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27 pages, 8829 KiB  
Article
Extensive Bioinformatics Analyses Reveal a Phylogenetically Conserved Winged Helix (WH) Domain (Zτ) of Topoisomerase IIα, Elucidating Its Very High Affinity for Left-Handed Z-DNA and Suggesting Novel Putative Functions
by Martin Bartas, Kristyna Slychko, Jiří Červeň, Petr Pečinka, Donna J. Arndt-Jovin and Thomas M. Jovin
Int. J. Mol. Sci. 2023, 24(13), 10740; https://doi.org/10.3390/ijms241310740 - 27 Jun 2023
Cited by 3 | Viewed by 2698
Abstract
The dynamic processes operating on genomic DNA, such as gene expression and cellular division, lead inexorably to topological challenges in the form of entanglements, catenanes, knots, “bubbles”, R-loops, and other outcomes of supercoiling and helical disruption. The resolution of toxic topological stress is [...] Read more.
The dynamic processes operating on genomic DNA, such as gene expression and cellular division, lead inexorably to topological challenges in the form of entanglements, catenanes, knots, “bubbles”, R-loops, and other outcomes of supercoiling and helical disruption. The resolution of toxic topological stress is the function attributed to DNA topoisomerases. A prominent example is the negative supercoiling (nsc) trailing processive enzymes such as DNA and RNA polymerases. The multiple equilibrium states that nscDNA can adopt by redistribution of helical twist and writhe include the left-handed double-helical conformation known as Z-DNA. Thirty years ago, one of our labs isolated a protein from Drosophila cells and embryos with a 100-fold greater affinity for Z-DNA than for B-DNA, and identified it as topoisomerase II (gene Top2, orthologous to the human UniProt proteins TOP2A and TOP2B). GTP increased the affinity and selectivity for Z-DNA even further and also led to inhibition of the isomerase enzymatic activity. An allosteric mechanism was proposed, in which topoII acts as a Z-DNA-binding protein (ZBP) to stabilize given states of topological (sub)domains and associated multiprotein complexes. We have now explored this possibility by comprehensive bioinformatic analyses of the available protein sequences of topoII representing organisms covering the whole tree of life. Multiple alignment of these sequences revealed an extremely high level of evolutionary conservation, including a winged-helix protein segment, here denoted as Zτ, constituting the putative structural homolog of Zα, the canonical Z-DNA/Z-RNA binding domain previously identified in the interferon-inducible RNA Adenosine-to-Inosine-editing deaminase, ADAR1p150. In contrast to Zα, which is separate from the protein segment responsible for catalysis, Zτ encompasses the active site tyrosine of topoII; a GTP-binding site and a GxxG sequence motif are in close proximity. Quantitative Zτ-Zα similarity comparisons and molecular docking with interaction scoring further supported the “B-Z-topoII hypothesis” and has led to an expanded mechanism for topoII function incorporating the recognition of Z-DNA segments (“Z-flipons”) as an inherent and essential element. We further propose that the two Zτ domains of the topoII homodimer exhibit a single-turnover “conformase” activity on given G(ate) B-DNA segments (“Z-flipins”), inducing their transition to the left-handed Z-conformation. Inasmuch as the topoII-Z-DNA complexes are isomerase inactive, we infer that they fulfill important structural roles in key processes such as mitosis. Topoisomerases are preeminent targets of anti-cancer drug discovery, and we anticipate that detailed elucidation of their structural–functional interactions with Z-DNA and GTP will facilitate the design of novel, more potent and selective anti-cancer chemotherapeutic agents. Full article
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Graphical abstract

Graphical abstract
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<p>Comparative structures of alternative conformations of dsDNA: <b>left</b>, B-DNA; <b>right</b>, Z-DNA; <b>center</b>, a B-Z composite DNA with an intervening junction. Black dashed arrows indicate handedness (B-DNA, <b>right</b>; Z-DNA, <b>left</b>). Horizontal arrows indicate transitions between depicted dsDNA conformations. The figure was constructed with UCSF Chimera: B-DNA and Z-DNA are modeled structures, and B/Z-DNA is a crystal structure (PDB: 5zup). The helical pitch of B-DNA is 33 nm (10.5 bp/turn), and for Z-DNA, it is 46 nm (12 bp/turn).</p>
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<p>Prior bioinformatic and biochemical modeling instigating the search for a Z-DNA recognition domain of topoII. (<b>A</b>) Representative molecular docking of human HOP2 Zα region (aa 1–74) to Z-DNA [<a href="#B26-ijms-24-10740" class="html-bibr">26</a>]. Potential key amino acid interactions are depicted by thin blue lines. (<b>B</b>) Example of topoII as an allosteric ZBP (left and right). It is subject to competition by molecules (middle) exerting isomerase activity on nsc B-DNA segments. The relaxation process (ellipse with arrow, long curved line) abrogates the Z-conformation (short curved line) in the designated topologically linked segments. The affinity of topoII for Z-DNA is much greater than for B-DNA and increases further in the presence of GTP (topoII*), which also inhibits isomerase function (property 12, <a href="#ijms-24-10740-t001" class="html-table">Table 1</a>). These binding sites are deemed to constitute potential clamps, barriers, and crosslinkers, for example, in chromatin remodeling and mitosis/meiosis. Adapted from Figure 9 of Ref. [<a href="#B8-ijms-24-10740" class="html-bibr">8</a>].</p>
