EP1550069A1 - Method for analysis of transcription variations in a set of genes - Google Patents

Abstract

The invention relates to a method for analysing the variations in concentration of RNA messengers obtained by transcription of a set of genes comprising the following steps:- measure the concentration of RNA messengers for each of the genes in the so-called reference cells and in test cells and report the results in a reference list and a test list, calculate a variation value for each gene which is a measure of the difference in concentration of m-RNA for said gene between the reference list and the test list, calculate a normalised variation value for each gene such that the cumulative frequency distribution of a sub-set of normalised variation values corresponding to genes has similar or identical m-RNA concentrations whatever the sub-set under consideration and identification of the genes with m-RNA concentration variations significantly different to normalised variation values.

Description

 METHOD OF ANALYSIS OF TRANSCRIPTION VARIATIONS OF AN ASSEMBLY

GENOA

The present invention relates to the analysis of variations in m-RNA concentrations of a set of genes carried out using DNA chips.

The analysis covers all types of living cells such as a bacteria, a brewer's yeast cell or a cell from a part of the human body. One or more DNA molecules are present in each cell. Each DNA molecule is made up of two complementary polynucleotide strands, an "antisense" strand (-) and a "sense" strand (+). Each polynucleotide strand consists of a polymeric chain of nucleotides. Each nucleotide consists of a phosphate, a sugar (deoxyribose) and a base, the bases possibly being a guanine (G), an adenine (A), a cytosine (C) and a thyine (T) . The two strands of the DNA molecule pair via hydrogen bonds between complementary bases, a guanine which can pair with a cytosine (G ≡ C) and an adenine which can pair with a thymine (A = T).

When a cell is active and living, each gene synthesizes RNA-messenger molecules, or mRNA, which are base-to-base copies of the sense (+) strand of the gene. This phenomenon is called transcription or expression of the gene. More precisely, the transcription of a gene is carried out only for certain groups of consecutive bases, or sequences, of the strand of the gene which is expressed, the sense strand (+). L ¹ mRNA produced by a gene is in fact a grouping of copies of sequences. Depending on the cell, not all genes are expressed in the same proportions. Thus, • the concentration of mRNA relative to a given gene can be zero, or vary between 1 and 10,000 per cell.

A known method for measuring the concentration of mRNA is to use DNA chips. Cells are taken from a culture or from a human body by biopsy. The transcription activity of these cells is then stopped, for example by freezing. A sample is then prepared containing the mRNA extracted from a certain number of cells in solution.

A DNA chip is also prepared, an example of which is illustrated in FIG. 1 in order to analyze a set of genes. On each chip, each gene is analyzed by means of two sets of around twenty hybridization units. A hybridization unit groups together a set of identical DNA strands called probes. These DNA strands are complementary strands of a gene sequence which is found in the mRNA of the cells analyzed. These DNA strands have sequences identical to those of the antisense (-) strand of the gene. A first set of hybridization units, called perfect (UP), contains probes which correspond to different sequences of a gene. A second set of hybridization units, called imperfect (IU), contains probes which differ from the probes of the first set for at least one of the bases, each perfect hybridization unit being associated with an imperfect hybridization unit. In the example of FIG. 1, a perfect hybridization unit 2 contains probes 3, 4, 5, 6 and 7. The perfect hybridization unit 2 is associated with an imperfect hybridization unit 10 which contains probes 11, 12, 13, 14 and 15 which differ by a base (A, G) compared to probes 3 to 7.

The messenger RNAs of the previously prepared sample are "labeled", for example rendered fluorescent. The fluorescence of the strands is represented by a cross in a circle attached to the fluorescent strand. The tagged RNA-messengers are called targets.

The DNA chip is then placed in the target sample under conditions favoring hybridization between complementary DNA strands. Thus, we can see in Figure 1 a total hybridization of targets 8 and 9 with two probes respectively 4 and 6 fixed on the perfect hybridization unit 2. It is possible that a partial hybridization occurs between a target 10 and a probe 5 not completely complementary. It is possible that a target 16 which is a messenger RNA perfectly complementary to one of the sequences of a gene represented by probes 3 to 7 of the perfect hybridization unit 2, may come to hybridize partially with a probe 12 of the imperfect hybridization unit 10. Similarly, it is possible that another target 17 may come to partially hybridize with a probe 13 of the imperfect hybridization unit 10. A washing step possibly makes it possible to dissociate the strands which are not very complementary and thus limit the number of false appearances. A photograph is then taken of each of the hybridization units of the DNA chip in order to determine for each hybridization unit a fluorescence intensity. After measuring the fluorescence intensities, two fluorescence intensity values iy and ± J are obtained for each pair of perfect and imperfect hybridization units corresponding to a gene sequence. A fluorescence intensity is calculated for each gene sequence equal to the difference between the fluorescence intensity values i-gp and iui- This method of measuring the fluorescence intensity of each sequence makes it possible to obtain a better signal ratio on noise. We calculate then a fluorescence intensity value for each gene by taking the average of the fluorescence intensities of each of the sequences of this gene. This gives a list showing a fluorescence intensity value for each of the genes. The intensity of fluorescence being proportional to the concentration of m-RNA resulting from the transcription of a gene, one can easily obtain a list reporting the concentration of m-RNA for each gene. In the case where a gene expresses very little, it is possible that the fluorescence intensity of the imperfect hybridization units is higher than that of the perfect hybridization units. The average fluorescence intensity of such a gene can be negative. In this case, it is generally considered that the discomfort is not expressed, and therefore that the associated concentration of mRNA is zero. Currently, we want to analyze the variations in mRNA concentrations between so-called reference cells and so-called test cells. It is this analysis of variations which will be the subject of the remainder of this description and of the invention. The reference cells could be, for example, healthy liver cells and the test cells, diseased liver cells. The same DNA chip models are used, and in both cases the sequence of operations described above is carried out. The study of variations in the concentration of m-RNA for each gene makes it possible to identify which genes have the concentration of m-RNA changed, following a modification of the transcription activity, or a change in the lifespan of mRNAs. The lifespan of mRNA fluctuates among other things as a function of more or less significant protein synthesis activity. Conventionally, the analysis of variations in mRNA concentrations for each of the genes is carried out by calculating the ratio of the mRNA concentrations of the same gene. This method is known as the "fold change" method. The change in m-RNA concentration is considered to be significant when the ratio of RN-m concentrations is above a predetermined threshold. This threshold is identical for all of the genes and this method therefore does not allow the specificity of each of them to be taken into account.

The processes of creation and destruction of m-RNA are interrupted randomly during the collection of cells and the concentration of m-RNA may fluctuate slightly from one cell to another. In the case where a gene produces on average 10 mRNA in each cell, a difference of only one

MRNA between two cells leads to a ratio of 1.1, or 10% difference, and the gene in question will be considered to have a significant difference in mRNA concentration. On the contrary for a gene having on average 1000 mRNA per cell, a difference of 10 mRNA leads to a ratio of 1.01, or 1% difference, and this will go unnoticed when it can be completely abnormal.

The "fold change" analysis is therefore unreliable because genes with a significant variation in their concentrations may not be identified.

In addition, the concentration of m-RNA relative to a gene can naturally vary in its own proportions. With a simple fold change analysis, it is impossible to know to what extent the variation in the concentration of m-RNA relative to a gene remains or not within acceptable proportions. One way of knowing the range of natural variation of the mRNA concentration relative to a gene, or more precisely the cumulative distribution of frequencies, would be to carry out a large number of mRNA concentration measurements, for each gene. from identical reference cells. In the case where 100 measurements have been made for each gene, it is possible to define threshold values corresponding to probabilities in increments of 0.01 so that the same discomfort associated with identical cells has a higher concentration of mRNA at these threshold values. When measuring the mRNA concentration of different cells, we can know what is the probability of obtaining a concentration of mRNA greater than the threshold value chosen without this concentration of mRNA being abnormal.

