### Abstract

Leap methods are very promising for accelerating stochastic simulation of a well stirred chemically reacting system, while providing acceptable simulation accuracy. In Gillespie's τ -leap method [D. Gillespie, J. Phys. Chem. 115, 1716 (2001)], the number of firings of each reaction channel during a leap is a Poisson random variable, whose sample values are unbounded. This may cause large changes in the populations of certain molecular species during a leap, thereby violating the leap condition. In this paper, we develop an alternative leap method called the K -leap method, in which we constrain the total number of reactions occurring during a leap to be a number K calculated from the leap condition. As the number of firings of each reaction channel during a leap is upper bounded by a properly chosen number, our K -leap method can better satisfy the leap condition, thereby improving simulation accuracy. Since the exact stochastic simulation algorithm (SSA) is a special case of our K -leap method when K=1, our K -leap method can naturally change from the exact SSA to an approximate leap method during simulation, whenever the leap condition allows to do so.

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

Article number | 074102 |

Journal | Journal of Chemical Physics |

Volume | 126 |

Issue number | 7 |

DOIs | |

State | Published - Feb 28 2007 |

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### ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics

### Cite this

*Journal of Chemical Physics*,

*126*(7), [074102]. https://doi.org/10.1063/1.2436869

**K -leap method for accelerating stochastic simulation of coupled chemical reactions.** / Cai, Xiaodong; Xu, Zhouyi.

Research output: Contribution to journal › Article

*Journal of Chemical Physics*, vol. 126, no. 7, 074102. https://doi.org/10.1063/1.2436869

}

TY - JOUR

T1 - K -leap method for accelerating stochastic simulation of coupled chemical reactions

AU - Cai, Xiaodong

AU - Xu, Zhouyi

PY - 2007/2/28

Y1 - 2007/2/28

N2 - Leap methods are very promising for accelerating stochastic simulation of a well stirred chemically reacting system, while providing acceptable simulation accuracy. In Gillespie's τ -leap method [D. Gillespie, J. Phys. Chem. 115, 1716 (2001)], the number of firings of each reaction channel during a leap is a Poisson random variable, whose sample values are unbounded. This may cause large changes in the populations of certain molecular species during a leap, thereby violating the leap condition. In this paper, we develop an alternative leap method called the K -leap method, in which we constrain the total number of reactions occurring during a leap to be a number K calculated from the leap condition. As the number of firings of each reaction channel during a leap is upper bounded by a properly chosen number, our K -leap method can better satisfy the leap condition, thereby improving simulation accuracy. Since the exact stochastic simulation algorithm (SSA) is a special case of our K -leap method when K=1, our K -leap method can naturally change from the exact SSA to an approximate leap method during simulation, whenever the leap condition allows to do so.

AB - Leap methods are very promising for accelerating stochastic simulation of a well stirred chemically reacting system, while providing acceptable simulation accuracy. In Gillespie's τ -leap method [D. Gillespie, J. Phys. Chem. 115, 1716 (2001)], the number of firings of each reaction channel during a leap is a Poisson random variable, whose sample values are unbounded. This may cause large changes in the populations of certain molecular species during a leap, thereby violating the leap condition. In this paper, we develop an alternative leap method called the K -leap method, in which we constrain the total number of reactions occurring during a leap to be a number K calculated from the leap condition. As the number of firings of each reaction channel during a leap is upper bounded by a properly chosen number, our K -leap method can better satisfy the leap condition, thereby improving simulation accuracy. Since the exact stochastic simulation algorithm (SSA) is a special case of our K -leap method when K=1, our K -leap method can naturally change from the exact SSA to an approximate leap method during simulation, whenever the leap condition allows to do so.

UR - http://www.scopus.com/inward/record.url?scp=33847220720&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33847220720&partnerID=8YFLogxK

U2 - 10.1063/1.2436869

DO - 10.1063/1.2436869

M3 - Article

VL - 126

JO - Journal of Chemical Physics

JF - Journal of Chemical Physics

SN - 0021-9606

IS - 7

M1 - 074102

ER -