Combinatorial regulation: characteristics of dynamic correlations

A cis-regulatory module often processes multiple regulatory inputs provided by transcription factors that bind to DNA and regulate the expression of the gene in a combinatorial logic manner. Here the authors analyse dynamic cross correlations between the regulator concentrations and the output of the gene using stochastic modelling, and show their characteristics for different logic operations. The authors find that the dynamic cross-correlation curve with respect to the correlation time near the peak close to the point of the zero correlation time is upwards convex in the case of AND logic whereas downwards convex in the case of OR logic, where intrinsic and extrinsic noise plays a distinct role. This result implies that the cross-correlation function is a useful and robust index for distinguishing super- and sub-additive gene regulatory scenarios (molecular analogues of AND and OR logic operations) that faithfully represent gene expression.