In practice, it is impossible to carry out as many measurements and the threshold value chosen is unreliable.

An object of the present invention is to provide a method for analyzing the variations in mRNA concentrations relating to a set of genes which makes it possible to take into account the specificity of each gene. Another object of the present invention is to provide such a method which makes it possible to identify genes exhibiting a significant variation in their mRNA concentrations with a limited number of measurements.

Another object of the present invention is to provide such a method which makes it possible to define a threshold value very precisely.

To achieve these objects, the present invention provides a method for analyzing variations in concentrations of messenger RNAs obtained by transcription of a set of genes comprising the following steps: a) measuring the concentration of messenger RNAs for each of the genes in so-called reference cells and report the results on a reference list (L _re f); b) measure the concentration of messenger RNA for each of the genes in so-called test cells and report the results on a test list (L ^ est) _• 'c) calculate for each gene a variation value (Var _j ) , k being an integer between 1 and n, which is a measure of the difference between the mRNA concentrations of said gene between the reference list (L _re f) and the test list

( ^L test) • 'd) classify genes into prime. and second groups, depending on whether the genes have variation values corresponding respectively to an increase or a decrease in their mRNA concentrations between the reference list and the test list; e) calculate for each gene of the second group a new variation value (Var ^) which is a measure of the difference between the concentrations of m-RNA of said gene between the test list and the reference list. f) calculate for each gene a normalized variation value (Z ^) such that the cumulative frequency distribution of a subset of normalized variation values corresponding to genes with close m-RNA concentrations is identical regardless either the subset considered; and g) identify genes exhibiting significant variations in mRNA concentrations from the normalized variation values.

According to an embodiment of the method of the present invention, the step of identifying the genes consists in selecting the genes whose normalized variation value is greater than a determined threshold value (Z _seυ j _] _). According to an embodiment of the method of the present invention, the determination of the threshold value (Z _seu j_) comprises the following steps: h) measuring the concentration of m-RNA for each of the genes of two identical groups of so-called calibration cells and report the respective results on first CL> etal l) and second (Iié al 2 ^ calibration lists; i) calculate for each gene a variation value (Vargtal k) according to the method of steps c ) to e) from the first (L _e t _a li) ^and second {I _* stall 2) calibration lists; j) calculating for each gene a normalized calibration variation value (Z _re fj according to the method of step f); k) construct the cumulative frequency distribution, called calibration, of the normalized calibration variation values associating with any calibration variation value normalized (Z _{re r} ] ς) a probability, called the probability of selection error (Pseuil, k) 'for there to be normalized calibration variation values greater than the normalized variation value considered; 1) choose the probability of selection error desired (p _S euil) _* ^and m) define the threshold value (Z _seu; j_ι) corresponding to the probability of selection error desired (Pseuil) ^ using the cumulative distribution of calibration frequencies. According to an embodiment of the method of the present invention, the step consisting in choosing the probability of selection error (p _S uil) comprises the following steps:

- define the maximum acceptable false positive rate for the identification of genes; and ^' - identify the probability of selection error

Pthr ^{and a} threshold value Z _seu - maximum to obtain an acceptable rate of false positive, the rate of false positive TFP being equal to:

pseuil * n TFP = - ^

(number of genes for which Z> Z threshold) where n is the number of genes considered.

According to an embodiment of the method of the present invention, the step of identifying the genes consists in selecting the genes whose normalized variation value is greater than a first threshold value for the genes of the first group and greater than a second threshold value for the genes of the second group.

According to an embodiment of the method of the present invention, the determination of the first and second threshold values consists in choosing first and second probabilities of selection error desired respectively for the first and second groups and in defining the first and second corresponding threshold values using the cumulative distribution of calibration frequencies. According to an embodiment of the method of the present invention, the choice of the first and second threshold values consists in carrying out the method of claim 4 successively for the first and the second group. According to an embodiment of the method of the present invention, the variation value Var ^ of a gene is equal to the difference between the concentrations of m-RNA of said gene for different cells.

According to an embodiment of the method of the present invention, the value of variation Var ^ - of a gene is equal to the ratio of the concentrations of m-RNA of said gene for different cells.

According to an embodiment of the method of the present invention, the method comprises for each list the following steps:

- classify the genes in ascending order of their mRNA concentrations;

- assign a zero rank value to all genes whose RN-m concentrations are less than or equal to a threshold concentration value;

- assign a unique rank value to each of the other genes whose mRNA concentration is greater than the threshold concentration value, the rank value being between 1 and ni, the rank R of a gene being d 'the higher the higher the m-RNA concentration of said gene; and

- normalize the values of ranks over a range from 0 to w, w being a positive integer, the rank r of a gene now being equal to (R * w) / n where n is the number of genes studied.

According to an embodiment of the method of the present invention, the variation value of a gene is equal to the difference between the ranks of the gene for the two lists analyzed.

According to an embodiment of the process of the present invention, the normalized variation value Z of each gene is obtained according to the following formula: Var - μ (g)

Z = σ (g) where Var is the variation value of said gene and μ (g) and σ (g) are respectively the mean and the standard deviation of a set of variation values corresponding to a set of genes having m-RNA concentrations close to the m-RNA concentration of said gene.

According to an embodiment of the method of the present invention, the normalized variation value is calculated according to the following steps: - assign a unique rank value r to each gene equal to the rank value of the reference list for the genes of the first group and equal to the rank value of the test list for genes of the second group.

- calculate the normalized variation value Z ^ of the gene according to the following formula: _{z =} Var -μ (r) σ (r) where Var is the variation of said gene, μ (r) and σ (r) are respectively the mean and the standard deviation of a set of variation values corresponding to a set of genes having ranks close to rank r of said gene.

According to a variant of the method of the present invention, the method aims to analyze the variations in m-RNA concentrations of a set of genes from m identical groups of so-called reference cells (GR ^ to G ^ and q groups identical to so-called test cells (GT _] _ to GTg), the method comprising the following steps:

- for all or part of the combinations of groups (C_ j) comprising a reference group (GRj) and a test group (GTj), carry out the following three steps: - construct the cumulative distribution of frequencies called calibration according to the method of steps h) to k) from first and second calibration groups (GR ^ tal 1 ^{and GR} etal, 2) P ^r i ^s both from the m reference groups or both from the q test groups, one of the groups possibly being the reference group (GR ^) or the test group (GTj) the combination of groups considered; - implementing steps a) to f) to determine a normalized variation value (Zj_, ₇ ]) for each gene; define for each gene a probability value, called probability of error (pi, j, k) 'corresponding to the normalized variation value of this gene (Z ^ j ^) from the cumulative distribution of calibration frequencies; calculate for each gene, a grouping value (R ^) according to a grouping method taking into account the set of error probabilities (pj_ _. j, k) of said gene obtained for each of the combinations (Cj_ _f j) of groups reference and test chosen; and identifying as having significant variations in mRNA concentrations the genes whose grouping value is greater than a determined threshold grouping value (R _S euil).

According to an embodiment of the method described above, the first and second calibration groups (GRétal i and Ggtal _X) are identical whatever the combination of groups considered. According to an embodiment of the method of the present invention, the normalized calibration variation values (Z _re fj are calculated according to the previously defined method _{z =} Var - μ (g) σ (g) and the variation values standardized between a test and reference list are calculated according to the following formula:

Var - μ prop (r) σ prop (r) where the functions μgtalW ^{and σ} ëtal ( ^r ) are obtained by smoothing the means μ (r) and standard deviations σ (r) calculated before the normalized calibration variation values. According to an embodiment of the present invention, the determination of the threshold grouping value (Rseuil) comprises the following steps:

- calculate for each gene, a calibration grouping value (Rétal k) according to the grouping method from the calibration error probabilities (Pétai k) of said gene obtained from the cumulative distributions of calculated calibration frequencies for each combination of groups (Cj ^ j) chosen;

- construct the cumulative frequency distribution, called grouping, from the calibration grouping values by associating with any calibration grouping value a probability, called the calibration grouping error probability, so that there exists calibration pool values greater than the relevant calibration pool value; - select the desired probability of selection of grouping error (p2 _seu iχ); and

- define the threshold grouping value (Rseuil) corresponding to the probability of selection grouping error (p2 _seuj _ _] _) using the cumulative distribution of grouping frequencies.

