The field of this invention relates to methods for using data from multiple repeated experiments to generate a confidence value for each data point, increase sensitivity, and eliminate systematic experimental bias.
There is currently an explosive increase in the generation of quantitative measurements of the levels of xe2x80x9ccellular constituentsxe2x80x9d. Cellular constituents include gene expression levels, abundance of mRNA encoding specific genes, and protein expression levels in a biological system. Levels of various constituents of a cell, such as mRNA encoding genes and/or protein expression levels, are known to change in response to drug treatments and other perturbations of the cell""s biological state. Measurements of a plurality of such xe2x80x9ccellular constituentsxe2x80x9d therefore contain a wealth of information about the affect of perturbations on the cell""s biological state. The collection of such measurements is generally referred to as the xe2x80x9cprofilexe2x80x9d of the cell""s biological state.
There may be on the order of 100,000 different cellular constituents for mammalian cells. Consequently, the profile of a particular cell is typically complex. The profile of any given state of a biological system is often measured after the biological system has been subjected to a perturbation. Such perturbations include experimental or environmental conditions(s) associated with a biological system such as exposure of the system to a drug candidate, the introduction of an exogenous gene, the deletion of a gene from the system, or changes in culture conditions. Comprehensive measurements of cellular constituents, or profiles of gene and protein expression and their response to perturbations in the cell, therefore have a wide range of utility including the ability to compare and understand the effects of drugs, diagnose disease, and optimize patient drug regimens. In addition, they have further application in basic life science research.
Within the past decade, several technological advances have made it possible to accurately measure cellular constituents and therefore derive profiles. For example, new techniques provide the ability to monitor the expression level of a large number of transcripts at any one time (see, e.g., Schena et al., 1995, Quantitative monitoring of gene expression patterns with a complementary DNA micro-array, Science 270:467-470; Lockhart et al., 1996, Expression monitoring by hybridization to high-density oligonucleotide arrays, Nature Biotechnology 14:1675-1680; Blanchard et al., 1996, Sequence to array: Probing the genome""s secrets, Nature Biotechnology 14, 1649; U.S. Pat. No. 5,569,588, issued Oct. 29, 1996 to Ashby et al. entitled xe2x80x9cMethods for Drug Screeningxe2x80x9d). In organisms for which the complete genome is known, it is possible to analyze the transcripts of all genes within the cell. With other organisms, such as humans, for which there is an increasing knowledge of the genome, it is possible to simultaneously monitor large numbers of the genes within the cell.
In another front, the direct measurement of protein abundance has been improved by the use of microcolumn reversed-phase liquid chromatography electrospray ionization tandem mass spectrometry (LC/MS/MS) to directly identify proteins contained in mixtures. This technology promises to push the dynamic range for which protein abundance can be measured in a biological system. Using LC/MS/MS, McCormack et al. have demonstrated that proteins presented in system mixtures can be readily identified with a 30-fold difference in molar quantity, that the identifications are reproducible, and that proteins within the mixture can be identified at low femtomole levels. McCormack et al., 1997, Direct analysis and identification of proteins in mixtures by LC/MS/MS and database searching at the low-femtomole level, Anal. Chem. 69:767-776. In a review of tandem mass spectrometry, Chait points out that an additional advantage of this technology is that it is orders of magnitude faster than more conventional approaches such as Edman sequencing. Chait, 1996, Trawling for proteins in the post-genome era, Nat. Biotech. 14:1544.
Other technological advances have provided for the ability to specifically perturb biological systems with individual genetic mutations. For example, Mortensen et al. describe a method for producing embryonic stem (ES) cell lines whereby both alleles are inactivated by homologous recombination. Using the methods of Mortensen et al., it is possible to obtain homozygous mutationally altered cells, i.e., double knockouts of ES cell lines. Mortensen et al. propose that their method may be generally applicable to other genes and to cell lines other than ES cells. Mortensen et al. 1992, Production of homozygous mutant ES cells with a single targeting construct, Cell Biol. 12:2391-2395.
In another promising technology Wach et al. provide a dominant resistance module for selection of S. cerevisiae transformants which entirely consists of heterologous DNA. The module can also be used to provide PCR based gene disruptions. Wach et al., 1994, New heterologous modules for classical or PCR-based gene disruptions in Saccharomyces cerevisiae, Yeast 10:1793-808.
Technological advances, such as the use of microarrays, are already being used in drug discovery (See e.g. Marton et al., 1998, Drug target validation and identification of secondary drug target effects using Microarrays, Nature Medicine in press; Gray et al., 1998, Exploiting chemical libraries, structure, and genomics in the search for kinase inhibitors, Science 281:533-538).
