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

TL;DR

This paper introduces a jump-diffusion approximation method for multi-scale biochemical reaction systems, providing error bounds and an efficient algorithm that couples stochastic differential equations with discrete chains to improve simulation efficiency.

Contribution

It proposes a novel jump-diffusion approximation for multi-scale Markov jump processes, including error bounds and a dynamic partitioning algorithm for efficient simulation.

Findings

The approximation accurately captures multi-scale reaction dynamics.

The dynamic partitioning algorithm improves computational efficiency.

Application to a signal transduction cascade demonstrates practical benefits.

Abstract

Biochemical reactions can happen on different time scales and also the abundance of species in these reactions can be very different from each other. Classical approaches, such as deterministic or stochastic approach, fail to account for or to exploit this multi-scale nature, respectively. In this paper, we propose a jump-diffusion approximation for multi-scale Markov jump processes that couples the two modeling approaches. An error bound of the proposed approximation is derived and used to partition the reactions into fast and slow sets, where the fast set is simulated by a stochastic differential equation and the slow set is modeled by a discrete chain. The error bound leads to a very efficient dynamic partitioning algorithm which has been implemented for several multi-scale reaction systems. The gain in computational efficiency is illustrated by a realistically sized model of a signal transduction cascade coupled to a gene expression dynamics.