According to an embodiment of the present invention, the step of selecting a probability of selection of grouping error _(if p2) comprises the steps of: - defining the maximum acceptable rate of false positive for one identification genes; and

- identify the probability of selection grouping error P2 threshold ^and 1 ^& maximum threshold Σ-threshold grouping value allowing an acceptable false positive rate to be obtained, the TFP false positive rate being equal to _{r ™} O2threshold * n

TFP = -

(number of genes for which Rk≥Rseuii) where n is the number of genes considered.

According to an embodiment of the present invention, the grouping method comprises the following steps:

- distribute the combinations of groups in different sets; calculating for each set an intermediate value for each gene equal to the product or to the sum of the error probabilities (Pi j] ς) of the gene obtained for each of the combinations of groups of the set;

- calculate for each annoyance a grouping value (Rk) equal to the average of the intermediate values calculated for each set. According to a variant of the method of the present invention, the method aims to analyze the variations in mRNA concentrations of a set of genes from m identical groups of so-called reference cells (GRη_ to GR _j ^) and q identical groups of so-called test cells (GT _] _ to GTg), the method comprising the following steps:

- carry out steps a) and b) for each of the reference and test groups giving m reference lists and q test lists;

define for each of the lists a rank value for each gene according to the method described above;

- define a global reference list associating with each gene a unique rank equal to the average of its ranks in the reference lists;

- define a global test list associating each gene with a unique rank equal to the average of its ranks in the test lists;

- carry out steps c) to g) from the global reference and test lists, the variation values being equal to the difference in ranks and the variation values normalized being calculated according to one of the methods previously described.

According to an embodiment of the method of the present invention, one or more reference, test or calibration lists are obtained according to a method of creating an artificial data set comprising the following steps:

- implementing steps h) to k) making it possible to obtain a cumulative distribution of calibration frequencies;

define for each gene a normalized variation value by making a random draw from the cumulative distribution of calibration frequencies, all the normalized variation values thus defined having a cumulative distribution of frequencies identical to that of calibration. These objects, characteristics and advantages, as well as others of the present invention will be explained in detail in the following description of particular embodiments given without limitation in relation to the attached figures, among which: FIG. 1 represents a chip DNA; FIG. 2 is a representation of variation values of m-RNA concentration relating to a set of genes used according to a first step of the invention; FIG. 3 is a representation of normalized mRNA concentration variation values relating to a set of genes used according to a second step of the invention; FIG. 4A represents a cumulative frequency distribution of RN-m concentration variation values for a first set of genes; Figure 4B shows a cumulative frequency distribution of mRNA concentration variation values for a second set of genes; FIG. 4C is a "quantile versus quantile" curve of the variation values of m-RNA concentrations of the first and second sets of genes; FIG. 5A represents a set of "quantile against quantile" curves of non-normalized variation values obtained according to a "fold change"method; FIG. 5B represents a set of "quantile against quantile" curves of non-normalized variation values obtained according to a row shift method; FIG. 6A represents a set of curves

"quantile against quantile" of normalized variation values obtained according to a fold change method; and FIG. 6B represents a set of "quantile against quantile" curves of normalized variation values obtained according to a row shift method.

The method of analysis of the present invention provides for using DNA chips to analyze a set of n genes and to study the variations in m-RNA concentrations between reference cells and test cells. In the first part, an analysis of the variations between a group of test cells and a group of reference cells will be described.

In a second part, we will describe a means of determining a threshold value which makes it possible to select genes having significant variations.

In a third part, the advantages of the invention compared to the prior art will be demonstrated.

In a fourth part, the method according to the invention will be generalized to the analysis of several groups of test and reference cells.

In a fifth part, we will describe a method of constructing artificial data sets.

In a sixth part, an application of the method according to the invention will be described which consists in analyzing the variations in m-RNA concentration as a function of time (study of kinetics) or according to successive modifications of the culture conditions of a set of cells (experiment of the dose / response type).

1. Comparison between a test group and a reference group

The method of analysis of the present invention provides for using DNA chips to analyze a set of n genes and to study the variations in m-RNA concentrations between a group of reference cells and a group of test cells. The concentration of mRNA Ck relative to each gk gene (k being a number between 1 and n) is measured beforehand and the values are reported on reference lists L _re f and test £ _eS .

The method of analysis begins with the calculation for each of the genes of a value of variation of mRNA concentration, or value of variation Var, which can be equal to the difference of the concentrations of mRNA of each gene between the reference and test groups ref ^{or c} k test and Ck ref respectively the mRNA concentrations of the gk gene on the test and reference lists) or also equal to the ratio of the mRNA concentrations (Va ^ ≈ Ck test / ^c k ref) <• ^which corresponds to the method "fold change" described above.

According to the present invention and before calculating the variation values, the genes are classified in ascending order of their mRNA concentrations for each of the reference and test lists. A value of zero rank is then assigned to all the genes whose mRNA concentration is equal to zero or more broadly to all the genes whose mRNA concentration is less than a threshold concentration value corresponding to a estimation of measurement noise. Each of the ni other genes is then assigned a unique rank value, the rank value being between 1 and ni. The set of rank values forms a continuous series of integers between 0 and ni. The higher the rank of a gene, the higher its mRNA concentration. In addition, variations in the method of measuring the concentration of mRNA from DNA chips results in a greater or lesser variation in the values of RNA concentration. Two identical groups of cells can have concentration values varying between 10 and 10,000 for the first group and between 50 and 11,000 for the second group.

In order to realign the ranges of values of m-RNA concentrations and to overcome the possible differences between the numbers n_ of genes for which the RN-m concentration is greater than a given threshold concentration value, we proceed to a normalization of the values of ranks over a range going for example from 0 to 100. The rank r of a gene g is now equal to (Rkxl00) / n, where Rk is the non-normalized rank of the gene gk- According to the present invention the variation value of each gene is expressed as being the difference between the rank of the gene in the reference list and the rank of the gene in the test list. The variation value, Vark, of each gk gene is calculated as follows: ^Var k ^≈ r _test , k - r _re f, k ⁽ D where r ^ st k ^{and r} ref k are respectively the ranks of the gk gene from the lists of test and reference.

This way of expressing the variation values according to the invention is hereinafter called "row shift" method. FIG. 2 represents a set of positive Vrk variation values calculated according to the "row shift" method. The rows are indicated on the abscissa. The variations are indicated on the ordinate. Each variation value of a gene is represented by a cross whose abscissa corresponds to the rank of this gene for the reference list. Although this is not visible in Figure 2 ^'because of the large number of genes considered, each value of x-axis (row) corresponds to a single gene, and thus to a single value of variation.

It will be noted that the genes whose rank is small have a greater amplitude of average variation than genes with a high rank value. This corresponds, as indicated above, to the fact that, for genes expressing little, the variations are likely to be greater. Thus, a method consisting, as in the prior art, of fixing an identical threshold variation value for the genes which express little and those which express a lot would lead to consider that the genes exhibiting a significant variation are the only genes having a low rank and therefore a low concentration of mRNA. To overcome this drawback, the present invention provides for defining a threshold variation value which is a function of the rank of the discomfort. More particularly, the analysis method of the present invention includes a normalization method. Genes are classified into two groups. The genes whose variation value indicates an increase in their mRNA concentrations between the reference list and the test list are placed in a first group. The others ^" are put in a second group and a new variation value is calculated for these genes by inverting the test and reference lists.

