Stochastic Simulation of Chemical Kinetics

Daniel T. Gillespie
2007 Annual review of physical chemistry (Print)  
Stochastic chemical kinetics describes the time evolution of a wellstirred chemically reacting system in a way that takes into account the fact that molecules come in whole numbers and exhibit some degree of randomness in their dynamical behavior. Researchers are increasingly using this approach to chemical kinetics in the analysis of cellular systems in biology, where the small molecular populations of only a few reactant species can lead to deviations from the predictions of the deterministic
more » ... differential equations of classical chemical kinetics. After reviewing the supporting theory of stochastic chemical kinetics, I discuss some recent advances in methods for using that theory to make numerical simulations. These include improvements to the exact stochastic simulation algorithm (SSA) and the approximate explicit tau-leaping procedure, as well as the development of two approximate strategies for simulating systems that are dynamically stiff: implicit tau-leaping and the slow-scale SSA. 35 Annu. Rev. Phys. Chem. 2007.58:35-55. Downloaded from arjournals.annualreviews.org by Los Alamos National Laboratory -Research Library on 07/24/07. For personal use only. Reaction-rate equation (RRE): the set of coupled, first-order, ordinary differential equations traditionally used to describe the time evolution of a well-stirred chemical system 36 Gillespie Annu. Rev. Phys. Chem. 2007.58:35-55. Downloaded from arjournals.annualreviews.org by Los Alamos National Laboratory -Research Library on 07/24/07. For personal use only. www.annualreviews.org • Stochastic Simulation of Chemical Kinetics 37 Annu. Rev. Phys. Chem. 2007.58:35-55. Downloaded from arjournals.annualreviews.org by Los Alamos National Laboratory -Research Library on 07/24/07. For personal use only. www.annualreviews.org • Stochastic Simulation of Chemical Kinetics 39 Annu. Rev. Phys. Chem. 2007.58:35-55. Downloaded from arjournals.annualreviews.org by Los Alamos National Laboratory -Research Library on 07/24/07. For personal use only. www.annualreviews.org • Stochastic Simulation of Chemical Kinetics 51 Annu. Rev. Phys. Chem. 2007.58:35-55. Downloaded from arjournals.annualreviews.org by Los Alamos National Laboratory -Research Library on 07/24/07. For personal use only.
doi:10.1146/annurev.physchem.58.032806.104637 pmid:17037977 fatcat:syonvd5tbnep7mvynnf2d3och4