Picture of two heads

Open Access research that challenges the mind...

The Strathprints institutional repository is a digital archive of University of Strathclyde research outputs. Strathprints provides access to thousands of Open Access research papers by University of Strathclyde researchers, including those from the School of Psychological Sciences & Health - but also papers by researchers based within the Faculties of Science, Engineering, Humanities & Social Sciences, and from the Strathclyde Business School.

Discover more...

Chemical master versus chemical langevin for first-order reaction networks

Higham, Desmond J. and Khanin, Raya (2008) Chemical master versus chemical langevin for first-order reaction networks. Open Applied Mathematics Journal, 2. pp. 59-79. ISSN 1874-1142

PDF (strathprints015053.pdf)

Download (180kB) | Preview


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 rst-order. 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 rst-order reaction network. Moreover, we show that these moments exactly match those of the under-lying 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.