TY - JOUR
T1 - Unbiased τ -leap methods for stochastic simulation of chemically reacting systems
AU - Xu, Zhouyi
AU - Cai, Xiaodong
N1 - Funding Information:
This work was supported by the National Science Foundation (NSF) under NSF CAREER Award No. 0746882.
PY - 2008
Y1 - 2008
N2 - The τ -leap method first developed by Gillespie [D. T. Gillespie, J. Chem. Phys. 115, 1716 (2001)] can significantly speed up stochastic simulation of certain chemically reacting systems with acceptable losses in accuracy. Recently, several improved τ -leap methods, including the binomial, multinomial, and modified τ -leap methods, have been developed. However, in all these τ -leap methods, the mean of the number of times, Km, that the mth reaction channel fires during a leap is not equal to the true mean. Therefore, all existing τ -leap methods produce biased simulation results, which limit the simulation accuracy and speed. In this paper, we analyze the mean of Km based on the chemical master equation. Using this analytical result, we develop unbiased Poisson and binomial τ -leap methods. Moreover, we analyze the variance of Km, and then develop an unbiased Poisson/Gaussian/binomial τ -leap method to correct the errors in both the mean and variance of Km. Simulation results demonstrate that our unbiased τ -leap method can significantly improve simulation accuracy without sacrificing speed.
AB - The τ -leap method first developed by Gillespie [D. T. Gillespie, J. Chem. Phys. 115, 1716 (2001)] can significantly speed up stochastic simulation of certain chemically reacting systems with acceptable losses in accuracy. Recently, several improved τ -leap methods, including the binomial, multinomial, and modified τ -leap methods, have been developed. However, in all these τ -leap methods, the mean of the number of times, Km, that the mth reaction channel fires during a leap is not equal to the true mean. Therefore, all existing τ -leap methods produce biased simulation results, which limit the simulation accuracy and speed. In this paper, we analyze the mean of Km based on the chemical master equation. Using this analytical result, we develop unbiased Poisson and binomial τ -leap methods. Moreover, we analyze the variance of Km, and then develop an unbiased Poisson/Gaussian/binomial τ -leap method to correct the errors in both the mean and variance of Km. Simulation results demonstrate that our unbiased τ -leap method can significantly improve simulation accuracy without sacrificing speed.
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U2 - 10.1063/1.2894479
DO - 10.1063/1.2894479
M3 - Article
C2 - 18433195
AN - SCOPUS:42449102270
VL - 128
JO - Journal of Chemical Physics
JF - Journal of Chemical Physics
SN - 0021-9606
IS - 15
M1 - 154112
ER -