Chi square tests for gene expression

Abstract

The present invention relates to systems and methods that utilize statistical means for analyzing expression of biological samples. Statistical concepts employed include population determinations, normal distributions, correlations between related measures, parameters utilized, Chi Square analysis, degrees of freedom, mean, variance and standard deviations from the mean.

Description

FIELD OF THE INVENTION

[0002] The present invention relates to systems and methods that utilize statistical means for analyzing expression information of biological samples.

BACKGROUND OF THE INVENTION

[0003] Gene expression varies within populations and even within what appears to be a homogeneous population. The most challenging aspects of presenting gene expression data involve the quantification and qualification of expression values, including standard statistical significance tests and confidence intervals. The current state-of-the-art in array-based studies precludes obtaining standard statistical indices (e.g., confidence intervals, outlier delineation) and performing standard statistical tests (e.g., t-tests, analyses-of-variance) that are used routinely in other scientific domains, because the number of replicates typically present in such studies would ordinarily be considered insufficient for these purposes. Thus, statistical indices and tests are required so estimates can be made about the reliability of observed differences between expression conditions. The key question in these kinds of comparisons is whether it is likely that observed differences in measured values reflect random error only or random error combined with treatment effect (i.e., “true difference”).

SUMMARY OF THE INVENTION

[0004] It is an object of this invention to provide a computer program for gene expression that may be applied to time-series analysis and to drug dose-response studies. It is another object of this invention to use Chi Square analysis to show that variation in gene expression is dependent only upon the average expression level of a gene and not upon the gene per se.

[0005] It is yet a further object of this invention to show that Chi Square analysis more clearly distinguishes a low dose from a high dose of a drug when compared to a correlation metric approach that could also be used to analyze identical data.

[0006] In one aspect of this invention, expression information of biological samples, as well as their response to external factors is recorded on computer readable media, and is processed by a computer system executing the analysis program of the present invention, or modules thereof. In one aspect, the entry and processing of information is iterative, and a user of the computer system can further manipulate the processing of the expression information. In a preferred embodiment, the processor is capable of producing a model of gene expression patterns based on Chi Square tests, that compares expression of a plurality biological samples in the presence or absence of external factors, and fits a significance value to the model using the Chi Square analysis.

[0007] In one aspect, the invention relates to a system for analyzing expression information of biological samples and evaluating statistical variation in expression patterns. In one aspect the biological samples are hybridized on an array. The system involves computer readable media or other such similar reading means that enables the user to cause the system to read expression information of one or more samples from plurality of data sources. The system further involves a processor or similar analyzing means that enables the user to analyze the expression information of the one or more samples, wherein the analysis is performed by estimating variation of expression data. The computer system further involves an interface and selection means that enables the user to select one or more samples presented by the computer system by utilizing the estimated variation in expression patterns from the analyzing means. The system also has a presenting means, such as for example, a CRT or printer that enables the user to cause the system to present the expression information, and the significance of variation of expression of the samples.

[0008] In one embodiment, the expression information is obtained from biological samples, which can include a plurality of polynucleotides or polypeptides. In some embodiments, the expression information is obtained from biological samples in the absence of external treatment (X0) and from biological samples treated or otherwise affected by one or more external factors, such as drugs or environmental conditions. The gene expression information is evaluated in view of a plurality of conditions or levels including high (Xt) and low (Yt) levels corresponding to time (t). The variation in gene expression is thus estimated by the analyzing means using a Chi Square analysis, wherein the algorithms for such analyses may be read from the computer readable media into the processor or analyzing means, and the results are communicated to the interface, output device or presenting means.

[0009] In another embodiment, the computer system calculates the Chi Square value between the samples Xt and X0, which is calculated using standard deviation (SD) according to the relation:

Chi Square=(Xt−X0)2/SD2

[0010] In yet another embodiment, the computer system calculates the Chi Square value between the samples Yt and X0, which is calculated using standard deviation (SD) according to the relation:

Chi Square=(Yt−X0)2/SD2

[0011] In still another embodiment, the computer system calculates the Chi Square value between the samples Xt and Yt, which is calculated using standard deviation (SD) according to the relation:

Chi Square=(Xt−Yt)2/SD2

[0012] In one embodiment, the computer system provides a selection means that further enables the user to select the expression of biological samples showing a probability value of false positive equivalent to 1/(total number of biological samples). In one embodiment, the variation is estimated by the processor or analyzing means, and is due to influence of one or more biological samples. In another embodiment, the variation is estimated by the analyzing means, and is due to one or more external factors, (e.g., physical, chemical or biological factors, drugs, genetic or environmental factors) influencing biological samples, or one or more error sources in the process of producing and measuring the samples, including but not limited to, those obtained from hybridization arrays.

[0013] In another embodiment, the system is integrated with plurality of processes of array hybridization, image capturing, image analysis, statistical analysis and laboratory information management systems. In another embodiment, the system is integrated with plurality of storage means, such as computer readable media, to store the information from analyzing means. In another embodiment, the selection means and presenting means are a graphical user interface (GUI).

[0014] In one embodiment, the system is computer based, and involves a standalone computer. In another embodiment, the system is computer based, and involves one or more networked computers. In this aspect, the analysis can be performed on a plurality of computers in communication with the network.

[0015] In still another aspect, the invention provides for methods for analyzing expression information of biological samples, such as array hybridized samples. The method involves the steps of reading expression information of one or more samples from plurality of data sources; analyzing expression information of one or more samples, wherein the analysis is performed by estimating statistical variation; selecting one or more samples by utilizing estimated variation from the analysis; and presenting expression information of one or more biological samples.