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<p>Canonical triple-gate isomerase mechanism for topoII. A double-helical DNA segment (G) binds to the topoII homodimer (upper left), is bent in the process, and is then cleaved, resulting in covalent protein (tyrosine)-DNA intermediates demarcating a double-strand break (DSB). A second “captured” DNA segment (T) traverses the DSB and is then released, while the G segment is religated, thereby restoring the integrity of the double helix. The intricate, sequential, concerted process is under allosteric control [<a href="#B48-ijms-24-10740" class="html-bibr">48</a>] mediated by ATP binding and turnover ([<a href="#B49-ijms-24-10740" class="html-bibr">49</a>], colored asterisks), divalent cations [<a href="#B50-ijms-24-10740" class="html-bibr">50</a>,<a href="#B51-ijms-24-10740" class="html-bibr">51</a>], and protein domains subject to post-translational modification, notably of the CTD [<a href="#B48-ijms-24-10740" class="html-bibr">48</a>]. The open and closed clamps of stages 1 and 3, respectively, are well depicted in a model of the tobacco enzyme (Figure 6 of Ref. [<a href="#B52-ijms-24-10740" class="html-bibr">52</a>]). Each cycle comprises a dual strand passage and thus changes the topological linking number <span class="html-italic">Lk</span> by ±2. The juxtaposition (a more appropriate term might be apposition) of the G and T segments at the crossover locus is dictated by the 3D structure of the local DNA domain, leading to numerous alternative topological outcomes [<a href="#B53-ijms-24-10740" class="html-bibr">53</a>]: resolution/simplification (relaxation, disentanglement) of plectonemic and toroidal supercoiled (+,−) substructures and reversal/formation of knots and catenanes arising during the processes of DNA transcription, replication, repair, recombination, higher-order chromosomal restructuring during mitosis and meiosis, and processing of closed circular DNA. Interference with DSB formation and resealing is highly genotoxic, and thus, steps 2 and 3 are key targets of antimicrobial and anticancer drugs [<a href="#B54-ijms-24-10740" class="html-bibr">54</a>,<a href="#B55-ijms-24-10740" class="html-bibr">55</a>,<a href="#B56-ijms-24-10740" class="html-bibr">56</a>,<a href="#B57-ijms-24-10740" class="html-bibr">57</a>,<a href="#B58-ijms-24-10740" class="html-bibr">58</a>]. Adapted from Figure 4 of Ref. [<a href="#B30-ijms-24-10740" class="html-bibr">30</a>].</p>
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<p>Structural comparison of Zα domain from human ADAR1p150 and putative Z???? domain from human topoII. (<b>A</b>) Crystal structure of Zα in complex with d(CACGTG) (PDB: 3f21). (<b>B</b>) Cryo-EM structure of the human TOP2A DNA-binding/cleavage domain in State 1 (PDB: 6zy5). Zα or Z???? domains are colored in hot pink, and DNA is colored according to NDB standards (A in red, T in blue, C in yellow, and G in green). (<b>C</b>) Superposition of Zα (ADAR1p150, red) and Z???? (TOP2A 722–812, cyan) domains, canonical designation of helices and β-sheets is indicated. (<b>D</b>) Graph of FATCAT [<a href="#B60-ijms-24-10740" class="html-bibr">60</a>] chaining result intuitively showing structural similarity across all 91 aa-long alignment (thick red diagonals); three gaps are depicted using thin vertical red lines, and non-significant structural similarity is depicted by gray diagonals.</p>
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<p>Domain composition of topoII together with putative Z-DNA-binding domains, Zτ (red), and predicted GTP-binding sites. ATP-binding sites (HATPase_c) and TOP (TOP4C) were annotated using a SMART web server [<a href="#B68-ijms-24-10740" class="html-bibr">68</a>]. (<b>A</b>) Known and newly identified features (Zτ, GTP-binding site, and deleterious SNPs, here depicted as Ds) in human TOP2A. (<b>B</b>) Zτ sequence (722–812), secondary structure, including the proposed “Z-discrimination region” (775–796, underlined residues; <a href="#ijms-24-10740-t003" class="html-table">Table 3</a> below). (<b>C</b>) Evolutionary conservation of Zτ and GTP-binding sites in diverse eukaryotic species.</p>
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<p>Multiple sequence alignment of TOP2 protein sequence in representative species showing very high conservation of the region Zτ constituting the Zα structural homolog (bounded by green and red triangle marks) and putative GTP-binding site. The purple asterisk mark highlights the locus critical for DNA bending. Experimentally validated ATP, Mg<sup>2+</sup>, and DNA-binding sites, together with the critical tyrosine 805 active site, are depicted as well. Columns highlighted in red and yellow show evolutionarily conserved regions/amino acid positions (primary sequence); the resulting consensus sequence is displayed in the bottom row, using criteria from MultAlin [<a href="#B69-ijms-24-10740" class="html-bibr">69</a>]: uppercase is identity, lowercase is consensus level &gt; 0.5, ! is any-one of IV, <span>$</span> is anyone of LM, % is anyone of FY, # is anyone of NDQE.</p>
