JP4947573B2 - Microarray data analysis method and analyzer - Google Patents

Description

  The present invention relates to a method and an apparatus for analyzing data obtained by a microarray experiment.

  Affymetrix's GeneChip type microarrays, also called DNA chips, are capable of simultaneously and quantitatively measuring the concentration of thousands of DNA / RNA. It is formed by arranging DNA molecules (probes) at high density on a small substrate.

  The concentration of the target can be known by hybridizing the probe on the microarray and the target to be analyzed, measuring the signal obtained from each probe, digitizing it, and analyzing it. Conventionally, various apparatuses and methods have been researched and developed as data analysis techniques in microarray experiments (see Patent Documents 1 to 3, etc.).

  When microarrays are used to measure very many types of DNA fragments, such as transcriptomes, various targets that partially match the sequence bind, not the complementary target corresponding to the probe sequence ( Non-specific binding, hereinafter referred to as “cross-hybridization”).

  This cross-hybridization adds the target target to the true signal value bound to the probe, so that it is treated as a noise component in the measurement value. In particular, when the concentration of the target of interest in the sample is low, it is difficult to distinguish between the signal component due to the true target and the signal component due to the effect of cross-hybridization, reducing the reliability of the measurement results. It is a big factor.

  As a method for solving such a problem, there is an algorithm using a mismatch probe implemented in analysis software of Affymetrix.

  The Affymetrix GeneChip (registered trademark) microarray has a mismatch that has a sequence that differs from the PM probe sequence by one base in addition to a probe that has a sequence complementary to the target of interest (Perfect Match (PM) probe). MisMatch (MM)) probe is synthesized. This algorithm assumes that there is not much difference in the effect of cross-hybridization between the PM probe and MM probe, and the effect of cross-hybridization can be canceled by subtracting the signal value of the MM probe from the signal value of the PM probe. Based on the idea.

Japanese Patent Laid-Open No. 2004-016131 JP 2004-013573 A International Publication No. WO2002 / 001477 Specification

  However, in practice, the effects of cross-hybridization often differ greatly between PM probes and MM probes, so the values obtained by the above algorithm are not necessarily signal values that exclude the effects of cross-hybridization. It does not reflect. As a result, the error appears as large noise, which is a factor of reducing the reliability of data. In particular, a target having a low concentration has been conventionally difficult to measure because a signal to be measured is buried in noise.

  The present invention has been made to solve the above-mentioned problems, and the object of the present invention is an analysis method for improving the accuracy of gene expression level analysis by removing the influence of noise from the signal value in a microarray experiment, and To provide an analysis device.

  In a first aspect of the present invention, there is provided a microarray analysis method for obtaining a concentration of a target contained in a solution using a microarray in which a plurality of probes are arranged.

  In the analysis method, the microarray includes a plurality of measurement probes having a base sequence corresponding to the base sequence of the target to be analyzed, and a plurality of random probes having a base sequence not corresponding to the base sequence of the target to be analyzed. .

The microarray analysis method includes the following steps:
1) a step of hybridizing a solution containing the target and each probe of the microarray,
2) a step of measuring the fluorescence intensity of each probe, and a step of determining the amount (t ^ns ) of a background target that is a target non-specifically bound to the probe from the measurement value of the fluorescence intensity of the random probe;
3) predicting the degree of influence (NS _i ) of cross-hybridization on the measurement value of the fluorescence intensity of the measurement probe based on the amount of the background target and the binding energy of each probe;
4) A step of obtaining the amount (t ^t _i ) of the target to be analyzed by excluding the degree of influence of cross hybridization from the measured value (I ^m _i ) of the fluorescence intensity of the measurement probe.

In the microarray analysis method, a model indicating an equilibrium between possible states of the probe may be defined, and the amount (t ^ns ) of the background target may be obtained using the model. The state of the probe in the model includes a state where the probe is free in solution, a state where the probe and the background target are non-specifically bound, and a state where the probe is folded by self-hybridization and has a secondary structure. May be included. In this case, the microarray analysis method further includes a step of hybridizing only a sample obtained by fragmenting the genome to be analyzed with a probe on the microarray, a step of measuring the fluorescence intensity of the random probe by the hybridization, and a measurement value thereof. And determining parameters (w ^pf , ε ^ns ) for determining the equilibrium constant of the model.

Or, the probe is further in a state where the target is free in solution, the target is folded by self-hybridization and has a secondary structure, and the probe and the background target are specifically bound. A state may be included. At this time, the binding energy is a parameter for obtaining the equilibrium constant of the model. In this case, the microarray analysis method further comprises a step of hybridizing a mixture of a sample obtained by fragmenting the genome to be analyzed and a DNA whose concentration has been determined with a probe on the microarray, and the fluorescence intensity of the measurement probe by hybridization. And a step of ^obtaining parameters (w ^tf , ε ^s ) for ^obtaining the binding energy based on the measured value.

  In the microarray analysis method described above, a step of hybridizing a part of a plurality of random probes with a DNA having a base sequence corresponding to the base sequence of the part of the probe and having a determined concentration; Measuring the fluorescence intensity of the probe, and determining a proportionality constant between the fluorescence intensity of the probe and the target concentration based on the measured value of the fluorescence intensity of some probes and the determined value of the DNA concentration. May be included.

  In a second aspect of the present invention, there is provided a microarray analyzer for analyzing a signal from a microarray in which a plurality of probes are arranged to determine the concentration of a target in a sample solution.

The analysis apparatus includes data storage means for storing information on a model used for analysis, and input means for inputting a measurement value of the fluorescence intensity of each probe obtained as a result of hybridization of a solution containing the target and each probe of the microarray. And processing means for calculating a target concentration (t ^t _i ) from the inputted measurement value of the fluorescence intensity using information on the model. The processing means obtains the amount (t ^ns ) of the background target, which is a target that non-specifically binds to the probe, from the measurement value of the fluorescence intensity of the input random probe, and the amount of the background target and the binding energy of each probe. Based on the above, the degree of influence of cross-hybridization (NS _i ) on the measurement value of fluorescence intensity of the measurement probe is predicted, and the degree of influence of cross-hybridization is excluded from the measurement value of fluorescence intensity (I ^m _i ) of the measurement probe. Thus, the amount (t ^t _i ) of the target to be analyzed is obtained.

