JP2003028862A - Dna microarray data correcting method - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a DNA microarray data correcting method. SOLUTION: The DNA microarray data correcting method for examining the difference between the gene expression levels of two types of samples on every gene through the use of a DNA microarray includes (A) a process for obtaining the average amounts of expression for every gene on the two types of samples by averaging measurement data for every gene on the two types of samples obtained from the DNA microarray, (B) a process for obtaining the difference between the amounts of expression for every gene on the two types of samples by obtaining differences for every gene from the measurement data on the two types of samples obtained form the DNA microarray, (C) a process for obtaining a simultaneous distribution with the average amounts of expression obtained in the process (A) and the difference between the amounts of expression obtained in the process (B) as random variables, and (D) a process for converting the simultaneous distribution obtained in the process (C) into a previously determined distribution or a statistically expected distribution.

Description

Detailed Description of the Invention

[0001]

TECHNICAL FIELD The present invention relates to a method for correcting DNA microarray data, a microarray data correction apparatus using the method, and a gene expression analyzer incorporating the DNA microarray data correction apparatus.

[0002]

2. Description of the Related Art Advances in gene analysis research represented by the Genome Project have increased the need for efficient analysis methods in place of conventional Northern blotting, competitive RT-PCR and the like. A DNA microarray (also referred to as a DNA chip) has been developed as a tool capable of rapidly and comprehensively examining gene expression. A DNA microarray is a method of measuring expression changes of each gene by aligning and fixing hundreds to tens of thousands of DNA probes on an array substrate and hybridizing a target prepared from mRNA to be analyzed to this. Is.

Using this method, a large amount of information can be obtained by a single measurement experiment. Therefore, systematic gene expression analysis can be performed based on the gene structure information obtained by genome analysis. It is possible. Studies using DNA microarrays are still in their infancy, and the methods for processing raw data have not been thoroughly investigated.

By the way, usually, in a gene expression analysis experiment using a DNA microarray, after two fluorescent labeling methods, that is, mRNAs derived from two types of cells are extracted and purified, and labeled with different fluorescent substances (for example, Cy3 and Cy5). , Competitive hybridization is performed on a DNA microarray, and each fluorescence intensity at different excitation wavelengths is measured. Then, by generally quantifying and comparing the fluorescence intensities of the respective fluorescent substances obtained from the respective spots on the array, it is general to obtain information on the ratio of the gene expression levels in the two types of cells.

However, in ordinary measurement, mRNAs are separately extracted and purified from different samples and labeled with different fluorescent substances for detection, so that the raw data obtained must be corrected if necessary. . Specifically, for example, when it is considered that there is not much difference in the expression levels of the two types of cells such as comparison of changes over time, it is considered that the total gene expression level does not change, and the fluorescence signal obtained from each spot is Method for calculating the correction coefficient from the total or median value and correcting the fluorescence intensity of each spot signal [Wilson, M. et al.:Proc. N
atl. Acad. Sci. USA, 96: 12833-12838 (1999)], and when the expression levels of the two types of cells are considered to be different, the expression level in each cell is considered to be constant. Method of calculating the correction coefficient from the fluorescence signal value of the gene (eg, housekeeping gene) to be corrected, and correcting the fluorescence intensity of each spot signal [Heller, RA et al .: Pr
oc. Natl. Acad. Sci. USA, 94: 2150-2155 (1997)] and the like have been adopted.

However, in a DNA microarray, a large number of DNA probes are usually present on one array, and the simple correction as described above is not sufficient. Recently, Yang et al. Have found that in order to perform more precise correction in microarrays, it is effective to correct the difference in pins when spotting the probe and the method of correcting the average distribution of expression levels depending on the expression levels. Reported [Yang, YH et al .: Normalizatio
n for cDNA Microarray Data.SPIE BiOS 2001, San Jo
se, California, January 2001]. However, the use of such correction is still not sufficient.

