Interpreting patterns of gene expression: signatures of coregulation, the data processing inequality, and triplet motifs.

Various methods of reconstructing transcriptional regulatory networks infer transcriptional regulatory interactions (TRIs) between strongly coexpressed gene pairs (as determined from microarray experiments measuring mRNA levels). Alternatively, however, the coexpression of two genes might imply that they are coregulated by one or more transcription factors (TFs), and do not necessarily share a direct regulatory interaction. We explore whether and under what circumstances gene pairs with a high degree of coexpression are more likely to indicate TRIs, coregulation or both. Here we use established TRIs in combination with microarray expression data from both Escherichia coli (a prokaryote) and Saccharomyces cerevisiae (a eukaryote) to assess the accuracy of predictions of coregulated gene pairs and TRIs from coexpressed gene pairs. We find that coexpressed gene pairs are more likely to indicate coregulation than TRIs for Saccharomyces cerevisiae, but the incidence of TRIs in highly coexpressed gene pairs is higher for Escherichia coli. The data processing inequality (DPI) has previously been applied for the inference of TRIs. We consider the case where a transcription factor gene is known to regulate two genes (one of which is a transcription factor gene) that are known not to regulate one another. According to the DPI, the non-interacting gene pairs should have the smallest mutual information among all pairs in the triplets. While this is sometimes the case for Escherichia coli, we find that it is almost always not the case for Saccharomyces cerevisiae. This brings into question the usefulness of the DPI sometimes employed to infer TRIs from expression data. Finally, we observe that when a TF gene is known to regulate two other genes, it is rarely the case that one regulatory interaction is positively correlated and the other interaction is negatively correlated. Typically both are either positively or negatively correlated.