Ortiz Zuazaga, Humberto

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    Discrete methods for microarray analysis
    (2008) Ortiz Zuazaga, Humberto; Moreno de Ayala, Oscar; College of Engineering; Bollman, Dorothy; Corrada Bravo, Carlos; Pericchi, Luis; Department of Electrical and Computer Engineering; García Arrarás, Jose E.
    Microarrays allow researchers to simultaneously measure the expression of thousands of genes. They give invaluable insight into the transcriptional state of biological systems, and can be important in understanding physiological as well as diseased conditions. However, the analysis of data from many thousands of genes, from only a few replications is very difficult. We have devised a novel method of correcting errors in microarray experiments, that also clusters genes into groups, and categorizes their measurements into coarse divisions, suitable for discrete techniques for reverse engineering. These techniques are based on finite fields and algebraic coding theory. We test these new techniques on a data set obtained from behavioral training experiments on rats, and identify two novel genes that may be involved in learning and memory. We extend this method to work with “probe level” microarray data, where each gene is represented by multiple probes. We have applied the error correction procedure to two data sets, one Affymetrix, one NimbleGen, having either 14 (Affymetrix) or approximately 10 (NimbleNen) probes per gene, derived from an odor avoidance experiment on Drosophila. The experiment is designed to validate analysis procedures by examining the degree of concordance the procedures produce across the data sets. For this data we devise a method to measure the concordance quantitatively. We have developed a technique based on mutual information to compare results obtained across the two data sets. Our results show that our error correction techniques result in a greater amount of shared information between data sets than traditional approaches based on averaging of probes and gene expression levels across repetitions. We show how our results can be extended to sets with finer gradations in expression values, and present the analysis of the Drosophila data discretized to 5 separate expression values. Finally, we present some future applications, such as using finite fields to encode expression values, allowing us to use the algebraic properties of finite fields to perform reverse engineering of gene regulatory networks.