### Abstract

Gillespie's exact stochastic simulation algorithm (SSA) [J. Phys. Chem. 81, 2350 (1977)] has been widely used to simulate the stochastic dynamics of chemically reacting systems. In this algorithm, it is assumed that all reactions occur instantly. While this is true in many cases, it is also possible that some chemical reactions, such as gene transcription and translation in living cells, take certain time to finish after they are initiated. Thus, the product of such reactions will emerge after certain delays. Apparently, Gillespie's SSA is not an exact algorithm for chemical reaction systems with delays. In this paper, the author develops an exact SSA for chemical reaction systems with delays, based upon the same fundamental premise of stochastic kinetics used by Gillespie in the development of his SSA. He then shows that an algorithm modified from Gillespie's SSA by Barrio et al. [PLOS Comput. Biol. 2, 1017 (2006)] is also an exact SSA for chemical reaction systems with delays, but it needs to generate more random variables than the author's algorithm.

Original language | English |
---|---|

Article number | 124108 |

Journal | Journal of Chemical Physics |

Volume | 126 |

Issue number | 12 |

DOIs | |

State | Published - Apr 8 2007 |

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### ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics

### Cite this

**Exact stochastic simulation of coupled chemical reactions with delays.** / Cai, Xiaodong.

Research output: Contribution to journal › Article

*Journal of Chemical Physics*, vol. 126, no. 12, 124108. https://doi.org/10.1063/1.2710253

}

TY - JOUR

T1 - Exact stochastic simulation of coupled chemical reactions with delays

AU - Cai, Xiaodong

PY - 2007/4/8

Y1 - 2007/4/8

N2 - Gillespie's exact stochastic simulation algorithm (SSA) [J. Phys. Chem. 81, 2350 (1977)] has been widely used to simulate the stochastic dynamics of chemically reacting systems. In this algorithm, it is assumed that all reactions occur instantly. While this is true in many cases, it is also possible that some chemical reactions, such as gene transcription and translation in living cells, take certain time to finish after they are initiated. Thus, the product of such reactions will emerge after certain delays. Apparently, Gillespie's SSA is not an exact algorithm for chemical reaction systems with delays. In this paper, the author develops an exact SSA for chemical reaction systems with delays, based upon the same fundamental premise of stochastic kinetics used by Gillespie in the development of his SSA. He then shows that an algorithm modified from Gillespie's SSA by Barrio et al. [PLOS Comput. Biol. 2, 1017 (2006)] is also an exact SSA for chemical reaction systems with delays, but it needs to generate more random variables than the author's algorithm.

AB - Gillespie's exact stochastic simulation algorithm (SSA) [J. Phys. Chem. 81, 2350 (1977)] has been widely used to simulate the stochastic dynamics of chemically reacting systems. In this algorithm, it is assumed that all reactions occur instantly. While this is true in many cases, it is also possible that some chemical reactions, such as gene transcription and translation in living cells, take certain time to finish after they are initiated. Thus, the product of such reactions will emerge after certain delays. Apparently, Gillespie's SSA is not an exact algorithm for chemical reaction systems with delays. In this paper, the author develops an exact SSA for chemical reaction systems with delays, based upon the same fundamental premise of stochastic kinetics used by Gillespie in the development of his SSA. He then shows that an algorithm modified from Gillespie's SSA by Barrio et al. [PLOS Comput. Biol. 2, 1017 (2006)] is also an exact SSA for chemical reaction systems with delays, but it needs to generate more random variables than the author's algorithm.

UR - http://www.scopus.com/inward/record.url?scp=34047136657&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=34047136657&partnerID=8YFLogxK

U2 - 10.1063/1.2710253

DO - 10.1063/1.2710253

M3 - Article

VL - 126

JO - Journal of Chemical Physics

JF - Journal of Chemical Physics

SN - 0021-9606

IS - 12

M1 - 124108

ER -