the previous layer may range from about one covalent linkage per molecule to about 32 covalent linkages per molecule. In some embodiments, the number of covalent bonds between a branched polymer molecule of the new layer and molecules of the previous layer may be at least 1, at least 2, at least 3, at least 4, at least 5, at least 6, at least 7, at least 8, at least 9, at least 10, at least 12, at least 14, at least 16, at least 18, at least 20, at least 22, at least 24, at least 26, at least 28, at least 30, or at least 32 covalent linkages per molecule.

[00810] Any reactive functional groups that remain following the coupling of a material layer to the surface may optionally be blocked by coupling a small, inert molecule using a high yield coupling chemistry. For example, in the case that amine coupling chemistry is used to attach a new material layer to the previous one, any residual amine groups may subsequently be acetylated or deactivated by coupling with a small amino acid such as glycine.

[00811] The number of layers of low non-specific binding material, e.g., a hydrophilic polymer material, deposited on the surface, may range from 1 to about 10. In some embodiments, the number of layers is at least 1, at least 2, at least 3, at least 4, at least 5, at least 6, at least 7, at least 8, at least 9, or at least 10. In some embodiments, the number of layers may be at most 10, at most 9, at most 8, at most 7, at most 6, at most 5, at most 4, at most 3, at most 2, or at most 1. Any of the lower and upper values described in this paragraph may be combined to form a range included within the present disclosure, for example, in some embodiments the number of layers may range from about 2 to about 4. In some embodiments, all of the layers may comprise the same material. In some embodiments, each layer may comprise a different material. In some embodiments, the plurality of layers may comprise a plurality of materials. In some embodiments at least one layer may comprise a branched polymer. In some embodiment, all of the layers may comprise a branched polymer. [00812] One or more layers of low non-specific binding material may in some cases be deposited on and/or conjugated to the substrate surface using a polar protic solvent, a polar or polar aprotic solvent, a nonpolar solvent, or any combination thereof. In some embodiments the solvent used for layer deposition and/or coupling may comprise an alcohol (e.g., methanol, ethanol, propanol, etc.), another organic solvent (e.g., acetonitrile, dimethyl sulfoxide (DMSO), dimethyl formamide (DMF), etc.), water, an aqueous buffer solution (e.g., phosphate buffer, phosphate buffered saline, 3-(N-morpholino)propanesulfonic acid (MOPS), etc.), or any combination thereof. In some embodiments, an organic component of the solvent mixture used may comprise at least 1%, 5%, 10%, 15%, 20%, 25%, 30%, 35%, 40%, 45%, 50%, 55%, 60%, 70%, 75%, 80%, 85%, 90%, 95%, 98%, or 99% of the total, with the balance made up of water or an aqueous buffer solution. In some embodiments, an aqueous component of the solvent mixture used may comprise at least 1%, 5%, 10%, 15%, 20%, 25%, 30%, 35%, 40%, 45%, 50%, 55%, 60%, 70%, 75%, 80%, 85%, 90%, 95%, 98%, or 99% of the total, with the balance made up of an organic solvent. The pH of the solvent mixture used may be less than 6, about 6, 6.5, 7, 7.5, 8, 8.5, 9, or greater than pH 9.

[00813] Fluorescence imaging may be performed using any of a variety of fluorophores, fluorescence imaging techniques, and fluorescence imaging instruments known to those of skill in the art. Examples of suitable fluorescence dyes that may be used (e.g., by conjugation to nucleotides, oligonucleotides, or proteins) include, but are not limited to, fluorescein, rhodamine, coumarin, cyanine, and derivatives thereof, including the cyanine derivatives Cyanine dye-3 (Cy3), Cyanine dye-5 (Cy5), Cyanine dye-7 (Cy7), etc. Examples of fluorescence imaging techniques that may be used include, but are not limited to, fluorescence microscopy imaging, fluorescence confocal imaging, two-photon fluorescence, and the like. Examples of fluorescence imaging instruments that may be used include, but are not limited to, fluorescence microscopes equipped with an image sensor or camera, confocal fluorescence microscopes, two-photon fluorescence microscopes, or custom instruments that comprise a suitable selection of light sources, lenses, mirrors, prisms, dichroic reflectors, apertures, and image sensors or cameras, etc. A non-limiting example of a fluorescence microscope equipped for acquiring images of the disclosed low-binding support surfaces and clonally-amplified colonies (polonies) of template nucleic acid sequences hybridized thereon is the Olympus 1X83 inverted fluorescence microscope equipped with ) 20x, 0.75 NA, a 532 nm light source, a bandpass and dichroic mirror filter set optimized for 532 nm long-pass excitation and Cy3 fluorescence emission filter, a Semrock 532 nm dichroic reflector, and a camera (Andor sCMOS, Zyla 4.2) where the excitation light intensity is adjusted to avoid signal saturation. Often, the support surface may be immersed in a buffer (e.g., 25 mM ACES, pH 7.4 buffer) while the image is acquired.

[00814] In some instances, the performance of nucleic acid hybridization and/or amplification reactions using the disclosed reaction formulations and low non-specific binding supports may be assessed using fluorescence imaging techniques, where the contrast- to-noise ratio (CNR) of the images provides a key metric in assessing amplification specificity and non-specific binding on the support. CNR is commonly defined as: CNR = (Signal - Background) / Noise. The background term is commonly taken to be the signal measured for the interstitial regions surrounding a particular feature (diffraction limited spot, DLS) in a specified region of interest (ROI). While signal-to-noise ratio (SNR) is often considered to be a benchmark of overall signal quality, it can be shown that improved CNR can provide a significant advantage over SNR as a benchmark for signal quality in applications that require rapid image capture (e.g., sequencing applications for which cycle times must be minimized), as shown in the example below. The surfaces of the instant disclosure are also provided in International Application Serial No. PCT/US2019/061556, which is hereby incorporated by reference in its entirety.

[00815] In most ensemble-based sequencing approaches, the background term is typically measured as the signal associated with ‘interstitial’ regions. In addition to “interstitial” background (Binter), “intrastitial” background (Bintra) exists within the region occupied by an amplified DNA colony. The combination of these two background signals dictates the achievable CNR, and subsequently directly impacts the optical instrument requirements, architecture costs, reagent costs, run- times, cost/genome, and ultimately the accuracy and data quality for cyclic array -based sequencing applications. The Binter background signal arises from a variety of sources; a few examples include auto-fluorescence from consumable flow cells, non-specific adsorption of detection molecules that yield spurious fluorescence signals that may obscure the signal from the ROI, the presence of non-specific DNA amplification products (e.g., those arising from primer dimers). In typical next generation sequencing (NGS) applications, this background signal in the current field-of-view (FOV) is averaged over time and subtracted. The signal arising from individual DNA colonies (i.e., (S) - Binter in the FOV) yields a discernable feature that can be classified. In some instances, the intrastitial background (Bintra) can contribute a confounding fluorescence signal that is not specific to the target of interest, but is present in the same ROI thus making it far more difficult to average and subtract.

[00816] The implementation of nucleic acid amplification on the low-binding substrates of the present disclosure may decrease the Binter background signal by reducing non-specific binding, may lead to improvements in specific nucleic acid amplification, and may lead to a decrease in non-specific amplification that can impact the background signal arising from both the interstitial and intrastitial regions. In some instances, the disclosed low-binding support surfaces, optionally used in combination with the disclosed hybridization buffer formulations, may lead to improvements in CNR by a factor of 2, 5, 10, 100, or 1000-fold over those achieved using conventional supports and hybridization, amplification, and/or sequencing protocols. Although described here in the context of using fluorescence imaging as the read-out or detection mode, the same principles apply to the use of the disclosed low non-specific binding supports and nucleic acid hybridization and amplification formulations for other detection modes as well, including both optical and non-optical detection modes. [00817] The disclosed low-binding supports, optionally used in combination with the disclosed hybridization and/or amplification protocols, yield solid-phase reactions that exhibit: (i) negligible non-specific binding of protein and other reaction components (thus minimizing substrate background), (ii) negligible non-specific nucleic acid amplification product, and (iii) provide tunable nucleic acid amplification reactions.

