BNMC Seminar:  Stochastic Chemical Kinetics

Dan Gillespie

The time evolution of a well-stirred chemically reacting system is traditionally modeled by a set of coupled ordinary differential equations called the reaction rate equation (RRE). The resulting picture of continuous deterministic evolution is, however, valid only for infinitely large systems. That condition is usually well approximated in laboratory test tube systems. But in biological systems formed by single living cells, the small population numbers of some reactant species can result in dynamical behavior that is noticeably discrete rather than continuous, and stochastic rather than deterministic. In that case, a more physically accurate mathematical modeling is obtained by using the machinery of Markov process theory, specifically, the chemical master equation (CME) and the stochastic simulation algorithm (SSA). This talk will review the theoretical foundations of stochastic chemical kinetics, and then discuss some recent efforts to (1) approximate the SSA by a faster simulation procedure, and (2) establish the formal connection between the CME/SSA description and the RRE description.

--------

About Dr. Gillespie: In the 1970's, Dan Gillespie developed an exact stochastic simulation approach for chemical kinetics that has since become the gold-standard algorithm for the field.  This work has also been the starting point for a variety of modern efforts by many groups worldwide to accelerate stochastic simulation beyond what is possible using the basic Gillespie algorithm.  Recent joint work involving Caltech and UCSB has been producing a steady stream of leading-edge results.

About the BNMC: The Beckman Institute Biological Network Modeling Center (BNMC; http://bnmc.caltech.edu) is a new interdisciplinary effort whose goal it is to bring together Caltech biologists, bioengineers, mathematicians, and computer scientists to develop and apply state-of-the-art computational tools for modeling and analyzing complex biological systems.  Its key members come from multiple Caltech divisions and groups, including Biology, Control and Dynamical Systems, and CACR (the Center for Advanced Computing Research).  As part of its mission, the BNMC has begun a regular seminar series on topics relevant to computational modeling in biology.

http://bnmc.caltech.edu/Events/8/stochastic-chemical-kinetics