Relating network rigidity, time scale hierarchies, and expression noise in gene networks.

Fluctuation-dissipation theorems can be used to predict characteristics of noise from characteristics of the macroscopic response of a system. In the case of gene networks, feedback control determines the "network rigidity," defined as resistance to slow external changes. We propose an effective Fokker-Planck equation that relates gene expression noise to topology and to time scales of the gene network. We distinguish between two situations referred to as normal and inverted time hierarchies. The noise can be buffered by network feedback in the first situation, whereas it can be topology independent in the latter.