[00818] In some embodiments, fluorescence images of the disclosed low background surfaces when used in nucleic acid hybridization or amplification applications to create polonies of hybridized or clonally-amplified nucleic acid molecules (e.g., that have been directly or indirectly labeled with a fluorophore) exhibit contrast-to-noise ratios (CNRs) of at least 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150, 160, 170, 180, 190, 20, 210, 220, 230, 240, 250, or greater than 250.

[00819] In some embodiments, a fluorescence image of the surface exhibits a contrast-to- noise ratio (CNR) of at least 20 when a sample nucleic acid molecule or complementary sequences thereof are labeled with a Cyanine dye-3 (Cy3) fluorophore, and when the fluorescence image is acquired using an inverted fluorescence microscope (e.g., Olympus 1X83) with a 20 x 0.75 NA objective, a 532 nm light source, a bandpass and dichroic mirror filter set optimized for 532 nm excitation and Cy3 fluorescence emission, and a camera (e.g., Andor sCMOS, Zyla 4.2) under non-signal saturating conditions while the surface is immersed in a buffer (e.g., 25 mM ACES, pH 7.4 buffer).

Sample Indexes for Improved Base Calling

[00820] In some aspects, the present disclosure provides methods for improving base calling using at least one sample index sequence (e.g., (170) and/or (160)) comprising a short random sequence (e.g., NNN) for sequencing any of the immobilized concatemer template molecules described herein, including sequencing compact DNA nanoballs, batch sequencing, reiterative sequencing and/or re-seeding methods. Generally, it is desirable to prepare nucleic acid libraries that will be distributed onto a support (e.g., a coated flow cell), where the library molecules are converted into concatemer template molecules that are immobilized at a high density to the support for massively parallel sequencing. For concatemer template molecules that are immobilized at high densities at random locations on the support, the challenge of resolving high density fluorescent images for accurate base calling during sequencing runs becomes challenging.

[00821] The nucleotide diversity of a population of concatemer template molecules generally refers to the relative proportion of nucleotides A, G, C and T that are present in each sequencing cycle. An optimal high diversity library will generally include one or more sequence-of-interest (insert) regions having approximately equal proportions of all four nucleotides represented in each cycle of a sequencing run. A low diversity library will generally include sequence-of-interest (insert) regions having a high proportion of certain nucleotides and low proportion of other nucleotides. To overcome the problem of low diversity libraries, a small amount of a high diversity library prepared from PhiX bacteriophage is typically mixed with the library-of-interest (e.g., PhiX spike-in library) and sequenced together on the same flow cell. While the PhiX library spike-in library provides nucleotide diversity it also occupies space on the flow cell, thereby replacing the target libraries carrying the sequence-of-interest and reduces the amount of sequencing data obtainable from the target libraries (e.g., reduces sequencing throughput). Another method to overcome the problem of low diversity libraries may be to prepare library molecules having at least one sample index sequence that is designed to be color-balanced. However, it may be desirable to design a large number of sample index sets, for example a set of single index sample sequences or paired index sample sequences for 16-plex, 24-plex, 96-plex or larger plexy levels. It is challenging to design sample index sequences, as a single or paired sample indexes, for large sample index sets where all of the sample index sequences are color- balanced (e.g., see FIG. 29).

[00822] An alternative method to overcome the challenges of sequencing low diversity library molecules (e.g., at high density on the support) is (1) to prepare libraries having at least one sample index sequence (e.g., (170) or (160)) comprising a short random sequence (e.g., NNN) linked directly to a universal sample index sequence, where the short random sequence provides nucleotide diversity and color balance, and/or (2) to prepare libraries having at least one batch barcode sequence comprising a short random sequence (e.g., NNN) linked directly to the barcode sequence, e.g., a batch barcode sequence, where the short random sequence provides nucleotide diversity and color balance. In a population of library molecules each molecule comprising a sample index sequence (e.g., (170) or (160)) and/or a batch barcode sequence, the short random sequence (e.g., NNN) provides high nucleotide diversity which includes approximately equal proportions of all four nucleotides (e.g., A, G, C, T and/or U) that will be represented in each cycle of a sequencing run (see FIG. 28). The high nucleotide diversity of the short random sequence also provide color balance during each cycle of the sequencing run. The advantage of designing sample indexes (e.g., (170) or (160)) to include a short random sequence (e.g., NNN) is that, in a low-plexy population of library molecules (e.g., 2-plex or 4-plex), the universal sample index sequences that identify the two or four different samples need not exhibit nucleotide diversity (e.g., see FIG. 28). Additionally, the nucleotide diversity of the short random sequence (e.g., NNN) can obviate the need to include a PhiX spike-in library, or permits use of a reduced amount of PhiX spike-in library to be distributed onto the flow cell and sequenced.

[00823] The library molecule can include at least one sample index sequence (e.g., (170) or (160)) which include a short random sequence (e.g., NNN). In some embodiments, the sequencing data from the sample index sequence (e.g., (170) or (160)) can be used for polony mapping and template registration because the short random sequence (e.g., NNN) provides sufficient nucleotide diversity and color balance. The sequencing data from the sample index sequence (e.g., (170) and/or (160)), which can be a universal sample index sequence, can be used to distinguish sequences of interest obtained from different sample sources in a multiplex assay.

[00824] In some embodiments, the library molecule comprises two sample index sequences (e.g., (170) and (160)). In some embodiments, the sequencing data from only one of the sample index sequences (e.g., (170) or (160)) can be used for polony mapping and/or template registration because the short random sequence provides sufficient nucleotide diversity and color balance. The sequencing data from the right sample index sequence (e.g., (170)) and the left sample index sequence (e.g., (160)), one or both of which can be a universal sample index sequence, can be used as dual sample indexes to distinguish sequences of interest obtained from different sample sources in a multiplex assay. In some embodiments, the second sample index sequence (e.g., (160)) may or may not include a second short random sequence (e.g., NNN).

[00825] The order of sequencing the sequence-of-interest region and the sample index region(s) can also be used to improve the challenges of sequencing low diversity library molecules. For example, the sample index region (e.g., (170) or (160)) can be sequenced first before sequencing the sequence-of-interest region, and the sample index sequence (e.g., (170) or (160)) can be associated with the sequence-of-interest region. For example, the sample index region (e.g., (170) or (160)) can be sequenced first including sequencing the short random sequence (e.g., NNN) and optionally sequencing at least a portion of the universal sample index, and then sequencing the sequence-of-interest region. In some embodiments, the batch barcode region can be sequenced first before sequencing the sequence-of-interest region, and the batch barcode region can be associated with the sequence-of-interest region. For example, the batch barcode region can be sequenced first including sequencing the short random sequence (e.g., NNN) and optionally sequencing at least a portion of the batch barcode, and then sequencing the sequence-of-interest region. In a population of library molecules, the short random sequence (e.g., NNN) provides nucleotide diversity which may not be provided the sequence-of-interest regions of the library molecules. The short random sequence (e.g., NNN) provides improved nucleotide diversity and color balance for polony mapping and template registration.