Thus in the case where the variation value is expressed according to the row shift method, the genes of the first group are the p _OS genes whose variation is positive or zero (r ^ is k ^{=> r} ref k for a gk gene ), the genes of the second group are the n _ne g genes whose variation is strictly negative (^ is k ^<r ref k For a g gene). For each gene of the second group we recalculate a variation value V ^ - equal to the opposite of the initial value. All variation values are now positive. In the case where the variation value is expressed according to the "fold change" method, the variation values of the genes exhibiting a decrease in their concentration (value less than 1) between the reference group and the test group are replaced by 1 inverse of the initial values. The variation values are therefore all greater than 1. According to an embodiment of the normalization method of the present invention, a set of neighboring rows, or else "window" of rows, is selected for each gene gk of rank ^. We then calculate the average value of the variation values corresponding to this row window which constitutes a local average μ (g) •

We also calculate a local standard deviation σ (g) of the variation values for each discomfort gk using the same window as for the calculation of the local average. The curves 20 and 21 in FIG. 2 respectively represent the general shape of the values μ (g) and σ (g) after smoothing.

From the values μ (gk) and σ (g). preferably taken after smoothing, a normalized variation value Zk is calculated for each of the gk genes according to the following formula: _z Vark ~ μ (9k) σ ⁽ g) According to a variant implementation of the method of the present invention, the normalization process is carried out separately for each of the first and second groups of genes. The values μ (gk) and σ (g) are calculated for each group from the variation values of a set of genes from the same group.

FIG. 3 represents the set of normalized variation values Z obtained for each of the variation values Vark ^ ^e l ⁱⁿ FIG. 2. As in FIG. 2, the abscissa designates the rows and a value of abscissa corresponds to a single value of normalized variation. The curves 30 and 31 correspond respectively to the local means and to the local standard deviations, not smoothed, calculated from the Z values in the same way as that had been done previously from the Vark values, and described above. Curves 30 and 31 show that the local means and the local standard deviations are now substantially constant whatever the rank, which means that genes with different mean mRNA concentrations have normalized variation values that follow the same cumulative frequency distribution.

In general, any normalization method can be used such that the cumulative frequency distribution of a subset of normalized variation values corresponding to genes in the same row window is substantially identical regardless of the subset. considered.

At one end of one stage of standardization, it is determined a threshold value _seu j_ι, possibly different for the first and the second group of genes, and selecting the genes whose standardized variation value exceeds the threshold value.

According to a fundamental aspect of the present invention, this threshold value is identical for all the genes and the selection criterion is homogeneous whatever the rank of the genes analyzed, that is to say regardless of their concentration of RNA- m average.

An advantage of the analysis method according to the present invention is that it makes it possible to identify genes exhibiting a significant variation in their mRNA concentrations from a limited number of measurements.

2. Determination of a threshold value

The present invention also proposes to define a threshold value according to the method below.

A calibration step is carried out which consists in determining the variations in the normal RN-m concentrations of each of the genes by studying two groups of identical cells called calibration, the concentration of m-RNA of each gene being plotted on two calibration lists Lg al 1 ^{and L} êtal 2 •

A calculation of normalized calibration variation values is carried out according to the row offset method and the normalization method previously described. One of the two calibration lists Lg ^ al 1 ^{and L} étal 2 ^is considered as a test list and the other as a reference list. We obtain and a calibration variation value Var _e t _a k P τ_ ° ^ur each gk gene and a normalized calibration variation value ^z k stall for each of the genes.

Here again, a set of normalized calibration variation values is obtained whose local means and local standard deviations are substantially constant.

In one embodiment of the method of the present invention, local averages are smoothed used for the calculation of Zetal k- ® ⁿ obtains two calibration curves representing the mean μetal ( ^r ) ^and the standard deviation r ^ tal ^) of the variations in calibration as a function of rank, any reference to a given gene being deleted . During a comparison between a test group and a reference group, the normalized variation values Z are calculated from these calibration curves according to the formula:

₌ Vaq _{: - μétalW ^σ étal (^ k)

The groups of calibration cells can be reference cells, test cells or other cells deemed suitable. The choice of cells used is dictated by the effect of the μêt values ^{(r) and σ} stall ^{(r) are} normalized ^on variation values Z - These are even smaller than the mean values and standard type are great. The values μetal ( ^r ) ^{and σ} etal ( ^r ) depend on the one hand on the reproducibility of the experimental conditions (DNA chips not perfectly identical) and on the other hand on the stability of the biological system of the chosen cells. The experimental conditions are assumed reproducible biological system μétal present values ^{(r) and σ} stall ^(r) all the greater that it is unstable. Thus calibration from two cancer cells will give higher μetal ( ^r ) ^e ^ ^σ cal ( ^r ) values compared to those obtained from two normal cells. Consequently, the calibration must be performed on a biological system which has the same stability characteristics as the system constituted by the test and the reference.

In the case where the test and the reference have both been duplicated, the calibration curves are constructed independently for each of the pairs, which leads to two pairs of calibration curves (^ test ' ^σ test) ^and ^ ref' ^σ ref) • ⁰ⁿ then evaluates which of the two systems is more unstable (μ or / and σ higher). This assessment can be done in different ways. One can for example calculate two sets of standard variation values using respectively (μtest ^'σ test) ^and (f ^ ref' ^σ ref) • P ^{0l1 was} F ^or example build for each set a cumulative frequency distribution. We compare the two normalized variation values corresponding for example to the 75 ^th percentile (probability equal to 0.75). The system with the highest value is the most unstable. In general, the results of the analysis method of the present invention are better if the calibration curves constructed from the most unstable system are used.

According to one aspect of the present invention, a cumulative distribution of calibration frequencies is constructed from all the normalized variation values. Normalized variation values for all genes, regardless of their rank, follow this cumulative distribution of calibration frequencies. Indeed, as will be established more precisely in relation to FIG. 6B, any subset of normalized calibration variation values corresponding to genes of the same row window follows the same cumulative distribution of frequencies and it is therefore possible to construct a single cumulative distribution of frequencies from all the normalized calibration variation values. Given the large number of genes studied and therefore the large number of normalized calibration variation values obtained, the cumulative distribution of resulting calibration frequencies is very precise. From this cumulative distribution calibration frequencies, is associated with all normalized calibration variation value ^z Stall, k ^Probability, called p selection error probability _is uil k 'for that there are values of normalized calibration variation naturally greater than the latter.

During a comparative analysis between test and reference cells according to the method previously described in relation to FIGS. 2 and 3, the probability of error can now be defined using the cumulative distribution of calibration frequencies. p _is uil selection corresponding to the probability that it exists naturally standard variation values greater than the threshold value _seu ^; L chosen to select genes. An advantage of the analysis method according to the present invention is that it makes it possible to associate a probability of selection error with any threshold value Z _seu j_τ_ chosen.

Another advantage of the analysis method according to the present invention is that it allows to choose a threshold value _{seu j_.} very precise with a limited number of measurements.

From the cumulative distribution frequency of calibration, it is possible to define a set of statistical parameters, knowledge to choose the best p selection error probability _is UIL Knowing the number of genes studied, one can know the proportion of "normal" genes among all the genes identified as having a normalized variation value k greater than Z _seu -. This proportion of normal discomfort is called the TFP false positive rate and is defined as follows:

TFP = ₇ ^^,

[number of genes for which Z ZseuilJ

In the case of a separate analysis of the first and second groups of genes, a first and a second false positive rate are defined. We replace n by the number of genes of the first group np _OS or of the second group n _ne g, the threshold Pseuil / ^z values possibly being different for each group of genes.

One can choose a very small Pseuil selection error probability allowing to obtain a very low false positive rate. Nevertheless, it may be beneficial to choose a probability p _is pleased uil large and thus a Z _seu i] _ smaller in order to select and therefore subsequently studied more genes.