[0007]

DISCLOSURE OF THE INVENTION The present invention is directed to a method for correcting data obtained from a DNA microarray (also referred to as DNA microarray data), a DNA microarray data correction apparatus using the method, and gene expression incorporating the correction apparatus. An object is to provide an analyzer.

[0008]

As a result of intensive studies to solve the above-mentioned problems, the inventors of the present invention corrected each data based on a correction curve, and simply statistically calculated the entire data. As a result, they have found that it is possible to perform correction with higher accuracy than the conventional correction method which is dealt with in (1), and thus completed the present invention. That is, the present invention is the following (1)
~ (7).

(1) A method for correcting measurement data in the case of examining the difference in gene expression level between two kinds of samples for each gene using a DNA microarray, which comprises the following steps: (A) DNA A step of obtaining the average expression level of each gene between the two types of samples by averaging the measurement data of the two types of samples obtained from the microarray, for each gene, (B) the two types of samples obtained from the DNA microarray The process of obtaining the difference in the expression level of each gene between two types of samples by taking the difference of the measurement data for each gene from the measurement data of the sample, and (C) the average expression level obtained in step (A) A step of obtaining a joint distribution with the difference in expression amount obtained in step (B) as a random variable, and
(D) a step of converting the simultaneous distribution obtained in step (C) into a distribution known in advance or a distribution expected statistically, correction of the DNA microarray data, Method.

(2) The method for correcting DNA microarray data according to (1) above, wherein the simultaneous distribution is a conditional distribution. (3) The method for correcting DNA microarray data according to (2) above, wherein the conditional distribution is an error distribution. (4) The method for correcting DNA microarray data according to (3) above, wherein the error distribution is a normal distribution.

(5) A recording medium recording a program for executing the method for correcting DNA microarray data according to any one of (1) to (4) above. (6) A DNA microarray data correction device containing the recording medium of (5) above. (7) A gene expression analysis device incorporating the DNA microarray data correction device of (6) above. Hereinafter, the present invention will be described in detail.

[0012]

BEST MODE FOR CARRYING OUT THE INVENTION One of the reasons why the accuracy of the conventional correction method is not sufficient is that the detection accuracy of each probe on the DNA microarray prepared for acquiring a large amount of data is as follows. Although the characteristics such as are not uniform, we have pointed out that the entire data obtained from them are regarded as subject to one random variable.
Therefore, by correcting each piece of data by the method described below, it has succeeded in correcting with high accuracy as compared with the conventional correction method in which the entire data is simply treated statistically. That is, the correction method of the present invention calculates the expression data obtained by the microarray, calculates the average expression level and the difference between the expression levels for each probe, and calculates the joint distribution using the difference between the average expression level and the expression level as a random variable. Then, the expression data is corrected by converting the distribution into a distribution known in advance or a distribution expected statistically.
Here, the "random variable" is a variable whose value is stochastically determined, specifically, the "simultaneous distribution".
The term "corresponding to a set of values that two or more random variables can take" and the occurrence probability of the set of values. The correction method of the present invention will be described more specifically as follows.

The data of the expression level of the same gene in two kinds of samples (for example, a cell sample derived from a normal mouse and a cell sample derived from a mouse in which a specific gene is destroyed) obtained by the DNA microarray are defined as X1 and Y1, respectively. Here, one data pair will be described, but it is actually necessary to perform the same operation on all the obtained data. Of the two types of samples, one is usually the sample to be investigated and the other is the control sample. The measurement value of the expression level is influenced by the experimental system and the measurement system. When the correction curve is obtained, it can be corrected by the correction curves f (x) and g (x) as follows.