  In a third aspect of the present invention, there is provided an analysis program for causing a computer to execute a process of analyzing a signal from a microarray in which a plurality of probes are arranged and obtaining a target concentration in a sample solution.

The analysis program inputs a measurement value of the fluorescence intensity of each probe obtained as a result of hybridization of the solution containing the target and each probe of the microarray and the measurement value of the fluorescence intensity of the input random probe to the probe. Cross-hybridization in the measurement value of the fluorescence intensity of the measurement probe based on the step of ^obtaining the amount (t ^ns ) of the background target that is a non-specific binding target and the amount of the background target and the binding energy of each probe the impact and the step of predicting (NS _i), the measurement value of the fluorescence intensity of the measuring probe (I ^m _i) to exclude the influence of cross-hybridization of the amount of target to be analyzed (t ^t _i) And causing the computer to execute

  According to the present invention, the amount of a target (background target) that causes cross-hybridization is calculated from the fluorescence intensity of a probe (random probe) having a base sequence that does not correspond to the target to be analyzed. Then, based on the binding energy of each probe, the influence of the background target on the fluorescence intensity is evaluated, and the concentration of the target to be analyzed is obtained in a form that excludes this influence. According to this method, since the influence (noise) due to the background target can be eliminated in the measured value of the fluorescence intensity, the true target concentration can be accurately obtained. In particular, it is possible to appropriately evaluate a low concentration target that has been buried in noise due to cross hybridization and cannot be measured.

  Embodiments of a microarray analysis method and an analysis apparatus according to the present invention will be described below with reference to the accompanying drawings.

  The microarray analysis method and analysis apparatus of the present invention predict the magnitude of the effect of cross-hybridization (non-specific binding) based on the binding energy of the base sequence of the probe of the microarray, and the actual fluorescence intensity signal value. It is possible to obtain the concentration of the target to be analyzed with high accuracy. In the following description, an RNA / DNA fragment in a sample that binds to a probe randomly regardless of the base sequence of the target of interest is referred to as a “background target”.

1. Microarray FIG. 1 shows a probe configuration of a microarray used in the microarray analysis method of the present invention. The microarray 10 is designed to include three types of probes: a measurement probe 11, a random probe 13, and a control probe 15.

  The measurement probe 11 is a probe having a base sequence complementary to the genome of a target cell for use in the original measurement, and basically the same probe as that of a conventional microarray can be used.

  The random probe 13 is a probe for evaluating the influence of cross hybridization. The random probe is a probe having a sequence artificially created based on a random number so that the corresponding base sequence is not included in the genome of the target cell. Align each random probe with the genome of the target cell as an indicator that “the corresponding sequence is not included in the genome of the target cell”, and the average length of the consecutive partial sequences matched Is less than 1/2 of the probe length. Since the corresponding DNA / RNA is not contained in the sample to be measured, it is considered that the fluorescence intensity exhibited by the random probe 13 is entirely due to the influence of cross hybridization.

  A part of the random probe 13 is assigned as the control probe 15. Control probe 15 is used to compare the intensity of the signal with the absolute amount of the target concentration. That is, an oligonucleotide having a corresponding sequence is artificially synthesized with respect to the control probe, and this is added to the sample at a constant concentration to bind to the control probe. At this time, by comparing the intensity of the signal obtained from the control probe with the absolute amount of the concentration of the oligonucleotide having the corresponding sequence, a correlation between the signal intensity and the absolute amount of the target concentration is obtained.

2. Microarray Analysis Method Hereinafter, details of the microarray analysis method of the present invention will be described.

2.1 Evaluation of Cross-Hybridization Effect In the present invention, first, the amount of target bound by cross-hybridization is predicted. Specifically, the total amount of binding when an unspecified number of targets partially bind to one type of probe is modeled in the form of an average binding energy of the unspecified number of targets. . After that, a preliminary experiment is performed, and various parameters of the model are optimized by a numerical analysis method so as to minimize an error between the actually measured value of the preliminary experiment and the predicted value of the model. Based on the parameters, the actual measurement values are corrected while evaluating the influence of cross-hybridization on each probe.

2.1.1 Model First, a model for evaluating the influence of cross hybridization will be described.

  A model for predicting the fluorescence intensity of the probe i when the base sequence of the probe i (i-th probe) is given will be described. Here, a model of the fluorescence intensity of the random probe 13 due to the influence of cross hybridization is considered, and a target having a base sequence corresponding to the base sequence of the random probe 13 is not included in the sample solution.

In this embodiment, as shown in FIG. 2, the probe can be in a free state P ^fr _i (FIG. 2 (a)), a background target (non-specific target) by cross-hybridization. ) In a non-specifically bound state PT ^ns _i (FIG. 2 (c)) and a state P ^fo _i (FIG. 2 (b)) in a secondary structure folded by self-hybridization. Think about two states. Then, consider the following three equilibria in the model.

-Equilibrium between linear / folded states due to probe self-hybridization (see equation (1))
-Equilibrium between single strands / double strands by cross-hybridization between probe and target (see equation (2)).

From the relationship of the above equation, the following equation is obtained.

Ｒは気体定数、Ｔはハイブリダイゼーション条件の絶対温度である。 The equilibrium constants K ^pf _i and K ^ns _i can be obtained by the following equations if the free energy ΔG of each reaction is given.

R is the gas constant and T is the absolute temperature of the hybridization conditions.

Let v be the volume of the effective space on the microarray 10 where the sample and probe interact. The total amount of the probe i can be expressed by p ^t v. p ^t v is considered to be a constant independent of the type of probe. The effective concentration [P ^fr _i ] of the probe in the free state in the space v is p _i, and the effective concentration [T ^ns ] of the entire target that interacts non-specifically with the probe i is t ^ns . deep. Since the total amount t ^ns v background target is considered to be sufficiently larger than the total p ^t v of the probe i, if t ^ns is considered constant, equation (3), the following equation (4) and mass conservation law give It is done.

