Geometric characteristics of dynamic correlations for combinatorial regulation in gene expression noise

Knowing which mode of combinatorial regulation (typically, AND or OR logic operation) that a gene employs is important for determining its function in regulatory networks. Here, we introduce a dynamic cross-correlation function between the output of a gene and its upstream regulator concentrations for signatures of combinatorial regulation in gene expression noise. We find that such a correlation function with respect to the correlation time near the peak close to the point of the zero correlation time is always upward convex in the case of AND logic whereas is always downward convex in the case of OR logic, whichever sources of noise (intrinsic or extrinsic or both). In turn, this fact implies a means for inferring regulatory synergies from available experimental data. The extensions and applications are discussed.