Coherent organization in gene regulation: a study on six networks.

Structural and dynamical fingerprints of evolutionary optimization in biological networks are still unclear. Here we analyze the dynamics of genetic regulatory networks responsible for the regulation of cell cycle and cell differentiation in three organisms or cell types each, and show that they follow a version of Hebb's rule which we have termed coherence. More precisely, we find that simultaneously expressed genes with a common target are less likely to act antagonistically at the attractors of the regulatory dynamics. We then investigate the dependence of coherence on structural parameters, such as the mean number of inputs per node and the activatory/repressory interaction ratio, as well as on dynamically determined quantities, such as the basin size and the number of expressed genes.