Jump-Diffusion Approximation of Stochastic Reaction Dynamics: Error Bounds and Algorithms

Abstract

Biochemical processes in living cells are comprised of reactions with vastly varying speeds and molecular counts of the reactant species. Classical deterministic or stochastic approaches to modeling often fail to exploit this multiscale nature of the reaction systems. In this paper, we propose a jump-diffusion approximation to these types of multiscale systems that couples the two traditional modeling approaches. An error bound of the proposed approximation is derived and used to partition the reactions into two sets, where one set is modeled by continuous stochastic differential equations and the other by discrete state processes. The methodology leads to a very efficient dynamic partitioning algorithm which has been implemented for several multiscale reaction systems. The gain in computational efficiency is evident in all these examples, which include a realistically sized model of a signal transduction cascade coupled to a gene expression dynamics.