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<p>DNA Topoisomerase type IIA diversity (<b>A</b>) and GTP-binding (<b>B</b>,<b>C</b>). (<b>A</b>) Known diversity of Topoisomerase type IIA (IPR001241). According to InterPro Database, there are more than 10<sup>5</sup> protein sequences in more than 50,000 different species across the whole tree of life. (<b>B</b>) GTP docked to the crystal structure of human topoII (PDB: 4fm9). Only the immediate surrounding of the docked GTP molecule is shown, but it comprises both the predicted GTP-binding region (in green) and Z????. The tyrosine active site of TOP2A is in red. (<b>C</b>) Sequence logo of the region corresponding to the putative GTP-binding site, and the GxxG/GxxxG motif(s) based on seed alignment of the DNA topoisomerase IV (PF00521) domain. The logo was produced using the Skylign tool [<a href="#B71-ijms-24-10740" class="html-bibr">71</a>].</p>
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<p>Molecular docking for various interacting protein–DNA pairs. The left column is for Zτ from the human protein TOP2A and the right column for Zα from the human protein ADAR1p150, both docked to the indicated nucleic acid structures (B-DNA, Z-DNA, B/Z-DNA, and Z-RNA).</p>
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<p>“B-Z-TopoII”: expanded reaction mechanism of topoII incorporating Z-DNA binding and a postulated conformase activity in addition to its canonical isomerase function. (<b>A</b>) Functional scheme, explained in the text. (<b>B</b>) Details of intermediate states (in square brackets) and outcomes of the isomerase and conformase pathways. The gray shaded area comprises the “DNA manifold” with interconversions between linear and bent conformations that depend on sequence, topological state, solution conditions, and external factors. Straight lines denote interactions between binding partners, leading to reactions (lines with arrows; in reversible reactions, a larger arrowhead indicates preferential state). Configurations of the topoII homodimer: <b>T<sub>o</sub></b>, free; <b>T<sub>B</sub></b>; bound bent (<b>B<sub>b</sub></b>) B-DNA (G-segment); <b>T<sub>Z</sub></b>; configuration bound to bent (<b>Z<sub>b</sub></b>) (G-segment); <b>T<sub>BA</sub></b>, <b>T<sub>B</sub></b> with bound ATP; <b>T<sub>ZG</sub></b>, <b>T<sub>Z</sub></b> with bound GTP. Adapted from Figure 1 in Ref. [<a href="#B78-ijms-24-10740" class="html-bibr">78</a>].</p>
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21 pages, 3045 KiB  
Article
Iridium Complexes with BIAN-Type Ligands: Synthesis, Structure and Redox Chemistry
by Nikolai F. Romashev, Ivan V. Bakaev, Veronika I. Komlyagina, Pavel A. Abramov, Irina V. Mirzaeva, Vladimir A. Nadolinny, Alexander N. Lavrov, Nikolai B. Kompan’kov, Artem A. Mikhailov, Iakov S. Fomenko, Alexander S. Novikov, Maxim N. Sokolov and Artem L. Gushchin
Int. J. Mol. Sci. 2023, 24(13), 10457; https://doi.org/10.3390/ijms241310457 - 21 Jun 2023
Cited by 8 | Viewed by 1729
Abstract
A series of iridium complexes with bis(diisopropylphenyl)iminoacenaphtene (dpp-bian) ligands, [Ir(cod)(dpp-bian)Cl] (1), [Ir(cod)(NO)(dpp-bian)](BF4)2 (2) and [Ir(cod)(dpp-bian)](BF4) (3), were prepared and characterized by spectroscopic techniques, elemental analysis, X-ray diffraction analysis and cyclic voltammetry (CV). [...] Read more.
A series of iridium complexes with bis(diisopropylphenyl)iminoacenaphtene (dpp-bian) ligands, [Ir(cod)(dpp-bian)Cl] (1), [Ir(cod)(NO)(dpp-bian)](BF4)2 (2) and [Ir(cod)(dpp-bian)](BF4) (3), were prepared and characterized by spectroscopic techniques, elemental analysis, X-ray diffraction analysis and cyclic voltammetry (CV). The structures of 13 feature a square planar backbone consisting of two C = C π-bonds of 1,5-cyclooctadiene (cod) and two nitrogen atoms of dpp-bian supplemented with a chloride ion (for 1) or a NO group (for 2) to complete a square-pyramidal geometry. In the nitrosyl complex 2, the Ir-N-O group has a bent geometry (the angle is 125°). The CV data for 1 and 3 show two reversible waves between 0 and -1.6 V (vs. Ag/AgCl). Reversible oxidation was also found at E1/2 = 0.60 V for 1. Magnetochemical measurements for 2 in a range from 1.77 to 300 K revealed an increase in the magnetic moment with increasing temperature up to 1.2 μB (at 300 K). Nitrosyl complex 2 is unstable in solution and loses its NO group to yield [Ir(cod)(dpp-bian)](BF4) (3). A paramagnetic complex, [Ir(cod)(dpp-bian)](BF4)2 (4), was also detected in the solution of 2 as a result of its decomposition. The EPR spectrum of 4 in CH2Cl2 is described by the spin Hamiltonian Ĥ = gβHŜ with S = 1/2 and gxx = gyy = 2.393 and gzz = 1.88, which are characteristic of the low-spin 5d7-Ir(II) state. DFT calculations were carried out in order to rationalize the experimental results. Full article
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Graphical abstract

Graphical abstract
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<p>Synthetic routes toward complexes <b>1</b>–<b>4</b>.</p>
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<p>Molecular structures of (<b>1</b>), cation of (<b>2</b>) and cation of (<b>3</b>) determined by X-ray diffraction analysis.</p>