[00826] Additionally, when sequencing the sample index region first, the length of the sequenced sample index region is relatively short (e.g., less than 30 nucleotides in length) so that de-hybridization of the product of the sequenced sample index region is more complete. In some embodiments, when sequencing the batch barcode region first, the length of the sequenced batch barcode region is relatively short (e.g., less than 30 nucleotides in length) so that de-hybridization of the product of the sequenced batch barcode region is more complete. Gentler de-hybridization conditions can be used to remove most or all of the product of the sequenced sample index region and batch barcode region which reduces the level of residual signals from any sequencing products remaining hybridized to the template molecules. By contrast, the sequence-of-interest region is typically much longer than the sample index region and the batch barcode region (e.g., more than 100 nucleotides in length). When the sequence-of-interest region is sequenced before the sample index region and the batch barcode region, the product of the sequenced sequence-of-interest region must be subjected to harsher de-hybridization conditions to remove any products remaining hybridized to the template molecules which may damage the template molecules.

[00827] In some aspects, the present disclosure provides linear single stranded library molecules (100) each comprising at least one sample index sequence that can be used to distinguish sequences of interest obtained from different sample sources in a multiplex assay, where the at least one sample index sequence comprises a short random sequence (e.g., NNN) linked to a universal sample index sequence. In some embodiments, the left sample index (160) comprises a short random sequence (e.g., NNN) linked to a universal left sample index sequence and/or the batch right sample index (170) comprises a short random sequence (e.g., NNN) linked to a right universal sample index sequence. The at least one sample index sequence can include sequence diversity for improved base calling. The at least one sample index sequence can be used to improve base calling accuracy.

[00828] In some aspects, the present disclosure provides linear single stranded library molecules (100) each comprising at least one batch barcode sequence, where the at least one batch barcode sequence comprises a short random sequence (e.g., NNN) linked to the batch barcode sequence. The at least one batch barcode sequence can include sequence diversity for improved base calling. The at least one batch barcode sequence can be used to improve base calling accuracy. [00829] In some embodiments, the short random sequence (e.g., NNN) is positioned upstream of the sample index sequence (e.g., (170) and/or (160)) so that during a sequencing run the random sequence portion is sequenced before the sample index sequence. In some embodiments, the sample index sequence comprises a universal sample index sequence. In some embodiments, the short random sequence is positioned downstream of the universal sample index sequence so that during a sequencing run the random portion is sequenced after the universal sample index sequence.

[00830] In some embodiments, the short random sequence (e.g., NNN) is positioned upstream of the batch barcode sequence so that during a sequencing run the random sequence portion is sequenced before the batch barcode sequence. In some embodiments, the short random sequence is positioned downstream of the batch barcode sequence so that during a sequencing run the random portion is sequenced after the batch barcode sequence.

[00831] In some embodiments, in the random sequence each base “N” at a given position is independently selected from A, G, C, T or U. In some embodiments, the random sequence lacks consecutive repeat sequences having 2 or 3 of the same nucleo-base, for example AA, TT, CC, GG, UU, AAA, TTT, CCC, GGG or UUU. In some embodiments, in a population of library molecules the sample index sequences (e.g., (170) and/or (160)) include a short random sequence having a high diversity sequence which includes approximately equal proportions of all four nucleotides (e.g., A, G, C, T and/or U) that will be represented in each cycle of a sequencing run. In some embodiments, the sample index sequences comprise universal sample index sequences. In some embodiments, in a population of library molecules the batch barcode sequences include a short random sequence having a high diversity sequence which includes approximately equal proportions of all four nucleotides (e.g., A, G, C, T and/or U) that will be represented in each cycle of a sequencing run.

[00832] In some embodiments, the short random sequence (e.g., NNN) comprises 3-20 nucleotides, or 3-10 nucleotides, or 3-8 nucleotides, or 3-6 nucleotides, or 3-5 nucleotides, or 3-4 nucleotides.

[00833] In some embodiments, the short random sequence (e.g., NNN) includes, but is not limited to, AGC, AGT, GAC, GAT, CAT, CAG, TAG, TAC. The skilled artisan will recognize that many more random sequences can be prepared (e.g., 64 possible combinations) where each base “N” at a given position in the random sequence is independently selected from A, G, C, T or U.

[00834] In some embodiments, the universal sample index sequence comprises 5-20 nucleotides, or 7-18 nucleotides, or 9-16 nucleotides. [00835] In some embodiments, in a population of library molecules the short random sequence (e.g., NNN) has an overall base composition of about 25% or about 20-30% of all four nucleotide bases (e.g., A, G, C and T/U) to provide nucleotide diversity at each sequencing cycle during sequencing the short random sequence (e.g., NNN).

[00836] In some embodiments, in the population of library molecules the proportion of adenine (A) at any given position in the short random sequence is about 20-30% or about 15- 35% or about 10-40%. In some embodiments, the proportion of guanine (G) at any given position in the short random sequence is about 20-30% or about 15-35% or about 10-40%. In some embodiments, the proportion of cytosine (C) at any given position in the short random sequence is about 20-30% or about 15-35% or about 10-40%. In some embodiments, the proportion of thymine (T) or uracil (U) at any given position in the short random sequence is about 20-30% or about 15-35% or about 10-40%.

[00837] In some embodiments, the proportion of adenine (A) and thymine (T), or the proportion of adenine (A) and uracil (U), at any given position in the short random sequence is about 10-65%. In some embodiments, the proportion of guanine (G) and cytosine (C) at any given position in the short random sequence is about 10-65%.

[00838] In some embodiments, the sequence diversity of the short random sequences ensures that no sequencing cycle is presented with fewer than four different nucleotide bases during sequencing at least the short random sequence (e.g., NNN).

[00839] Exemplary sample index sequences (e.g., (170) and/or (160)) that include a short random sequence NNN linked directly to a universal sample index sequence include but are not limited to: NNNGTAGGAGCC; NNNCCGCTGCTA; NNNAACAACAAG; NNNGGTGGTCTA; NNNTTGGCCAAC; NNNCAGGAGTGC; and NNNATCACACTA. The skilled artisan will recognize that the universal sample index can be any length and have any sequence that can be used to distinguish sequences of interest obtained from different sample sources in a multiplex assay. In a population of a given sample index, for example NNNGTAGGAGCC, the population contains a mixture of individual sample index molecules each carrying the same universal sample index sequence (e.g., GTAGGAGCC) and a different short random sequence (e.g., NNN), where up to 64 different short random sequences may be present in the population of the given sample index.

[00840] In some embodiments, a sequencing reaction includes use of polymerases and nucleotides (e.g., nucleotide analogs) that are labeled with a different fluorophore that corresponds to the nucleo-base. In some embodiments, sequencing the short random sequence (e.g., NNN) using labeled nucleotides provides a balanced ratio of fluorescent colors that correspond to the nucleo-bases adenine, cytosine, guanine, thymine and/or uracil in each cycle of a sequencing run. In some embodiments, sequencing the short random sequence (e.g., NNN) and at least a portion of the universal sample index sequence using labeled nucleotides provides a balanced ratio of fluorescent colors that correspond to nucleo- bases adenine, cytosine, guanine, thymine and/or uracil (e.g., see FIG. 28). In some embodiments, sequencing the short random sequence (e.g., NNN) and at least a portion of the batch barcode sequence using labeled nucleotides provides a balanced ratio of fluorescent colors that correspond to nucleo-bases adenine, cytosine, guanine, thymine and/or uracil. The labeled nucleotides emit fluorescent signals during the sequencing reactions. In some embodiments, the sequencing reaction is conducted on a sequencing apparatus having a detector that captures fluorescent images from sequencing reactions on the immobilized concatemer template molecules. The sequencing apparatus can be configured to relay the fluorescent imaging data captured by the detector to a computer system that is programmed to determine the location (e.g., mapping) of the immobilized concatemer template molecules on the flow cell. The computer system can generate a map of the locations of the immobilized concatemer template molecules based on the fluorescent imaging data of only the random sequence (e.g., NNN), or based on the random sequence (e.g., NNN) and at least a portion the universal sample index sequence and/or the batch barcode sequence. Thus, the few numbers of sequencing cycles used to sequence the random sequence (e.g., NNN) and optionally a portion of the universal sample index sequence and/or optionally a portion the batch barcode sequence can be used to generate a map of the location of the immobilized concatemer template molecules. The computer system can be configured to extract the fluorescent color and intensity of only the random sequence (e.g., NNN), or from the random sequence (e.g., NNN) and at least a portion of the universal sample index sequence, or the random sequence (e.g., NNN) and at least a portion of the batch barcode sequence. The computer system can be configured to use the location of a given immobilized concatemer template molecule and the fluorescent color and intensity associated with the given template molecule (which were established while sequencing the random sequence) for base calling while sequencing the insert region (110). The computer system can be configured to detect phasing and prephasing while sequencing the random sequence (e.g., NNN) and the universal sample index sequence, and the insert region (110). In some embodiments, the balanced ratio of fluorescent colors provided by the random sequence (e.g., NNN) at each sequencing cycle can improve the quality of the data which is processed from the fluorescent images captured by the detector, and can in turn improve the capability by the computer system to determine the location of the immobilized concatemer template molecules on the flow cell, and the color and intensity, all of which can improve base calling accuracy and quality scores of the sequenced insert region (110).

