The convergent reaction-diffusion master equation (CRDME) was recentlydeveloped to provide a lattice particle-based stochastic reaction-diffusionmodel that is a convergent approximation in the lattice spacing to anunderlying spatially-continuous particle dynamics model. The CRDME was designedto be identical to the popular lattice reaction-diffusion master equation(RDME) model for systems with only linear reactions, while overcoming theRDME's loss of bimolecular reaction effects as the lattice spacing is taken tozero. In our original work we developed the CRDME to handle bimolecularassociation reactions on Cartesian grids. In this work we develop severalextensions to the CRDME to facilitate the modeling of cellular processes withinrealistic biological domains. Foremost, we extend the CRDME to handlereversible bimolecular reactions on unstructured grids. Here we develop ageneralized CRDME through discretization of the spatially continuous volumereactivity model, extending the CRDME to encompass a larger variety ofparticle-particle interactions. Finally, we conclude by examining severalnumerical examples to demonstrate the convergence and accuracy of the CRDME inapproximating the volume reactivity model.
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