[0014]

[Equation 1]

[0015]

[Equation 2]

Here, X0 and Y0 are the expression levels obtained by the correction before being influenced by the experimental system and the measurement system. In the analysis, it is important to check whether there is a difference in the expression level between the two samples, and rather than analyzing X1 and Y1 as they are, variable conversion is performed and the part of the change that should be noted and the part that is not related to the change Divide into As a result, the part having a notable difference can be expressed as the difference in expression level, and the part unrelated to the change can be expressed as the average expression level. The average expression level A1 before correction and the difference in expression level M1 are

[0017]

[Equation 3]

[0018]

[Equation 4] Given in.

Corrected average expression level A0 and difference in expression level
M0 uses the correction curves f (x) and g (x),

[0020]

[Equation 5]

[0021]

[Equation 6] Becomes

Here, considering Taylor expansion around A1 and approximation up to the first order,

[Equation 7] Becomes Here, f '(A1) and g' (A1) are x = A1 of f (x) and g (x)
Is a differential coefficient in.

Here, the measurement data is obtained by taking advantage of the fact that an extremely large amount of expression is obtained at one time, and the random distribution a is fixed in the simultaneous distribution p1 (a, m) of A1 and M1 and the simultaneous distribution. Consider the resulting conditional distribution p1 (m | a). When M1 is regarded as a random variable in Expression (7), it can be seen that the conditional distribution p1 (m1 | a1) has a different mean value and variance than the corrected conditional distribution p0 (m0 | a1). In other words, if the mean and variance of the true distribution before being affected by the experimental and measurement systems are known, the correction function values f (A1), g (A1) and their differential coefficients f '(A1), g' Even if you do not know (A1), you can correct it only by the average value and variance. Where a0 and a1 are almost equal,
Or p0 (a, m) does not change much with changes in a,
That is

[0024]

[Equation 8] Was assumed.

As a concrete calculation, the equation (7) is used as a correction function. First, the data is divided into sections according to the size of A1, and the average value and variance of M1 are calculated for each section to create a list. For the calculation of the average value and the variance, not only the data of the section to be calculated but also the data of the section around it can be used to use the smoothed value. This is effective because it is possible to reduce the influence of the statistical error of the data by using the smoothed value. As the smoothing, there is a local weighted least squares method or the like. Based on the obtained list, correction is performed using equation (7) so that the true distribution becomes equal to the mean value and variance for each section.

In the above calculation, Taylor expansion is performed and high-order terms are ignored in order to make the explanation easy to understand.
Generally, it is a non-linear transformation. If not only the average value and the variance of the conditional distribution p0 (m | a) but also the shape of the distribution is known in detail, nonlinear conversion can be performed, and more accurate correction can be performed. The correction can be performed by obtaining a conversion function that converts p1 (m | a) into p0 (m | a). In general, a conversion function from an arbitrary distribution to another arbitrary distribution can be obtained by creating a list that associates probability points where the lower probabilities of two distributions are equal. First, the section in which the average expression level A1 is distributed is divided into two or more sections. The width of the section may be uniform or non-uniform. Here, the value is uniform and dA.

[0027] Of the data, the average expression level A1 is in the interval [A, A + dA]
The set of expression difference M1 as shown in is extracted. By sorting the retrieved measurement data in ascending order, a list whose sorted order corresponds to the lower probability of the distribution is created. In addition, the lower probability {(1-0.5) / N,…, (N-0.5) / N} according to the distribution p0 (m | a) consisting of the same number as the number N of extracted measurement data
Create a list of probability points for. By combining the two lists, it is possible to create a corresponding list of probability points in which the probability points having the same lower probability are in the same order. This list is the interval
It is the conversion function at [A, A + dA]. This list of all A1
By creating for the section of, the conversion function of all the sections can be obtained.

Further, the simultaneous distribution p1 is used instead of the conditional distribution.
In the case of (a, m), it is possible to transform by repeating the above transformations several times alternately until the simultaneous distributions of the conditional distribution p1 (m | a) and the conditional distribution p1 (a | m) converge. .

