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Int. J. Mol. Sci. 2010, 11(9), 3472-3500; doi:10.3390/ijms11093472
Review

The Chemical Master Equation Approach to Nonequilibrium Steady-State of Open Biochemical Systems: Linear Single-Molecule Enzyme Kinetics and Nonlinear Biochemical Reaction Networks

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Received: 15 August 2010; Accepted: 14 September 2010 / Published: 20 September 2010
(This article belongs to the Special Issue Quantitative Modelling in Molecular System Bioenergetics)
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Abstract: We develop the stochastic, chemical master equation as a unifying approach to the dynamics of biochemical reaction systems in a mesoscopic volume under a living environment. A living environment provides a continuous chemical energy input that sustains the reaction system in a nonequilibrium steady state with concentration fluctuations. We discuss the linear, unimolecular single-molecule enzyme kinetics, phosphorylation-dephosphorylation cycle (PdPC) with bistability, and network exhibiting oscillations. Emphasis is paid to the comparison between the stochastic dynamics and the prediction based on the traditional approach based on the Law of Mass Action. We introduce the difference between nonlinear bistability and stochastic bistability, the latter has no deterministic counterpart. For systems with nonlinear bistability, there are three different time scales: (a) individual biochemical reactions, (b) nonlinear network dynamics approaching to attractors, and (c) cellular evolution. For mesoscopic systems with size of a living cell, dynamics in (a) and (c) are stochastic while that with (b) is dominantly deterministic. Both (b) and (c) are emergent properties of a dynamic biochemical network; We suggest that the (c) is most relevant to major cellular biochemical processes such as epi-genetic regulation, apoptosis, and cancer immunoediting. The cellular evolution proceeds with transitions among the attractors of (b) in a “punctuated equilibrium” manner.
Keywords: chemical kinetics; chemical master equation; stochastic dynamics; biochemical reaction; systems biology chemical kinetics; chemical master equation; stochastic dynamics; biochemical reaction; systems biology
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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MDPI and ACS Style

Qian, H.; Bishop, L.M. The Chemical Master Equation Approach to Nonequilibrium Steady-State of Open Biochemical Systems: Linear Single-Molecule Enzyme Kinetics and Nonlinear Biochemical Reaction Networks. Int. J. Mol. Sci. 2010, 11, 3472-3500.

AMA Style

Qian H, Bishop LM. The Chemical Master Equation Approach to Nonequilibrium Steady-State of Open Biochemical Systems: Linear Single-Molecule Enzyme Kinetics and Nonlinear Biochemical Reaction Networks. International Journal of Molecular Sciences. 2010; 11(9):3472-3500.

Chicago/Turabian Style

Qian, Hong; Bishop, Lisa M. 2010. "The Chemical Master Equation Approach to Nonequilibrium Steady-State of Open Biochemical Systems: Linear Single-Molecule Enzyme Kinetics and Nonlinear Biochemical Reaction Networks." Int. J. Mol. Sci. 11, no. 9: 3472-3500.



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