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<p>CV of <b>1</b> in CH<sub>2</sub>Cl<sub>2</sub> in the −1.6–1.4 V region at a potential scan rate of 100 mV/s (blue spectrum—reduction part, red spectrum—oxidation part).</p>
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<p>EPR spectra of <b>4</b> in CH<sub>2</sub>Cl<sub>2</sub> recorded in the x-band at 77 K (a—experimental, b—simulated).</p>
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<p>(<b>a</b>) Temperature dependence of the magnetic susceptibility, <span class="html-italic">χ</span>, measured for <b>2</b> at the magnetic field <span class="html-italic">H</span> = 10 kOe. (<b>b</b>) Temperature dependences of the effective moment, <span class="html-italic">μ</span><sub>eff</sub> (green symbols), and <span class="html-italic">χ</span><sub>p</sub><span class="html-italic">T</span> (red symbols) for <b>2.</b> The depicted <span class="html-italic">μ</span><sub>eff</sub> was calculated given an assumption of non-interacting magnetic moments (<span class="html-italic">θ</span> = 0). The estimated additive contribution of paramagnetic impurities to <span class="html-italic">χ</span><sub>p</sub><span class="html-italic">T</span> is indicated by the blue dashed line.</p>
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<p>View of selected orbitals: (<b>a</b>) HOMO and LUMO for <b>1</b>, (<b>b</b>) HOMO and LUMO for cation [Ir(cod)(NO)(dpp-bian)]<sup>2+</sup> of <b>2</b>, (<b>c</b>) HOMO-1 and HOMO for triplet state of cation [Ir(cod)(NO)(dpp-bian)]<sup>2+</sup> of <b>2</b>, and (<b>d</b>) HOMO and LUMO for cation [Ir(cod)(dpp-bian)]<sup>+</sup> of <b>3</b>.</p>
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<p>Two isomers of [Ir(cod)(NO)(dpp-bian)]<sup>2+</sup> (cation of <b>2</b>).</p>
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<p>Spin density for paramagnetic <b>v1</b> isomer of [Ir(cod)(NO)(dpp-bian)]<sup>2+</sup> (cation of <b>2</b>) and [Ir(cod)(dpp-bian)]<sup>2+</sup> (cation of <b>4</b>).</p>
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12 pages, 2613 KiB  
Article
Folding Mechanism and Aggregation Propensity of the KH0 Domain of FMRP and Its R138Q Pathological Variant
by Daniele Santorelli, Francesca Troilo, Francesca Fata, Francesco Angelucci, Nicola Demitri, Giorgio Giardina, Luca Federici, Flavia Catalano, Adele Di Matteo and Carlo Travaglini-Allocatelli
Int. J. Mol. Sci. 2022, 23(20), 12178; https://doi.org/10.3390/ijms232012178 - 12 Oct 2022
Cited by 1 | Viewed by 1836
Abstract
The K-homology (KH) domains are small, structurally conserved domains found in proteins of different origins characterized by a central conserved βααβ “core” and a GxxG motif in the loop between the two helices of the KH core. In the eukaryotic KHI type, additional [...] Read more.
The K-homology (KH) domains are small, structurally conserved domains found in proteins of different origins characterized by a central conserved βααβ “core” and a GxxG motif in the loop between the two helices of the KH core. In the eukaryotic KHI type, additional αβ elements decorate the “core” at the C-terminus. Proteins containing KH domains perform different functions and several diseases have been associated with mutations in these domains, including those in the fragile X mental retardation protein (FMRP). FMRP is an RNA-binding protein crucial for the control of RNA metabolism whose lack or mutations lead to fragile X syndrome (FXS). Among missense mutations, the R138Q substitution is in the KH0 degenerated domain lacking the classical GxxG motif. By combining equilibrium and kinetic experiments, we present a characterization of the folding mechanism of the KH0 domain from the FMRP wild-type and of the R138Q variant showing that in both cases the folding mechanism implies the accumulation of an on-pathway transient intermediate. Moreover, by exploiting a battery of biophysical techniques, we show that the KH0 domain has the propensity to form amyloid-like aggregates in mild conditions in vitro and that the R138Q mutation leads to a general destabilization of the protein and to an increased fibrillogenesis propensity. Full article
(This article belongs to the Section Molecular Biophysics)
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Figure 1

Figure 1
<p>Superposition of the three-dimensional structure of the KH0 (green) and KH0-R138Q domain (magenta) of FMRP represented as a cartoon (from pdb codes 4QVZ and 4QW2, respectively). The residues Arg138/Gln138 and Phe189 are shown in stick representation. Secondary structure elements are labeled. The blow-up shows that Arg138 engages in a salt bridge with Glu135 and makes a Pi-cation interaction with Tyr166.</p>
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<p>(<b>a</b>) Far-UV CD spectra recorded at different temperatures of KH0 measured in 20 mM sodium phosphate pH 7.2, 100 mM NaCl. (<b>b</b>) CD thermal denaturation profile of KH0 (full circles) and KH0-R138Q (empty squares) monitored by CD at 222 nm. The curves, fitted to a sigmoidal function, provided an app-T<sub>m</sub> of 68 ± 1 °C and 48 ± 2 °C for KH0 and KH0-R138Q, respectively. (<b>c</b>) Urea-induced denaturation of KH0 (full circles) and KH0-R138Q (empty squares). Fitting of the reversible transitions (black lines) provided the thermodynamic stability (ΔG<sub>DN</sub>) of the two proteins (ΔG<sub>DN</sub> = 5.7 ± 0.3 and 4.7 ± 0.2 kcal mol<sup>−1</sup> for KH0 and KH0-R138Q, respectively). The <span class="html-italic">m</span> value was shared during fitting procedure for both proteins (<span class="html-italic">m</span> = 1.25 ± 0.06 kcal mol<sup>−1</sup> M<sup>−1</sup>).</p>
