Based on a stochastic, nonlinear, open biochemical reaction system perspective, we present an analytical theory for cellular biochemical processes. The chemical master equation (CME) approach provides a unifying mathematical framework for cellular mod- eling. We apply this theory to both self-regulating gene networks and phosphorylation- dephosphorylation signalingmodules with feedbacks. Two types of bistability are illustrated in mesoscopic biochemical systems: one that has a macroscopic, deterministic counterpart and another that does not. In certain cases, the latter stochastic bistability is shown to be a “ghost” of the extinction phenomenon.We argue the thermal fluctuations inherent in mole- cular processes do not disappear in mesoscopic cell-sized nonlinear systems; rather they manifest themselves as isogenetic variations on a different time scale. Isogenetic biochem- ical variations in terms of the stochastic attractors can have extremely long lifetime. Tran- sitions among discrete stochastic attractors spend most of the time in “waiting”, exhibit punctuated equilibria. It can be naturally passed to “daughter cells” via a simple growth and division process. The CME system follows a set of nonequilibrium thermodynamic laws that include non-increasing free energy F(t) with external energy drive Qhk ≥ 0, and total entropy production rate ep =−dF/dt +Qhk ≥ 0. In the thermodynamic limit, with a sys- tem’s size being infinitely large, the nonlinear bistability in the CME exhibits many of the characteristics of macroscopic equilibrium phase transition.
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