[00841] In some embodiments, a sequencing reaction includes use of polymerases and multivalent molecules that are labeled with a different fluorophore that corresponds to the nucleo-base (e.g., adenine, guanine, cytosine, thymine or uracil) of the nucleotide moieties that are attached to the nucleotide arms in a given multivalent molecule. In some embodiments, the core of individual multivalent molecules is attached to a fluorophore which corresponds to the nucleotide moieties (e.g., adenine, guanine, cytosine, thymine or uracil) that are attached to the nucleotide arms in a given multivalent molecule (e.g., see FIGS. 1-4). In some embodiments, at least one of the nucleotide arms of the multivalent molecule comprises a linker and/or nucleotide base that is attached to a fluorophore. In some embodiments, the fluorophore which is attached to a given linker or nucleotide base corresponds to the nucleotide base (e.g., adenine, guanine, cytosine, thymine or uracil) of the nucleotide arm. In some embodiments, sequencing the random sequence (e.g., NNN) by conducting the two-stage sequencing method using labeled multivalent molecules provides a balanced ratio of fluorescent colors that correspond to the nucleo-bases adenine, cytosine, guanine, thymine and/or uracil in each cycle of a sequencing run. In some embodiments, sequencing the random sequence (e.g., NNN) and at least a portion of the universal sample index sequence and/or at least a portion of the batch barcode sequence using labeled multivalent molecules provides a balanced ratio of fluorescent colors that correspond to nucleo-bases adenine, cytosine, guanine, thymine and/or uracil (e.g., see FIG. 28). The labeled multivalent molecules emit fluorescent signals during the sequencing reactions. In some embodiments, the sequencing reaction is conducted on a sequencing apparatus having a detector that captures fluorescent images from sequencing reactions on the immobilized concatemer template molecules. The sequencing apparatus can be configured to relay the fluorescent imaging data captured by the detector to a computer system that is programmed to determine the location (e.g., mapping) of the immobilized concatemer template molecules (polonies) on the flow cell. The computer system can generate a map of the locations of the immobilized concatemer template molecules based on the fluorescent imaging data of only the random sequence (e.g., NNN), or based on the random sequence (e.g., NNN) and at least a portion of the universal sample index sequence and/or at least a portion of the batch barcode sequence. Thus, the few numbers of sequencing cycles used to sequence the random sequence (e.g., NNN) and optionally a portion of the universal sample index sequence can be used to generate a map of the location of the immobilized concatemer template molecules. The computer system can be configured to extract the fluorescent color and intensity of only the random sequence (e.g., NNN), or from the random sequence (e.g., NNN) and the universal sample index sequence and/or batch barcode sequence. The computer system can be configured to use the location of a given immobilized concatemer template molecule and the fluorescent color and intensity associated with the given template molecule (which were established while sequencing the random sequence) for base calling while sequencing the insert region (110). The computer system can be configured to detect phasing and prephasing while sequencing the random sequence (e.g., NNN) and the universal sample index sequence, and the insert region (110). In some embodiments, the balanced ratio of fluorescent colors provided by the random sequence (e.g., NNN) at each sequencing cycle can improve the quality of the data which is processed from the fluorescent images captured by the detector, and can in turn improve the capability by the computer system to determine the location of the immobilized concatemer template molecules on the flow cell, and the color and intensity, all of which can improve base calling accuracy and quality scores of the sequenced insert region (110).

EXAMPLES

[00842] The following examples are meant to be illustrative and can be used to further understand embodiments of the present disclosure and should not be construed as limiting the scope of the present teachings in any way.

Example 1: Two-Plex Batch Sequencing Concatemer Template Molecules Prepared with Single-stranded Splint or Double-Stranded Adaptors

[00843] Covalently closed circular libraries containing phiX insert regions (as the sequence of interest) were prepared by hybridizing linear library molecules to either singlestranded splints (e.g., FIG. 26A) or double-stranded adaptors (e.g., FIG. 27A).

[00844] For the single-stranded splint workflow: briefly, linear single-stranded nucleic acid library molecules (100) included the following components (e.g., FIG. 26A): (i) a surface pinning primer binding site sequence (120); (ii) a left sample index sequence (160); (iii) a forward sequencing primer binding site sequence (140); (iv) a sequence of interest (e.g., an insert sequence) (110); (v) a reverse sequencing primer binding site sequence (150); (vi) a right sample index sequence (170); and (vii) a surface capture primer binding site sequence (130). The single-stranded library molecules were hybridized with single-stranded splint strands (200) to generate library-splint complexes (300) having one nick. The nick was ligated to generate covalently closed circular library molecules (400). The single-stranded splint strand (200) was removed enzymatically. The forward sequencing primer binding site sequence (1 0) was an ss- Splint sequencing primer having the sequence 5’- CGTGCTGGATTGGCTCACCAGACACCTTCCGACAT -3’ (SEQ ID NO: 161). [00845] For the double-stranded splint workflow: single-stranded nucleic acid library molecules (100) included the following components (e.g., FIG. 27A): (i) a surface pinning primer binding site sequence (120); (ii) a left sample index sequence (160); (iii) a forward sequencing primer binding site sequence (140); (iv) a sequence of interest (e.g., an insert sequence) (110); (v) a reverse sequencing primer binding site sequence (150); (vi) a right sample index sequence (170); and (vii) a surface capture primer binding site sequence (130). The single-stranded library molecules were hybridized with double-stranded splint adaptors (500) to generate library-splint complexes (800) having two nicks. The nicks were ligated to generate covalently closed circular library molecules (900). The first splint strand (600) was removed enzymatically. The forward sequencing primer binding site sequence (140) was TruSeq (HP 10) having the sequence

[00846] 5’-ACACTCTTTCCCTACACGACGCTCTTCCGATCT -3’ (SEQ ID NO: 150). [00847] The two types of covalently closed circular library molecules (400) and (900) were mixed at 1 : 1 ratio and 20 pM was distributed onto a flow cell having a plurality of surface capture and pinning primers immobilized thereon. The surface capture primer was designed to capture both types of covalently closed circular library molecules (e.g., (400) and (900)). The loaded covalently closed circular library molecules (400) and (900) were subjected to on-support rolling circle amplification using the immobilized surface capture primers as amplification primers, thereby generating two types of concatemer template molecules. The rolling circle amplification reaction was conducted in the presence of compaction oligonucleotides to generated compact DNA nanoballs. The pinning primer was designed to pin down both types of concatemer template molecules resulting from rolling circle amplification. In other experiments, 30 and 40 pM of covalently closed circular library molecules (400) and (900) were loaded onto a flow cell to increase the density of immobilized concatemer template molecules.

