A numerical scheme for optimal transition paths of stochastic chemical kinetic systems

Journal of Computational Physics

Volumn 227, Issue 19, 2008, Pages 8672-8684

  Liu, Di ^a  

^a MICHIGAN STATE UNIVERSITY   (United States)

Author keywords

Constraint optimization; Large Deviation Theory; Numerical methods; Stochastic chemical kinetic systems; Stochastic processes; Transition paths and transition rates

Indexed keywords

CONSTRAINED OPTIMIZATION; ESCHERICHIA COLI; KINETICS; RANDOM PROCESSES; STOCHASTIC SYSTEMS;

CHEMICAL KINETIC SYSTEMS; CONSTRAINT OPTIMIZATIONS; LARGE DEVIATIONS THEORY; NUMERICAL SCHEME; OPTIMAL TRANSITION; STOCHASTIC CHEMICAL KINETIC SYSTEM; STOCHASTIC CHEMICAL KINETICS; TRANSITION PATH AND TRANSITION RATE; TRANSITION PATHS; TRANSITION RATES;

NUMERICAL METHODS;

EID: 49449097807     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2008.06.010     Document Type: Article

References (32)

1. MacAdams H.H., and Arkin A. It's a noisy business! Genetic regulation at the nanomolar scale. Trends Genet. 15 (1999) 65-69
2. Fedoroff N., and Fontana W. Small numbers of big molecules. Science 297 (2002) 1129-1131
3. Hänggi P., Talkner P., and Borkovec M. Reaction-rate theory: fifty years after Kramers. Rev. Mod. Phys. 62 (1990) 251-341
4. Bortz A.B., Kalos M.H., and Lebowitz J.L. A new algorithm for Monte Carlo simulation of Ising spin systems. J. Comp. Phys. 17 (1975) 10-18
5. Gillespie D. A general method for numerically simulating the stochastic time evolution of coupled chemical reactions. J. Comp. Phys. 22 (1976) 403-434
6. Gillespie D. Exact stochastic simulation of coupled chemical reactions. J. Phys. Chem. 81 (1977) 2340-2361
7. Alberts B., et al. Essential Cell Biology. second ed. (2004), Garland Science, New York
8. Wang S. Multistability and multicellularity: cell fates as high-dimensional attractors of Gene Regulatory Networks. In: Kriete A., and Eils R. (Eds). Computational System Biology (2006), Elsevier Academic Press, New York 293-326
9. Arkin A., Ross J., and MacAdams H. Stochastic kinetic analysis of the developmental pathway bifurcation in phase λ-infected Escherichia coli cells. Genetics 149 (1998) 1633-1648
10. Gardner T.S., Cantor C.R., and Collins J.J. Construction of a genetic toggle switch in Escherichia coli. Nature 403 (2000) 339-342
11. Novick A., and Winer M. Enzyme induction as an all-or-none phenomenon. PNAS 43 (1957) 553-567
12. Chung J.D., and Stephanopoulos G. On physiological multiplicity and population of biological systems. Chem. Eng. Sci. 51 (1996) 1509-1521
13. Dykman M., Mori E., Ross J., and Hunt P. Large fluctuations and optimal paths in chemical kinetics. J. Chem. Phys. 100 (1994) 5735-5750
14. Roma D., O'Flanagan R., Ruckenstein A., Sengupta A., and Mukhopadhay R. Optimal path to epigenetic switching. Phys. Rev. E 71 (2005) 011901
15. Aurell E., and Sneppen K. Epigenetics as a first exit problem. Phy. Rev. Lett. 88 (2002) 048101
16. Zhu X., Yin L., Hood L., and Ao P. Calculating biological behaviors of epigenetic states in the phage λ life cycle. Funct. Integr. Cemonics 4 (2004) 188-195
17. Liu D. Optimal transition paths of stochastic chemical kinetic systems. J. Chem. Phys. 124 (2006) 164104
18. Wentzell A.D. Limit Theorems on Large Deviations for Markov Stochastic Processes (1990), Kluwer Academic Publishers., Boston, London
19. Shwartz A., and Weiss A. Large Deviations for Performance Analysis: Queues, Communications, and Computing (1995), Chapman and Hall, London, New York
20. Shwartz A., and Weiss A. Large deviations with diminishing rates. Math. Operat. Res. 30 (2005) 281-310
21. E W., Ren W., and Vanden-Eijnden E. Minimum action method for the study of rare events. Comm. Pure Appl. Math. 57 (2004) 637-656
22. Heymann M., and Vanden-Eijnden E. The geometric minimum action method: a lest action principle on the space of curves. Comm. Pure Appl. Math. LXI (2008) 1052-1117
23. Kurtz T. Strong approximation theorems for density dependent Markov chains. Stoc. Proc. Appl. 6 (1978) 223-240
24. Van Kampen N.G. Stochastic Processes in Physics and Chemistry (1981), Elsevier North-Holland Publishing, New York
25. Freidlin M.I., and Wentzell A.D. Random Perturbations of Dynamical Systems. second ed. (1998), Springer, New York
26. Nocedal J., and Wright S.J. Numerical Optimization (1999), Springer, New York
27. E W., Liu D., and Vanden-Eijnden E. Nested stochastic simulation algorithm for chemical kinetic systems with disparate rates. J. Chem. Phys. 123 (2005) 194107
28. E W., Liu D., and Vanden-Eijnden E. Nested stochastic simulation algorithms for chemical kinetic systems with multiple time scales. J. Comput. Phys. 221 (2007) 158-180
29. Haseltine E.L., and Rawlings J.B. Approximate simulation of coupled fast and slow reactions for stochastic chemical kinetics. J. Chem. Phys. 117 (2002) 6959-6969
30. Puchalka J., and Kierzek A.M. Bridging the gap between stochastic and deterministic regimes in the kinetic simulations of the biochemical reaction networks. Biophys. J. 86 (2004) 1357-1372
31. Salis H., and Kaznessis Y. Accurate hybrid stochastic simulation of a system of coupled chemical or biological reactions. J. Chem. Phys. 122 (2005) 054103
32. Zhou Z., Ren W., and E W. Adaptive minimum action method for the study of rare events. J. Chem. Phys. 128 (2008) 104111