Higham, Desmond J. and Khanin, Raya (2008) Chemical master versus chemical langevin for firstorder reaction networks. Open Applied Mathematics Journal, 2. pp. 5979. ISSN 18741142

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Abstract
Markov jump processes are widely used to model interacting species in circumstances where discreteness and stochasticity are relevant. Such models have been particularly successful in computational cell biology, and in this case, the interactions are typically rstorder. The Chemical Langevin Equation is a stochastic dierential equation that can be regarded as an approximation to the underlying jump process. In particular, the Chemical Langevin Equation allows simulations to be performed more eectively. In this work, we obtain expressions for the rst and second moments of the Chemical Langevin Equation for a generic rstorder reaction network. Moreover, we show that these moments exactly match those of the underlying jump process. Hence, in terms of means, variances and correlations, the Chemical Langevin Equation is an excellent proxy for the Chemical Master Equation. Our work assumes that a unique solution exists for the Chemical Langevin Equation. We also show that the moment matching re sult extends to the case where a gene regulation model of Raser and O'Shea (Science, 2004) is replaced by a hybrid model that mixes elements of the Master and Langevin equations. We nish with numerical experiments on a dimerization model that involves second order reactions, showing that the two regimes continue to give similar results.
Item type:  Article 

ID code:  15053 
Keywords:  birthanddeath process, chemical master equation, chemical kinetics, correlation matrix, gene regulation network, stochastic simulation algorithm, Mathematics, Applied Mathematics 
Subjects:  Science > Mathematics 
Department:  Faculty of Science > Mathematics and Statistics 
Depositing user:  Mrs Irene Spencer 
Date Deposited:  26 Jan 2010 12:18 
Last modified:  12 Dec 2015 14:25 
Related URLs:  
URI:  http://strathprints.strath.ac.uk/id/eprint/15053 
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