Particle-based stochastic reaction-diffusion (PBSRD) models are a popular approach for studying biological systems involving both noise in the reaction process and diffusive transport. In this work we derive coarse-grained deterministic partial integro-differential equation (PIDE) that provide mean field approximation to volume reactivity PBSRD model, model commonly used cellular processes. We ...

We consider a class of semi-linear differential Volterra equations with memory terms, polynomial nonlinearities and random perturbation. For broad nonlinearities, we show that the system in concern admits unique weak solution. Also, any statistically steady state must possess regularity compatible Moreover, if sufficiently many directions are stochastically forced, employ generalized coupling a...

Many cellular and subcellular biological processes can be described in terms of diffusing and chemically reacting species (e.g. enzymes). Such reaction-diffusion processes can be mathematically modelled using either deterministic partial-differential equations or stochastic simulation algorithms. The latter provide a more detailed and precise picture, and several stochastic simulation algorithm...

As quantitative biologists get more measurements of spatially regulated systems such as cell division and polarization, simulation of reaction and diffusion of proteins using the data is becoming increasingly relevant to uncover the mechanisms underlying the systems. Spatiocyte is a lattice-based stochastic particle simulator for biochemical reaction and diffusion processes. Simulations can be ...