In addition to the false positive rate, it is possible to know the sensitivity of the selection. The cumulative frequency distribution of the normalized variation values Zk obtained during the comparison between test and reference cells is constructed beforehand. From this distribution, it is possible to associate with any normalized variation value k a probability, called probability of observation Pobs k 'so that normalized variation values greater than the latter are observed.

From the values of probability of selection error p _seu ii ^and of probability of observation p ₀ £, sk of each gene, it is possible to define the fraction F of genes for which the value of variation Vark ^has increased relative at the value of calibration variation Variai k- ^The fraction F is defined as being the maximum value of the set of values Pobs k ~ Pseuil k calculated for each gene gk . If Pseuil, k ^is the probability of selection error chosen, the false positive rate can be defined as being equal to Pseuil k / Pobs k- When we choose a pair of values Pseuil / ^Z threshold 'l ^has sensitivity, equal to (Pobs k "Pseuil k) / ^F 'makes it possible to know if among the selected genes, the number of genes actually showing significant variations is representative of the number of genes whose variation values have increased (Vark> ariai) •

An advantage of the analysis method according to the present invention is that it allows to associate a false positive rate and a sensitivity value of any threshold value _seu i] _ and therefore to any Pseuil selection error probability value chosen.

3. Demonstration of the advantages of the invention

FIGS. 4A to 4C illustrate the construction of a "quantile against quantile" curve. FIG. 4A represents a cumulative distribution of frequencies C ^ of a first subset of variation values taken from the set of variation values (Var) obtained during a comparative study. The variation values are plotted on the abscissa. We indicate on the ordinate the probability (proba) so that there are variation values lower than the variation value on the abscissa.

FIG. 4B is another cumulative distribution of frequencies C2 of a second set of variation values taken from the set of variation values of the comparative study.

FIG. 4C is a "quantile against quantile" curve C3 obtained from curves C1 and C2 in FIGS. 4A and 4B. The variation values of the first studied set are represented on the ordinate, and the variation values of the second studied set are represented on the abscissa. The curve

"quantile against quantile" is obtained by taking for each probability value (between 0 and 1) the corresponding variation values on the curves C1 and C2 and by defining a point having these two values respectively for ordinate and abscissa. The point 40 of the curve C3 has the abscissa VI 'and the ordinate VI, VI and VI' being respectively the values of variation of the curves Cl and C2 corresponding to the probability 0.1. Similarly, the points 41 and 42 of the curve C3 have the respective abscissa V2 'and V3' and for the ordinate V2 and V3, the variation values V2, V3 of the curve Cη_ and

V2 ', V3' of curve C2 having respective probabilities 0, 5 and 0.9. A “quantile against quantile” curve is thus obtained for two subsets of variation values. In the example of FIG. 4C, the curve C3 is relatively far from the diagonal drawn in dotted lines, which means that the first and second subsets of variation values have different distribution functions.

FIG. 5A represents a set of "quantile against quantile" curves obtained by studying different subsets of variation values calculated according to a Fold Change method. The most flattened curves are obtained by taking subsets of variation values whose respective ranks are very far apart. This demonstrates that genes with different ranks have variation values that follow different distribution functions.

FIG. 5B likewise represents a set of "quantile against quantile" curves obtained by studying different subsets of non-normalized variation values calculated according to a row shift function. We can also observe a difference between the distribution functions for genes with very distant ranks.

FIG. 6A represents a set of "quantile against quantile" curves obtained by studying different subsets of normalized variation values calculated according to the Fold Change function and the normalization method of the present invention. The curves approach the diagonal which means that genes with different ranks have normalized variation values which follow relatively similar distribution functions. However, there are relatively large divergences for the values corresponding to high probabilities.

FIG. 6B represents a set of "quantile against quantile" curves obtained by studying different subsets of normalized variation values calculated according to the row shift method and the normalization method of the present invention. The curves are all very close to the diagonal, which means that the set of normalized variation values follows the same cumulative frequency distribution. This demonstrates that, by combining a calculation of the variation values according to the row shift method of the invention and a normalization of these values according to the normalization method of the invention, a set of normalized variation values is obtained which follow the same cumulative distribution of reference frequencies.

As a result, thanks to the analysis method according to the present invention, it is possible to study each gene individually from only three measurements of m-RNA concentrations with DNA chips when a large number of measurements was necessary. before. 4. Comparison between several test and reference groups

In the case where several measurements of ARN-m concentrations for each gene are available and obtained from m reference groups GR_ to GR ^ and q test groups GT ^ to GTg, a method of multiple analysis according to the present The invention aims to identify more precisely which genes exhibit the most significant variations in mRNA concentrations. The multiple analysis method includes multiple analyzes of variation between reference and test lists. For all or ^"part of the combinations C i j comprising a reference group GR ^ and a test group GT is calculated for each gene gk, an amount of change Var ^ j ^ according to the offset method of ranks and an amount of change normalized Zj_ jk according to the normalization process of the invention.

In parallel, a calibration step identical to that described above is carried out. After selecting two GR ^ calibration groups have] _ and ^ al GR 2 among the m reference groups, is calculated for each gene g a normalized calibration variation value Zgtal k by ^means of the offset method of rows and of the standardization process of the invention. A cumulative distribution of calibration frequencies is constructed from all the variation values calibration standards. It is thus possible to associate with a normalized value of variation of calibration Zg ^ al k ^a probability, called probability of error of calibration Pétai k 'so that there exist values of normalized variation naturally higher than this last.

According to an alternative embodiment, a cumulative distribution of grouping frequencies is constructed for each combination C- ^ j chosen from two reference groups one of which is the GRi group or two test groups whose one of them is the group GT-j of the combination Cj_ considered.

From the cumulative distributions of calibration frequencies, a probability is defined for each gene gk, called the probability of error Pi k _/ corresponding to the normalized variation value Z j _{k of} said gene. In the case where only a cumulative calibration frequency distribution is available, the error probabilities Pi j, k are all equal.

According to an alternative embodiment, it is determined whether the values of variation of a gene obtained for each CL H combination corresponds to an increase (positive variation) or to a decrease (negative variation) in the mRNA concentrations between the group of reference cells GRj_ and the group of test cells GTj. For a particular gk gene, some of the probabilities Pi -1 k correspond to positive variations and other values Pk i correspond to negative variations. The product Prodpp _OS of the values Pi, j, k corresponding to positive variations is compared to the product Prodp _n gg of the values Pi, j, k corresponding to negative values. If Prodp _OS is less than Prod _n £ g we consider that the variation of the gene is positive and all the probabilities Pi, k corresponding to negative variations take the value 1 (conversely if Prodp _OS > Prod _n gg, the variation of the discomfort is considered negative and all the probabilities Pi H k take the value 1). In general, the result is homogeneous, i.e. the variation of the k gene is considered to be positive (or negative) for all combinations. If for a minority of sets the assignment procedure has resulted in giving the gk gene a sense of opposite variation, this is explained by the presence of an abnormal variation called artefactual which is easily detectable. These values are eliminated, which leads to a correct reassignment of the direction of variation.

Next, a grouping value Rk is calculated for each gene g from the gene error probabilities according to a grouping method. According to the same method, is calculated for each gene gk worth RETAL calibration combination, k ^using the calibration petai error probabilities, i, j, k corresponding to the normalized variation values Zêtal, i, k each gene obtained from the cumulative frequency distributions previously calculated. According to an embodiment of the grouping method of the present invention, the combinations chosen are distributed in different sets. We could for example constitute sets of independent combinations, two combinations Ci ^ ji and C 2 _r j2 being independent if the groups GRϋ and GR2 are different and if the groups GTji and

G j2 are different. In the case where there are as many reference groups as there are test groups (m = q), we could for example constitute m! sets of m independent combinations (if m <q we can constitute q! / m! sets of m independent comparisons). We then carry out for each set the product (or the sum) of all the error probabilities Pi k of the same gene gk in each set and we obtain an intermediate value for each set. Then computed for each ^'discomfort gk Rk a grouping value by taking the average of the intermediate values of each set.

