Haseltine, Eric L. and Rawlings, James B. (2005) On the origins of approximations for stochastic chemical kinetics. Journal of Chemical Physics, 123 (16). Art. no. 164115. ISSN 0021-9606 http://resolver.caltech.edu/CaltechAUTHORS:HASjcp05
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This paper considers the derivation of approximations for stochastic chemical kinetics governed by the discrete master equation. Here, the concepts of (1) partitioning on the basis of fast and slow reactions as opposed to fast and slow species and (2) conditional probability densities are used to derive approximate, partitioned master equations, which are Markovian in nature, from the original master equation. Under different conditions dictated by relaxation time arguments, such approximations give rise to both the equilibrium and hybrid (deterministic or Langevin equations coupled with discrete stochastic simulation) approximations previously reported. In addition, the derivation points out several weaknesses in previous justifications of both the hybrid and equilibrium systems and demonstrates the connection between the original and approximate master equations. Two simple examples illustrate situations in which these two approximate methods are applicable and demonstrate the two methods' efficiencies.
|Additional Information:||©2005 American Institute of Physics (Received 20 June 2005; accepted 18 August 2005; published online 27 October 2005) One of the authors (E. L. H.) was supported by an NLM training grant to the Computation and Informatics in Biology and Medicine Training Program (NLM 5T15LM007359). We gratefully acknowledge the financial support of the industrial members of the Texas-Wisconsin Modeling and Control Consortium. All simulations were performed using OCTAVE (http://www.octave.org). OCTAVE is freely distributed under the terms of the GNU General Public License.|
|Subject Keywords:||reaction kinetics theory; stochastic processes; chemical reactions; probability; master equation|
|Usage Policy:||No commercial reproduction, distribution, display or performance rights in this work are provided.|
|Deposited By:||Archive Administrator|
|Deposited On:||10 Jan 2006|
|Last Modified:||26 Dec 2012 08:43|
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