Interaction among the gene products contributes to the regulation of gene expression.

Owing to its complexity, the mechanism of gene regulation for the whole genome is not easily probed with the conventional gene-level analysis. Models of gene regulatory networks (GRN) that are based on a course-grained view of gene regulation, where genes with similar expression profile are grouped in clusters, can aid the inference of important correlations between genes. We propose a model of gene regulation which incorporates the effects of interaction among gene products on the transcription rates. We introduce for that purpose a non-constant rate of gene product degradation which depends on the concentrations of other gene products. Guided by previous reports on the sparseness of GRNs we employ a method of parameter reduction based on interpolating polynomials. We test our model on DNA microarray time series data of Escherichia coli during a glucose-lactose diauxie and report good agreement between data and theory. Our analysis shows that on going from glucose to lactose phase the system becomes highly connected and becomes again sparsely connected in the lactose phase. Out of the many compatible GRNs that our model predicts we chose the ones that satisfy criteria based on robustness, behavior near a fixed point, and fit of the data.