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Sam Isaacson (Boston University), Applied Mathematics Colloquium
February 3, 2017 @ 4:00 pm - 5:00 pm
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.