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• W2073162756 abstract "The nonlinear dynamics of biochemical reactions in a small-sized system on the order of a cell are stochastic. Assuming spatial homogeneity, the populations of n molecular species follow a multi-dimensional birth-and-death process on . We introduce the Delbrück–Gillespie process, a continuous-time Markov jump process, whose Kolmogorov forward equation has been known as the chemical master equation, and whose stochastic trajectories can be computed via the Gillespie algorithm. Using simple models, we illustrate that a system of nonlinear ordinary differential equations on emerges in the infinite system size limit. For finite system size, transitions among multiple attractors of the nonlinear dynamical system are rare events with exponentially long transit times. There is a separation of time scales between the deterministic ODEs and the stochastic Markov jumps between attractors. No diffusion process can provide a global representation that is accurate on both short and long time scales for the nonlinear, stochastic population dynamics. On the short time scale and near deterministic stable fixed points, Ornstein–Uhlenbeck Gaussian processes give linear stochastic dynamics that exhibit time-irreversible circular motion for open, driven chemical systems. Extending this individual stochastic behaviour-based nonlinear population theory of molecular species to other biological systems is discussed." @default.
• W2073162756 created "2016-06-24" @default.
• W2073162756 creator A5027668881 @default.
• W2073162756 date "2011-04-21" @default.
• W2073162756 modified "2023-09-30" @default.
• W2073162756 title "Nonlinear stochastic dynamics of mesoscopic homogeneous biochemical reaction systems—an analytical theory" @default.
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• W2073162756 doi "https://doi.org/10.1088/0951-7715/24/6/r01" @default.
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