Adaptive Time-Stepping Using Control Theory for the Chemical Langevin Equation

[摘要] Stochastic modeling of biochemical systems has been the subject of intense research in recent years due to the largenumber of important applications of these systems. A critical stochastic model of well-stirred biochemical systems inthe regime of relatively large molecular numbers, far from the thermodynamic limit, is the chemical Langevin equation. This model is represented as a system of stochastic differential equations, with multiplicative and noncommutativenoise. Often biochemical systems in applications evolve on multiple time-scales; examples include slow transcriptionand fast dimerization reactions. The existence of multiple time-scales leads to mathematical stiffness, which is a majorchallenge for the numerical simulation. Consequently, there is a demand for efficient and accurate numerical methods toapproximate the solution of these models. In this paper, we design an adaptive time-stepping method, based on controltheory, for the numerical solution of the chemical Langevin equation. The underlying approximation method is theMilstein scheme. The adaptive strategy is tested on several models of interest and is shown to have improved efficiencyand accuracy compared with the existing variable and constant-step methods.

[学科分类] 应用数学