[00848] A first batch sequencing reaction was conducted using the TruSeq (HP 10) sequencing primer and the two-stage sequencing reaction. Thirty-one sequencing cycles were conducted, and fluorescent images were acquired after reacting the concatemer template molecules with labeled multivalent molecules (exemplified in FIG. 4) and non-labeled chain terminator nucleotides. After 31 sequencing cycles, the first batch sequencing read products were removed.

[00849] A second batch sequencing reaction was conducted using an ss-Splint sequencing primer and the two-stage sequencing reaction. Thirty-one sequencing cycles were conducted and fluorescent images were acquired after reacting the concatemer template molecules with labeled multivalent molecules (exemplified in FIG. 4) and non-labeled chain terminator nucleotides. After 31 sequencing cycles, the second batch sequencing read products were removed.

[00850] Table 1 below shows the number of millions of reads, quality scores (%Q30), and percent error.

Table 1:

Example 2: Four-Plex and Eight-Plex Batch Sequencing of Concatemer Template Molecules Prepared with Single-Stranded Splints

[00851] Four sub-populations of linear single-stranded library molecules (100) were prepared having a PhiX sequence of interest where individual library molecules included: (i) a surface pinning primer binding site sequence (120); (ii) a left sample index sequence (160) (e.g., one of four different sample indexes which are 9 bases in length); (iii) a forward sequencing primer binding site sequence (140) (e.g., one of four different batch-specific forward sequencing primer binding site sequences); (iv) a sequence of interest (110) (e.g., PhiX); (v) a reverse sequencing primer binding site sequence (150) (e.g., a batch-specific reverse sequencing primer binding site sequence); (vi) a right sample index sequence (170) (e.g., one of four different sample indexes having a random sequence 3-mer (e.g., NNN) and a 9-base sample index sequence); and (vii) a surface capture primer binding site sequence (130). The linear library molecules did not include a unique molecular index (UMI). The arrangement of the linear single-stranded library molecules (100) is shown in FIG. 26A.

[00852] Single-stranded splint strands (200) were prepared having: (i) a first region (210) that hybridizes with the surface pinning primer binding site sequence (120) of the linear single-stranded library molecule (100), and a second region (220) that hybridizes with the surface capture primer binding site sequence (130) of the single-stranded library molecule (100). The arrangement of the single-stranded splint strands (200) is shown in FIG. 26A. [00853] In four separate reactions, the linear single stranded library molecules (100) were hybridized with single-stranded splint strands (200) to generate four sub-populations of library-splint complexes (300) with a nick (e.g., see FIG. 26A). The library-splint complexes (300) in the four sub-populations carried one of four different forward sequencing primer binding site sequences.

[00854] The library-splint complexes (300) were subjected to separate ligation reaction to generate four sub-populations of covalently closed circular library molecules (400) where individual covalently closed circular library molecules included: (i) a surface pinning primer binding site sequence (120), which can be universal; (ii) a left sample index sequence (160) (e.g., one of four different sample indexes which are 9 bases in length); (iii) a forward sequencing primer binding site sequence (140) (e.g., one of four different batch-specific forward sequencing primer binding site sequences); (iv) a sequence of interest (110) (e.g., PhiX); (v) a reverse sequencing primer binding site sequence (150) (e.g., a batch-specific reverse sequencing primer binding site sequence); (vi) a right sample index sequence (170) (e.g., one of four different sample indexes having a random sequence 3-mer (e.g., NNN) and a 9-base sample index sequence); and (vii) a surface capture primer binding site sequence (130), which can be universal.

[00855] The four sub-populations of covalently closed circular library molecules (400) were mixed at 1 : 1 : 1 : 1 ratio and 200 pM of the mixture was distributed onto a flow cell having a plurality of surface capture and pinning primers immobilized thereon. The loaded covalently closed circular library molecules (400) were subjected to on-support rolling circle amplification using the immobilized surface capture primers as amplification primers, thereby generating four sub-populations of concatemer template molecules, where the concatemers in the different sub-populations carried one of four different forward sequencing primer binding site sequence. The rolling circle amplification reaction was conducted in the presence of compaction oligonucleotides to generate compact concatemers (e.g., DNA nanoballs; polonies).

[00856] The density of each sub-population of polonies on the flow cell was measured to be about 400K/mm² to about 450K/mm², resulting in a total polony density of about 1600K/mm².

[00857] A first batch sequencing reaction was conducted using a first batch forward sequencing primer and the two-stage sequencing reaction to sequence the PhiX insert region. Thirty-one sequencing cycles were conducted and fluorescent images were acquired after reacting the concatemer template molecules with labeled multivalent molecules (e.g., FIG. 4) and non-labeled chain terminator nucleotides. After 31 sequencing cycles, the first batch sequencing read products were removed.

[00858] A second batch sequencing reaction was conducted using a second batch forward sequencing primer and the two-stage sequencing reaction to sequence the PhiX insert region. Thirty-one sequencing cycles were conducted and fluorescent images were acquired after reacting the concatemer template molecules with labeled multivalent molecules (e.g., FIG. 4) and non-labeled chain terminator nucleotides. After 31 sequencing cycles, the second batch sequencing read products were removed.

[00859] The sequencing reactions were repeated using the third and fourth batch forward sequencing primers as described above. The quality scores of the sequencing reads were determined to be about 96% at Q30 and 85% at Q40.

[00860] In a similar manner, an 8-plex library prep, circularization and sequencing workflow was conducted using eight sub-populations of libraries that were prepared using eight different batch-specific forward sequencing primer binding site sequences (140) and eight different batch-specific reverse sequencing primer binding site sequence (150). The sequences of the eight different forward sequencing primer binding site sequences (140) in the linear library molecules are listed in Table 2 below.

Table 2:

[00861] The eight sub-populations of covalently closed circular library molecules (400) were mixed at equal ratio (e.g., each at 8.5 pM, 12.5 pM or 25 pM) and the mixture was distributed onto a flow cell having a plurality of universal capture and pinning primers immobilized thereon. Thus, 68 pM, 100 pM or 200 pM of the covalently closed circular library molecules were loaded onto a flow cell. Rolling circle amplification reaction was conducted. The density of each sub-population of polonies on the flow cell was measured to be about 270K/mm² to about 290K/mm², resulting in a total polony density of about 2100K/mm². Eight rounds of batch sequencing were conducted in a manner similar to that described above using eight different batch sequencing primers and conducting 31 sequencing cycles for each batch. The quality scores of the sequencing reads of the eight different sub-populations are listed in Table 3 below.

Table 3:

Example 3: Eight-Plex Batch Sequencing of Concatemer Template Molecules Prepared with Single-Stranded Splints

[00862] Eight sub-populations of linear single stranded library molecules (100) were prepared having an E. coli sequence of interest (e.g., insert region) where individual library molecules included: (i) a surface pinning primer binding site sequence (120); (ii) a left sample index sequence (160) (e.g., one of eight different sample indexes which are 9 bases in length); (iii) a forward sequencing primer binding site sequence (140) (e.g., one of eight different batch-specific forward sequencing primer binding site sequences); (iv) a sequence of interest (110) (e.g., from E. coli) (v) a reverse sequencing primer binding site sequence (150) (e.g., a batch-specific reverse sequencing primer binding site sequence); (vi) a right sample index sequence (170) (e.g., one of eight different sample indexes having a random sequence 3-mer (e.g., NNN) and a 9-base sample index sequence); and (vii) a surface capture primer binding site sequence (130). The library molecules did not include a unique molecular index (UMI). The arrangement of the single stranded linear library molecules (100) is shown in FIG. 26 A. The sequences of the eight different forward sequencing primer binding site sequences (140) in the linear library molecules are listed in Table 4 below.

