Salis Howard, Kaznessis Yiannis
Department of Chemical Engineering and Materials Science, and Digital Technology Center, University of Minnesota, Minneapolis, MN 55455, USA.
J Chem Phys. 2005 Feb 1;122(5):54103. doi: 10.1063/1.1835951.
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.
由主方程描述的充分混合的非线性随机化学动力学系统的动力学解，可以使用随机模拟算法精确计算。然而，由于计算成本随反应发生次数而增加，对于具有一个或多个“快速”反应的系统，模拟成本会变得很高。本文描述了一种混合随机方法，该方法将系统划分为快速反应和慢速反应子集，使用化学朗之万方程将快速反应近似为连续马尔可夫过程，并使用随机模拟算法的“下一个反应”变体的积分形式精确描述慢速动力学。该方法的关键创新在于其能够在模拟连续、随机或确定性过程动力学的同时，有效监测慢速离散事件发生的机制。此外，通过引入一种近似，即在化学朗之万方程的数值积分时间步长内可能发生多个慢速反应，混合随机方法的执行速度大幅提高，而精度仅略有下降。使用精确方法和本文提出的混合方法以及作为比较的先前混合随机方法，对包括生物脉冲发生器和大规模系统基准在内的多个示例进行了模拟。比较了解的概率分布并计算了前两阶矩的弱误差。一般来说，这些混合方法可应用于由随机微分方程、常微分方程和主方程描述的系统动力学模拟。
