Mesoscopic Modeling of Random Walk and Reactions in Crowded Media

We develop a mesoscopic modeling framework for diffusion in a crowded environment, particularly with applications in the description of living cells. Through homogenization techniques we effectively coarse-grain a detailed microscopic description into a previously developed internal state diffusive framework. In turn, in a certain deterministic limit this framework connects to macroscopic fractional partial differential equations. Similarly, the mesoscopic model also corresponds to partial differential equations driven by stochastically varying diffusion fields in space and time. Analytical solutions and numerical experiments illustrate the modeling framework.