Constraint structure analysis of gene expression

A microarray experiment gives a snapshot of the state of an organism in terms of the relative abundances of its mRNA transcripts, locating the organism at a point in a high dimensional state space where each axis represents the relative expression level of a single gene. Multiple experiments generate a cloud of points in this gene expression space. We present a geometric approach to analyzing the covariational properties of such a cloud and use a dataset from Saccharomyces cerevisiae as an illustration. In particular, we use singular value decomposition to identify significant linear sub-structures in the data and analyze the contributions of both individual genes and functional classes of genes to these major directions of variation. Analyzing the publicly available yeast expression data, we show that under all experimental conditions the variation in expression is limited to a small number of linear dimensions. Projections of individual gene axes onto the significant dimensions can order the contribution of individual genes to variation in expression within an experiment. We show that no particular groups of genes characterize particular experimental conditions. Instead, the particular structure of the coordinated expression of the entire genome characterizes a particular experiment.