ここで、Ｃはスケーリングの比例定数、bgは計測機器の機械的な影響によるバックグラウンドを表す。 Assuming that the fluorescence intensity of the probe is proportional to the amount of bound target [PT ^ns _i ] v, the fluorescence intensity of probe i by cross-hybridization can be obtained from the following equations from equations (4) and (6).

Here, C is a proportional constant of scaling, and bg is a background due to the mechanical influence of the measuring device.

C, p ^t , and bg can be considered as constants independent of experiments. The value of bg simply given by the minimum value of all signal values, also the product C · p ^t the target is present in excess, the probe corresponds to the maximum fluorescence intensity when saturated. Therefore, if the background target amount t ^ns and the K ^pf _i and K ^ns _{i of} the probe _i are known, the expected fluorescence intensity I ^ns _i can be calculated.

2.1.2 Evaluation of the free energy in the folded state In order to calculate the equilibrium constant K ^pf _i for evaluating the amount of the probe in the folded state, the free energy ΔG ^pf _i of the secondary structure of the probe is obtained. Previous studies have shown that the free energy of RNA and DNA secondary structures can be predicted from a given base sequence using a dynamic programming technique (D. Mathews, J. Sabina, M. Zuker, and D. Turner. Expanded sequence dependence of thermodynamic parameters improves prediction of rna secondary structure. J. Mol. Biol., 288 (5): 91140, 1999.), a prediction program MFOLD1 based on that algorithm was released Yes. In the present invention, this program is used to predict the secondary structure of the DNA of each probe, and the equilibrium constant obtained from the free energy is used to evaluate the influence of the secondary structure of the probe. However, the model used in MFOLD1 is based on experiments with free DNA molecules in solution, and the conditions differ from molecules immobilized on solid surfaces such as microarray probes. In the present invention, a value obtained by multiplying the free energy obtained by MFOLD1 by a weighting coefficient w ^pf is used for actual evaluation.
Free energy ΔG ^pf _i used for evaluation
= (Free energy of the secondary structure of the probe determined by MFOLD1) × w ^pf

2.1.3 Nonspecific Nearest Neighbor Model In order to calculate the equilibrium constant K ^ns _i for assessing the amount of non-specifically bound probe, the binding energy ΔG ^{ns of the} probe / background target cross-hybridization _{Find i} .

  According to previous studies, it is known that the binding energy of hybridization between a probe and a target can be predicted from a probe base sequence by a calculation method called a Nearest Neighbor (NN) model (J. SantaLucia. A unified view of polymer, Dumbbell, and oligonucleotide dna nearest-neighbor thermodynamics. Proc. Natl. Acad. Sci. USA, 95 (4): 14605, 1998.). In the present invention, the concept of this model is expanded, and the total amount of partial binding between the probe and an unspecified number of targets is approximately obtained in the form of their average binding energy.

In this embodiment, the non-specific binding energy ε ^ns for each base of the probe is considered as an amount depending on the combination of the base and the bases before and after the base, and the total binding energy ΔG is calculated as the sum. If the type of the k-th base in the probe is given by b _k , the binding energy ΔG ^ns is obtained by the following equation.

For example, when the base sequence “ATGCTTCG” is given, the average binding energy of the probe is calculated as follows.

There are 32 combinations of the three base combinations when the sequences that can be regarded as the same combination are inverted by reversing the combinations such as “ATG” and “CAT” out of all 64 combinations. In addition to this, when considering the case where the end of the sequence is included as in “AT” as another combination, the required parameter ε ^ns is 48.

2.2 Evaluation of Signal Excluding Cross-Hybridization Effect Next, based on the above-described cross-hybridization evaluation model, a signal (target high-frequency signal) excluding the influence of cross-hybridization from the fluorescence intensity in the actual measurement. A model for obtaining a fluorescence intensity measurement value by hybridization will be described.

2.2.1 When a target corresponding to the sequence of the model probe i is included in the sample, a model that predicts the fluorescence intensity including the influence of cross-hybridization is constructed. Consider the following four equilibria in the model:

-Equilibrium between linear (Fig. 2 (a)) / folded state (Fig. 2 (b)) by probe self-hybridization (see equation (10))
-Equilibrium between linear (figure 2 (f)) / folded state (figure 2 (e)) by target self-hybridization (see equation (11))
-Equilibrium between single-stranded (Fig. 2 (a), (f)) / double-stranded (Fig. 2 (d)) by specific hybridization of the probe with the target of interest (formula (12) reference)
-Equilibrium between single strand (Fig. 2 (a), (g)) / double strand (Fig. 2 (c)) by cross-hybridization between probe and background target (see formula (13)) )

The following relationship is obtained from these state transition models.

ただし、バックグラウンドターゲットの総量ｔ^nsｖはプローブiの総量ｐ^tｖより十分に多いと考えられるのでｔ^nsは一定と見なしている。プローブの蛍光強度Ｉ^s _iは、特異的に結合したターゲットの量とクロスハイブリダイゼーションの量の和([ＰＴ^s _i]+[ＰＴ^ns _i])ｖに比例すると考えると、実効的な平衡定数Ｋ^ef _iを用いて式（２１）〜式（２３）で得られる。

Similar to section 2.1, the volume of the effective space sample and probe to interact on the microarray 10 v, the total amount of probe i and expressed by p ^t v, p ^t v does not depend on the type of probe constants I believe that. The effective concentration of the probe in the free state [P ^fr _i] of in space v p _i Distant, effective concentration of the entire target that interact probe i and nonspecific [T ^ns] a t ^ns far. The concentration of the charged target that interact specifically with probe i in the sample and t ^t _i, when the concentration of free target in solution and expressed by t ^fr _i, the equation (14) to (17) Weight The following relation holds from the law of conservation.

