Stochastic Bistability in Chemical Reaction Systems with Resampling
John McSweeney (Mathematical Biosciences Institute, The Ohio State University)
(April 10, 2012 10:30 AM - 11:20 AM)
Classical mathematical formulation of the dynamics of chemical reaction systems involves setting up and analyzing a system of ODEs, or PDEs if spatial effects are considered. However, a system may be sensitive to the stochasticity inherent in the mechanism of chemical reactions, for example due to having small numbers of molecules, or reaction rates which vary over several orders of magnitude. We consider such a reaction system in a cellular environment, and also impose a 'global' cell division mechanism, which adds noise to the concentrations of chemical species along a given lineage, and find parameter regimes for which this produces a qualitative change in the dynamics. We model these reaction and division processes as Jump Markov Processes, and discuss some toy models in which the stochasticity can allow the system to exhibit behavior that is not possible with a deterministic formulation. One such behavior is bistability, for which we find two processes that have similar macroscopic signatures but whose underlying causes are fundamentally different; one such case leads to the Large-Deviation theory of Freidlin and Wentzell. Such bistability is characteristic of many gene expression systems that effectively incorporate an ON/OFF switch, but the framework is very general and is applicable in other areas, such as population genetics, where bistability may represent alternating dominance of allelic types in a population. This is joint work with Lea Popovic of Concordia University (Montreal).