As for a simple analysis between a reference list and a test list, a threshold grouping value R _S euil is defined in order to select the genes having grouping values greater than the latter. To this end, a cumulative distribution of frequencies, called grouping frequencies, from all the calibration grouping values. To any grouping value R _{k there} corresponds a probability, known as the theoretical probability Pthéo k 'so that there are grouping values greater than R. We can then associate a probability of group selection error P2seuil any threshold grouping value Rgeuil chosen. R _S ^and Pthr euil be chosen ^{according to} the false positive rate and the desired sensitivity.

This multiple analysis method makes it possible to increase the power of the analysis because it makes it possible to select genes whose variations in the concentration of mRNA are small and not significant in all the comparisons taken individually, but become significant when all possible comparisons are taken into account. b. Analysis of averages

The method of multiple analysis by analysis of means consists in constructing for the groups G] _ to GR _j n and GTτ_ to GTg a single group GR and GT. The concentration values of mRNA-m of the groups GR ^ to GR _j n and GT _X to GTq are expressed in the form of rank values, normalized on a scale of 0 to 100, as described in chapter 1. We construct two new ^L test ^{and L} ref lists indicating for each gene a unique rank value equal to the average of the rank values of the test groups and of the reference groups respectively. Calibration both lists is then constructed étall ^ k and _T k t l2 ^from two sets of N groups of identical cells (reference to test or otherwise), with N≈m if m <= q, or N = p if p <= m, according to the method described above. The same analysis process is then carried out as that used during a comparison between a single test group and a single reference group, the cumulative distribution of calibration frequencies being constructed from the two calibration lists. L _{étall / k} and Lêtal2, * 5. Construction of an artificial dataset

According to one aspect of the present invention, the cumulative distribution of frequencies of the variations of transcription signal normalized for a biological system makes it possible to construct artificial data sets, in the form of an artificial list _ar t associating with each gene a concentration value, the data set having the same statistical characteristics as the actual data used for the calibration. From two identical groups of Gl cells and

G2, the smoothed calibration curves μetal (9k) ^{and σ} cal (9) 'are constructed as described above, as well as the cumulative frequency distribution of the normalized calibration variation values. We then build an artificial data set either from Gl or G2 exclusively or from Gl and G2, used in turn. If we take for example Gl as the basis for artificially generating a data set, we consider the rank r of the gene gk- We do a random drawing of a number from a linear distribution over the interval [0, 1]. By interpolating this darkness on the cumulative distribution of calibration frequencies, we obtain a normalized variation value Z for the gene gk- If the gene increases between G] _ and G2, this normalized variation value is transformed into the value of variation according to formula:

Van ^, = Z * σétal () + μétal () and we deduce the new rank, rj _eu? k of the gene g by the formula ^r game, k ^{= r} k ^{+ Var} k

If j _{eU /} is greater than 100, we give it the value 100. If the gene gk decreases between G] _ and G2, we must find the new rank rj _{eU /} k such that:

Vark = ^z k * σ _eta l (rje, k) + μetal (rjeu, k) ^{and r} game, k = ^~ Va ± εr where εrest a constant to be determined. One of the possibilities for finding rj _eUf k consists in successively calculating, starting from the value immediately below rk, the absolute value of ε _r for any value ^r game, k less than r and taking the rank ^r game for new rank. , k for which the absolute value of ε _r reaches the first local minimum (ie when the absolute value of ε _r at the rank immediately below the rj _{eU /} considered becomes larger than at the rank rj _{eU /} k) •

If we arrive at rank zero without having satisfied the second condition, we choose rj _had equal to zero.

The new set of values thus obtained can be easily transformed into mRNA concentration values by the reverse transformation of that which gives the rank. The concentration of mRNA of each gene being reported on the artificial list L _ar t.

It is possible to generate several artificial lists according to the method described above. These lists can be used when comparing several groups of test and reference cells, especially when the number of test groups and the number of reference groups differ. In general, an artificial dataset can replace any group of cells used during the analyzes described above. 6. Analysis of kinetics or dose / response experiments In the case where several measures of transcription activity are available and obtained from several n + 1 sets of groups, n being an integer. The first group GCO contains ± _Q groups GCO ^ to GC0 ₀ , the second group GC1 contains i] _ groups GCl ^ to GClϋ, the last group GCn contains i _n groups GCn ^ to GChi _n . A multiple method according to the present invention plans to identify more precisely the genes exhibiting the most significant transcription variations. The groups GC1 to GCn can represent measurements carried out on the same biological system but at different and increasing times (kinetics experiment), or subjected to a stimulus of strictly increasing or decreasing intensity (dose / response experiments). The common characteristic of these two types of experiment is that it is sought for each gk gene whether there has been a significant variation in transcription signal over the entire interval of the independent variable VI (time in kinetics or dose of a product in the case of a dose / response). The values of the independent variable are taken arbitrarily equal to VI = 0.1, ... n. In a first phase of the analysis, all the analyzes concerning the groups for which VI = i and VI = i + 1 are carried out independently, according to the methods described above. For example, one of the analyzes will relate to the GCO and GC1 groups, another to the GC1 and GC2 groups, and the last will relate to the GCn-1 and GCn groups. For each test and for each gene the Pthéor k is determined (° ^u l ^es Pthr k ^s' ϋ there is only one group) and p s k _OD ⁰ⁿ selects genes that have undergone an RNA concentration variation -m significant using the selection parameters such as the probability of grouping selection error, the false positive rate or the sensitivity. We then obtain for each gene a sequence of ordered results, S _meaning k Ç which indicates for each interval of VI whether the gene has been detected as non-variant or varying positively or negatively, and another sequence of ordered results, S _se τ_ k Φ ^ - indicates if the variation is significant. So for the gk gene we could have the sequence ^s sense, k = + / + 0, -, -, - ₇ +, + and the sequence S _s g] _ ^ k ⁼ 1 / 1,0,0,0, 0,0,0. Note that here as for the following, a position for which no variation has been detected (0 in Ssens, k) always remains at zero in S _s gχ *

Then, if there exists at least one gene gi for which there is a zero at two consecutive positions of S _{S (} §JL i, without there being a zero at one of the corresponding positions in ^s sense i ^we perform independently all analyzes concerning the groups for which VI = i and VI = i + 2, and for which there are genes such as the g gene, according to the methods described above. For example, one of the analyzes will relate to the GCO and GC2 groups, another to the GC1 and GC3 groups, and the last will relate to the GCn-2 and GCn groups. Likewise, the genes having undergone significant variation are selected. The S _sense list is not modified. The list ^s sel k ^is completed as follows: if a significant variation has been detected between the values i and i + 2 of VI, and if the positions i and i + 1 were at zero in the previous step, then we changes positions i and i + 1 to one. If one of the positions were already at one, the new result is not considered significant with regard to the second position. Thus the new suite for k could be ^s Sel k≈ ^{1 '1' 0 '1' 1 '1} -' ^{0 '0} - ^The positions 4,5 and 6 were set to 1, because the analysis of the groups corresponding to VI = 3 and VI = 5 resulted in the selection of the g gene, as well as

1 analysis on the groups corresponding to VI = 4 and VI = 6.

The analysis continues at the orders of higher degrees, such as the order of degree 3 (VI = i and VI = i + 3), etc. as long as it is necessary (existence of at least one gene i, having a sequence of zero of the same degree in S _s g _] _ and no zero in one of the corresponding positions in S _sense ).

At the end of the analysis process, we select all the genes having at least one position set to one in S _s êχ. This procedure effectively filters genes that have shown significant variation over an interval of contiguous IV values. These genes can then be grouped more finely by a grouping method.