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<p>Chevron plot of the observed (un)folding rate constants as a function of urea concentration determined by SF (full symbols) or TJ experiments (empty symbols) for (<b>a</b>) W-KH0 and (<b>b</b>) W-KH0-R138Q . The solid black line represents the fit to a three-state model with an on-pathway intermediate.</p>
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<p>Fluorescence spectra recorded after adding a stoichiometric amount of ThT in pre-incubated samples at 70 °C and 20 °C of 20 μM KH0 (<b>a</b>) and KH0-R138Q (<b>b</b>) in 20 mM sodium phosphate pH 7.2 100 mM NaCl. TEM analysis. Transmission electron micrograph of heat-induced fibrils after 2 h incubation at 55 °C of 50 μM KH0 (<b>c</b>) and 50 μM KH0-R138Q (<b>d</b>) The scale bars correspond to 100 nm in both panels. X-ray analysis. X-ray diffraction analysis of KH0 (<b>e</b>) and KH0-R138Q (<b>f</b>); samples (100 μM) were heated at 37 °C for 50 h.</p>
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<p>Kinetics of fibril formation followed by ThT fluorescence analysis at 482 nm (λ<sub>ex</sub> = 440 nm) of KH0 (full squares) and R138Q (empty squares) incubated at 55 °C (<b>a</b>) and 37 °C (<b>b</b>) in 20 mM sodium phosphate pH 7.2, 100 mM NaCl.</p>
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<p>Proposed model for the enhanced aggregation propensity of KH0-R138Q mutant. In the case of KH0-R138Q mutant, a more populated intermediate state (I), due to a higher energy barrier between the I and N state (TS2), could facilitate KH0-R138Q reaching the fibrillar state. It cannot be excluded that the destabilization of the native state of KH0-R138Q with respect to KH0 (N) also plays a role in the fibrillogenesis process.</p>
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24 pages, 5455 KiB  
Article
Comparative Phosphoproteomic Analysis of Sporulated Oocysts and Tachyzoites of Toxoplasma gondii Reveals Stage-Specific Patterns
by Ze-Xiang Wang, Liang Che, Rui-Si Hu and Xiao-Lin Sun
Molecules 2022, 27(3), 1022; https://doi.org/10.3390/molecules27031022 - 2 Feb 2022
Cited by 2 | Viewed by 2556
Abstract
Toxoplasma gondii is an obligate intracellular protozoan of severe threat to humans and livestock, whose life history harbors both gamic and apogamic stages. Chinese 1 (ToxoDB#9) was a preponderant genotype epidemic in food-derived animals and humans in China, with a different pathogenesis from [...] Read more.
Toxoplasma gondii is an obligate intracellular protozoan of severe threat to humans and livestock, whose life history harbors both gamic and apogamic stages. Chinese 1 (ToxoDB#9) was a preponderant genotype epidemic in food-derived animals and humans in China, with a different pathogenesis from the strains from the other nations of the world. Posttranslational modifications (PTMs) of proteins were critical mediators of the biology, developmental transforms, and pathogenesis of protozoan parasites. The phosphoprotein profiling and the difference between the developmental phases of T. gondii, contributing to development and infectivity, remain unknown. A quantitative phosphoproteomic approach using IBT integrated with TiO2 affinity chromatography was applied to identify and analyze the difference in the phosphoproteomes between the sporulated oocysts and the tachyzoites of the virulent ToxoDB#9 (PYS) strain of T. gondii. A total of 4058 differential phosphopeptides, consisting of 2597 upregulated and 1461 downregulated phosphopeptides, were characterized between sporulated the oocysts and tachyzoites. Twenty-one motifs extracted from the upregulated phosphopeptides contained 19 serine motifs and 2 threonine motifs (GxxTP and TP), whereas 16 motifs identified from downregulated phosphopeptides included 13 serine motifs and 3 threonine motifs (KxxT, RxxT, and TP). Beyond the traditional kinases, some infrequent classes of kinases, including Ab1, EGFR, INSR, Jak, Src and Syk, were found to be corresponding to motifs from the upregulated and downregulated phosphopeptides. Remarkable functional properties of the differentially expressed phosphoproteins were discovered by GO analysis, KEGG pathway analysis, and STRING analysis. S8GFS8 (DNMT1-RFD domain-containing protein) and S8F5G5 (Histone kinase SNF1) were the two most connected peptides in the kinase-associated network. Out of these, phosphorylated modifications in histone kinase SNF1 have functioned in mitosis and interphase of T. gondii, as well as in the regulation of gene expression relevant to differentiation. Our study discovered a remarkable difference in the abundance of phosphopeptides between the sporulated oocysts and tachyzoites of the virulent ToxoDB#9 (PYS) strain of T. gondii, which may provide a new resource for understanding stage-specific differences in PTMs and may enhance the illustration of the regulatory mechanisms contributing to the development and infectivity of T. gondii. Full article