[0016] In yet another aspect, the invention relates to a computer system for analyzing expression information of array hybridized biological samples, the system including computer readable code (also known as an instruction set) including an algorithm capable of instructing the system processor, reading modules to read expression information of one or more biological samples from a plurality of data sources; analyzing modules to analyze the expression information of the one or more samples, wherein the analysis is performed by estimating stastistical variation; selection modules to select for the one or more analyzed samples by estimating variation from the analyzing modules; and presenting modules to cause the system to present to a user, the expression information of the one or more selected biological samples.

[0017] In another aspect, the invention relates to a system including an electronic storage medium having an algorithm, or computer readable code disposed on a data storage means, which allows a user to analyze expression information of biological samples. In this aspect, the storage medium involves computer readable code having an algorithm that enables a processor to allow a user to read expression information of one or more biological samples from a plurality of data sources; computer readable code that enables a processor to allow a user to analyze the expression information of one or more samples, wherein the analysis is performed by estimating statistical variation; computer readable code that enables a processor to allow a user to select one or more samples by utilizing estimated variation from analyzing means; and computer readable code that enables a processor to allow a user to cause the computer system to present the expression information of one or more samples. In one embodiment, the algorithm has one or more modules or subroutines. In another embodiment, the computer system includes a reading means capable of reading physically measured information from a plurality of array locations having biological samples, i.e., a plurality of replications of the samples. In yet another embodiment, the computer system includes an array of biological samples, wherein the biological samples are hybridized to their reverse complement sequences or fragments thereof, and the hybridization is carried out on a glass substrate.

[0018] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs. Although methods and materials similar or equivalent to those described herein can be used in the practice or testing of the present invention, suitable methods and materials are described below. All publications, patent applications, patents, and other references mentioned herein are incorporated by reference in their entirety. In the case of conflict, the present specification, including definitions, will control. In addition, the materials, methods, and examples are illustrative only and are not intended to be limiting.

[0019] Other features and advantages of the invention will be apparent from the following detailed description and claims.

BRIEF DESCRIPTION OF THE DRAWINGS

[0020] FIG. 1 illustrates standard deviation in band intensity for 13K bands versus the intensity of each band.

[0021] FIG. 2 shows bands that exhibited a difference in p-value of <10−5 in at least 2 of the following 3 comparisons: low dose versus vehicle, high dose versus vehicle, and low dose versus high dose, for at least 2 drugs.

[0022] FIG. 3 illustrates band clustering using “k-clustering” means for all 13K bands.

[0023] FIG. 4 illustrates band clustering using “k-clustering” means for the 2K bands that meet the significance and filter tests shown in FIG. 2.

[0024] FIG. 5 shows Chi Square metric and traditional correlation coefficient interpretations of results from all 13K bands.

[0025] FIG. 6 shows a comparison of analytic tests done on only the best 2K bands, and the better distinction between high and low dose levels provided by the Chi Square metric.

DETAILED DESCRIPTION OF THE INVENTION

[0026] Chi Square analysis is a statistical calculation used in genetics studies. A calculated value of Chi Square compares the frequencies of various kinds of items in a random sample to the expected frequencies of those items if the population from which the items are drawn is what an investigator has hypothesized. That is, Chi Square analysis will tell how well the hypothesized frequency fits with the set of frequencies obtained from a random sample.

[0027] Integral to Chi Square analysis is the concept of standard deviation from the mean. Standard deviation is an index of variability that shows dispersion among measures within a given population. Variation in levels of gene expression are held to depend on any number of factors, not the least of which is the gene per se, and its expression according to biologic influences impacting it, such as, for example, drugs.

[0028] As used herein, “biological samples” refers to polynucleotides, including polyribonucleotides and polydeoxyribonucleotides, as well as polypeptides. Biological samples include, derivatives of polypeptides and polynucleotides, as well as other varients, for example allelic polymorphisms and single nucleotide polymorphisms (SNP's). According to the present invention, the biological samples can be processed, for example in an array format, such as an array or matrix of immobilized polynucleotides that are probed or hybridized to their reverse complement sequence, or a portion thereof.

[0029] As used herein, the term “statistical variation” refers to Chi Square analysis, population determinations, normal distributions, correlations between related measures, parameters utilized, degrees of freedom, mean, variance and standard deviations from the mean.

[0030] As used herein, the terms “a computer-based system” or “computer system” are used interchangeably and refer to the hardware means, software means, and data storage means used to analyze the expression levels of genes. The minimum hardware means of the computer-based systems of the present invention include a central processing unit (CPU), input means, output means, and data storage means. Those skilled in the art will readily appreciate that any of the currently available computer-based systems are suitable for use in the present invention. It is understood that any general or special purpose system includes a processor in electrical communication with both a memory and at least one input/output device, such as a terminal. Such a system may include, but is not limited to, personal computers, workstations or mainframes. The processor may be a general purpose processor or microprocessor or a specialized processor executing programs located in RAM memory. The programs may be placed in RAM from a storage device, such as a disk or preprogrammed ROM memory. In one embodiment, the RAM memory is used both for data storage and program execution. The term computer system also embraces systems where the processor and memory reside in different physical entities but which are in electrical communication by means of a network.

