  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
the correlation function is always upwards convex for the AND operation whereas
downwards convex for the OR operation, 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.
