The slow-scale stochastic simulation algorithm

TLDR

Chemical systems often involve reactions on vastly different time scales, with fast reactions occurring far more frequently than slow ones, and because fast and slow reactions share species, simulating all events is computationally inefficient when stiffness is present. The paper aims to develop a systematic approximate theory that enables stochastic advancement of the system by simulating only slow reaction events. The authors implement this theory by devising an effective strategy that selectively simulates slow reactions while accounting for fast reaction effects. When applied to two simple systems, this approach yields substantial increases in simulation speed, demonstrating its practical feasibility.

Abstract

Reactions in real chemical systems often take place on vastly different time scales, with “fast” reaction channels firing very much more frequently than “slow” ones. These firings will be interdependent if, as is usually the case, the fast and slow reactions involve some of the same species. An exact stochastic simulation of such a system will necessarily spend most of its time simulating the more numerous fast reaction events. This is a frustratingly inefficient allocation of computational effort when dynamical stiffness is present, since in that case a fast reaction event will be of much less importance to the system’s evolution than will a slow reaction event. For such situations, this paper develops a systematic approximate theory that allows one to stochastically advance the system in time by simulating the firings of only the slow reaction events. Developing an effective strategy to implement this theory poses some challenges, but as is illustrated here for two simple systems, when those challenges can be overcome, very substantial increases in simulation speed can be realized.