When the joint distribution p0 (a, m) is not known, the optimum joint distribution p0 is determined in consideration of the experimental system and the measurement system.
By assuming the functional form of (a, m), the correction can be performed in the same way as when the distribution is known. In DNA microarrays, where a large amount of data can be obtained at one time, there are many genes whose expression levels do not differ. Therefore, considering that the shape of the distribution is determined by such data, the conditional distribution p0 (m | a) can be regarded as the distribution of the error difference between X0 and Y0. In many cases, the distribution of error and error difference can be treated as a normal distribution. However, this does not mean that the error distribution considered in the present invention is not limited to the normal distribution.

On the other hand, it is necessary to examine the correction curves f (x) and g (x) representing the characteristics of the experimental system and the measurement system and obtain an appropriate functional form for detailed evaluation of the experimental system and the measurement system. And difficult. However, in the present invention, the correction can be performed only by examining the functional form of the distribution of p0 (a, m), which is easier than the case of obtaining the correction curve. Moreover, based on the above-mentioned theoretical grounds, it is expected that the accuracy will be improved in the same manner as when the correction curve is used. As a method of examining the true co-distribution in advance, the distribution of average expression levels can be estimated by preliminarily measuring the expression levels of several targets using competitive RT-PCR, etc. The distribution of the difference in expression amount can be estimated from the accuracy of reverse transcription of mRNA when preparing a sample and the reading accuracy of a measuring device. Also,
In many cases, the distribution form of the difference in expression amount is an error distribution, and it is easy to properly assume the functional form.

Referring to the flow chart shown in FIG. 2, the DNA microarray data correction apparatus of the present invention is shown in FIG.
The operation of will be described. In FIG. 1, data from the storage means (101) for each expression data 1-N of genes 1-N derived from cell A and the storage means (102) for each expression data 1-N of genes 1-N derived from cell B are shown. X1 [i], Y1 [i] and probe information ID
Input [i] (S1). The subsequent calculation is performed by the correction means (103). Average expression level A1 [i] and expression level difference M1 [i]
Is calculated (S2). Where [i] is the i-th gene,
i takes a value from 1 to N. Next, input the number of sections that divide A1 [i] into sections (S3), substitute A1 [i] into A1 [j] [k] divided for each section (S4), and obtain the corresponding M1 [i] Substitute for M1 [j] [k] (S5).
Here, [j] represents the j-th section of A1 [i], and [k] represents the number associated with the data in that section. Here, the processing is divided into the case where the correction is performed by the average value and the variance of the distribution and the case where the correction is performed using the functional form of the distribution (S6). When correcting with the mean and variance of the distribution, enter the mean M0M [j] and variance M0D [j] in each section j of the distribution M0 (S7), and enter the distribution M
Calculate the mean M1M [j] and variance M1D [j] in each interval j of 1 (S
8) Calculate the corrected distribution and substitute it into M0 [j] [k] (S9).
When performing correction using the functional form of distribution, M1 [j] of each section
Substituting the number of elements of [k] into N1 [j] (S10), inputting the functional form of the distribution M0 (S11), the lower probability of the distribution of M0 in each interval {(1-0.
5) / N1 [j], ..., (N1 [j] -0.5) / N1 [j]}
Substituting into Q [j] [k] (S12), substituting a list of M1 distributions M1 [j] [k] in ascending order into M1S [j] [k] (S13), and correcting The calculated distribution is calculated and substituted into M0 [j] [k] (S14). Substituting M0 [j] [k] thus obtained into one-dimensional array M0 [i]
(S15), corrected expression difference M0 [i] and probe information ID
[i] is output through the output means (104) (S16).

If a recording medium recording a program for realizing the above-described processing of FIG. 2 is prepared and the computer is controlled by the program recorded in the recording medium, the DNA microarray data will be obtained in the same manner as above. It is clear that a correction of can be made. As the recording medium, various recording media other than the semiconductor memory and the magnetic disk device can be used.

The DNA microarray data correction device shown in FIG. 1 can be incorporated into a DNA microarray system to construct a gene expression analysis device.