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Figure 1

Figure 1
<p>Large-scale information regarding the phosphoproteomic research between sporulated oocysts and tachyzoites of the <span class="html-italic">T. gondii</span> PYS strain. (<b>A</b>) The distribution of phosphopeptides on different peptide lengths. (<b>B</b>) The proportion of mono-phosphosites and multi-phosphosites among total phosphopeptides showed that a large part of the phosphopeptides have single phosphosites. (<b>C</b>) Proportion of the pSer/pThr/pTyr phosphoproteome. Phospho-pSer, phospho-pThr, and phospho-pTyr accounted for 86.27% of all phosphosites, 9.28% of all phosphosites, and 0.42% of all phosphosites, respectively. (<b>D</b>) Distribution of phosphosites on phosphoproteins. Most phosphoproteins included single phosphosites.</p>
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<p>Repeatability analysis of the phosphopeptide quantification founded on the value of CV (coefficient of variation). The <span class="html-italic">x</span>-axis represents the percentage values of CV. The quantities of phosphopeptides and the accumulative proportion of phosphopeptides are indicated by the left and right <span class="html-italic">y</span>-axis, respectively.</p>
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<p>Quantitative analysis of characterized phosphopeptides. (<b>A</b>) Scatter plot of quantified phosphopeptides. The log<sub>2</sub> fold change value and −log<sub>10</sub> <span class="html-italic">p</span> value of phosphopeptides are indicated by the <span class="html-italic">x</span>-axis and the <span class="html-italic">y</span>-axis, respectively. The red circles and green circles denote upregulated and downregulated DEPs, respectively. (<b>B</b>) Distribution of upregulated DEPs and downregulated DEPs between the sporulated oocysts and tachyzoites on different levels. The <span class="html-italic">x</span>-axis and <span class="html-italic">y</span>-axis indicate the values of changes and the quantity of DEPs. The red color and green color represent upregulated DEPs and downregulated DEPs, respectively.</p>
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<p>Hierarchical clustering analysis of DEPs. Log1.5 fold change value of DEPs is denoted by different colors.</p>
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<p>Phosphorylation site motif analysis of the upregulated DEPs using Motif-X. The degree of amino acids emerging at specific locations is represented by the elevation of the symbols.</p>
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<p>Phosphorylation site motif analysis of the downregulated DEPs using Motif-X. The degree of amino acids emerging at specific locations is represented by the elevation of the symbols.</p>
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<p>GO enrichment analysis of DEPs. (<b>A</b>) GO enrichment analysis of upregulated DEPs. (<b>B</b>) GO enrichment analysis of downregulated DEPs. The number of DEPs and GO terms are displayed on the horizontal axis and vertical axis, respectively.</p>
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<p>KEGG pathway enrichment analysis of DEPs between sporulated oocysts and tachyzoites. The <span class="html-italic">y</span>-axis indicates the KEGG pathways DEPs significantly enriched and the <span class="html-italic">x</span>-axis denotes the rich factors of the pathways. Rich factor implies the proportion of DEPs among total phosphoproteins in the pathway. Greater degrees of enrichment are indicated by higher rich factors. The color and size of the node represent the <span class="html-italic">p</span> value and quantity of phosphoproteins of the corresponding pathways.</p>
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<p>Protein–protein interaction (PPI, combined score ≥ 0.9) network of the DEPs between sporulated oocysts and tachyzoites. The nodes indicate DEPs and the lines between the nodes refer to the interactors between DEPs. The color of the edge symbolizes the combined score of the interacting partners.</p>
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<p>Network of kinase-phosphopeptide partners and potential phosphor- reliant interactions determined by correlation analysis. Light red nodes denoted phosphoproteins and edges represented interactors between phosphoproteins. The gray arrow denotes protein interactions which are presumed to be activated by the phosphorylation and green arrows represents protein interactions that are presumed to be inactivated by the phosphorylation.</p>
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26 pages, 1707 KiB  
Article
About the Use of Generalized Forms of Derivatives in the Study of Electromagnetic Problems
by Giulio Antonini, Giuseppe Dattoli, Fabrizio Frezza, Silvia Licciardi and Fabrizio Loreto
Appl. Sci. 2021, 11(16), 7505; https://doi.org/10.3390/app11167505 - 16 Aug 2021
Cited by 1 | Viewed by 1454
Abstract
The use of non-local operators, defining Riemann–Liouville or Caputo derivatives, is a very useful tool to study problems involving non-conventional diffusion problems. The case of electric circuits, ruled by non-integer derivatives or capacitors with fractional dielectric permittivity, is a fairly natural frame of [...] Read more.