[0031] As used herein, the term “computer readable media” refers to any data storage medium which can be read and accessed directly by a computer. Such media include, but are not limited to: magnetic storage media, such as floppy discs, hard disc storage medium, and magnetic tape; optical storage media such as CD-ROM; electrical storage media such as RAM and ROM; and hybrids of these categories such as magnetic/optical storage media. A skilled artisan can readily appreciate how any computer readable media can be used to create a manufacture comprising computer readable medium having recorded thereon a program of the present invention. The choice of the data storage medium will generally be based on the means chosen to access the stored information.

[0032] As used herein, the term “data storage means” refers to memory which can store expression information of the present invention, or a memory access means which can access manufactures having recorded thereon the expression information of the present invention.

[0033] As used herein, the term “recorded” refers to a process for storing information on computer readable medium. A skilled artisan can readily adopt any known method for recording information on computer readable medium to generate manufactures involving the program information of the present invention. A variety of data storage structures are available to a skilled artisan for creating a computer readable medium having recorded thereon a computer readable program or algorithm of the present invention. In addition, a variety of data processor programs and formats can be used to store the information of the present invention on computer readable medium.

[0034] As used herein the term “external factors” refers to physical, chemical, biological, or environmental factors that modulate the expression or activity of biological samples. “External treatment” refers to the exposure of one or more biological samples to one or more external factors. An example of a chemical external factor is a naturally occuring or synthesized agent, that is not itself a native component of the biological samples, including but not limited to, a drug or toxin. An example of a biological external factor is a agent normally present in a living cell, that is not itself a native component of the biological samples but that acts on the biological samples, for example but not limited to a hormone or a gene product such as one from one or more genes in an upstream metabolic pathway relative to the biological samples, or a gene product of a microorganism (i.e., a bactrium, a virus, a fungus, or microbe). An example of an environmental external factor is a naturally occuring or manufactured agent or stimulus, that is not itself a native component of the biological samples, for example but not limited to radiation such as UV, electromagnetic energy, or the like. An example of a phycical external factor is heat, cold, or pressure. One skilled in the art will recognize, for example, that an external factor may be both a chemical and biological factor, or an environmental and chemical factor, or an environmental and biological factor, or all three.

[0035] The output of the computer system can be represented in a word processing text file, formatted in commercially-available software such as WordPerfect® and Microsoft Word®, or represented in the form of an ASCII file, stored in a database application, such as DB2, Sybase, Oracle, or the like. A skilled artisan can readily adapt any number of data processor structuring formats (e.g. text file or database) in order to obtain computer readable medium having recorded thereon the expression information of the present invention.

[0036] Chi Square analysis provides a system and method for determining statistical variation in gene expression levels that depends upon the average expression level of the gene and not upon the gene per se. That is, two genes with the same mean expression level exhibit the same statistical variation from sample to sample, which can be detected and interpreted by the system of the present invention.

[0037] The determination of expression levels for polynucleotides and polypeptides are well known in the art. For example, RT-PCR provides a quantitative method for determining expression of one or more genes. The quantitative expression of various biological samples is assessed using, for example microtiter plates containing RNA samples from a variety of normal and pathology-derived cells, cell lines and tissues using real time quantitative PCR (RTQ PCR). RTQ PCR is performed, e.g., an Applied Biosystems ABI PRISM® 7700 or an ABI PRISM® 7900 HT Sequence Detection System. The capabilities of RT-PCR in determining gene expression information from biological samples is well known to those trained in the field. RT-PCR is accomplished using primers of standard designs to skilled artisans.

[0038] Southern or Northern blotting provides another method of detecting the presence and the expression of one or more genes, and such hybridizations can additionally be perfomed on arrays or in matrix format, e.g. dot blots or hybridization on glass arrays as part of a high throughput screen. These techniqies are well described in the scientific literature. Probes useful to these techniques are reverse complements of the target sequences, including fragments of these greater than 20 nucleotides in length. The creation and use of such probes are well known to skilled artisans.

[0039] Alternatively, fluorescent activated cell sorting (FACS) or Western blotting provide two non-limiting examples of methods for determining expression levels of polypeptides. One example of the use of fluorescence detection for cancer screening is U.S. Pat. No. 5,270,171 to Cercek, et al, which teaches a method to identify, separate and purify the factor or factors that provoke a response by SCM (structuredness of the cytoplasmic matrix) responding lymphocytes. Also, U.S. Pat. No. 5,554,505 to Hajek, et al. discloses an optical screening method and apparatus for identifying both the morphology and selective characteristics or properties expressed by cells. Similarly, U.S. Pat. No. 5,562,114 to Chu, et al. discloses a diagnostic immunoassay method using monoclonal antibodies. Each of the above references are hereby incorporated hirein in their entireties.

[0040] Depending upon the size of the biological sample, the collected sample within the specimen could be processed, for example on a standard flow cytometer even prior to initial observation under the fluorescence microscope. In the case of large volumes of fluid contained within a biological sample, such as one would obtain on a screen for uterine cervix or colon cancer, a flow cytometer can process large volumes of cells in a very short period of time. Commercially available flow cytometers may be used. Manufacturers of such devices include Coulter, Becton-Dickenson, and Cytomation. As well understood in the art, flow cytometry involves the suspension of individual cells in a solution, followed by the movement of the cells through a tubular system which only allows one cell at a time to flow. The cells pass through a chamber in the system where there is a selection of lasers of selected different frequencies of light to conduct a number of measurements, including cell counts, cell measurements as to overall size and other parameters.