However, the total amount t ^ns v of the background target is t ^ns since it is considered to be sufficiently larger than the total amount p ^t v of the probe i is regarded as a constant. Considering that the fluorescence intensity I ^s _i of the probe is proportional to the sum of the amount of specifically bound target and the amount of cross-hybridization ([PT ^s _i ] + [PT ^ns _i ]) v, an effective equilibrium constant Using K ^ef _i , it can be obtained from formula (21) to formula (23).

Therefore, the amount t ^ns background target amount t ^t _i complementary target and probe are the object of measurement, and K ^pf _i probe _{^{i, K tf i, K ns}} i, if K ^s _i are known, it is possible to expect the fluorescence intensity I ^s _i tailored specific hybridization and cross-hybridization. Conversely, given the t ^t _i other than the value of the parameter and the actual fluorescence intensity I ^s _i, the amount of target t ^t _i, i.e., it is possible to determine the concentration of target in the sample.

Therefore, in the present invention, in advance to determine the values of the parameters other than t ^t _i in advance by performing a preliminary experiment, then, from the measured value I ^s _i of the fluorescence intensity of the target in the sample by using the determined parameter Determine the concentration. Since the target concentration thus determined is determined by eliminating the influence of cross hybridization, it is a highly accurate value.

Evaluation equilibrium constant 2.2.2 folding free energy K ^tf _i, to calculate the obtained free energy .DELTA.G ^tf _i of the secondary structure of the target. Since the target DNA molecule is complementary in sequence to the probe, its secondary structure is expected to be essentially the same as the secondary structure of the probe. However, the actual target is different from the probe in that the target is a fragment of a base sequence with different lengths and that it can move freely in solution. Therefore, as the data for estimation, the free energy value of the secondary structure calculated using MFOLD1 from the probe array is used as in the previous section, but the weighting coefficient is set to w ^tf instead of w ^pf as the target. The free energy of the secondary structure of
Free energy ΔG ^tf _i used for evaluation
= (Free energy of secondary structure of target obtained by MFOLD1) × w ^tf

2.2.3 Nearest Neighbor Model Similar to the case of non-specific binding, the free energy of hybridization due to specific binding can be estimated approximately from the combination of sequences. In addition to ε ^ns in the previous section, another set of 48 parameters ε ^s is prepared, and the sum of contributions from each base pair is calculated as in the previous section.

2.3 Parameter Determination Method Of the parameters in the above model, the values of w ^pf , w ^tf , ε ^s and ε ^ns excluding t ^ns are considered to be constants independent of experiments. For this reason, the values of these parameters are determined in advance by performing the following experiments 1 and 2 as a preliminary experiment. The parameter determination method will be described below.

<Experiment 1>
First, only a sample obtained by fragmenting the genome of a target cell using the microarray 10 is hybridized, and the parameters (w ^pf , ε ^ns) in the cross-hybridization model are based on the fluorescence intensity of the random probe 13 obtained as a result. ).

The number of random probe 13 included in the microarray 10 used in the experiment and N ^r. A sample of a target cell is measured using the microarray 10 including the random probe 13, and the fluorescence intensity of the random probe 13 obtained by the measurement is defined as I ^r _i (1 ≦ i ≦ N ^r ). Consider an error R ^r between this I ^r _i and the expected value I ^ns _i (see equation (7)). Note that the expected value I ^ns _i based on the model is obtained by Equation (7), but a temporary value is set for the proportionality constant C in Equation (7).

Then, t ^ns , w ^pf , and 48 values of ε ^ns that minimize the error R ^r are determined using numerical optimization techniques such as Newton's method, quasi-Newton's method, and Nelder-Mead's method. To do. Specifically, the following process is performed.
(1) Appropriate initial values are given to t ^ns , w ^pf and ε ^ns , and R ^r is calculated.
(2) Then, the value of each parameter is changed so that R ^r decreases.
(3) Calculate R ^r again.
While changing the parameters, the processes (2) and (3) are repeated until the error R ^r becomes equal to or less than a predetermined value close to 0, and finally converged values are used as the values of the respective parameters.

Thus, the parameters w ^pf and ε ^ns are obtained.

<Experiment 2>
Next, a solution in which a sample obtained by fragmenting the genome of a target cell in a microarray and a DNA whose concentration with respect to the control probe 15 has been determined (hereinafter referred to as “control sample”) is hybridized, and parameter w ^tf and Optimize the value of ε ^s .

(1) First, the concentration of the background target is estimated based on the measured value of the fluorescence intensity of the random probe 13 obtained as a result of Experiment 2. Specifically, K ^pf _i and K ^ns _i of each probe are calculated based on the parameters w ^pf and ε ^ns obtained in Experiment 1, and R ^r obtained from the equation (25) is minimized. Then, the value of t ^ns is obtained by numerical optimization. The value of t ^ns obtained in this way is set as the effective total amount of the background target.

(2) Since the concentration of the fragmented cell genome is measured, it can be assumed that the target concentrations t ^t _i corresponding to all measurement probes are constant. Optimal t ^t _i using the values of parameters obtained in the Experiments 1 and 2 (1), w ^tf, obtaining the value of epsilon ^s. Specifically, using the following equation (26), the error R ^s is t ^t _i so as to minimize the expected value I ^s _i and measured values I _i of the fluorescence intensity, w ^tf, the value of epsilon ^s Optimize. The expected value I ^s _i is given by the equation (23).

As described above, the amount t ^{ns of the} background target and the parameters w ^tf and ε ^s are obtained.

(3) Finally, the concentration of the control sample is calculated from the parameters w ^tf and ε ^s obtained by optimization and the measured fluorescence intensity of the control probe 15. The value of the scaling proportional constant C is determined so that the calculated concentration is equal to the concentration of the actually supplied control sample.

2.4 Evaluation of Target Concentration After the parameters are determined as described above, the fluorescence intensity of the microarray is actually measured, and the target amount t ^t to be analyzed using the above parameters from the actually measured value I ^m _{i. i,} ie, the concentration of the target in the sample. Specifically, it is as follows.