The use of non-local operators, defining Riemann–Liouville or Caputo derivatives, is a very useful tool to study problems involving non-conventional diffusion problems. The case of electric circuits, ruled by non-integer derivatives or capacitors with fractional dielectric permittivity, is a fairly natural frame of relevant applications. We use techniques, involving generalized exponential operators, to obtain suitable solutions for this type of problems and eventually discuss specific problems in applications. Full article
(This article belongs to the Special Issue Advanced Technologies in Electromagnetic Compatibility)
Show Figures

Figure 1

Figure 1
<p>Solution <math display="inline"><semantics> <mrow> <mi>F</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo>,</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> </semantics></math> of Equation (<a href="#FD21-applsci-11-07505" class="html-disp-formula">21</a>) at different times <span class="html-italic">t</span>, for <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>=</mo> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> </semantics></math> and initial function <math display="inline"><semantics> <mrow> <mi>f</mi> <mo stretchy="false">(</mo> <mo>.</mo> <mo stretchy="false">)</mo> </mrow> </semantics></math> being a Gaussian.</p>
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<p>Comparison between the solutions of Equations (<a href="#FD17-applsci-11-07505" class="html-disp-formula">17</a>) and (<a href="#FD23-applsci-11-07505" class="html-disp-formula">23</a>) for <math display="inline"><semantics> <mrow> <mi>v</mi> <mo>=</mo> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> </semantics></math> and different values of <span class="html-italic">t</span>. (<b>a</b>) <span class="html-italic">t</span> = 0.5; (<b>b</b>) <span class="html-italic">t</span> = 1.</p>
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<p>Comparison between the solutions of Equation (<a href="#FD17-applsci-11-07505" class="html-disp-formula">17</a>) for different values of <span class="html-italic">α</span> and <span class="html-italic">t</span>. (<b>a</b>) <span class="html-italic">t</span> = 0.5; (<b>b</b>) <span class="html-italic">t</span> = 1.</p>
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<p>Equation (<a href="#FD29-applsci-11-07505" class="html-disp-formula">29</a>) for different values of <span class="html-italic">β</span>, <math display="inline"><semantics> <mrow> <mi>v</mi> <mo>=</mo> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> </semantics></math> and <span class="html-italic">f</span>(<span class="html-italic">x</span>) Gaussian or super-Gaussian function. (<b>a</b>) <math display="inline"><semantics> <mrow> <mi>f</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>=</mo> <msup> <mi>e</mi> <msup> <mrow> <mo>−</mo> <mi>x</mi> </mrow> <mn>2</mn> </msup> </msup> </mrow> </semantics></math> (<b>b</b>) <math display="inline"><semantics> <mrow> <mi>f</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>=</mo> <msup> <mi>e</mi> <msup> <mrow> <mo>−</mo> <mi>x</mi> </mrow> <mn>4</mn> </msup> </msup> </mrow> </semantics></math>.</p>
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<p>Equation (<a href="#FD29-applsci-11-07505" class="html-disp-formula">29</a>) for different values of <span class="html-italic">β</span>, <math display="inline"><semantics> <mrow> <mi>v</mi> <mo>=</mo> <mfrac> <mn>1</mn> <mn>3</mn> </mfrac> </mrow> </semantics></math> and <span class="html-italic">f</span>(<span class="html-italic">x</span>) Gaussian or super-Gaussian function. (<b>a</b>) <math display="inline"><semantics> <mrow> <mi>f</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>=</mo> <msup> <mi>e</mi> <msup> <mrow> <mo>−</mo> <mi>x</mi> </mrow> <mn>2</mn> </msup> </msup> </mrow> </semantics></math> (<b>b</b>) <math display="inline"><semantics> <mrow> <mi>f</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>=</mo> <msup> <mi>e</mi> <msup> <mrow> <mo>−</mo> <mi>x</mi> </mrow> <mn>4</mn> </msup> </msup> </mrow> </semantics></math>.</p>
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<p>Equation (<a href="#FD29-applsci-11-07505" class="html-disp-formula">29</a>) for different values of <span class="html-italic">β</span>, <math display="inline"><semantics> <mrow> <mi>v</mi> <mo>=</mo> <mfrac> <mn>2</mn> <mn>3</mn> </mfrac> </mrow> </semantics></math> and <span class="html-italic">f</span>(<span class="html-italic">x</span>) Gaussian or super-Gaussian function. (<b>a</b>) <math display="inline"><semantics> <mrow> <mi>f</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>=</mo> <msup> <mi>e</mi> <msup> <mrow> <mo>−</mo> <mi>x</mi> </mrow> <mn>2</mn> </msup> </msup> </mrow> </semantics></math> (<b>b</b>) <math display="inline"><semantics> <mrow> <mi>f</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>=</mo> <msup> <mi>e</mi> <msup> <mrow> <mo>−</mo> <mi>x</mi> </mrow> <mn>8</mn> </msup> </msup> </mrow> </semantics></math>.</p>
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<p>Solutions of RC circuit (<a href="#FD38-applsci-11-07505" class="html-disp-formula">38</a>) in ordinary and fractional cases with initial function <span class="html-italic">f</span>(.) = cos(.). (<b>a</b>) Potential across the capacitor (<a href="#FD40-applsci-11-07505" class="html-disp-formula">40</a>) (<span class="html-italic">Q</span>(<span class="html-italic">t</span>)) and external potential (<span class="html-italic">V</span>(<span class="html-italic">t</span>)); (<b>b</b>) Fractional case for potential across the capacitor (Π(<span class="html-italic">t</span>)) for different values of <span class="html-italic">γ</span>.</p>
