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Issue 24, 2009
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Stochastic bifurcation, slow fluctuations, and bistability as an origin of biochemical complexity

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Abstract

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.

Graphical abstract: Stochastic bifurcation, slow fluctuations, and bistability as an origin of biochemical complexity

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Article information


Submitted
07 Jan 2009
Accepted
26 Feb 2009
First published
08 Apr 2009

Phys. Chem. Chem. Phys., 2009,11, 4861-4870
Article type
Paper

Stochastic bifurcation, slow fluctuations, and bistability as an origin of biochemical complexity

H. Qian, P. Shi and J. Xing, Phys. Chem. Chem. Phys., 2009, 11, 4861
DOI: 10.1039/B900335P

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