“Final All Possible Steps” Approach for Accelerating Stochastic Simulation of Coupled Chemical Reactions

ZHUO Wen; PENG Xin-jun; LIU Xiang; YAN Zheng-lou; WANG Yi-fei

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Article Navigation > Applied Mathematics and Mechanics > 2008 > 29(3): 342-350

ZHUO Wen, PENG Xin-jun, LIU Xiang, YAN Zheng-lou, WANG Yi-fei. “Final All Possible Steps” Approach for Accelerating Stochastic Simulation of Coupled Chemical Reactions[J]. Applied Mathematics and Mechanics, 2008, 29(3): 342-350.

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“Final All Possible Steps” Approach for Accelerating Stochastic Simulation of Coupled Chemical Reactions

1.
Department of Mathematics, Shanghai University, Shanghai 200444, P. R. China;
Department of Mathematics, Anhui Normal University, Wuhu 241000, P. R. China

Received Date: 2007-08-03
Rev Recd Date: 2008-01-29
Publish Date: 2008-03-15

Abstract

Abstract

A modified accelerated stochastic simulation method for chemically reacting systems, called the "final all possible steps" (FAPS) method is developed. The reliable statistics of all species were obtained in any time during the time course with fewer simulation times. Moreover, the FAPS method can be incorporated into the leap methods, which makes the simulation of larger systems more efficient. Numerical results indicate that the proposed methods can be applied to a wide range of chemically reacting systems with a high-precision level and a significant improvement can be obtained on efficiency over the existed methods.
- “final all possible steps” approach,
- stochastic simulation algorithm,
- chemically reacting system

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References(21)

References

[1]	McAdams H H,Arkin A.Stochastic mechanisms in gene expression[J].Proc Natl Acad Sci U S A,1997,94(3):814-819. doi: 10.1073/pnas.94.3.814
[2]	Arkin A,Ross J,McAdams H H.Stochastic kinetic analysis of developmental pathway bifurcation in phage λ-infected E coli cells[J].Genetics,1998,149(4):1633-1648.
[3]	Fedoroff N,Fontana W. Small numbers of large molecules[J].Science,2002,297(5584):1129-1130. doi: 10.1126/science.1075988
[4]	Van Kampen N G.Stochastic Process in Physics and Chemistry[M].Amsterdam:North-Holland,1981.
[5]	Gillespie D T. A general method for numerically simulating the stochastic time evolution of coupled chemical reactions[J].J Comput Phys,1976,22(4):403-434. doi: 10.1016/0021-9991(76)90041-3
[6]	Gillespie D T. Exact stochastic simulation of coupled chemical reactions[J].J Chem Phys,1977,81(25):2340-2361. doi: 10.1021/j100540a008
[7]	Gibson M, Bruck J. Efficient formulation of the stochastic simulation algorithm for chemically reacting systems[J].J Chem Phys,2000,104(9):1876-1889. doi: 10.1021/jp993732q
[8]	McCollum J M, Peterson G D,Cox C D,et al.The sorting direct method for stochastic simulation of biochemical systems with varying reaction execution behavior[J].Comput Biol Chem,2006,30(1):39-49. doi: 10.1016/j.compbiolchem.2005.10.007
[9]	Gillespie D T.Approximate accelerated stochastic simulation of chemically reacting systems[J].J Chem Phys,2001,115(4):1716-1733. doi: 10.1063/1.1378322
[10]	Gillespie D T,Petzold L R.Improved leap-size selection for accelerated stochastic simulation[J].J Chem Phys,2003,119(16):8229-8234. doi: 10.1063/1.1613254
[11]	Rathinam M,Petzold L R,Cao Y,et al.Stiffness in stochastic chemically reacting systems: The implicit tau-leaping method[J].J Chem Phys,2003,119(24):12784-12794. doi: 10.1063/1.1627296
[12]	Tian T, Burrage K.Binomial leap methods for simulating stochastic chemical kinetics[J].J Chem Phys,2004,121(21):10356-10364. doi: 10.1063/1.1810475
[13]	Chatterjee A, Vlachos D G, Katsoulakis M A.Binomial distribution based τ-leap accelerated stochastic simulation[J].J Chem Phys,2005,122(2): 024112. doi: 10.1063/1.1833357
[14]	Peng X J, Zhou W,Wang Y F. Efficient binomial leap method for simulating chemical kinetics[J].J Chem Phys,2007,126(22):1-9.
[15]	Cai X D, Xu Z Y.K-leap method for accelerating stochastic simulation of coupled chemical reactions[J].J Chem Phys,2007,126(7):1.
[16]	Auger A ,Chatelain P,Koumoutsakos P.R-leaping: Accelerating the stochastic simulation algorithm by reaction leaps[J].J Chem Phys,2006,125(8):084103. doi: 10.1063/1.2218339
[17]	Cao Y, Gillespie D T,Petzold L R.Efficient step size selection for the tau-leaping simulation method[J].J Chem Phys,2006,124(4):044109. doi: 10.1063/1.2159468
[18]	Cao Y, Petzold L R.Accuracy limitations and the measurement of errors in the stochastic simulation of chemically reacting systems[J].J Comput Phys,2006,212(1):6-24. doi: 10.1016/j.jcp.2005.06.012
[19]	Cao Y, Li H,Petzold L R. Efficient exact stochastic simulation algorithm for chemically reacting systems[J].J Comput Phys,2004,121(9):4059-4067.
[20]	Cao Y, Gillespie D T,Petzold L R. Avoiding negative populations in explicit poisson tau-leaping[J].J Chem Phys,2005,123(5):054104. doi: 10.1063/1.1992473
[21]	Lipshtat A.“All possible steps” approach to the accelerated use of Gillespie's algorithm[J].J Chem Phys,2007,126(18):184103. doi: 10.1063/1.2730507