One can also make an additional selection and a first qualitative grouping of the variation curves as a function of VI, by applying the sequence S _s gτ_ k on the sequence ^s direction k as follows: for any position of S _s gι k equal to one, we keep the values at the corresponding positions of SgéT _^ k 'and for any position of Sg ^ ik equal to zero, we put in parentheses the values at the positions correspondents of S _s gχ k _* Thus S _s gi] ς = LL, 1, 0, 1,1,1, 0, 0 and ^s sense, k = +, +, 0 - / -'- '+ / + will give S _{senS /} k = +. +, (0), -, -, -, (+), (+).

This representation allows an additional selection on simple criteria. For example, in a dose / response experiment, it can be imposed as an additional condition that the variation be monotonic. In this case the gk gene such as ^s sense ^~ k _. ^{= +} _> + r (0), -, -, -, (+), (+) would not be retained. On the other hand, the gj gene such as S _{senS /} j = +, +, (+), (0), (-), +, (+), (+) would be retained because all the significant variations are positive. Likewise, if biological or other arguments suggest that starting, for example, from the fourth value of VI

(marked by | in the continuation) one must have a change of the direction of variation, one would be led to preserve the gene 1 such as S _direction] _ = +, +, (+), | (-), (-), -, (+), -. and to eliminate the gene m such that S _sense m = -, -, (+), | (+), (+), -, (-), -.

This representation. also allows for rapid pooling of comparable mRNA concentration signal profiles. For example, we will group together genes such as S _sen g _n = +, +, (+), (-), (-), -, (+), - and such that ^s meaning '° ^{= +} ' ⁺ ' ( ⁺ ) '( ⁺ )' ( ⁺ ) '"' ( ^~ ) '" S ^J ^ - ^{there are} significant positive variations at the same positions 1 and 2, and significant negative variations at the same positions 6 and 8.

Of course, the present invention is susceptible of various variants and modifications which will appear to one skilled in the art. In particular, the method of the present invention can be applied to the analysis of variations in the number of different proteins present in living cells.

In addition, the analysis method of the present invention can be implemented from the concentrations of m-RNA noted for each of the gene sequences studied corresponding to a hybridization unit of the DNA chip used. We will therefore not study the variations in the concentration of mRNA relating to a gene but that relating to a given sequence. In addition, a different definition of variation values can be used. Likewise, other normalization methods can be provided which satisfy the requirement of uniformity of the cumulative frequency distributions of any subset of normalized variation values. In addition, those skilled in the art will be able to define the optimal grouping process making it possible to identify the genes having the most significant values of variation in mRNA concentrations.

Claims

1. A method of analyzing variations in concentrations of messenger RNA obtained by transcription of a set of genes comprising the following steps: a) measuring the concentration of messenger RNA for each of the genes in so-called reference cells and transfer the results to a reference list (L _re f); b) measure the concentration of messenger RNA for each of the genes in so-called test cells and report the results on a test list (L ^ est) _< 'c) calculate a variation value for each gene

(Var) 'k being an integer between 1 and n, which is a measure of the difference between the m-RNA concentrations of said gene between the reference list (L _re f) and the test list

( ^L test); d) classifying the genes into first and second groups, depending on whether the genes have variation values corresponding respectively to an increase or to a decrease in their mRNA concentrations between the reference list and the test list; e) calculate for each gene of the second group a new variation value (Vark) Φ- ¹ ^, ie a measurement of the difference between the mRNA concentrations of said gene between the test list and the reference list. f) calculate for each gene a normalized variation value (Zk) such that the cumulative frequency distribution of a subset of normalized variation values corresponding to genes with close m-RNA concentrations is identical whatever the subset considered; and g) identify genes exhibiting significant variations in mRNA concentrations from the normalized variation values.

2. Method according to claim 1, in which the step of identifying the genes consists in selecting the genes whose standardized variation value is greater than a threshold value (Z i_ _seu).

3. The method of claim 2, wherein determining the threshold value (Z _seu iχ) comprises the following steps: h) measuring the concentration of mRNA for each of the two identical groups of genes of cells known to calibration and report the respective results on the first (Lg ^ al l) and second (Lgtal 2) calibration lists; i) calculate for each ^" gene a calibration variation value (ar _e t _a ik) according to the method of steps c) to e) from the first (Lgtal l) ^e t second (Lg al 2) lists calibration; j) calculate for each gene a normalized calibration variation value (Z _re fk) according to the method of step f); k) construct the cumulative frequency distribution, called calibration, of the variation values d 'normalized calibration associating with any value of normalized calibration variation (Z _re fk) a probability, called probability of selection error (Pseuil k)' so that there are values of normalized calibration variation greater than the value normalized variation considered;

1) selecting the desired probability of selection error _(S euil) / ^"and m) determining the threshold value _(seu ϋ) corresponding to the desired probability of selection error _(S euil) ^has the idea ^has of the cumulative distribution of calibration frequencies.

4. Method according to claim 3, in which the step consisting in choosing the probability of selection error (Pseuil) comprises the following steps:

- define the maximum acceptable false positive rate for the identification of genes; and identifying the probability of Pthr selection error ^and the threshold value Z _seu allowing maximum _ obtain an acceptable false positive rate, the TFP false positive rate being equal to:

TFP = - pseuil * n

(number of genes for which Zk> Zseml) where n is the number of genes considered.

5. Method according to claim 1, in which the step of identifying the genes consists in selecting the genes whose normalized variation value is greater than a first threshold value for the genes of the first group and greater than a second value of threshold for genes in the second group ^" .

6. Method according to claims 3 and 5, in which the determination of the first and second threshold values consists in choosing first and second probabilities of selection error desired respectively for the first and second groups and in defining the first and second values threshold values using the cumulative distribution of calibration frequencies.

7. The method of claim 6 for which the choice of the first and second threshold values consists in carrying out the method of claim 4 successively for the first and the second group.

8. Method for analyzing variations in m-RNA concentrations of a set of genes from m identical groups of so-called reference cells (GR.χ to GR _m ) and q identical groups of so-called test cells ( Glχ to GTg), the method comprising the following steps: a2) measuring, for each reference group, the concentration of messenger RNA for each of the genes and plotting the results on m reference lists (L _re f to L _re f2 ); b2) measure, for each test group, the concentration of messenger RNA for each of the genes and report the results on q test lists (Lt _es tχ to Ltest2) ' ^* - for all or part of the combinations of groups (C _^ j) comprising a reference group (GR) and a test group (GTj), carry out steps c2 to 12 as follows:

- c2) calculate for each gene a variation value (Vark) '^ being an integer between 1 and n, which is a measure of the difference between the RN-m concentrations of said gene between the reference list ( L _re fi) and the test list (L _test j);

- d2) classify the genes into first and second groups, according to whether the genes have variation values corresponding respectively to an increase or to a decrease in their mRNA concentrations between the reference list (L _re i) and the test list (Ltestj) _• '

- e2) calculate for each gene of the second group a new variation value (Vax ± _f jk) Ç [u is a measure of the difference between the mRNA concentrations of said gene between the test list (Ltest) ^and the reference list (L _re fi);

- f2) calculating for each gene a ^normalized variation value (± Z k) such that the cumulative frequency distribution of a sub-set of standard variation values corresponding to genes having concentrations of mRNA near is identical regardless of the subset considered;

- h.2) choose first and second calibration groups (Ggtal, iij and GR ^^ al 2, i, j) p is both among the m reference groups or both among the q test groups, one of the groups possibly being the reference group (GRi) or the test group (GTj) of the combination of groups considered; - i2) calculate for each gene a calibration variation value (Variai, i, j, k) according to. process of steps c2) to e2) from first (T-> éttal, li, k) ^and second

( ^L cal, 2, j, k) calibration lists corresponding to the first and second calibration groups; - j2) calculate for each gene a normalized calibration variation value (ref, i, j, k) according to the method of step f2);

- k2) .construct the cumulative frequency distribution, called calibration, of the normalized calibration variation values associating with any normalized calibration variation value (Z _re fi, j,) ^uae probability, called probability of selection error (Pseuil, i, jk) _• So that there are normalized calibration variation values greater than the normalized variation value considered;

- 12) define for each gene a probability value, said error probability (p j, k) corresponding to the normalized change in value of this gene (i ^) ^from the cumulative distribution calibration frequencies; - m2) calculate for each gene, a grouping value (Rk) according to a grouping method taking into account the set of error probabilities (pi, j, k) of said gene obtained for each of the combinations ( ^c i, j ) selected reference and test groups; and - n2) identifying as having significant variations in mRNA concentrations the genes whose grouping value is greater than a determined threshold grouping value (R _S euil).

