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Cellular biology in terms of stochastic nonlinear biochemical dynamics: Emergent properties, isogenetic variations and chemical system inheritability. (English) Zbl 1205.82118

Summary: Based on the 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 modeling. We apply this theory to both self-regulating gene networks and phosphorylation-dephosphorylation signaling modules 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 molecular processes do not disappear in mesoscopic cell-sized nonlinear systems; they rather manifest themselves as isogenetic variations on a different time scale. Isogenetic biochemical variations in terms of the stochastic attractors can have extremely long lifetime. Transitions 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 \(Q_{hk} \geq 0\), and total entropy production rate \(e_{p }= - dF/dt+Q _{hk} \geq 0\). In the thermodynamic limit, with an infinitely large system size, the nonlinear bistability in the CME exhibits many of the characteristics of macroscopic equilibrium phase transition.

MSC:

82C35 Irreversible thermodynamics, including Onsager-Machlup theory
82C26 Dynamic and nonequilibrium phase transitions (general) in statistical mechanics
92C40 Biochemistry, molecular biology
92C37 Cell biology
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