[00863] Single-stranded splint strands (200) (universal single-stranded splint strands) were prepared having: (i) a first region (210) that hybridizes with the surface pinning primer binding site sequence (120) of the linear single-stranded library molecule (100), and a second region (220) that hybridizes with the surface capture primer binding site sequence (130) of the linear single-stranded library molecule (100). The arrangement of the single-stranded splint strands (200) is shown in FIG. 26A.

Table 4: [00864] In eight separate reactions, the linear single stranded library molecules (100) were hybridized with universal single-stranded splint strands (200) to generate eight subpopulations of library-splint complexes (300) with a nick (e.g., see FIG. 26A). The librarysplint complexes (300) in the eight sub-populations carried one of eight different forward sequencing primer binding site sequences.

[00865] The library-splint complexes (300) were subjected to separate ligation reactions to generate eight sub-populations of covalently closed circular library molecules (400) where individual covalently closed circular library molecules included: (i) a surface pinning primer binding site sequence (120), which can be universal; (ii) a left sample index sequence (160) (e.g., one of eight different sample indexes which are 9 bases in length); (iii) a forward sequencing primer binding site sequence (1 0) (e.g., one of eight different batch-specific forward sequencing primer binding site sequences); (iv) a sequence of interest (110) (e.g., from E. coliy, (v) a reverse sequencing primer binding site sequence (150) (e.g., a batchspecific reverse sequencing primer binding site sequence); (vi) a right sample index sequence (170) (e.g., one of eight different sample indexes having a random sequence 3-mer (e.g., NNN) and a 9-base sample index sequence); and (vii) a surface capture primer binding site sequence (130), which can be universal.

[00866] Equal amounts of the eight sub-populations of covalently closed circular library molecules (400) were mixed together and 56 pM of the mixture was distributed onto a flow cell having a plurality of capture and pinning primers immobilized thereon. The loaded covalently closed circular library molecules (400) were subjected to on-support rolling circle amplification using the immobilized surface capture primers as amplification primers, thereby generating eight sub-populations of concatemer template molecules, where the concatemers in the different sub-populations carried one of eight different forward sequencing primer binding site sequences. The rolling circle amplification reaction was conducted in the presence of compaction oligonucleotides to generate compact concatemers (e.g., DNA nanoballs; polonies).

[00867] The density of each sub-population of polonies on the flow cell was measured to be about 200 K/mm² to about 450 K/mm², resulting in a total polony density of about 3,500 K/mm².

[00868] A first batch sequencing reaction was conducted using a first batch forward sequencing primer and the two-stage sequencing reaction to sequence the E. coli insert region. Thirty-one sequencing cycles were conducted and fluorescent images were acquired after reacting the concatemer template molecules with labeled multivalent molecules (e.g., FIG. 4) and non-labeled chain terminator nucleotides. After 31 sequencing cycles, the first batch sequencing read products were removed.

[00869] A second batch sequencing reaction was conducted using a second batch forward sequencing primer and the two-stage sequencing reaction to sequence the E. coli insert region. 31 sequencing cycles were conducted, and fluorescent images were acquired after reacting the concatemer template molecules with labeled multivalent molecules (e.g., FIG. 4) and non-labeled chain terminator nucleotides. After 31 sequencing cycles, the second batch sequencing read products were removed.

[00870] The two-stage sequencing reactions were repeated separately using the third, fourth, fifth, sixth, seventh and eighth batch forward sequencing primers as described above. [00871] The quality scores of the sequencing reads of the eight different sub-populations are listed in Table 5 below.

Table 5:

Example 4: Preparing and Sequencing Compact DNA Nanoballs Generated with Soluble Amplification Primers

[00872] Covalently closed circular libraries were prepared by preparing covalently closed circular library molecules, individual covalently closed circular library molecules carrying: (i) a surface pinning primer binding site sequence (120), which can be universal; (ii) a left sample index sequence (160); (iii) a forward sequencing primer binding site sequence (140);

(iv) a sequence of interest (e.g., an insert region) (110); (v) a reverse sequencing primer binding site sequence (150), which can be universal; (vi) a right sample index sequence (170); and (vii) a surface capture primer binding site sequence (130). The forward and reverse sequencing primer binding site sequences were universal sequences.

[00873] 8 pM of the covalently closed circular library molecules (400) were distributed onto a flow cell having a plurality of capture and pinning primers immobilized thereon. The loaded covalently closed circular library molecules (400) were subjected to on-support rolling circle amplification using the immobilized capture primers as amplification primers, thereby generating a plurality of concatemer template molecules immobilized to the flow cell. The rolling circle amplification reaction was conducted in the presence of compaction oligonucleotides, and one or two different soluble amplification primers, to generate compact DNA nanoballs (e.g., DNA polonies). A control rolling circle amplification reaction included compaction oligonucleotides and lacked any soluble amplification primers. For example, the different soluble amplification primers hybridized to a universal binding site in the covalently closed circular library molecule, including the forward sequencing primer binding site sequence (1 0) or the reverse sequencing primer binding site sequence (150).

[00874] Pairwise sequencing was then conducted. The forward sequencing reaction was conducted using universal forward sequencing primers and the two-stage sequencing reaction to sequence the insert region. About 150 sequencing cycles were conducted, and fluorescent images were acquired after reacting the compact DNA nanoballs with labeled multivalent molecules (e.g., FIG. 4) and non-labeled chain terminator nucleotides. The reverse sequencing reaction was conducted using universal reverse sequencing primers and the two- stage sequencing reaction to sequence the insert region. About 150 sequencing cycles were conducted, and fluorescent images were acquired after reacting the compact DNA nanoballs with labeled multivalent molecules (e.g., FIG. 4) and non-labeled chain terminator nucleotides.

[00875] A comparison of normalized signal intensities of the images of the compact DNA nanoballs was obtained. The histogram of FIG. 22A compares normalized signal intensities of the forward sequencing run generated using 1 or 3 soluble amplification primers. The histogram of FIG. 22B compares normalized signal intensities of the reverse sequencing run generated using 1 or 3 soluble amplification primers.

[00876] A comparison of sequencing quality scores was obtained. In the boxplots of FIGS. 23 A-23B and 24A-24B, the x-axis indicates the base position in the forward (FIGs. 23A and 23B) and reverse (FIGS. 24A and 24B) reads, and the y-axis indicates the quality scores. The boxplot of FIG. 23A shows the quality scores at each base position in the forward sequencing run using 1 soluble amplification primer. The boxplot of FIG. 23B shows the quality scores at each base position in the forward sequencing run using 3 soluble amplification primers. The boxplot of FIG. 24A shows the quality scores at each base position in the reverse sequencing run using 1 soluble amplification primer. The boxplot of FIG. 24B shows the quality scores at each base position in the reverse sequencing run using 3 soluble amplification primers.

Table 6: Compaction Oligonucleotides Table 6 (continued): Compaction Oligonucleotides Table 6 (continued): Compaction Oligonucleotides Table 6 (continued): Compaction Oligonucleotides Table 6 (continued): Compaction Oligonucleotides

Table 6 (continued): Compaction Oligonucleotides

INCORPORATION BY REFERENCE

[00877] Throughout this application various publications, patents, and/or patent applications are referenced. The disclosures of the publications, patents and/or patent applications are hereby incorporated by reference in their entireties into this application in order to more fully describe the state of the art to which this disclosure pertains.

EQUIVALENTS

[00878] The details of one or more embodiments of the disclosure are set forth in the accompanying description above. Although any methods and materials similar or equivalent to those described herein can be used in the practice or testing of the present disclosure, the preferred methods and materials are now described. Other features, objects, and advantages of the disclosure will be apparent from the description and from the claims. In the specification and the appended claims, the singular forms include plural referents unless the context clearly dictates otherwise. Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this disclosure belongs. All patents and publications cited in this specification are incorporated by reference.

