Generalized singular value decomposition for comparative analysis of genome-scale expression data sets of two different organisms

Abstract

We describe a comparative mathematical framework for two genome-scale expression data sets. This framework formulates expression as superposition of the effects of regulatory programs, biological processes, and experimental artifacts common to both data sets, as well as those that are exclusive to one data set or the other, by using generalized singular value decomposition. This framework enables comparative reconstruction and classification of the genes and arrays of both data sets. We illustrate this framework with a comparison of yeast and human cell-cycle expression data sets.DNA microarrays ͉ cell cycle ͉ yeast Saccharomyces cerevisiae ͉ human HeLa cell line R ecent advances in high-throughput genomic technologies enable acquisition of different types of molecular biological data, e.g., DNA-sequence and mRNA-expression data, on a genomic scale. Comparative analysis of these data among two or more model organisms promises to enhance fundamental understanding of the universality as well as the specialization of molecular biological mechanisms. It also may prove useful in medical diagnosis, treatment, and drug design. Comparisons of the DNA sequence of entire genomes already give insights into evolutionary, biochemical, and genetic pathways.Comparative analysis of mRNA-expression data requires mathematical tools that are able to distinguish the similar from the dissimilar among two or more large-scale data sets. These tools should provide mathematical frameworks for the description of the data, where the variables and operations may represent some biological reality. Recently we showed that singular value decomposition (SVD) provides such a framework for genome-wide expression data (refs. 1-3; see also refs. 4-7). Now we show that generalized SVD (GSVD) (8) provides a comparative mathematical framework for two genome-scale expression data sets. GSVD is a linear transformation of the two data sets from the two genes ϫ arrays spaces to two reduced and diagonalized ''genelets'' ϫ ''arraylets'' spaces. The genelets are shared by both data sets. Each genelet is expressed only in the two corresponding arraylets, with a corresponding ''angular distance'' indicating the relative significance of this genelet, i.e., its significance, in one data set relative to that in the other.We show that a genelet of equal significance in both data sets may represent a process common to both data sets. The two corresponding arraylets may represent the cellular states in each data set that correspond to this common process. A genelet of no significance in one data set relative to the other may represent a process exclusive to the latter data set. The corresponding arraylet of this data set may represent the cellular state that corresponds to this exclusive process.We also show that mathematical reconstruction of gene expression in a subset of genelets may simulate experimental observation of only the process that these genelets are inferred to represent. Similarly, reconstruction of array expression in the subset of corresponding arr...

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