Comparison of profiles with other profiles in a database (see, e.g., U.S. Pat. No. 5,777,888, issued Jul. 7, 1998 to Rine et al. entitled xe2x80x9cSystems for generating and analyzing stimulus-response output signal matricesxe2x80x9d) or clustering of profiles by similarity can give clues to the molecular targets of drugs and related functions, efficacy and toxicity of drug candidates and/or pharmacological agents. Such comparisons may also be used to derive consensus profiles representative of ideal drug activities or disease states. Profile comparison can also help detect diseases in a patient at an early stage and provide improved clinical outcome projections for a patient diagnosed with a disease.
The use of two fluorophores has been described by Shalon et al. Shalon et al., 1996, A microarray system for analyzing complex DNA samples using two-color fluorescent probe hybridization, Genome Research 6:629-645. The problem with the approach put forth by Shalon is that each species of mRNA molecule has a bias in its measured color ratio due to interaction of the fluorescent labeling molecule with either the reverse transcription of the mRNA or with the hybridization efficiency or both. Without any error correction scheme to account for this bias, the data from a single microarray experiment, or even a plurality of nominal repeats of a microarray experiment in which the various results are averages, will produce an unacceptable error rate. As used herein, the term nominal repeat or nominally repeated experiment refers to experiments that are run under essentially the same or similar experimental conditions such that it would be useful to combine the results of the repeated experiments.
While the technological advances have allowed for the generation of quantitative measurements of the levels cellular constituents, the experiments are expensive. A single microarray experiment, or a single gel electrophoresis place, can cost in the neighborhood of $100-$1000 and higher. Also, it has only become apparent after many initial attempts to apply the data to actual commercial needs that individual experiments suffer from high levels of false positives in the sense of declaring significance where there really is none. Because of the expense involved, and the high rate of false positives, no description of robust methods for repeating and statistically combining multiple, nominally identical experiments for the express purpose of data quality improvement have been provided in the prior art.
The power of genome-wide cell profiling accomplished with microarrays is in its ability to survey response to known perturbations across essentially the entire set of cellular mechanisms. However, in any given experiment, typically only a small number of cellular constituents may have dramatic changes in abundance, where the vast majority are unchanged. There are exceptions, but cells have specific, biologically fairly insulated responses to stimuli, and so most profiles involve a large set of constituents with xe2x80x98no-changexe2x80x99, and a much smaller set that are either up or down regulated. For this reason, even a small false alarm rate in the measurements can severely compromise their utility. For example, if one percent of cellular constituents actually respond in a typical experiment, the resolution in the measurement is twofold, and the errors exceed twofold one percent of the time, then there will be as many false alarms as true detections above a twofold threshold.
In general, the art has underappreciated the extensive amount of errors that are present in individual cellular constituent quantification experiments such as microarray or protein gel experiments. In addition to the difficulty posed by the fairly insulated response biological systems have to any given perturbation, a substantial amount of error is present in any nominal microarray experiment due to artifacts such as unevenly printed DNA probe spots on the microarray, scratches dust and artifacts on the microarray, uneveness in signal brightness across the microarray due to nonuniform DNA hybridization, and color stripes due fluorophore-specific biases of fluorophores used in the microarray process.
One method to reduce the effects of these serious errors is to repeat the experiment under identical conditions and to average the data. However, simple averaging of the data without any consideration of the nature of the underlying experimental errors does not provide an adequate solution to the problems the experimental errors introduce. If only simple averaging of the data is performed, an excessive number of nominal repeats would be required in order to reduce the effects of error down to an acceptable level. However, because of the expense involved in performing each cellular constituent quantification experiment, this is not a feasible solution. Accordingly, what is needed in the art are robust methods for combining the experimental results of repeated cellular constituent quantification experiments so that a minimal set of nominal repeats can provide an acceptable error rate.
Discussion or citation of a reference herein shall not be construed as an admission that such citation is prior art to the present invention.
This invention provides solutions for minimizing the number of times a cellular constituent quantification experiment must be repeated in order to produce data that has acceptable error levels. Accordingly, the methods of the present invention provide a novel method for fluorophore bias removal. This allows for the attenuation of fluorophore specific biases to acceptable levels based on only two nominal repeats of a cellular constituent quantification experiment. The present invention further provides methods for combining nomimal repeats of a cellular constituent quantification experiment based on rank order of up-regulation or down-regulation. In these methods, cellular constituent up- or down-regulation data determined from nominal repeats of cellular constituent quantification experiments are expressed by a novel metric that is free of intensity dependent errors. Application of this metric before combining based on rank order provides a powerful method for removing error from weakly expressing cellular constituents without an excessive number of nominal repetitions of the expensive cellular constituent quantification experiment.