Claims

CLAIMS What is claimed:

1. A method for generating and sequencing a plurality of compact DNA nanoballs immobilized to a support, comprising: a) providing a support comprising:

(i) a plurality of capture primers immobilized to the support, wherein individual capture primers comprise a 3’ extendible end;

(ii) a plurality of pinning primers immobilized to the support, wherein individual pinning primers comprise a 3’ non-extendible end; and

(iii) a plurality of covalently closed circular polynucleotide molecules, wherein individual covalently closed circular polynucleotide molecules are hybridized to individual capture primers, thereby forming a plurality of immobilized circular molecule-capture primer duplexes; b) contacting the plurality of immobilized circular molecule-capture primer duplexes with a plurality of soluble amplification primers under a condition suitable for hybridizing at least one soluble amplification primer to an individual immobilized circular molecule-capture primer duplex thereby forming a plurality of immobilized circular molecule-capture primer duplexes; c) conducting a rolling circle amplification (RCA) reaction on the plurality of immobilized circular molecule-capture primer duplexes of step (b) in the presence of a plurality of compaction oligonucleotides, thereby generating a plurality of compact DNA nanoballs immobilized to the support,

• wherein individual compact DNA nanoballs comprise (i) a concatemer template molecule generated by RCA-extension of an immobilized capture primer and (ii) at least one concatemer template molecule generated by RCA-extension of a soluble amplification primer,

• wherein at least a portion of individual compact DNA nanoballs is hybridized to a pinning primer, thereby generating a plurality of compact DNA nanoballs immobilized to the support; d) removing the plurality of covalently closed circular polynucleotide molecules and retaining the plurality of compact DNA nanoballs; and e) sequencing the plurality of the compact DNA nanoballs of step (d).

2. The method of claim 1, wherein the support comprises glass, plastic and/or a polymer material.

3. The method of claim 1 or 2, wherein the support is passivated with at least one hydrophilic polymer coating.

4. The method of claim 3, wherein the plurality of capture primers and the plurality of pinning primers are covalently joined to the at least one hydrophilic polymer coating.

5. The method of claim 3, wherein the at least one hydrophilic polymer coating has a water contact angle of no more than 45 degrees.

6. The method of any one of claims 1-5, wherein the plurality of capture primers is immobilized to the support at random locations or immobilized to the support at predetermined locations.

7. The method of any one of claims 1-6, wherein the plurality of pinning primers is immobilized to the support at random locations or immobilized to the support at predetermined locations.

8. The method of any one of claims 1-7, wherein the plurality of capture primers is immobilized to the support at a density of about 10² - 10¹⁵ capture primers per mm².

9. The method of any one of claims 1-8, wherein the plurality of pinning primers is immobilized to the at a density of about 10² - 10¹⁵ pinning primers per mm².

10. The method of any one of claims 1-9, wherein the support lacks partitions or barriers that separate regions of the support.

11. The method of any one of claims 1-10, wherein the plurality of covalently closed circular polynucleotide molecules comprises RNA or DNA, optionally wherein the DNA comprises complementary DNA (cDNA).

12. The method of any one of claims 1-11, wherein individual covalently closed circular polynucleotide molecules comprise a sequence of interest that is 200 - 2000 nucleotides in length.

13. The method of any one of claims 1-11, wherein individual covalently closed circular polynucleotide molecules comprise a sequence of interest and lack a universal adaptor sequence.

14. The method of any one of claims 1-13, wherein individual covalently closed circular polynucleotide molecules comprise a sequence of interest and any one or any combination of two or more of:

(i) a universal sequence for binding a pinning primer or a complementary sequence thereof,

(ii) a universal sequence for binding a capture primer or a complementary sequence thereof,

(iii) at least one universal sequence for binding a first sequencing primer or a complementary sequence thereof,

(iv) at least one universal sequence for binding a second sequencing primer or a complementary sequence thereof,

(v) at least one universal sequence for binding a soluble amplification primer or a complementary sequence thereof and/or

(vi) a universal sequence for binding a compaction oligonucleotide or a complementary sequence thereof.

15. The method of claim 14, wherein individual soluble amplification primers provided on step (b) bind to any one or more of:

(i) the sequence of interest,

(ii) the universal sequence for binding a pinning primer or a complementary sequence thereof, (iii) the universal sequence for binding a capture primer or a complementary sequence thereof,

(iv) the universal sequence for binding a first sequencing primer or a complementary sequence thereof,

(v) the universal sequence for binding a second sequencing primer or a complementary sequence thereof,

(vi) the universal sequence for binding a compaction oligonucleotide or a complementary sequence thereof; or

(vii) a combination thereof.

16. The method of any one of claims 1-15, wherein individual covalently closed circular polynucleotide molecules are further hybridized to 1, 2, 3, 4, 5, 6, 7, 8, 9 or 10 soluble amplification primers.

17. The method of any one of claims 14-16, wherein the at least one soluble amplification primer of step (b) is hybridized to any one or more of:

(i) the sequence of interest,

(ii) the universal sequence for binding a capture primer or a complementary sequence thereof,

(iii) the universal sequence for binding a pinning primer or a complementary sequence thereof,

(iv) the universal sequence for binding a first sequencing primer,

(v) the universal sequence for binding a second sequencing primer, and/or

(vii) a combination thereof.

18. The method of any one of claims 1-17, wherein the RCA reaction comprises contacting the plurality of the immobilized circular molecule-capture primer duplexes with a plurality of strand displacing polymerases, and a plurality of nucleotides.

19. The method of claim 18, wherein the plurality of nucleotides comprises at least one nucleotide having a scissile moiety that can be cleaved to generate an abasic site in the immobilized compact DNA nanoball.

20. The method of claim 19, wherein the at least one nucleotide having a scissile moiety comprises uridine, 8-oxo-7,8-dihydrogunine or deoxyinosine.

21. The method of any one of claims 1-20, wherein the plurality of compaction oligonucleotides comprises at least a first and a second compaction oligonucleotide, wherein

(i) the first compaction oligonucleotide comprises a first binding region that hybridizes to a first portion of the concatemer template molecule generated in step (c), and a second binding region that hybridizes to a second portion of the same concatemer template molecule thereby pulling together distal portions of the concatemer molecule causing compaction of the concatemer template molecule, and

(ii) the second compaction oligonucleotide comprises a first binding region that hybridizes to a first portion of the concatemer template molecule generated in step (c), and a second binding that hybridizes to a second portion of the same concatemer template molecule thereby pulling together distal portions of the concatemer molecule causing compaction of the concatemer template molecule.

22. The method of claim 21, wherein the first and the second compaction oligonucleotides comprise the same sequence or different sequences.

23. The method of any one of claims 1-22, wherein the plurality of compact DNA nanoballs is immobilized to the support at a high density, wherein at least some of the immobilized compact DNA nanoballs comprise nearest neighbor compact DNA nanoballs that touch each other and/or overlap each other when viewed from any angle of the support including above, below or side views of the support.

24. The method of any one of claims 1-23, wherein the sequencing comprises contacting individual compact DNA nanoballs with a plurality of sequencing primers, a plurality of sequencing polymerases and a plurality of detectably labeled multivalent molecules, individual detectably labeled multivalent molecules comprising (a) a core and (b) a plurality of nucleotide arms and wherein individual polymer arms comprise at least one nucleotide moiety.

25. The method of any one of claims 1-24, wherein the sequencing comprises:

(i) binding the concatemer template molecules of step (c) with a plurality of sequencing primers, a plurality of sequencing polymerases, and a plurality of detectably labeled multivalent molecules, and/or

(ii) binding the concatemer template molecules of step (c) with a plurality of sequencing primers, a plurality of sequencing polymerases, and a plurality of detectably labeled multivalent molecules, thereby generating a compact DNA nanoball immobilized to the support that emits a detectable signal.