[0034]

EXAMPLES Examples of the present invention will be specifically described below, but the scope of the present invention is not limited thereto. [Example 1] Correction of DNA microarray data by the correction method of the present invention DNA microarray data was corrected by the correction method of the present invention. For DNA microarray data, see the website http://www.stat.berkeley.edu/users/terry/zarray/
The measurement data published in Html / apodata.html was used. This data was obtained from an experiment using a knockout mouse of apolipoprotein AI gene and a normal mouse as a sample source. Specifically, the target prepared from the mRNAs of the two kinds of samples labeled with different fluorescent dyes was competitively hybridized with one DNA microarray, and the difference in the expression level was relatively compared. is there. The data obtained are two types of fluorescence intensity for each spot, and the difference in expression level is reflected as the difference in intensity.

Two kinds of fluorescence intensity are digitized for each spot in the data (these two kinds of data are referred to as Cy5 and Cy3). The data without correction is shown in FIG. In FIG. 3, the horizontal axis is L of the fluorescence intensity of Cy5 and Cy3 for each spot.
It is the average value (average expression level) of og2, and is calculated by the following formula.

[0036]

[Equation 9]

The vertical axis represents the difference in Log2 of fluorescence intensity of Cy5 and Cy3 for each spot (difference in expression level), which is calculated by the following formula.

[0038]

[Equation 10]

FIG. 4 shows the data obtained by finding the smoothed value of M by the local weighted least squares method for each data spotted on the same pin and subtracting it from M for this data.
Et al [YH Yang, S. Dudoit, P. Luu and TP Speed.
Normalization for cDNA Microarray Data. SPIE BiOS
2001, San Jose, California, January 2001].

The results of using the correction method of the present invention are shown below. The data M does not depend on the average expression level A, and it is assumed that the average is zero and the variance is constant. This is a natural assumption that the normal distribution shown in the embodiment of the invention is the error distribution. Under this assumption, first, in order to make the average value zero by the correction proposed by Yang et al., And then to make the variance of M constant independent of A, the local weighted least squares method of the absolute value of M is used. A smooth value was obtained and M was divided by the smooth value to remove the A dependence of the variance. Further, FIG. 5 shows data obtained by multiplying by an appropriate value so that the overall variance does not change from the data before correction.

In FIGS. 4 and 5, the diamonds (♦) are the top 5% data in which the absolute value of the difference in expression level is large. In FIG. 5 corrected by the present invention as compared with FIG. 4 corrected by Yang et al., It can be seen that a point where the absolute value of the difference in expression level is large over a wide range of A can be selected. When the present invention is used, the average expression level becomes too low or conversely too large due to a design error of the probe or technical difficulty, and it is possible to extract information of change even for data with a small difference in expression level.

Next, using a plurality of array data, the t value was obtained for each spot in order to investigate the gene whose expression level was different between the knockout mouse and the normal mouse by a statistical method, and the actual t value was calculated. 6 and 7 are plots of probability points-probability points using the distribution and the t distribution which is the theoretical distribution. The “t value” is a value obtained by performing a t-test that tests whether or not the average values of two sets of data are equal, and the greater the absolute value of the t-value, the more the P-value obtained from the t-value. The value becomes smaller. It means that the smaller the P value is, the higher the probability that the average values of the two sets of data are different. A function that associates the t value with the P value is called a t distribution. FIG. 6 shows the result of the correction proposed by Yang et al., And FIG. 7 shows the result of the correction according to the present invention. Comparing the two figures, it can be seen that the result according to the present invention clearly distinguishes the straight line portion and the point deviated from the straight line. Table 1 lists t values and P values of 12 genes in ascending order of t value. In FIG. 6, there are four points on the left side of the straight line that are slightly displaced (Nos. 8, 9, 10, and 11 in Table 1), and it is difficult to distinguish them. In FIG. 7, it is clear that 3 out of 4 points are on the straight line and 1 point is off the straight line. In this case, one point deviated from the straight line can be judged to be data having a different property from the remaining three points. A point deviating from the straight line means that it is out of the t distribution, and it can be concluded that there is a difference in the expression level between the knockout mouse and the normal mouse. That is, it is shown that whether or not the expression level is statistically significantly changed can be discriminated with higher accuracy by the t-test and the outlier of the distribution of the t-values.