(1) already determined parameters w ^pf, binding energy .DELTA.G ^pf _i of each probe based on the epsilon ^{ns _{like, ΔG ns i, ΔG tf i}} , computes the .DELTA.G ^s _i. Equilibrium constants K ^pf _i , K ^ns _i , K ^tf _i , and K ^s _i are obtained from their binding energies.

(2) The amount of the background target that binds to each probe nonspecifically as a background from the measured value of the fluorescence intensity of the random probe 13 that does not have a corresponding sequence in the sample, using Equation (7). ^tns is obtained.

(3) From the measured value I ^m _i of the fluorescence intensity of each measurement probe 11, the value of the target concentration t ^t _i is obtained using the amount t ^{ns of the} background target and each value calculated above. Specifically, in the equation (26), the target values are set so that the difference between the measured value I ^m _i of the fluorescence intensity of each measurement probe 11 and the theoretical value I ^s _i of the fluorescence intensity of the target target is minimized. concentration values t ^t _i numerically analytically determined. The theoretical value I ^s _i of the fluorescence intensity by the target is obtained by using the background target amount t ^ns , the equilibrium constant obtained in step S32, and other known values (proportional constant C etc.). Calculated from (23).

The target concentration t ^t _i obtained in this way is obtained by eliminating the influence (NS _i ) of the background target, that is, the noise component, from the signal I ^m _i of the measurement probe 11. It is a highly accurate value that depends only on 11 specific bindings.

3. Microarray analysis system
3.1 System Configuration A microarray analysis system to which the above microarray analysis method is applied will be described. FIG. 1 shows a configuration example of the microarray analysis system of the present invention. The microarray analysis system 100 includes a scanner 20 that reads the fluorescence state of each probe of the microarray 10 and outputs the image information as an electrical signal (signal), and an analysis device 50 that processes the image information from the scanner 20.

  The analysis device 50 includes a display unit 51 that displays measurement data, analysis results, and the like on a screen, a data storage unit 53 that stores predetermined data, a processor 55 that executes analysis processing according to a control program, and a user that performs analysis. An operation unit 57 for operating the apparatus, a scanner interface 58 for inputting image information from the scanner 20, and an external interface 59 for exchanging data with an external device or the like are included.

  The display unit 51 is composed of a liquid crystal display (LCD) or the like, and can display input data and analysis results. The processor 55 is, for example, an MPU or CPU, and controls the operation of the entire analysis apparatus 50 by executing a predetermined program. The operation unit 57 includes operation buttons, switches, a keyboard, a mouse, and the like, and the user operates the analysis device 50 via the operation unit 57. The external interface 59 is an interface that enables data transmission / reception between the analysis apparatus and an external device such as a network or a printer. The analysis device 50 is constituted by a personal computer, for example. The scanner 20 and the analysis device 50 may be integrated.

  The data storage unit 53 includes a semiconductor storage device such as a hard disk and a flash memory, and a recording medium such as a CD and a DVD, and stores data necessary for processing of the analysis device 50 such as measurement data, analysis results, and control programs. The data storage unit 53 stores mathematical formula information and parameters relating to the model used for the above-described analysis as model information.

3.2 Processing Flow A specific operation of the microarray analysis system 100 will be described.

3.2.1 Parameter Determination Processing Parameter determination processing of the microarray analysis system 100 will be described with reference to the flowchart of FIG.

  First, only the sample obtained by fragmenting the genome of the target cell is hybridized with the probe of the microarray 10 (Experiment 1).

  The fluorescence intensity of the random probe 13 according to Experiment 1 is read by the scanner 20. The processor 50 inputs the measured value of the fluorescence intensity from the scanner 20 as an electrical signal (S11). The input measurement value of the fluorescence intensity is stored in the data storage unit 53.

The processor 50 determines parameters (w ^pf , ε ^ns ) by a numerical optimization technique using the equation (25) based on the input measurement value of the fluorescence intensity of the random probe 13 (S12).

  Next, a solution in which a sample obtained by fragmenting the genome of a target cell and a DNA (control sample) whose concentration is determined with respect to the control probe 15 is mixed with the probe of the microarray 10 (Experiment 2).

The processor 55 inputs the measurement value of the fluorescence intensity according to the experiment 2 from the scanner 20 (S13), and based on the input measurement value of the fluorescence intensity of the random probe 13 and the already obtained parameter, the background is obtained using the equation (25). The target concentration t ^ns is obtained (S14).

The processor 55 determines parameters (w ^tf , ε ^s ) using the equation (25) based on the measured fluorescence intensity of the measurement probe 11 and the parameters already obtained (S15). Finally, the proportionality constant C is determined based on the measured value of the fluorescence intensity of the control probe 15, the measured value of the concentration of the control sample, and the theoretical value (S16). As described above, each parameter used for the model is determined and stored in the data storage unit 53.

3.2.2 Concentration Analysis Processing The concentration analysis processing of the microarray analysis system 100 will be described with reference to the flowchart of FIG.

  A sample obtained by fragmenting the genome of a target cell is hybridized with a probe of the microarray 10.

The processor 55 inputs the measurement value of the fluorescence intensity of the probe resulting from the hybridization from the scanner 20 (S31). Processor 55, the parameters stored in the data storage unit 53 (w ^pf, ε ^ns, etc.) binding energy .DELTA.G ^pf _i of each probe on the basis _{^{of, ΔG ns i, ΔG tf i}} , calculate the ΔG ^s _i (S32). At this time, the equilibrium constants K ^pf _i , K ^ns _i , K ^tf _i , and K ^s _i are obtained from these binding energies and stored in the data storage unit 53.

Subsequently, the processor 55 binds to each probe non-specifically as a background from the measured value I ^r _i of the fluorescence intensity of the random probe 13 that does not have a corresponding sequence in the sample, using Equation (7). The amount t ^{ns of the} background target coming is obtained (S33).

