Speaker: Sam Isaacson (Courant Institute, NYU)
Title:  Incorporating Diffusion in Complex Geometries into Stochastic
        Chemical Kinetics Simulations

Abstract:
At sufficiently low concentrations deterministic mass-action kinetics
can no longer accurately model the time evolution of biochemical systems.
Stochastic chemical kinetics, based on a master equation formulation of
the dynamics, provides a means to account for the underlying fluctuations
in such systems. Traditionally, spatial effects are ignored in both types
of models by assuming the biochemicals making up the system are well-mixed
(i.e. equally probable to be in any subregion of the total volume of
interest). Corresponding to deterministic mass-action kinetics,
reaction-diffusion equations can be used to model biochemical systems in
which spatial effects are important.

We will present an overview of stochastic chemical kinetics, and a method
for incorporating diffusion in complex geometries into the master
equation formulation. The method is based on an embedded boundary
discretization of the diffusion equation for the probability density of a
single particle. Movement of particles between cells of the mesh are then
approximated as first order reactions with jump rates determined from the
discretization. Numerical convergence results for the method will be
presented. An application of the method to 2D and 3D models for
eukaryotic transcription, nuclear export of mRNA, translation, nuclear
import of protein, and gene regulation will be discussed.