Title: Stochastic Chemical Kinetics
Abstract: 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 by test tube size systems. But in biological systems formed by single living cells, the small molecular populations 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 physically more 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). In this tutorial talk, we will outline the theoretical foundations of stochastic chemical kinetics. In particular, we will show how two sequential approximate procedures for accelerating the SSA turn out to form a logical bridge from the discrete-stochastic CME/SSA formalism to the continuous-deterministic RRE formalism.
Dan Gillespie is a physicist, with a B.A. from Rice University and a Ph.D. from Johns Hopkins University. His graduate work in high energy physics, and also his postdoctoral work at the University of Maryland in classical transport theory, featured extensive use of Monte Carlo methods, and that has colored much of his later research. For three decades he was a civilian research scientist for the U. S. Navy in China Lake, California. Since his retirement from there in 2001, he has been a private consultant in computational biochemistry, working< mainly with the Petzold Group at the University of California at Santa Barbara. This work has been aimed at developing better ways of numerically modeling biochemical systems, improving and extending some stochastic simulation approaches he developed earlier. His research publication list also contains articles on raindrop formation in clouds, light scattering in aerosols, random variable theory, Brownian motion, thermal electrical noise, applied stochastic process theory,and quantum mechanics. He is the author of “A Quantum Mechanics Primer” (in print from 1970-1986) and “Markov Processes: An Introduction for Physical Scientists” (Academic Press, 1992). He has just co-authored with Effrosyni Seitaridou (Oxford College of Emory University), a new book entitled “Simple Brownian Diffusion: An introduction to the standard theories of how solute molecules move in a sea of many smaller solvent molecules”, which will be published later this year by Oxford University Press.