  The reaction-diffusion master equation (RDME) is commonly used to model
processes where both the spatial and stochastic nature of chemical reactions
need to be considered. We show that the RDME in many cases is inconsistent with
a microscopic description of diffusion limited chemical reactions and that this
will result in unphysical results. We describe how the inconsistency can be
reconciled if the association and dissociation rates used in the RDME are
derived from the underlying microscopic description. These rate constants will
however necessarily depend on the spatial discretization. At fine spatial
resolution the rates approach the microscopic rate constants defined at the
reaction radius. At low resolution the rates converge to the macroscopic
diffusion limited rate constants in 3D, whereas there is no limiting value in
2D. Our results make it possible to develop spatially discretized
reaction-diffusion models that correspond to a well-defined microscopic
description. We show that this is critical for a correct description of 2D
systems and systems that require high spatial resolution in 3D.