26. The method of claim 25, wherein individual detectably labeled multivalent molecules comprise (a) a core; and (b) a plurality of nucleotide arms comprising (i) a core attachment moiety, (ii) a spacer, (iii) a linker, and (iv) a nucleotide moiety, wherein the core is attached to the plurality of nucleotide arms via their core attachment moiety, wherein the core attachment moiety is attached to the spacer, wherein the spacer is attached to the linker, and wherein the linker is attached to the nucleotide moiety.

27. The method of claim 24, wherein individual nucleotide arms comprise (i) a core attachment moiety, (ii) a spacer and (iii) a nucleotide moiety, wherein the core is attached to the plurality of nucleotide arms via their core attachment moiety, wherein the core attachment moiety is attached to the spacer, wherein the spacer is attached to the nucleotide moiety.

28. The method of claim 27, wherein the linker comprises an aliphatic chain having 2-6 subunits or an oligo ethylene glycol chain having 2-6 subunits.

29. The method of claim 26 or 27, wherein the plurality of nucleotide arms attached to an individual core has the same type of nucleotide moiety selected from the group consisting of dATP, dGTP, dCTP, dTTP and dUTP.

30. The method of claim 26 or 27, wherein individual detectably labeled multivalent molecules have the same type of nucleotide moiety selected from the group consisting of dATP, dGTP, dCTP, dTTP and dUTP.

31. The method of any one of claims 24-30, wherein the plurality of detectably labeled multivalent molecules comprises a mixture of two or more types of detectably labeled multivalent molecules, individual types of detectably labeled multivalent molecules having nucleotide moieties selected from the group consisting of dATP, dGTP, dCTP, dTTP and dUTP

32. The method of claim 24, wherein individual detectably labeled multivalent molecules in the plurality comprise

• a core attached to a fluorophore,

• a nucleotide arm attached to a fluorophore, and/or

• a nucleotide moiety attached to a fluorophore.

33. The method of any one of claims 1-32, wherein the sequencing further comprises contacting individual compact DNA nanoballs with a plurality of non-catalytic divalent cations that inhibit polymerase-catalyzed nucleotide incorporation, wherein the non- catalytic divalent cations comprise strontium, calcium or barium.

34. The method of any one of claims 1-24, wherein the sequencing comprises: a) binding a first sequencing primer, a first sequencing polymerase, and a first multivalent molecule to a first portion of the concatemer template molecule of step (c) thereby forming a first binding complex, wherein a first nucleotide moiety of the first multivalent molecule binds to the first sequencing polymerase; and b) binding a second sequencing primer, a second sequencing polymerase, and the first multivalent molecule to a second portion of the same concatemer template molecule thereby forming a second binding complex, wherein a second nucleotide moiety of the first multivalent molecule binds to the second sequencing polymerase, and wherein the first and second binding complexes which include the same multivalent molecule form an avidity complex.

35. The method of any one of claims 1-24, wherein the sequencing comprises: a) contacting different portions of the concatemer template molecule of step (c) with a first plurality of sequencing polymerases and a first plurality of sequencing primers to form at least a first and a second polymerase complex on the same concatemer template molecule; b) contacting a plurality of detectably labeled multivalent molecules with the at least first and second polymerase complexes on the same concatemer template molecule to bind a single multivalent molecule to the first and the second polymerase complexes, wherein at least a first nucleotide moiety of the single multivalent molecule is bound to the first polymerase complex thereby forming a first binding complex, and wherein at least a second nucleotide moiety of the single multivalent molecule is bound to the second polymerase complex thereby forming a second binding complex,

• wherein the contacting is conducted under a condition suitable to inhibit polymerase-catalyzed incorporation of the bound first and second nucleotide moieties in the first and second binding complexes, and

• wherein the first and second binding complexes which are bound to the same multivalent molecule form an avidity complex; c) detecting the first and the second binding complexes on the same concatemer template molecule; and d) identifying the first nucleotide moiety in the first binding complex thereby determining the sequence of the first portion of the concatemer template molecule, and identifying the second nucleotide moiety in the second binding complex thereby determining the sequence of the second portion of the concatemer template molecule.

36. The method of any one of claims 24-35, wherein contacting individual compact DNA nanoballs with a plurality of labeled nucleotides comprises:

(i) binding the concatemer template molecule of step (c) with a plurality of sequencing primers, a plurality of sequencing polymerases, and a plurality of detectably labeled nucleotides, and

(ii) binding the concatemer template molecule of step (c) with a plurality of sequencing primers, a plurality of sequencing polymerases, and a plurality of detectably labeled nucleotides, thereby generating a compact DNA nanoball immobilized to the support that emits a detectable signal.

37. The method of claim 36, wherein individual detectably labeled nucleotides in the plurality comprise an aromatic base, a five-carbon sugar, and 1-10 phosphate groups.

38. The method of claim 36 or 37, wherein the plurality of detectably labeled nucleotides comprises one type of nucleotide selected from the group consisting of dATP, dGTP, dCTP, dTTP and dUTP.

39. The method of claim 36, wherein the plurality of detectably labeled nucleotides comprises two or more types of nucleotides selected from the group consisting of dATP, dGTP, dCTP, dTTP and dUTP.

40. The method of any one of claims 36-39, wherein at least one detectably labeled nucleotide in the plurality is labeled with a fluorophore.

41. The method of any one of claims 36-40, wherein at least one nucleotide in the plurality lacks a fluorophore label.

42. The method of claim 36, wherein at least one of the detectably labeled nucleotides comprises a removable chain terminating moiety attached to the 3’ carbon position of the sugar group, wherein the removable chain terminating moiety comprises an alkyl group, an alkenyl group, an alkynyl group, an allyl group, an aryl group, a benzyl group, an azide group, an azido group, an O-azidomethyl group, an amine group, an amide group, a keto group, an isocyanate group, a phosphate group, a thio group, a disulfide group, a carbonate group, a urea group, an acetal group or a silyl group, and wherein the removable chain terminating moiety is cleavable with a chemical compound to generate an extendible 3 ’OH moiety on the sugar group.

43. The method of any one of claims 34-42, wherein the sequencing further comprises contacting individual compact DNA nanoballs with a plurality of catalytic divalent cations that promote polymerase-catalyzed nucleotide incorporation, wherein the catalytic divalent cations comprise magnesium or manganese.

44. A method for generating a plurality of compact DNA nanoballs, comprising: a) providing a support comprising: (i) a plurality of capture primers immobilized to the support, wherein individual capture primers comprise a 3’ extendible end;

(iii) a plurality of covalently closed circular polynucleotide molecules, wherein individual covalently closed circular polynucleotide molecules are hybridized to individual capture primers, thereby forming a plurality of immobilized circular molecule-capture primer duplexes; b) contacting the plurality of immobilized circular molecule-capture primer duplexes with a plurality of soluble amplification primers under a condition suitable for hybridizing at least one soluble amplification primer to individual immobilized circular molecule-capture primer duplexes; c) conducting a rolling circle amplification (RCA) reaction on the plurality of immobilized circular molecule-capture primer duplexes of step (b) in the presence of a plurality of compaction oligonucleotides, thereby generating a plurality of compact DNA nanoballs immobilized to the support,

• wherein at least a portion of individual compact DNA nanoballs is hybridized to an immobilized pinning primer; d) removing the plurality of covalently closed circular polynucleotide molecules and retaining the plurality of compact DNA nanoballs immobilized to the support.

45. The method of claim 44, further comprising sequencing the plurality of immobilized compact DNA nanoballs.