[0041] As applied to the method of this invention, the flow cytometer would have a selection of lasers which provide light to match the excitation frequency of the particular compound used to produce fluorescence in the cell sample. By this fluorescent tagging, the flow cytometer is able to accurately count the number of cells which fluoresce. In order to actually separate fluorescing versus non-fluorescing cells, the FACS must be conducted. The FACS involves the inducement of a charge (positive or negative) on the cell surface of each cell which passes through the flow cytometer. By this induced charge, the fluorescing cells are separated from non-fluorescing cells. Accordingly, the fluorescing cells would be placed into a separate container from the non-fluorescing cells. As discussed above, this concentrated sample of fluorescing cells makes viewing easier under a fluorescence microscope, and for easier photographing of the fluorescing cells. Often, it is desirable first to attempt to locate fluorescing cells by simply viewing them under a fluorescence microscope. The capabilities of flow cytometers and fluorescence activated cell sorters are well known to those trained in the field. However, it shall be understood that the invention is not limited to any particular sequence in terms of the use of the present flow cytometer, fluorescence microscope, or by determining expression by conducting a FACS analysis. Instead the present invention is concerned with obtaining a biological sample and assigning an initial estimate as to the expression of one or more genes from that sample, to determine the data fit of a meaningful hypothesis by Chi Square analysis.

[0042] To practice the invention, one skilled in the art obtains a source of biological samples, as well as expression information about the biological samples, i.e., expression information relative to one or more genes or polypeptides encoded therein. Data is collected for a particular phenotype appearing within a given population under study, whereby expression of that phenotype is to be determined within the biological sample under study. The phenotype is correlated to a specific genotype, which is then represented as a band with a given intentity, thus indicative of gene expression levels, and is then compared to control samples. Alternatively, the response of a gene to dosage with one or more drugs is determined by band intensity. The standard deviation from the mean (StdDev) is calculated for the control samples, and is fit to functional form in the following equation:

log(StdDev)=A+B log(intensity)

[0043] The Chi Square is then calculated for the significance of the gene under study, for example but not limited to, low or high dose of drug versus control, using the equation:

Chi Square=sum of (x(t)−x0)2/SD2

[0044] where x(t) is the dose of drug at time, t; x0 is the mean of the control values over all times; df is the number of times sampled; and p-value is the tail of the Chi Square distribution. When values are provided and calculations performed, it can be determined if there are significant differences between expression patterns, for example, gene expression in view of high and low drug doses versus control values.

[0045] To determine further if there is significance between high drug dose versus low drug dose, the following calculation is performed:

Chi Square=sum of (x(t)−y(t))2/SD2

[0046] where x(t) is the high dose of drug at time, t; y(t) is the low dose of drug at time, t; and df is 2×the number of times given.

[0047] In order to achieve a low, false-positive rate, a gene or feature is selected that shows “significance” at a p-value=1/(total number of genes or features). Ideally, it is required is that the same gene or feature shows significance for tests involving a minimum of 2 drugs, and for each drug tested, 2 of the following 3 parameters are triggered: low dose versus vehicle, high dose versus vehicle and low dose versus high dose.

[0048] With respect to filters used, the equation:

StdDev=A(Intensity)B+an allowance factor

[0049] provides a bias to high intensity. To avoid misrepresentations in data due to polymorphisms, it is important that the Chi Square value be significant. This can be achieved by ignoring the largest difference in calculating the Chi Square value. An appropriate filter is then selected by choosing the ratio of larger difference for: where 1 log(ratio) 1>log (2) provides a reasonable cut-off.

[0050] These equations are stored in computer readable media as part of a computer readable program written in a suitable language, for example C, C++, UNIX, FORTRAN, BASIC, PASCAL, or the like. The program provides an algorithm for performing the Chi Square analysis, as well as other functional elements contained in one or more modules or subroutines (e.g., relational database capabilities, search features, and user defined functions). An example of such an algorithm is provided as Example 1. The algorithm includes reading modules that enable the user to permit the system to read the expression information of one or more biological samples from plurality of data sources input by the user or by automated means; analyzing modules that enable the user to analyze the expression information of one or more biological samples, wherein the analysis is performed by estimating sample variation; selection modules that enable the user to select one or more samples by utilizing the estimated statistical variation from the analyzing modules; and presenting modules that enable the user to cause the system to present the expression information of one or more samples.

[0051] For example, data on gene expression, drug type and dosages, and the like is entered by a user into the computer system, (see, Example 2) where it is stored in memory and manipulated by the processor using the modules of the algorithm described. The output information is thus available to the user, and is visualized by an output device such as a graphical user interface, or a printed copy. The output information permits a determination of significance of a comparison of at least two biological samples.

EXAMPLE 1

Computer Algorithm for Determining Expression Variance

[0052] The following provides an implementation of the factorial experimental design of this invention as a computer program in the C language. This code can run on any computers recognizing this language, for example but not limited to PowerPC™ based Macintosh type computers and Pentium™ based PC type computers.

EXAMPLE 2

Determining Expression Variance

[0053] A multi-sample expression analysis was run using the program described in Example 1. For each drug run, only runs for genes producing bands with a p-value<10−5 in at least 2 of the following 3 comparisons were selected: low dose versus vehicle, high dose versus vehicle and low dose versus high dose. Bands that exhibited this difference for at least 2 drugs were chosen (FIG. 2). Since clusters found using all 13K bands included some of the best 2K bands, it was concluded that no essential signal was lost (see FIGS. 3 and 4). As seen in FIG. 5, Chi Square metric and traditional correlation coefficient interpretations of the results from all 13K bands. A comparison using the same analytic tests on only the best 2K bands. It can be seen that the Chi Square metric provides a better distinction between low and high doses than the correlation metric, which is not able to distinguish between the low dose and the high dose (see FIG. 6). The low-dose/high dose statistical variation is more pronounced when only the best 2K bands are selected.