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<p>Same comparison as <a href="#applsci-11-07505-f007" class="html-fig">Figure 7</a> between Θ(<span class="html-italic">t</span>) in (<a href="#FD56-applsci-11-07505" class="html-disp-formula">56</a>) and <span class="html-italic">f</span>(<span class="html-italic">t</span>) in (<a href="#FD55-applsci-11-07505" class="html-disp-formula">55</a>), for <span class="html-italic">α<sub>γ</sub></span> = 0.2 and <span class="html-italic">σ<sub>γ</sub></span> = 1. (<b>a</b>) Non-fractional RL circuit; (<b>b</b>) Solutions of fractional RL circuit, Θ(<span class="html-italic">t</span>), for different values of <span class="html-italic">γ</span>.</p>
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<p>Solution Θ<span class="html-italic"><sub>γ</sub></span>(<span class="html-italic">t</span>) with different <span class="html-italic">f</span>(<span class="html-italic">t</span>) and <span class="html-italic">γ</span> values. (<b>a</b>) Ordinary circuit (<a href="#FD40-applsci-11-07505" class="html-disp-formula">40</a>) with different <span class="html-italic">f</span>(<span class="html-italic">x</span>), Gaussian or Super-Gaussian; (<b>b</b>) Comparison between fractional and ordinary circuits for Equation (<a href="#FD57-applsci-11-07505" class="html-disp-formula">57</a>), with <math display="inline"><semantics> <mrow> <mi>f</mi> <mo stretchy="false">(</mo> <mi>η</mi> <mo stretchy="false">)</mo> <mo>=</mo> <msup> <mi>e</mi> <msup> <mrow> <mo>−</mo> <mi>η</mi> </mrow> <mn>2</mn> </msup> </msup> </mrow> </semantics></math> for different values of <span class="html-italic">γ</span>, and Equation (<a href="#FD40-applsci-11-07505" class="html-disp-formula">40</a>).</p>
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<p>Solutions of Equation (<a href="#FD58-applsci-11-07505" class="html-disp-formula">58</a>) for <math display="inline"><semantics> <mrow> <msub> <mi>y</mi> <mn>0</mn> </msub> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>f</mi> <mrow> <mo stretchy="false">(</mo> <mi>τ</mi> <mo stretchy="false">)</mo> </mrow> <mo>=</mo> <msup> <mi>e</mi> <mrow> <mo>−</mo> <msup> <mi>x</mi> <mn>2</mn> </msup> </mrow> </msup> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>γ</mi> <mo>=</mo> <mn>0.5</mn> </mrow> </semantics></math>.</p>
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<p>Equation (<a href="#FD59-applsci-11-07505" class="html-disp-formula">59</a>) for different values of <math display="inline"><semantics> <mi>γ</mi> </semantics></math>.</p>
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<p>Solution <math display="inline"><semantics> <mrow> <mover> <mi>i</mi> <mo stretchy="false">¯</mo> </mover> <mrow> <mo stretchy="false">(</mo> <mi>τ</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </semantics></math> for different values of <math display="inline"><semantics> <mrow> <mi>A</mi> <mo>=</mo> <msub> <mi>ω</mi> <mn>0</mn> </msub> <msub> <mi>τ</mi> <mi>L</mi> </msub> </mrow> </semantics></math>.</p>
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<p>Solution <math display="inline"><semantics> <mrow> <msub> <mover> <mi>i</mi> <mo stretchy="false">¯</mo> </mover> <mi>P</mi> </msub> <mrow> <mo stretchy="false">(</mo> <mi>τ</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </semantics></math> for different values of <span class="html-italic">A</span>, <span class="html-italic">α</span>, <span class="html-italic">γ</span>, <span class="html-italic">κ</span>. (<b>a</b>) Different values of <math display="inline"><semantics> <mrow> <mi>A</mi> <mo>=</mo> <msub> <mi>ω</mi> <mn>0</mn> </msub> <msub> <mi>τ</mi> <mi>L</mi> </msub> </mrow> </semantics></math> with <span class="html-italic">α</span> = 0.2, <span class="html-italic">γ</span> = <span class="html-italic">κ</span> = 0.5; (<b>b</b>) Different values of <span class="html-italic">α</span> with <span class="html-italic">A</span> = 1, <span class="html-italic">γ</span> = <span class="html-italic">κ</span> = 0.5; (<b>c</b>) Different values of <span class="html-italic">γ</span> with <span class="html-italic">A</span> = 1 and <span class="html-italic">α</span> = <span class="html-italic">κ</span> = 0.5; (<b>d</b>) Different values of <span class="html-italic">κ</span> with <span class="html-italic">A</span> = 1 and <span class="html-italic">α</span> = <span class="html-italic">γ</span> = 0.5.</p>
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<p>Normalized source voltage.</p>
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<p>Time-domain behavior of the normalized charge using the four dielectric laws proposed.</p>
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<p>Time-domain comparison for the normalized charge considering the Havriliak–Negami dielectric.</p>
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<p>Solution with <math display="inline"><semantics> <mrow> <mi>τ</mi> <mo>=</mo> <mn>153</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>=</mo> <mn>0.4</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>β</mi> <mo>=</mo> <mn>0.1</mn> </mrow> </semantics></math> and different values of <math display="inline"><semantics> <mi>κ</mi> </semantics></math>.</p>
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<p><math display="inline"><semantics> <mrow> <mo>∣</mo> <mi mathvariant="sans-serif">Ψ</mi> <mrow> <mo stretchy="false">(</mo> <mi>η</mi> <mo>,</mo> <mi>τ</mi> <mo stretchy="false">)</mo> </mrow> <msup> <mo>∣</mo> <mn>2</mn> </msup> </mrow> </semantics></math> vs. <math display="inline"><semantics> <mi>η</mi> </semantics></math> for different values of <math display="inline"><semantics> <mi>τ</mi> </semantics></math>, by reference to Equation (<a href="#FD89-applsci-11-07505" class="html-disp-formula">89</a>).</p>
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<p><math display="inline"><semantics> <mrow> <mo>∣</mo> <mi>ψ</mi> <mrow> <mo stretchy="false">(</mo> <mi>ξ</mi> <mo>,</mo> <mi>σ</mi> <mo stretchy="false">)</mo> </mrow> <msup> <mo>∣</mo> <mn>2</mn> </msup> </mrow> </semantics></math> vs. <math display="inline"><semantics> <mi>ξ</mi> </semantics></math> for different <math display="inline"><semantics> <mi>σ</mi> </semantics></math> values.</p>
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