From the above, it was found that the DNA microarray data correction method of the present invention has a higher accuracy than the conventional correction method.

[0044]

[Table 1]

[0045]

EFFECTS OF THE INVENTION The present invention provides a method for correcting raw data obtained from a DNA microarray with higher accuracy, a correction device for DNA microarray data using the method, and a gene expression analyzer incorporating the correction device. It According to the method of the present invention, the same effect as the improvement of measurement accuracy by the improvement of hardware such as a DNA microarray can be obtained. The correction method of the present invention has been accumulated to date.
By applying it to the raw data of the DNA microarray, it is possible to obtain more reliable gene expression information from the already obtained data without performing a new experiment.

[Brief description of drawings]

FIG. 1 is a block diagram showing one embodiment of a DNA microarray data correction device of the present invention.

FIG. 2 is a diagram showing a flowchart showing the operation of the embodiment.

FIG. 3 is a diagram showing a plot of the difference between the average expression level and the expression level of raw data without correction.

FIG. 4 is a diagram showing a plot of the difference between the average expression level and the expression level of the data whose average value is corrected.

FIG. 5 is a diagram showing a plot of the difference between the average expression level and the expression level of the data in which the average value and the variance are corrected.

FIG. 6 is a diagram showing a probability point-probability point plot of t-values obtained from data with corrected average values.

FIG. 7 is a diagram showing a probability point-probability point plot of t-values obtained from data obtained by correcting mean values and variances.

[Explanation of symbols]

101 Means for storing expression data 1-N of genes 1-N derived from cell A 102 Expression data 1-N of genes 1-N derived from cell B
Storage means 103 correction means 104 output means

─────────────────────────────────────────────────── ─── Continuation of front page (51) Int.Cl. ⁷ Identification code FI theme code (reference) G01N 37/00 102 C12N 15/00 FF term (reference) 4B024 AA11 CA01 HA12 HA19 4B029 AA07 AA21 AA23 BB20 CC03 FA10 FA15 4B063 QA01 QA12 QA17 QA18 QQ03 QQ13 QQ42 QR32 QR38 QR56 QR80 QR82 QS25 QS34 QS39 QX02

Claims (7)

[Claims] 1. A method for correcting measurement data, wherein the difference in gene expression level between two types of samples is examined for each gene using a DNA microarray, which comprises the following steps: (A) DNA microarray By averaging the measurement data of the two types of samples obtained from
The step of obtaining the average expression level of each gene between the two types of samples, (B) by measuring the difference of the measurement data for each gene from the measurement data of the two types of samples obtained from the DNA microarray A step of obtaining a difference in the expression amount of each gene between samples, (C) a step of obtaining a simultaneous distribution using a difference between the average expression amount obtained in step (A) and the expression amount obtained in step (B) as a random variable, And (D) process
(C) converting the joint distribution obtained in advance into a distribution known in advance or a statistically expected distribution,
The method for correcting DNA microarray data, which comprises: 2. The method for correcting DNA microarray data according to claim 1, wherein the simultaneous distribution is a conditional distribution. 3. The method for correcting DNA microarray data according to claim 2, wherein the conditional distribution is an error distribution. 4. The method for correcting DNA microarray data according to claim 3, wherein the error distribution is a normal distribution. 5. A recording medium recording a program for executing the method for correcting DNA microarray data according to any one of claims 1 to 4. 6. A DNA containing the recording medium according to claim 5.
Microarray data correction device. 7. A gene expression analysis device incorporating the DNA microarray data correction device according to claim 6.