TALK by K. Ball

Souther California Probability Symposium

December 3, 2005

Stochastic models for multiscale chemical reaction kinetics

Karen Ball (Center for Communications Research)

In this talk, we will look at models for the evolution of chemical reactions in a homogeneous, well-stirred environment. At laboratory and industrial scales, where all reactants are present in large enough quantities, such reactions are well-modeled by a system of ordinary differential equations. At the other extreme, if all reactants are present in small enough quantities, there is a Markov model for the system. We develop stochastic models for multiscale reactions lying between these two extremes, where the abundances of reactants may vary over several orders of magnitude. We obtain these models by taking appropriate scaling limits of the Markov model for chemical reactions. We then use this new family of models to analyze a simple model for the infection of a living cell by a virus. This is joint work with Tom Kurtz, Lea Popovic, and Greg Rempala.