Samuel Isaacson
Department of Mathematics and Statistics
Boston University
Boston, Massachusetts, USA
The Chemical Master Equation is a model for biochemical systems in which noise in the chemical reaction process is important. It is a more microscopic model for biochemical systems than ODE-based reaction-rate equations for chemical concentrations. In the Chemical Master Equation formalism chemical species are modeled as continuous-time integer-valued jump Markov processes. These processes are easily simulated through the use of the Gillespie method.
In this talk I will give an introduction to an extension of the chemical master equation, called the reaction-diffusion master equation (RDME), that allows for reaction and diffusion of chemical species. This extension goes back as far as the work of Gardiner in the 1970's, and has recently started being applied to models of biochemical systems within individual cells (where noise in the chemical reaction process has been shown experimentally to be of importance). In the RDME model spaced is discretized into a collection of voxels. How to choose the spatial discretization so as to obtain physically meaningful results is an important question. We will discuss the behavior of the RDME as the voxel size is varied, and demonstrate how the RDME can be interpreted as an approximation to several other spatially-continuous stochastic reaction-diffusion models for appropriately chosen voxel sizes.