DATA INPUT
nDim 3
Drug 9
ANIT
Methylenedianiline
Dichlorobenzene
Cyproterone
BCNU
BHT
CTFT
Corn Oil
Untx
Dose 3
Vehicle
Low
High
Time 4
1d
3d
7d
14d
nSample 59
0	15825	ANIT	High	1d
1	15842	ANIT	High	3d
2	15859	ANIT	High	7d
3	15873	ANIT	Low	14d
4	15826	ANIT	Low	1d
5	15841	ANIT	Low	3d
6	15858	ANIT	Low	7d
7	15834	BCNU	High	1d
8	15850	BCNU	High	3d
9	15833	BCNU	Low	1d
10	15849	BCNU	Low	3d
11	15866	BCNU	Low	7d
12	15880	BHT	High	14d
13	15832	BHT	High	1d
14	15848	BHT	High	3d
15	15865	BHT	High	7d
16	15878	BHT	Low	14d
17	15831	BHT	Low	1d
18	15847	BHT	Low	3d
19	15864	BHT	Low	7d
20	15877	CTFT	High	14d
21	15830	CTFT	High	1d
22	15846	CTFT	High	3d
23	15863	CTFT	High	7d
24	15876	CTFT	Low	14d
25	15829	CTFT	Low	1d
26	15845	CTFT	Low	3d
27	15862	CTFT	Low	7d
28	15884	Corn Oil	Vehicle	14d
29	15838	Corn Oil	Vehicle	1d
30	15855	Corn Oil	Vehicle	3d
31	15870	Corn Oil	Vehicle	7d
32	15882	Cyproterone	High	14d
33	15836	Cyproterone	High	1d
34	15853	Cyproterone	High	3d
35	15868	Cyproterone	High	7d
36	15835	Cyproterone	Low	1d
37	15852	Cyproterone	Low	3d
38	15867	Cyproterone	Low	7d
39	15872	Dichlorobenzene	High	14d
40	15824	Dichlorobenzene	High	1d
41	15840	Dichlorobenzene	High	3d
42	15857	Dichlorobenzene	High	7d
43	15871	Dichlorobenzene	Low	14d
44	15823	Dichlorobenzene	Low	1d
45	15839	Dichlorobenzene	Low	3d
46	15856	Dichlorobenzene	Low	7d
47	15875	Methylenedianiline	High	14d
48	15828	Methylenedianiline	High	1d
49	15844	Methylenedianiline	High	3d
50	15861	Methylenedianiline	High	7d
51	15874	Methylenedianiline	Low	14d
52	16303	Methylenedianiline	Low	1d
53	15843	Methylenedianiline	Low	3d
54	15860	Methylenedianiline	Low	7d
55	15883	Untx	Vehicle	14d
56	15837	Untx	Vehicle	1d
57	15854	Untx	Vehicle	3d
58	15869	Untx	Vehicle	7d
DATA OUTPUT
12955	F Pvalue  100670_Pooled_ANIT_-_High_-_1d
Band
	100686_Pooled_ANIT_-_High_-_3d
	100702_Pooled_ANIT_-_High_-_7d
	100716_Pooled_ANIT_-_Low_-_14d
	100669_Pooled_ANIT_-_Low_-_1d
	100685_Pooled_ANIT_-_Low_-_3d
	100701_Pooled_ANIT_-_Low_-_7d
	100678_Pooled_BCNU_-_High_-_1d
	100694_Pooled_BCNU_-_High_-_3d
	100677_Pooled_BCNU_-_Low_-_1d
	100693_Pooled_BCNU_-_Low_-_3d
	100709_Pooled_BCNU_-_Low_-_7d
	100722_Pooled_BHT_-_High_-_14d
	100676_Pooled_BHT_-_High_-_1d
	100692_Pooled_BHT_-_High_-_3d
	100708_Pooled_BHT_-_High_-_7d
	100721_Pooled_BHT_-_Low_-_14d
	100675_Pooled_BHT_-_Low_-_1d
	100691_Pooled_BHT_-_Low_-_3d
	100707_Pooled_BHT_-_Low_-_7d
	100720_Pooled_CTFT_-_High_-_14d
	100674_Pooled_CTFT_-_High_-_1d
	100690_Pooled_CTFT_-_High_-_3d
	100706_Pooled_CTFT_-_High_-_7d
	100719_Pooled_CTFT_-_Low_-_14d
	100673_Pooled_CTFT_-_Low_-_1d
	100689_Pooled_CTFT_-_Low_-_3d
	100705_Pooled_CTFT_-_Low_-_7d
	100727_Pooled_Corn_Oil_Vehicle_-_14d
	100682_Pooled_Corn_Oil_Vehicle_-_1d
	100698_Pooled_Corn_Oil_Vehicle_-_3d
	100713_Pooled_Corn_Oil_Vehicle_-_7d
	100725_Pooled_Cyproterone_-_High_-_14d
	100680_Pooled_Cyproterone_-_High_-_1d
	100696_Pooled_Cyproterone_-_High_-_3d
	100711_Pooled_Cyproterone_-_High_-_7d
	100679_Pooled_Cyproterone_-_Low_-_1d
	100695_Pooled_Cyproterone_-_Low_-_3d
	100710_Pooled_Cyproterone_-_Low_-_7d
	100715_Pooled_Dichlorobenzene_-_High_-_14d
	100668_Pooled_Dichlorobenzene_-_High_-_1d
	100684_Pooled_Dichlorobenzene_-_High_-_3d
	100700_Pooled_Dichlorobenzene_-_High_-_7d
	100714_Pooled_Dichlorobenzene_-_Low_-_14d
	100667_Pooled_Dichlorobenzene_-_Low_-_1d
	100683_Pooled_Dichlorobenzene_-_Low_-_3d
	100699_Pooled_Dichlorobenzene_-_Low_-_7d
	100718_Pooled_Methylenedianiline_-_High_-_14d
	100672_Pooled_Methylenedianiline_-_High_-_1d
	100688_Pooled_Methylenedianiline_-_High_-_3d
	100704_Pooled_Methylenedianiline_-_High_-_7d
	100717_Pooled_Methylenedianiline_-_Low_-_14d
	100671_Pooled_Methylenedianiline_-_Low_-_1d
	100687_Pooled_Methylenedianiline_-_Low_-_3d
	100703_Pooled_Methylenedianiline_-_Low_-_7d
	100726_Pooled_Untx_-_Series_1_-_14d
	100681_Pooled_Untx_-_Series_1_-_1d
	100697_Pooled_Untx_-_Series_1_-_3d
	100712_Pooled_Untx_-_Series_1_-_7d
b1i0_51.7	0	23.544892	30.103037	21.567616	81.997346
	30.702796	22.373736	20.666184	29.608189	30.974794
	24.268556	21.637515	19.759957	26.784709	24.213618
	25.0702	17.715696	18.314255	18.782205	18.023983
	12.127385	19.058594	17.270417	23.529339	13.918661
	32.701469	22.809197	30.635824	17.663446	15.672605
	21.538437	14.610615	20.769767	19.899767	35.069505
	32.34381	22.634416	19.269776	21.873214	12.769259
	21.769265	27.835384	10.749258	16.630761	23.430812
	28.93028	26.061803	16.565025	33.183899	23.54918
	27.879463	23.351387	71.331804	22.283294	27.013604
	21.369566	14.763453	27.838359	17.47643	18.055182
