Stochastic bifurcation, slow fluctuations, and bistability as an origin of biochemical complexity.
We present a simple, unifying theory for stochastic biochemical systems with multiple time-scale dynamics that exhibit noise-induced bistability in an open-chemical environment, while the corresponding macroscopic reaction is unistable. Nonlinear stochastic biochemical systems like these are fundamentally different from classical systems in equilibrium or near-equilibrium steady state whose fluctuations are unimodal following Einstein-Onsager-Lax-Keizer theory. We show that noise-induced bistability in general arises from slow fluctuations, and a pitchfork bifurcation occurs as the rate of fluctuations decreases. Since an equilibrium distribution, due to detailed balance, has to be independent of changes in time-scale, the bifurcation is necessarily a driven phenomenon. As examples, we analyze three biochemical networks of currently interest: self-regulating gene, stochastic binary decision, and phosphorylation-dephosphorylation cycle with fluctuating kinase. The implications of bistability to biochemical complexity are discussed.
Qian
Hong
H
Department of Applied Mathematics, University of Washington, Seattle, WA 98195, USA. qian@amath.washington.edu
Shi
Pei-Zhe
PZ
Xing
Jianhua
J
D053263:Gene Regulatory Networks; D008954:Models, Biological; D010766:Phosphorylation; D010770:Phosphotransferases / Q000378:metabolism; D013269:Stochastic Processes
D010770:Phosphotransferases