The processor 55 calculates the measured value I ^m _i of the fluorescence intensity of each measurement probe 11, the value of the concentration t ^t _i of the target based on the values calculated above. (S34). Specifically, in the equation (26), the target values are set so that the difference between the measured value I ^m _i of the fluorescence intensity of each measurement probe 11 and the theoretical value I ^s _i of the fluorescence intensity of the target target is minimized. concentration values t ^t _i numerically analytically determined. The theoretical value I ^s _i of the fluorescence intensity by the target is calculated by using the background target amount t ^ns , the equilibrium constant obtained in step S32 and other known values (proportional constant C, etc.) Calculate from (23).

  The obtained target concentration can be displayed on the display unit 51 or output as data via the external interface 59.

  Specific examples using the microarray analysis method of the present invention will be described below.

4.1 Design of Microarray In this example, a custom array designed based on the genome of Escherichia coli was used. This microarray is roughly divided into the following two types of probes.
1) Measurement probe covering E. coli gene (glnA, 1410bp) with 14mer step 2) Random probe based on artificially synthesized base sequence

4.2 Creation of Random Probe The procedure for designing the random probe used in this microarray will be described.
1) Generate a character string of length 25 such that each alphabet of A, T, G, and C appears with a probability of ¼ using random numbers.

  2) Nearest Neighbor model of previous research (see J. SantaLucia. A unified view of polymer, dumbbell, and oligonucleotide dna nearest-neighbor thermodynamics. Proc. Natl. Acad. Sci. USA, 95 (4): 14605, 1998.) Is used to calculate the free energy of hybridization of each sequence.

  3) From the sequence generated in 1), the free energy calculated in 2) is included in the three ranges of -28 ± 0.5 kcal / mol, -32 ± 0.5 kcal / mol, -36 ± 0.5 kcal / mol. Select 50 items each, 150 in total. If there are less than 50 selected arrays in one range, go back to 1) and add the arrays.

  4) Based on the array of 150 obtained in 3), an array with a length of 14 that has been deleted up to the 11th character, such as a character deleted from the left end, a character deleted from the left, etc. Up to 1800 sequences are generated together with the original sequence.

  5) For each of the 1800 sequences prepared in 4), a mismatch sequence is synthesized by substituting one base at each base from the 3 'end to 5' to obtain a total of 110700 probes.

  In this experiment, a 25-mer oligonucleotide complementary to each of the 150 sequences generated in 3) was synthesized and used as the control probe 15.

  The document adjustment, hybridization, washing, and scanning processes followed Affymetrix's Expression Analysis Technical Manual. Hybridization was performed using Affymetrix Hybridization Oven 640 at 45C for 16 hours at 60 rpm. Affymetrix Fluidics Station 450 was used for cleaning, and ProkGE_WS2_450 script was used. The microarray scan was measured using an Affymetrix GeneChip Scanner 3000, and the signal intensity value was obtained using Microarray Suite 5.0.

  For the analysis of data, use the statistical calculation language R (see R: A language for data analysis and graphics. Journal of Computational and Graphical Statistics, 5: 299314, 1996) and create an original script. And calculated. Unless otherwise specified in the analysis, the fluorescence intensity of each experiment is handled in logarithm (log 10).

4.3 Experimental Experiment 1: Extracted and fragmented total genomic DNA of E. coli was measured.
Experiment 2: A sample obtained by adding an oligonucleotide as a control sample to total genomic DNA of E. coli was measured. Different samples were prepared in 7 stages from the final oligonucleotide concentration of 1.4 fM to 1.4 nM in 10 stages, and measurement was performed 14 times in total, twice each.

4.4 Determination of parameters First, parameters related to cross-hybridization were determined by Experiment 1 in which only the genome was measured. Since no oligonucleotide is added, all signals of the random probe 13 can be regarded as due to cross-hybridization. The number of data points used for the measurement is 110,700. That is, 110,700 random probes 13 were used.

A background target amount t ^ns , a parameter w ^pf, and 48 values of ε ^ns were determined by fitting using an R optimization function. FIG. 6 shows a scatter diagram of predicted values and measured values based on the optimized model. The error R ^ns of the predicted value at this time is 0.044, and it can be said that the amount of cross hybridization can be predicted with high accuracy.

4.5 The number of data points used for fitting at the time of determining the fitting convergence parameter was changed, and the minimum number of random probes 13 required to construct a quantitative model was estimated. 50, 100, 200, 400, 800, 1600, and 3200 probes are sampled from random probes 13 by random numbers. A parameter of the model is determined based on each sample data, and a prediction error when the fluorescence intensity of all remaining random probes is predicted using the parameter is obtained. FIG. 7 shows the result of plotting the prediction error against the number used. The results of the two verifications that changed the way the samples were taken are displayed in an overlapping manner. When the sample data is too small, the prediction error increases due to overfitting, but it can be seen that the error converges if there are a sufficient number of samples. Taking into account variations in experiments, etc., it is preferable to use approximately 1000 or more probes for quantitative analysis.

4.6 Calibration by Control Probe Next, using the data of Experiment 2, the original concentration is calculated from the signal value of the control probe 15 using the method of the present invention, and the actual concentration of oligonucleotide added to the sample is calculated. Make a comparison. Based on the parameters determined in the previous section, concentration values were independently determined for each of seven experiments with different oligonucleotide concentrations. For the calculation, 150 probes with a length of 25mer were used. In actual gene expression analysis, since it is usually designed so that a plurality of probes match different parts of the same gene, for convenience, 150 probes are treated as 30 probe sets of 5 each. .

Five probes in each set is assumed to correspond to the same amount of the target, determine the concentration t ^t _i of the common target. Since the necessary parameters have already been obtained, t ^t _i is obtained by optimizing so that the error shown in equation (26) is minimized. Estimated concentrations from the model calculated for 7 inputs for each set were calculated independently. The result of comparing the relationship between the estimated amount and the actual input amount is shown in FIG.

  FIG. 8A shows an analysis result based on the Affymetrix algorithm as an existing method. For the calculation, the above 150 probes and the corresponding mismatch probe data are used, and the above 5 sets are used as the probe set. In the existing method, the variation in data is large, and the dispersion is particularly wide on the low concentration side. In addition, the Affymetrix algorithm excludes data with a larger MM probe signal than the PM probe. Therefore, if the influence of cross-hybridization is large, the reliability of the probe set data decreases.