b1i0_53.0	0	99.498789	84.157358	106.268871	54.672107
	121.830758	45.024387	108.124859	110.830028	118.438436
	117.109022	98.959691	104.154649	82.870158	104.264211
	101.737289	104.082898	96.381843	108.777447	87.177289
	104.467173	76.60183	96.215713	82.040827	93.627534
	91.49095	116.854083	111.788057	113.540644	103.105961
	79.614576	97.690274	114.849913	40.970251	93.392231
	99.723751	99.01235	111.604202	99.850245	99.008207
	95.421533	103.413865	48.520724	99.659889	116.359037
	127.083002	71.532666	113.83161	60.924121	101.131133
	98.113818	113.819446	55.869889	103.357971	101.135801
	111.54306	104.211595	88.659637	102.327053	100.549388
b1i0_54.5	0	102.162121	114.236918	95.668457	33.492072
	105.289908	111.329988	88.171497	112.394852	112.08911
	102.765858	103.605607	108.188735	93.418658	82.822941
	96.924635	81.737892	91.728547	93.969467	101.517293
	92.421443	79.055276	92.290305	88.546772	79.535788
	114.276011	107.896665	98.390101	102.227042	120.852053
	95.560027	89.0957	91.858273	69.777006	98.482402
	80.834446	81.205749	94.406498	93.730905	98.196724
	84.90956	91.994075	89.822644	80.917888	101.411635
	88.394326	128.360502	88.11377	51.093146	104.866521
	105.968709	82.178127	62.552039	123.714173	111.42007
	86.490276	112.252632	111.766402	94.787428	100.08862
b1i0_57.4	0	1272.181176	712.350351	685.827476	810.740232
	1209.0048	1266.179729	1302.501456	1153.585685	1296.093934
	1234.82714	1366.747949	1344.875534	1048.923128	1176.845905
	1234.732576	990.188001	1228.87043	1181.508899	1224.46485
	1156.307983	1118.740972	1069.945925	1131.011927	1134.759409
	1314.63168	1320.211382	1266.951876	1269.838966	1421.83629
	1212.104564	1374.303669	1609.013097	775.476752	1104.833598
	1020.813029	1104.711819	1285.38766	1337.738793	1436.846037
	1142.184413	1259.846692	1064.023452	1287.17738	1338.104131
	1300.991332	1352.070182	1297.569152	455.917146	1229.664203
	1406.835021	1183.591626	789.213457	1376.007231	1432.65909
	1280.075113	1124.261263	1188.88269	1169.56077	1431.349855
b1i0_60.7	0	74.318131	74.885892	72.634322	141.739709
	87.084708	67.382771	75.420732	78.554664	115.43014
	88.974793	80.086747	96.794687	68.414051	71.521922
	70.086835	62.308954	90.107901	72.362149	69.126883
	79.01462	66.335668	47.716031	61.290957	61.305902
	95.315202	80.425505	71.714776	83.221031	73.39388
	73.23158	80.209404	98.748627	57.479996	53.895513
	46.420581	73.60713	76.154166	72.42433	80.221557
	82.423227	79.936554	62.132235	77.865835	94.457296
	95.980356	58.606575	74.814424	158.258085	67.134602
	85.720582	82.440553	139.591736	66.657168	78.988282
	79.323633	66.614629	85.62878	79.061055	84.584349
b1i0_62.5	0	49.333039	93.55836	81.396541	249.285581
	68.444181	104.914862	91.612585	67.749485	84.846006
	69.477608	57.902516	82.577232	57.739134	81.055744
	56.242769	81.593016	63.696139	74.661691	70.37307
	62.541429	41.230387	65.175429	55.656819	77.005689
	66.074812	64.308598	67.003095	83.061617	64.193046
	54.851502	84.924007	72.738439	148.303315	49.192872
	64.931492	71.818063	62.408898	59.374251	70.853701
	64.49277	68.450513	97.82131	76.856718	68.637928
	73.54091	76.310018	88.914069	185.668673	59.418237
	70.638693	71.551375	207.597461	63.428999	69.922381
	86.010994	51.796498	65.940154	79.383289	76.349883
b1i0_63.7	0	50.086148	0.013986	147.855112	9.84461
	170.563405	7.244774	299.354374	98.176856	115.095918
	155.387462	104.211339	204.187792	41.881109	240.682376
	120.102063	313.443844	161.614678	152.614587	171.352528
	132.26082	70.808399	91.065597	90.26942	203.400877
	78.723363	113.76279	153.65371	214.990675	77.290828
	67.22041	215.288026	120.071582	18.516288	51.361368
	111.761376	154.734763	68.203119	110.350994	146.033635
	157.667328	128.994118	5.697943	224.273133	152.140783
	166.160213	24.943422	258.765787	2.07316	85.097835
	153.773953	144.320995	0.352662	24.89242	84.097621
	287.243053	32.43036	60.797084	160.349147	186.394024
b1i0_69.4	0	208.615745	284.116754	271.180949	748.935515
	276.30951	370.530811	305.405868	194.274676	219.097168
	254.034511	292.140705	325.132969	268.812266	241.720276
	251.241121	255.877557	286.544691	272.460758	190.569808
	282.903132	200.797981	70.194874	266.958137	223.117159
	388.812807	274.075638	351.831761	323.241725	356.574433
	106.637994	308.845886	219.856445	528.340834	254.857169
	250.680914	317.87817	243.165372	270.664752	326.261078
	311.303114	295.499652	393.194329	261.660532	333.2913
	130.611455	334.562355	304.302031	512.877262	262.228392
	329.88134	290.2061	714.823366	349.369569	349.278273
	303.138007	298.088233	242.026718	325.630603	293.444945

