Reversible-equivalent-monomolecular tau: A leaping method for "small number and stiff" stochastic chemical systems

Journal of Computational Physics

Volumn 224, Issue 2, 2007, Pages 897-923

  Rathinam, Muruhan ^a   El Samad, Hana ^b  

^a UNIVERSITY OF MARYLAND BALTIMORE COUNTY   (United States)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Chemical master equation; Stochastic chemical kinetics; Tau leaping

Indexed keywords

CONTINUOUS TIME SYSTEMS;

CHEMICAL MASTER EQUATION; CHEMICAL REACTION SYSTEMS; CHEMICAL SYSTEMS; LEAPING METHODS; MONOMOLECULARS; REVERSIBLE REACTION; STOCHASTIC CHEMICAL KINETICS; STOCHASTICS; TAU-LEAPING; TIME-STEPPING;

STOCHASTIC SYSTEMS;

EID: 34248583573     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2006.10.034     Document Type: Article

References (30)

1. Elowitz M., Levine A., Siggia E., and Swain P. Stochastic gene expression in a single cell. Science 297 August (2002) 1183-1186
2. Hasty J., Pradines J., Dolnik M., and Collins J. Noise-based switches and amplifiers for gene expression. PNAS 97 (2000) 2075-2080
3. Arkin A., Ross J., and McAdams H. Stochastic kinetic analysis of the developmental pathway bifurcation in phase λ-infected Escehrichia coli cells. Genetics 149 4 (1998) 1633-1648
4. Gillespie D.T. A rigorous derivation of the chemical master equation. Physica A 188 (1992) 404-425
5. Kampen N.V. Stochastic Processes in Physics and Chemistry (1992), Elsevier Science Publishing Company
6. Gillespie D.T. A general method for numerically simulating the stochastic time evolution of coupled chemical reactions. J. Comput. Phys. 22 (1976) 403-434
7. Gillespie D.T. Exact stochastic simulation of coupled chemical reactions. J. Phys. Chem. 81 (1977) 2340-2361
8. Munsky B., and Khammash M. The finite state projection algorithm for the solution of the chemical master equation. J. Chem. Phys. 124 (2006) 044144
9. Gillespie D.T. Approximate accelerated stochastic simulation of chemically reacting systems. J. Chem. Phys. 115 4 (2001) 1716-1733
10. Rathinam M., Petzold L., Cao Y., and Gillespie D. Stiffness in stochastic chemically reacting systems: The implicit tau-leaping method. J. Chem. Phys. 119 24 (2003) 12784-12794
11. Cao Y., Petzold L., Rathinam M., and Gillespie D. The numerical stability of leaping methods for stochastic simulation of chemically reacting systems. J. Chem. Phys. 121 24 (2004) 12169-12178
12. Chatterjee A., Vlachos D., and Katsoulakis M. Binomial distribution based τ-leap accelerated stochastic simulation. J. Chem. Phys. 122 (2005) 024112
13. Tian T., and Burrage K. Binomial leap methods for simulating stochastic chemical kinetics. J. Chem. Phys. 121 21 (2004) 10356-10364
14. Rathinam M., Petzold L., Cao Y., and Gillespie D. Consistency and stability of tau leaping schemes for chemical reaction systems. SIAM J. MMS 4 3 (2005) 867-895
15. Haseltine E., and Rawlings J. Approximate simulation of coupled fast and slow reactions for stochastic chemical kinetics. J. Chem. Phys. 117 15 (2002) 6959
16. Rao C., and Arkin A. Stochastic chemical kinetics and the quasi-steady-state assumption: application to the Gillespie algorithm. J. Chem. Phys. 118 11 (2003) 4999-5010
17. Cao Y., Gillespie D., and Petzold L. Multiscale stochastic simulation algorithm with stochastic partial equilibrium assumption for chemically reacting systems. J. Comput. Phys. 206 2 (2005) 395-411
18. Cao Y., Gillespie D., and Petzold L. The slow-scale stochastic simulation algorithm. J. Chem. Phys. 122 1 (2005) 014116
19. Goutsias J. Quasiequilibrium approximation of fast reaction kinetics in stochastic biochemical systems. J. Chem. Phys. 122 18 (2005) 184102
20. Segel L., and Slemrod M. The quasi-steady-state assumption: a case study in perturbation. SIAM Rev. 31 3 (1989) 446-477
21. Givon D., Kupferman R., and Stuart A. Extracting macroscopic dynamics: model problems and algorithms. Nonlinearity 17 (2004) 55-127
22. Gillespie D.T., and Petzold L. Improved leap-size selection for accelerated stochastic simulation. J. Chem. Phys. 119 (2003) 8229-8234
23. Y. Cao, L. Petzold, Trapezoidal tau-leaping formula for the stochastic simulation of biochemical systems, in: Proceedings of Foundations of Systems Biology in Engineering (FOSBE 2005), 2005, pp. 149-152.
24. Ross S. Introduction to Probability Models. eighth ed. (2002), Academic Press
25. Gillespie D.T. Markov Processes: An Introduction for Physical Scientists (1992), Academic Press
26. Ascher U.M., and Petzold L.R. Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations (1998), SIAM
27. Percus J. Small population effects in stochastic population dynamics. Bull. Math. Biol. 67 (2005) 1173-1194
28. McQuarrie D. Kinetics of small systems I. J. Chem. Phys. 38 2 (1963) 433-436
29. Cock K.D., Zhang X., Bugallo M.F., and Djuric P. Comment on stiffness in stochastic chemically reacting systems: the implicit tau-leaping method. J. Chem. Phys. 121 7 (2004) 3347-3348
30. Jachimowski C., and Russell M. Set-theoretic approach to reaction kinetics. J. Chem. Phys. 42 8 (1965) 2819-2822