On the Reaction Diffusion Master Equation in the Microscopic Limit

TL;DR

This paper analyzes the limitations of the Reaction-Diffusion Master Equation (RDME) in accurately modeling biochemical reaction networks at very fine spatial scales, revealing a fundamental limit on its applicability compared to the Smoluchowski model.

Contribution

It provides a new, simple argument demonstrating the breakdown of RDME at small voxel sizes, establishing a hard limit on its accuracy relative to the microscopic Smoluchowski model.

Findings

RDME becomes inaccurate at very fine mesh sizes

A fundamental limit exists on voxel size for RDME validity

RDME cannot fully replicate Smoluchowski model at small scales

Abstract

Stochastic modeling of reaction-diffusion kinetics has emerged as a powerful theoretical tool in the study of biochemical reaction networks. Two frequently employed models are the particle-tracking Smoluchowski framework and the on-lattice Reaction-Diffusion Master Equation (RDME) framework. As the mesh size goes from coarse to fine, the RDME initially becomes more accurate. However, recent developments have shown that it will become increasingly inaccurate compared to the Smoluchowski model as the lattice spacing becomes very fine. In this paper we give a new, general and simple argument for why the RDME breaks down. Our analysis reveals a hard limit on the voxel size for which no local RDME can agree with the Smoluchowski model.