EQUIVALENTS

[0054] From the foregoing detailed description of the specific embodiments of the invention, it should be apparent that a unique procedure to evaluate time-series and drug-dose responses in gene expression studies has been described. Although particular embodiments have been disclosed herein in detail, this has been done by way of example for purposes of illustration only, and is not intended to be limiting with respect to the scope of the appended claims that follows. In particular, it is contemplated by the inventor that substitutions, alterations, and modifications may be made to the invention without departing from the spirit and scope of the invention as defined by the claims.

Claims

1. A computer system for analyzing expression information of biological samples, the system comprising: reading means to read expression information of one or more samples from plurality of data sources; analyzing means to analyze the read expression information of the one or more samples, wherein the analysis is performed by estimating a statistical variation; selection means to select one or more analyzed biological samples by utilizing estimated variation from the analyzing means; and presenting means to cause the system to present the expression information of one or more samples.

2. The computer system of claim 1, wherein the expression information is obtained from biological samples having no external treatment (X0) and biological samples treated by one or more external factors at plurality of levels including high (Xt) and low (Yt) levels corresponding to time (t), and wherein the statistical variation is estimated by analyzing means using a Chi Square analysis.

3. The computer system according to claim 2, wherein a Chi Square value is calculated using standard deviation (SD) according to the relation

4. The computer system according to claim 2, wherein a Chi Square value is calculated using standard deviation (SD) according to the relation

5. The computer system according to claim 2, wherein a Chi Square value is calculated using standard deviation (SD) according to the relation

6. The computer system according to claim 1, wherein the selection means further selects the expression of biological samples showing a probability value of false positive equivalent to

7. The computer system according to claim 1, wherein the variation estimated by the analyzing means is due to influence of one or more external factors.

8. The computer system according to claim 1, wherein the variation estimated by the analyzing means is due to one or more biological factors influencing biological samples.

9. The computer system according to claim 1, wherein the variation estimated by the analyzing means is due to one or more error sources in the process of producing and measuring hybridized arrays.

10. The computer system according to claim 1, wherein the biological samples are a plurality of polynucleotides.

11. The computer system according to claim 1, wherein the biological samples are a plurality of polypeptides.

12. The computer system according to claim 8, wherein the external factor is a drug.

13. The computer system according to claim 1, wherein the system is integrated with plurality of processes consisting of array hybridization, image capturing, image analysis, statistical analysis and laboratory information management systems.

14. The computer system according to claim 1, wherein the system is integrated with a plurality of storage means to store the information from the analyzing means.

15. The computer system according to claim 1, wherein the selection means and the presenting means are in graphical user interface (GUI).

16. The computer system according to claim 1, wherein the system is run on a standalone computer.

17. The computer system according to claim 1, wherein the system in run on one or more networked computers.

18. A computer system for analyzing expression information of array hybridized biological samples, the system comprising: reading modules to read expression information of one or more biological samples from a plurality of data sources; analyzing modules to analyze the expression information of the one or more samples, wherein the analysis is performed by estimating stastistical variation; selection modules to select for the one or more analyzed samples by estimating variation from the analyzing modules; and presenting modules to cause the system to present the expression information of the one or more selected samples.

