Accurate hybrid stochastic simulation of a system of coupled chemical or biochemical reactions
Accurate hybrid stochastic simulation of a system of coupled chemical or biochemical reactions
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DOI：
10.1063/1.1835951
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发表时间：
2005-02-01
影响因子：
4.4
通讯作者：
Kaznessis, Y
中科院分区：
文献类型：
--
作者：
Salis, H;Kaznessis, Y
通过随机仿真算法，可以精确计算出良好混合的非线性随机化学动力学系统的动力解。但是，由于具有反应发生次数的计算成本量表，具有一个或多个“快速”反应的系统变得昂贵。本文描述了一种混合随机方法，该方法将系统划分为快速和缓慢反应的子集，使用化学Langevin方程将快速反应作为连续的Markov工艺近似，并使用“下一个反应”的积分形式准确地描述了缓慢的动态形式。 “随机仿真算法的变体。该方法的关键创新是其有效监测缓慢，离散事件的发生的机制，同时同时模拟连续，随机或确定性过程的动态。另外，通过引入一个近似值，在该近似值中，可以在化学兰格维素方程的数值整合的时间步骤中发生多个缓慢的反应，杂交随机方法的执行速度只有准确性的边缘降低。使用精确且建议的混合方法以及以前的混合随机方法进行了模拟，包括生物脉冲发生器和大规模系统基准在内的多个示例。比较解决方案的概率分布，并计算前两个矩的弱误差。通常，这些混合方法可以应用于由随机差分，普通差分和主方程描述的系统的动力学模拟。 （c）2005年美国物理研究所。
The dynamical solution of a well-mixed, nonlinear stochastic chemical kinetic system, described by the Master equation, may be exactly computed using the stochastic simulation algorithm. However, because the computational cost scales with the number of reaction occurrences, systems with one or more "fast" reactions become costly to simulate. This paper describes a hybrid stochastic method that partitions the system into subsets of fast and slow reactions, approximates the fast reactions as a continuous Markov process, using a chemical Langevin equation, and accurately describes the slow dynamics using the integral form of the "Next Reaction" variant of the stochastic simulation algorithm. The key innovation of this method is its mechanism of efficiently monitoring the occurrences of slow, discrete events while simultaneously simulating the dynamics of a continuous, stochastic or deterministic process. In addition, by introducing an approximation in which multiple slow reactions may occur within a time step of the numerical integration of the chemical Langevin equation, the hybrid stochastic method performs much faster with only a marginal decrease in accuracy. Multiple examples, including a biological pulse generator and a large-scale system benchmark, are simulated using the exact and proposed hybrid methods as well as, for comparison, a previous hybrid stochastic method. Probability distributions of the solutions are compared and the weak errors of the first two moments are computed. In general, these hybrid methods may be applied to the simulation of the dynamics of a system described by stochastic differential, ordinary differential, and Master equations. (C) 2005 American Institute of Physics.