Particle-based stochastic reaction diffusion methods have become a popular approach for studying the behavior of cellular processes in which both spatial transport and noise in the chemical reaction process can be important. While the corresponding deterministic, mean-field models given by reaction-diffusion PDEs are well-established, there are a plethora of different stochastic models that have been used to study biological systems, along with a wide variety of proposed numerical solution methods.
In this talk I will introduce our attempt to rectify the major drawback to one of the most popular particle-based stochastic reaction-diffusion models, the lattice reaction-diffusion master equation (RDME). We propose a modified version of the RDME that converges in the continuum limit that the lattice spacing approaches zero to an appropriate spatially-continuous model. I will then discuss some application areas to which we are applying these methods, focusing on how the complicated ultrastructure within cells, as reconstructed from X-ray CT images, might influence the dynamics of cellular processes.