Stochastic formulations of reaction-diffusion processes
Biological processes occurring at scales of a biological cell can be described in terms of diffusing and interacting molecules. At the level of particle-resolved descriptions, where molecules are represented by particles and chemical reactions are coupled to their spatial diffusion, there exist comprehensive numerical simulation schemes, while the corresponding mathematical formalization is relatively underdeveloped. In this work, we provide different frameworks to systematically formulate the probabilistic evolution equation, termed chemical diffusion master equation (CDME), that governs stochastic reaction-diffusion processes. These frameworks can be used to unify reaction-diffusion models at different scales, allowing the development of consistent multiscale simulation schemes and beyond.