Sam Isaacson (Boston University), Applied Mathematics Colloquium

Title:  Jump Process Approximation of Particle-Based Stochastic Reaction-Diffusion Models

Abstract:  Particle-based stochastic reaction-diffusion (PSRD) models have become a popular tool for modeling cellular processes in which both noise in chemical reactions and the spatial transport of molecules are important. I will briefly motivate our interest in such models by discussing the influence of volume exclusion due to organelles on the propagation of signals within cells, and by exploring a simple receptor signaling system where only spatial, stochastic models can correctly reproduce experimentally observed dynamics.

I will then introduce a general formulation of PSRD models that encompasses several of the most widely-used variants. To numerically solve a subset of these models, a hybrid finite element / finite volume discretization that has the form of a master equation for a jump process will be constructed. Exact realizations of the resulting jump process can be generated through the well-known stochastic simulation algorithm, enabling the accurate simulation of general PSRD models. Time-permitting, I will illustrate our method on several biological examples.