### Abstract

Language | English |
---|---|

Pages | 59-79 |

Number of pages | 20 |

Journal | Open Applied Mathematics Journal |

Volume | 2 |

DOIs | |

Publication status | Published - 2008 |

### Fingerprint

### Keywords

- birth-and-death process
- chemical master equation
- chemical kinetics
- correlation matrix
- gene regulation network
- stochastic simulation algorithm

### Cite this

*Open Applied Mathematics Journal*,

*2*, 59-79. https://doi.org/10.2174/1874114200802010059

}

*Open Applied Mathematics Journal*, vol. 2, pp. 59-79. https://doi.org/10.2174/1874114200802010059

**Chemical master versus chemical langevin for first-order reaction networks.** / Higham, Desmond J.; Khanin, Raya.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Chemical master versus chemical langevin for first-order reaction networks

AU - Higham, Desmond J.

AU - Khanin, Raya

PY - 2008

Y1 - 2008

N2 - 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.

AB - 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.

KW - birth-and-death process

KW - chemical master equation

KW - chemical kinetics

KW - correlation matrix

KW - gene regulation network

KW - stochastic simulation algorithm

U2 - 10.2174/1874114200802010059

DO - 10.2174/1874114200802010059

M3 - Article

VL - 2

SP - 59

EP - 79

JO - Open Applied Mathematics Journal

T2 - Open Applied Mathematics Journal

JF - Open Applied Mathematics Journal

SN - 1874-1142

ER -