9. The method of claim 8, wherein the first and second calibration groups (Ggt _a ] _ i and GRg ^ a _. 1,2) are identical regardless of the combination of groups considered.

10. The method of claim 8 or 9, wherein the determination of the threshold grouping value ( ^R threshold) comprises the following steps: calculating for each gene, a calibration grouping value (Rêtal, k) according to the method of regrouping from the calibration error probabilities (Petal, k) of said gene obtained from the distributions cumulative calibration frequencies calculated for each combination of groups (Ci _f j) chosen;

- construct the cumulative frequency distribution, called grouping, from the calibration grouping values by associating with any calibration grouping value a probability, known as the calibration grouping error probability, so that there is calibration pool values greater than the relevant calibration pool value; - select the desired probability of selection of grouping error (p2 _seu it); and

- set the threshold grouping value (R _S euil) corresponding to the probability of selection of grouping error (p2seuil) by ^means of the cumulative distribution grouping frequencies.

11. The method of claim 10, wherein the step of choosing a probability of selection pooling error (P ² threshold) comprises the following steps: - defining the maximum acceptable false positive rate for the identification of genes ; and

- identify the probability of selection grouping error P2seuil ^and the maximum threshold ^z threshold grouping value allowing an acceptable false positive rate to be obtained, the TFP false positive rate being equal to

_{mτ ^} p2threshold * n

TFP

(number of genes for which Rk≥Rsemi) where n is the number of genes considered.

12. The method of claim 8, wherein the grouping method comprises the following steps: - distributing the combinations of groups in different sets; calculate for each set an intermediate value for each gene equal to the product or the sum probabilities of error (Pi 4) of the gene obtained for each of the combinations of groups of the set;

- calculate for each gene a grouping value (Rk) equal to the average of the intermediate values calculated for each set.

13. The method of claim 1 or 8, wherein the variation value (Vark) of a gene is equal to the difference between the concentrations of m-RNA of said gene for different cells.

14. The method of claim 1 or 8, wherein the variation value (Vark) of a gene is equal to the ratio of the concentrations of m-RNA of said gene for different cells.

15. The method of claim 1 or 8 comprising for each list the following steps: - classifying the genes in ascending order of their concentrations of mRNA;

- assign a zero rank value to all genes whose mRNA concentrations are less than or equal to a threshold concentration value; - assign a unique rank value to each of the other genes whose mRNA concentration is greater than the threshold concentration value, the rank value being between 1 and ni, the rank R of a gene being d 'the higher the higher the m-RNA concentration of said gene; and - normalize the values of ranks over a range from 0 to w, w being a positive integer, the rank r of a gene now being equal to (R *) / n where n is the number of genes studied.

16. The method of claim 15, wherein the variation value of a gene is equal to the difference between the ranks of the gene for the two lists analyzed.

17. The method of claim 1 or 8 wherein the normalized variation value Z of each gene is obtained according to the following formula: _ _^ Var - μ (g) σ (g) where Var is the variation value of said gene and μ (g) and σ (g) are respectively the mean and the standard deviation of a set of variation values corresponding to a set of genes having concentrations of mRNA close to the concentration of mRNA of said gene.

18. Method according to claim 1 or 8, in which the normalized variation value is calculated according to the following steps:

- assign a unique rank r value to each gene equal to the rank value of the reference list for genes in the first group and equal to the rank value of the test list for genes in the second group.

- calculate the normalized variation value Z of the gene according to the following formula:

where Var is the variation of said gene, μ (r) and σ (r) are respectively the mean and the standard deviation of a set of variation values corresponding to a set of genes having ranks close to the rank r of said gene.

19. The method of claim 3 or 8, wherein the normalized calibration variation values (Z _re fk) are calculated according to the following method:

- assign a unique rank r value to each gene equal to the rank value of the reference list for genes in the first group and equal to the rank value of the test list for genes in the second group. calculate the normalized calibration variation value Z of the gene according to the following formula:

where Var is the calibration variation of said gene, μ (r) and σ (r) are respectively the mean and the standard deviation of a set of calibration variation values corresponding to a set of genes having ranks close to the r rank of said gene and in which the normalized variation values between a test list and a reference list are calculated according to the following formula:

_ Var - μ prop (r) σ prop (r) where the functions cal ( ^r ) ^e t ^σ cal ( ^r ) ^its t obtained by smoothing the means μ (r) and standard deviations σ (r) calculated beforehand from the values calibration variation.

20. Method for analyzing variations in m-RNA concentrations of a set of genes from m identical groups of so-called reference cells (GR ^ to GR _m ) and q identical groups of so-called test cells (GT ^ to GTg), the method comprising. the following steps: - measure, for each reference group, the concentration of messenger RNA for each of the genes and report the results on m reference lists (L _re f to L _re f2); measure, for each test group, the concentration of messenger RNA for each of the genes and report the results on q test lists (^ gg ^ i to Lj- _es t2);

- define for each of the lists a rank value for each gene according to the process comprising the following four steps:

- classify the genes in ascending order of their mRNA concentrations;

- assign a zero rank value to all genes whose mRNA concentrations are less than or equal to a threshold concentration value;

- assign a unique rank value to each of the other genes whose RN-m concentration is greater than the threshold concentration value, the rank value being between 1 and ni, the R rank of a gene being the higher the higher the m-RNA concentration of said gene; and - normalize the values of ranks over a range from 0 to w, w being a positive integer, the rank r of a gene now being equal to (R *) / n where n is the number of genes studied

- define a global reference list associating with each gene a unique rank equal to the average of its ranks in the reference lists;

- define a global test list associating each gene with a unique rank equal to the average of its ranks in the test lists; - calculate for each gene a variation value

(Var) equal to the difference between the rank of the gene for the global reference list and the rank of the gene for the global test list; classify the genes into first and second groups, according to whether the genes have variation values corresponding respectively to an increase or a decrease in their ranks between the global reference list and the global test list;

- calculate for each gene of the second group a new variation value (Vark) equal to the difference between the rank of the gene for the global test list and the rank of the gene for the global reference list;

- calculate for each gene a normalized variation value (Zk) according to the process comprising the following two steps:

- assign a unique rank r value to each gene equal to the rank value of the reference list for genes in the first group and equal to the rank value of the test list for genes in the second group. - calculate the normalized variation value Zk of the gene according to the following formula:

where Var is the variation of said gene, μ (r) and σ (r) are respectively the mean and the standard deviation of a set of variation values corresponding to a set of genes having - ranks close to the rank r of said gene ; and - identify the genes exhibiting significant variations in mRNA concentrations from the normalized variation values.

21. Method according to any one of the preceding claims, in which one or more reference, test or calibration lists are obtained according to a method for creating an artificial data set comprising the following steps: implementing the steps h) to k) of claim 3 making it possible to obtain a cumulative distribution of calibration frequencies; defining for each gene a normalized variation value by making a random draw from the cumulative distribution of calibration frequencies, all the normalized variation values thus defined having a cumulative frequency distribution identical to that of calibration.