Another aspect of the present invention is an improved method for computing a weighted average of individual cellular constituent measurements in nominally repeated cellular constituent quantification experiments. In particular, a novel method for calculating the error associated with each cellular constituent measurement is provided. By using this novel method for calculating error, the error bar in the weighted average is sharply attenuated. One skilled in the art will appreciate that these improved methods for computing a weighted average are applicable to two-fluorophore (two-color) or single fluorophore (one-color) protocols.
One embodiment of the present invention provides a method of fluorophore bias removal comprising the steps of:
(a) labeling a first pool of genetic matter, derived from a biological system representing a baseline state, with a first fluorophore to obtain a first pool of fluorophore-labeled genetic matter;
(b) labeling a second pool of genetic matter, derived from a biological system representing a perturbed state, with a second fluorophore to obtain a second pool of fluorophore-labeled genetic matter;
(c) labeling a third pool of genetic matter, derived from said biological system representing said baseline state, with said second fluorophore to obtain a third pool of fluorophore-labeled genetic matter;
(d) labeling a fourth pool of genetic matter, derived from said biological system representing said perturbed state, with said first fluorophore to obtain a fourth pool of fluorophore-labeled genetic matter;
(e) independently contacting said first pool of fluorophore-labeled genetic matter and said second pool of fluorophore-labeled genetic matter with a first microarray under conditions such that hybridization can occur and determining a first color ratio between said first pool of fluorophore-labeled genetic matter and said second pool of fluorophore-labeled genetic matter that binds to said microarray;
(f) independently contacting said third pool of fluorophore-labeled genetic matter and said fourth pool of fluorophore-labeled genetic matter with a second microarray under conditions such that hybridization can occur and determining a second color ratio between said third pool of fluorophore-labeled genetic matter and said fourth pool of fluorophore-labeled genetic matter; and
(g) computing an average color ratio by averaging said first color ratio and said second color ratio.
Another embodiment of the invention provides a method for determining a probability that an expression level of a cellular constituent in a plurality of paired differential microarray experiments is altered by a perturbation, wherein each paired differential microarray experiment in said plurality of paired differential microarray experiments comprises a first microarray experiment representing a baseline state of a first biological system, and a second microarray experiment representing a perturbed state of said first biological system, said method comprising the steps of
(a) determining an error distribution statistic by fitting a reference pair of microarray experiments with an intensity independent statistic, wherein said reference pair of microarray experiments comprises a first reference microarray experiment, and a second reference microarray experiment that is a nominal repeat of said first reference microarray experiment;
(b) selecting said cellular constituent from a set of cellular constituents measured in said plurality of paired differential microarray experiments, and, for each paired differential microarray experiment in said plurality of paired differential microarray experiments, determining an amount of change in expression level of said cellular constituent between the second microarray experiment and the first microarray experiment of said paired differential microarray experiment using said error distribution statistic; and
(c) determining said probability that said expression level of said cellular constituent in said plurality of paired differential microarray experiments is altered by said perturbation by combining said amount of change in expression level of said cellular constituent determined in step (b) for each paired differential microarray experiment in said plurality of paired differential microarray experiments using a rank based method.
Yet another embodiment of the invention is a method for determining a weighted mean differential intensity in an expression level of a cellular constituent in a biological system in response to a perturbation, the method comprising:
(a) determining an error distribution statistic by fitting a reference microarray experiment pair with an intensity independent statistic, wherein the reference microarray experiment pair comprises a first reference microarray experiment and a second reference microarray experiment which is a nominal repeat of the first reference microarray experiment;
(b) determining an amount of differential expression of the cellular constituent a plurality of times;
(c) for each amount of differential expression determined in accordance with (b), calculating a corresponding amount of error based on a magnitude derived by the error distribution statistic; and
(d) computing the weighted mean differential intensity by inversely weighting each amount of the differential expression of the cellular constituent determined in step (b) by the corresponding amount of error determined in step (c) according to the formula   X  =            ∑              (                              x            i                    /                      σ            i            2                          )                    ∑              (                  1          /                      σ            i            2                          )            
where x is the weighted mean differential intensity of the cellular constituent, xi is a differential expression measurement of the cellular constituent i and "sgr"i2 is a corresponding error for mean differential intensity xi.