The reaction-diffusion master equation (RDME) is a lattice stochastic reaction-diffusion model that has been used to study spatially distributed cellular processes. The RDME has been shown to have the drawback of losing bimolecular reactions in the continuum limit that the lattice spacing approaches zero (in two or more dimensions). In this work we derive a new convergent RDME (CRDME) that eliminates this problem. The CRDME is obtained by finite volume discretization of a spatially-continuous stochastic reaction-diffusion model. We demonstrate the empirical numerical convergence of reaction time statistics associated with the CRDME. Although the reaction time statistics of the RDME diverge as the lattice spacing approaches zero, we show they approach those of the CRDME for sufficiently large lattice spacings or slow bimolecular reaction rates . As such, the RDME may be interpreted as an approximation to the CRDME in several asymptotic limits.
The reaction-diffusion master equation (RDME) is a lattice stochastic reaction-diffusion model that has been used to study spatially distributed cellular processes. The RDME has been shown to have the drawback of losing bimolecular reactions in the limit that the lattice spacing approaches zero (in two or more dimensions). In this work we derive a new convergent RDME (CRDME) that eliminates this problem. The CRDME is obtained by finite volume discretization of a spatially-continuous stochastic reaction-diffusion model. We demonstrate the numerical convergence of reaction time statistics associated with the CRDME. For sufficiently large lattice spacings or slow bimolecular reaction rates , we also show the reaction time statistics of the CRDME may be approximated by those from the RDME. The original RDME may therefore be interpreted as an approximation to the CRDME in several asymptotic limits.
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continuum
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empirical
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Although the reaction time statistics of the RDME diverge as the lattice spacing approaches zero, we show they approach those of the CRDME for
For
R
. As such, the RDME may
, we also show the reaction time statistics of the CRDME may be approximated by those from the RDME. The original RDME may therefore