  In particular, at the lowest concentration, nearly half of the probes are excluded. On the other hand, as shown in FIG. 8 (b), in the present invention, it can be said that the plotted points are located almost on a straight line from the low concentration side to the high concentration side, and shows high agreement between the input amount and the estimated amount. (Correlation coefficient 0.989). Further, it can be said that the reliability is high because there is little dispersion between the probe sets. Since more accurate measurement is possible with a smaller number of probes, it is possible to increase the resolution of expression analysis using this method.

5. Summary According to the present invention, the amount of a target (background target) that causes cross-hybridization is calculated from the fluorescence intensity of a random probe that binds nonspecifically to the target to be analyzed, Based on the binding energy of the probe, the influence of the background target on the fluorescence intensity is evaluated, and the concentration of the target target is obtained in a form that eliminates this influence. Since the influence of the background target can be eliminated in this way, the true target concentration can be obtained with high accuracy. In particular, it is possible to appropriately evaluate a low concentration target that has been buried in noise due to cross hybridization and cannot be measured.

  In the above model, other states may be considered as possible states of the probe and the target. For example, a state in which probes are combined or a state in which a target to be analyzed and a background target are combined may be considered.

  In the above model, the Nearest Neighbor model using 48 parameters was used to obtain specific and nonspecific binding energies. The parameter may be ignored. For example, a method of adding an effect depending on the position of the base, or considering a combination of four or more bases in which the inverted sequences are not regarded as the same can be considered.

  In the above model, the calculated value by MFOLD is used to obtain the free energy of folding, but other methods may be used for this calculation.

  In this embodiment, an artificially generated sequence using random numbers was used for the design of a random probe, but this random probe is included in the genome of a different organism if it is not included in the genome of the cell to be measured. May be used.

  In this embodiment, hybridization was performed using the cell genome as a sample, but hybridization was performed using a sample obtained by reverse transcription of RNA extracted from the cell to obtain cloned DNA, or amplification by further RNA transcription therefrom. Thus, it is possible to analyze the intracellular concentration of the original RNA, that is, the expression level of each gene.

  The present invention is not limited to GeneChip type arrays, and can be applied to general measurement systems based on hybridization between oligonucleotide probes and target RNA / DNA.

The present invention can improve the analysis accuracy of gene expression using a microarray, and can increase the reliability of measurement data.
As an effect,
1) Reliable data can be obtained using a set of fewer probes.
2) Since a target with a low concentration can be measured more accurately, it is useful for quantitative analysis of a gene with a low expression level.
There are merits such as.

  By reducing the number of probes required for the probe set, the number of types of genes that can be analyzed with one microarray can be increased, so that improvement in analysis efficiency can be expected. In addition, since the expression level can be measured quantitatively from a small number of probes, it can be said that it is also effective for elucidating the action of short non-coding RNAs such as siRNA and miRNA. Application to gene therapy can be considered. In addition, being able to examine the behavior of genes with low expression levels in detail has great implications for elucidating the role of transcription factors in gene regulatory networks. For example, in the pharmaceutical industry, much attention has been paid to genomic drug discovery. In particular, it can be said that the development of toxicogenomics that comprehensively analyzes the mechanism of action of toxins or drugs at the gene expression level is very important. Microarray analysis is promising as a tool for analysis of transcription factor expression and accompanying genome network analysis. However, at present, it is difficult to accurately analyze a gene group having a low expression level such as a transcription factor, and therefore, there are various restrictions due to the low quality of data. If a detailed expression analysis is performed by using the analysis method of the present invention, it is considered that it can greatly contribute to the development of toxicogenomics and the accompanying prosperity of the genome drug discovery industry.

The figure which shows the probe structure of the microarray used with the microarray analysis method of this invention Diagram explaining possible states of target and probe in sample solution The figure which shows the structural example of the microarray analysis system of this invention Flowchart of parameter determination processing by microarray analysis system of the present invention Flow chart of concentration analysis processing by the microarray analysis system of the present invention Figure showing the comparison result of the predicted value of fluorescence intensity by the background target and the measured value (the predicted value on the horizontal axis, the measured value on the vertical axis, the unit on both axes is arbitrary unit (AU), the scale is logarithm (log10), thick (The broken line shows y = x, and the thin broken line shows y = 2x, x / 2.) Diagram showing the relationship between the number of data used for model optimization and model prediction errors A graph showing the comparison between the concentration of the input control and the concentration converted from the signal value by the model (the input concentration on the horizontal axis, the estimated amount on the vertical axis, the unit on both axes is fM, the scale is logarithm (log10), A thick broken line indicates y = x, (a) a figure showing an estimated value by an existing method, (b) a figure showing an estimated value according to the present invention).

Explanation of symbols

DESCRIPTION OF SYMBOLS 10 Microarray 11 Measurement probe 13 Random probe 15 Target probe 20 Scanner 50 Analyzer 51 Display part 53 Data storage part 55 Processor 57 Operation part 58 Scanner interface 59 External interface

Claims (13)

