Chemical Master Equation
 Prof. Hao Ge,
 Hong Qian
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Synonyms
Gillespie algorithm; Stochastic chemical kinetics
Definition
Chemical master equation is the stochastic counterpart of the chemical kinetic equation based on the law of mass action. It describes the kinetics of chemical reactions in a rapidly stirred tank with small volume in terms of stochastic reaction times giving rise to fluctuating copy numbers of reaction species.
Consider a system of fixed volume V at constant temperature T. Let there be wellstirred mixture of N ≥ 1 molecular species {S_{1}, …,S_{N}} and M ≥ 1 reactions {R_{1}, …, R_{M}}. One specifies the dynamical state of this system by X(t) = (X_{1}(t), …, X_{N}(t)), where X_{i}(t) is the copy number of molecular species S_{i} in the system at time t.
One describes the time evolution of X(t) from some given initial state X(t_{0}) = x_{0}. Both singlemolecule experimental measurements and theoretical investigations have shown that X(t) is a stochastic process because the time at which a particular reaction occurs is random.
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 Title
 Chemical Master Equation
 Reference Work Title
 Encyclopedia of Systems Biology
 Pages
 pp 396399
 Copyright
 2013
 DOI
 10.1007/9781441998637_278
 Print ISBN
 9781441998620
 Online ISBN
 9781441998637
 Publisher
 Springer New York
 Copyright Holder
 Springer Science+Business Media, LLC
 Additional Links
 Topics
 eBook Packages
 Editors

 Werner Dubitzky ^{(1)}
 Olaf Wolkenhauer ^{(2)}
 KwangHyun Cho ^{(3)}
 Hiroki Yokota ^{(4)}
 Editor Affiliations

 1. Biomedical Sciences Research Institute, University of Ulster
 2. Department of Computer Science, University of Rostock
 3. Department of Bio and Brain Engineering, Korea Advanced Institute of Science and Technology (KAIST)
 4. Department of Biomedical Engineering, Rensselaer Polytechnic Institute
 Authors

 Prof. Hao Ge ^{(02781)}
 Hong Qian ^{(02782)}
 Author Affiliations

 02781. School of Mathematical Sciences and Centre for Computational Systems Biology, Fudan University, No. 220 Handan Road, 200433, Shanghai, China
 02782. Department of Applied Mathematics, University of Washington, 352420, Seattle, WA, 98195, USA
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