EXACT STOCHASTIC SIMULATION OF COUPLED CHEMICAL-REACTIONS
EXACT STOCHASTIC SIMULATION OF COUPLED CHEMICAL-REACTIONS
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DOI：
10.1021/j100540a008
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发表时间：
1977-01-01
影响因子：
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通讯作者：
GILLESPIE, DT
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文献类型：
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作者：
GILLESPIE, DT
对于空间均质化学体系的时间行为，有两种数学描述方法：确定性方法认为时间演化是一个连续的、完全可预测的过程，由一组耦合的常微分方程控制（“反应速率方程”）;随机方法把时间演化看作是一种由单一的微分差分方程控制的随机行走过程（“主方程”）。相当简单的动力学理论论证表明，化学动力学的随机公式比确定性公式有更坚实的物理基础，但不幸的是，随机主方程往往是数学上难以解决的。然而，有一种方法可以在随机公式的框架内进行精确的数值计算，而不必直接处理主方程。它是一种相对简单的数字计算机算法，它使用严格推导的蒙特卡罗程序来数值模拟给定化学系统的时间演化。像主方程一样，这种“随机模拟算法”正确地解释了确定性公式中必然忽略的内在波动和相关性。此外，与大多数数值求解确定性反应速率方程的程序不同，该算法从不用有限时间步长Δ t近似无穷小的时间增量df。通过将其应用于几个著名的模型化学系统，包括洛特卡模型，Oregonator和Chronoselator的模拟算法的可行性和实用性进行了证明。
There are two formalisms for mathematically describing the time behavior of a spatially homogeneous chemical system: The deterministic approach regards thetime evolution as a continuous, wholly predictable process which is governedby a set of coupled, ordinary differential equations (the “reaction-rate equations”); the stochastic approach regards the time evolution as a kind of random-walk process which is governed by a single dif-ferential-difference equation (the “master equation”). Fairly simple kinetic theory arguments show that the stochastic formulation of chemical kinetics has a firmer physical basis than the deterministic formulation, but unfortunately thestochastic master equation is often mathematically intractable. There is, however, a way to make exact numerical calculations within the framework of the stochastic formulation without having to deal with the master equation directly. It is a relatively simple digital computer algorithm which uses a rigorously derived Monte Carlo procedure to numerically simulate the time evolution of the given chemical system. Like the master equation, this “stochastic simulation algorithm” correctly accounts for the inherent fluctuations and correlations that are necessarily ignored in the deterministic formulation. In addition, unlike most procedures for numerically solving the deterministic reaction-rate equations, this algorithm never approximates infinitesimal time increments df by finite time steps At. The feasibility and utility of the simulation algorithm are demonstrated by applying it to several well-known model chemical systems, including the Lotka model, the Brusselator, and the Oregonator.