A microarray analysis method for obtaining a concentration of a target contained in a sample solution using a microarray in which a plurality of probes are arranged,
a) The microarray includes a plurality of measurement probes having a base sequence corresponding to the base sequence of the target to be analyzed, and a plurality of random probes having a base sequence not corresponding to the base sequence of the target to be analyzed,
b) The microarray analysis method is as follows:
Hybridizing a solution containing the target and each probe of the microarray;
Measuring the fluorescence intensity of each probe;
Determining the amount (t ^ns ) of a background target that is a target non-specifically bound to the probe from the measurement value of the fluorescence intensity of the random probe;
Predicting the degree of influence of cross hybridization (NS _i ) on the measured fluorescence intensity of the measurement probe based on the amount of the background target and the binding energy of each probe;
And excluding the influence of the cross hybridization from the measured value (I ^m _i ) of the fluorescence intensity of the measurement probe to obtain the target amount (t ^t _i ) to be analyzed. Microarray analysis method. Define a model that shows the equilibrium between possible states of the probe, and use the model to determine the amount of the background target (t ^ns ),
The state of the probe in the model includes a state in which the probe is free in a solution, a state in which the probe and the background target are nonspecifically bound, and a probe that is folded by self-hybridization to have a secondary structure. State included,
The microarray analysis method according to claim 1, wherein: Hybridizing only a sample fragmented from the genome to be analyzed with probes on the microarray;
Measuring the fluorescence intensity of the random probe by the hybridization;
The method for analyzing a microarray according to claim 2, further comprising a step of determining parameters (w ^pf , ε ^ns ) for obtaining an equilibrium constant of the model based on the measured value. Define a model that shows the equilibrium between the possible states of the probe and target,
The state of the probe includes a state where the probe is free in a solution, a state where the probe is folded by self-hybridization and has a secondary structure, a state where the target is free in the solution, and a state where the target is self-hybridized. Includes a folded and secondary structure, a probe and background target non-specifically bound, and a probe and background target specifically bound,
2. The microarray analysis method according to claim 1, wherein the binding energy is a parameter for obtaining an equilibrium constant of the model. Hybridizing a mixture of a sample obtained by fragmenting the genome to be analyzed and a DNA having a determined concentration with a probe on the microarray;
Measuring the fluorescence intensity of the measurement probe by the hybridization;
5. The method of analyzing a microarray according to claim 4, further comprising a step of obtaining a parameter (w ^tf , ε ^s ) for obtaining the binding energy based on the measured value. Hybridizing a part of the plurality of random probes with a DNA having a base sequence corresponding to the base sequence of the part of the probe and having a determined concentration;
Measuring the fluorescence intensity of the partial probe;
The method further comprises the step of determining a proportionality constant between the fluorescence intensity of the probe and the target concentration based on the measured value of the fluorescence intensity of the partial probe and the determined value of the concentration of the DNA. Item 4. A microarray analysis method according to Item 1. A microarray analyzer that analyzes a signal from a microarray in which a plurality of probes are arranged to determine a target concentration in a sample solution,
a) The microarray includes a plurality of measurement probes having a base sequence corresponding to the base sequence of the target to be analyzed, and a plurality of random probes having a base sequence not corresponding to the base sequence of the target to be analyzed,
b) The analysis device
Data storage means for storing information about the model used for analysis;
An input means for inputting a measured value of the fluorescence intensity of each probe obtained as a result of hybridizing the solution containing the target and each probe of the microarray;
Processing means for calculating a target concentration (t ^t _i ) from the measured value of the input fluorescence intensity using information on the model,
c) The processing means includes:
From the measurement value of the fluorescence intensity of the input random probe, the amount (t ^ns ) of the background target that is a target non-specifically bound to the probe is determined.
Based on the amount of the background target and the binding energy of each probe, the degree of influence of cross-hybridization (NS _i ) on the measured fluorescence intensity of the measurement probe is predicted,
A microarray analyzer characterized in that the amount of target (t ^t _i ) to be analyzed is obtained by excluding the influence of the cross hybridization from the measured value (I ^m _i ) of the fluorescence intensity of the measurement probe. . The data storage means stores information about a model indicating an equilibrium between possible states of the probe,
The state of the probe in the model includes a state in which the probe is free in a solution, a state in which the probe and the background target are nonspecifically bound, and a probe that is folded by self-hybridization to have a secondary structure. State included,
The processing means obtains the amount (t ^ns ) of the background target using the model.
8. The microarray analysis apparatus according to claim 7, wherein The processing means is a parameter for obtaining an equilibrium constant of the model based on a measured value of fluorescence intensity of a random probe when only a sample obtained by fragmenting the genome to be analyzed is hybridized with a probe on the microarray ( ^9. The microarray analysis apparatus according to claim 8, further comprising determining w ^pf , ε ^ns ). The data storage means stores information relating to a model indicating an equilibrium between possible states of the probe and the target;
The state of the probe includes a state where the probe is free in a solution, a state where the probe is folded by self-hybridization and has a secondary structure, a state where the target is free in the solution, and a state where the target is self-hybridized. Includes a folded and secondary structure, a probe and background target non-specifically bound, and a probe and background target specifically bound,
8. The microarray analysis apparatus according to claim 7, wherein the binding energy is a parameter for obtaining an equilibrium constant of the model. The processing means is based on the measurement value of the fluorescence intensity of the measurement probe when a mixed solution of the sample fragmented from the genome to be analyzed and the DNA whose concentration has been determined is hybridized with the probe on the microarray. ^11. The microarray analysis apparatus according to claim 10, wherein parameters (w ^tf , ε ^s ) for ^obtaining the binding energy are obtained. The processing means is configured to hybridize a partial probe of the plurality of random probes and a DNA having a base sequence corresponding to the base sequence of the partial probe and having a determined concentration. 8. The microarray analyzer according to claim 7, wherein a proportionality constant between the probe fluorescence intensity and the target concentration is determined based on a measured value of the fluorescence intensity of the probe and a determined value of the concentration of the DNA. . An analysis program for analyzing a signal from a microarray in which a plurality of probes are arranged, and causing a computer to execute a process for obtaining a concentration of a target in a sample solution,
a) The microarray includes a plurality of measurement probes having a base sequence corresponding to the base sequence of the target to be analyzed, and a plurality of random probes having a base sequence not corresponding to the base sequence of the target to be analyzed,
b) The analysis program is
Inputting a measurement value of the fluorescence intensity of each probe obtained as a result of hybridization of the solution containing the target and each probe of the microarray;
Determining the amount (t ^ns ) of a background target that is a target that non-specifically binds to the probe from the measured fluorescence intensity of the input random probe;
Predicting the degree of influence of cross hybridization (NS _i ) on the measured fluorescence intensity of the measurement probe based on the amount of the background target and the binding energy of each probe;
Causing the computer to execute the step of determining the target amount (t ^t _i ) to be analyzed by excluding the influence of the cross hybridization from the measured value (I ^m _i ) of the fluorescence intensity of the measurement probe. A microarray analysis program.

Images