19. The computer system according to claim 18, wherein the expression information is obtained from biological samples having no external treatment (X0) and biological samples treated by one or more external factors at plurality of levels including high (Xt) and low (Yt) levels corresponding to time (t), and wherein the variation is estimated by analyzing means using a Chi Square analysis.

20. The computer system according to claim 19, wherein a Chi Square value is calculated using standard deviation (SD) according to the relation

21. The computer system according to claim 19, wherein a Chi Square value is calculated using standard deviation (SD) according to the relation

22. The computer system according to claim 19, wherein a Chi Square value is calculated using standard deviation (SD) according to the relation

23. The computer system according to claim 18, wherein the selection modules further enable the user to select the expression of biological samples showing a probability value of false positive equivalent to 1/(total number of biological samples).

24. The computer system according to claim 18, wherein the variation estimated by the analyzing modules is due to influence of one or more biological samples.

25. The computer system according to claim 18, wherein the variation estimated by analyzing modules is due to one or more external factors influencing the biological samples.

26. The computer system according to claim 18, wherein the variation estimated by the analyzing modules is due to one or more error sources in the process of producing and measuring hybridized arrays.

27. The computer system according to claim 18, wherein the biological samples are a plurality of polynucleotides.

28. The computer system according to claim 18, wherein the biological samples are a plurality of polypeptides.

29. The computer system according to claim 18, wherein the external factor is a drug.

30. The computer system according to claim 18, wherein the system is integrated with a plurality of processes further comprising array hybridization, image capturing, image analysis, statistical analysis and laboratory information management systems.

31. The computer system according to claim 18, wherein the system is integrated with a plurality of storage modules to store the information from the analyzing modules.

32. The computer system according to claim 18, wherein the selection modules and presenting modules are graphical user interfaces (GUI).

33. The computer system according to claim 18, wherein the system is run on a standalone computer.

34. The computer system according to claim 18, wherein the system in run on one or more networked computers.

35. A method for analyzing expression information of biological samples, the method comprising: reading expression information of one or more samples from plurality of data sources; analyzing the expression information of the samples, wherein the analysis is performed by estimating statistical variation; selecting one or more of the analyzed samples by utilizing estimated variation from the analysis; and presenting expression information of the selected samples.

36. The method according to claim 35, wherein the expression information is obtained from biological samples having no external treatment (X0) and biological samples treated by one or more external factors at plurality of levels including high (Xt) and low (Yt) levels corresponding to time (t), and wherein the variation is estimated by analyzing means using a Chi Square analysis.

37. The method according to claim 36, wherein a Chi Square value is calculated using standard deviation (SD) according to the relation

38. The method according to claim 36, wherein a Chi Square value is calculated using standard deviation (SD) according to the relation

39. The method according to claim 36, wherein a Chi Square value is calculated using standard deviation (SD) according to the relation

40. The method according to claim 35, wherein the step of selecting further selects the expression of biological samples showing a probability value of false positive equivalent to

41. The method according to claim 35, wherein the variation estimated by the analyzing means is due to influence of one or more biological samples.

42. The method according to claim 35, wherein the variation estimated by the analyzing means is due to one or more external factors influencing biological samples.

43. The method according to claim 35, wherein the variation estimated by the analyzing means is due to one or more error sources in the process of producing and measuring the array hybridized biological samples.

44. The method according to claim 35, wherein the biological samples are a plurality of polynucleotides.

45. The method according to claim 35, wherein the biological samples are a plurality of polypeptides.

46. The method according to claim 42, wherein the external factor is a drug.

47. A system comprising electronic storage medium having computer readable code contained therein, the electronic storage medium further comprising: computer readable code that instructs a processor to read expression information of one or more biological samples from a plurality of data sources; computer readable code that instructs a processor to analyze the expression information of the one or more samples, wherein the analysis is performed by estimating stasistical variation; computer readable code that instructs a processor to select one or more of the analyzed samples by utilizing the estimated stasistical variation from analyzing means; and computer readable code that instructs a processor to present the expression information of the biological samples to a user, whereby the computer readable code allows a user to analyze expression information of biological samples.

48. The electronic storage medium according to claim 47, wherein the expression information are obtained from biological samples with no external treatment (X0) and biological samples treated by one or more external factors at plurality of levels including high (Xt) and low (Yt) levels corresponding to time (t), and wherein the variation is estimated by analyzing means using a Chi Square analysis.

49. The electronic storage medium according to claim 48, wherein a Chi Square value is calculated using standard deviation (SD) according to the relation Chi Square=(Xt−X0)2/SD2

50. The electronic storage medium according to claim 48, wherein a Chi Square value is calculated using standard deviation (SD) according to the relation Chi Square=(Yt−X0)2/SD2.

51. The electronic storage medium according to claim 48, wherein a Chi Square value is calculated using standard deviation (SD) according to the relation Chi Square=(Xt−Yt)2/SD2.

52. The electronic storage medium according to claim 47, wherein the medium further comprises computer readable code that instructs a processor to enable a user to select the expression of biological samples showing a probability value of false positive equivalent to 1/(total number of biological samples).

53. A computer system according to claim 1, wherein reading means are capable of reading physically measured information from plurality of arrays having plurality of replications.

54. A computer system according to claim 1, wherein the biological samples are hybridized to their reverse complement sequences or fragments thereof, and the hybridization is carried out on a glass substrate.