Mathematical Biology seminar

Sam Isaacson
Courant Institute, NYU
"Incorporating Diffusion in Complex Geometries into Stochastic Chemical Kinetics Simulations"
Monday January 10, 2005
3:05pm in LCB 215

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.