On the Reaction Diffusion Master Equation in the Microscopic Limit
This provides a rigorous, general explanation for a known limitation of the RDME, which is important for researchers modeling stochastic reaction-diffusion systems in biophysics.
The paper identifies a fundamental limitation of the Reaction-Diffusion Master Equation (RDME) framework, proving that no local RDME can match the Smoluchowski model for arbitrarily fine mesh sizes, thus explaining the breakdown of RDME at small lattice spacings.
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.