  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.
