Modeling and simulating chemical reactions

SIAM Review

Volumn 50, Issue 2, 2008, Pages 347-368

  Higham, Desmond J ^a  

^a UNIVERSITY OF STRATHCLYDE   (United Kingdom)

Author keywords

Birth and death process; Chemical Langevin; Chemical master equation; Euler Maruyama; Gillespie; Kinetic Monte Carlo; Law of mass action; Michaelis Menten; Reaction rate equation; Stochastic simulation algorithm; Stoichiometric vector; Tau leaping

Indexed keywords

COMPUTATIONAL METHODS; MATLAB; ORDINARY DIFFERENTIAL EQUATIONS; PROBABILITY; REACTION RATES; STOICHIOMETRY;

BIRTH-AND-DEATH PROCESS; CHEMICAL LANGEVIN; CHEMICAL MASTER EQUATION; STOCHASTIC SIMULATION ALGORITHM; STOICHIOMETRIC VECTOR;

CHEMICAL REACTIONS;

EID: 44949114109     PISSN: 00361445     EISSN: None     Source Type: Journal    
DOI: 10.1137/060666457     Document Type: Article

References (41)

1. D. ADALSTEINSSON, D. MCMILLEN, AND T. C. ELSTON, Biochemical network stochastic simulator (BioNetS): Software for stochastic modeling of biochemical networks, BMC Bioinform., 5:24 (2004); available online from http://www.pubmedcentral.nih.gov/ articlerender.fcgi?artid=408466.
2. D. F. ANDERSON, Incorporating postleap checks with tau-leaping, J. Chem. Phys., 128 (2008), article 054103.
3. K. BALL, T. G. KURTZ, L. POPOVIC, AND G. REMPALA, Asymptotic analysis of multiscale approximations to reaction networks, Ann. Appl. Probab., 16 (2006), pp. 1925-1961.
4. A. B. BORTZ, M. H. KALOS, AND J. L. LEBOWITZ, A new algorithm for Monte Carlo simulation of Ising spin systems, J. Comput. Phys., 17 (1975), pp. 10-18.
5. D. BRATSUN, D. VOLFSON, L. S. TSIMRING, AND J. HASTY, Delay-induced stochastic oscillations in gene regulation, Proc. Natl. Acad. Sci. USA, 102 (2005), pp. 14593-14598.
6. Y. CAO, D. T. GILLESPIE, AND L. PETZOLD, The slow-scale stochastic simulation algorithm, J. Chem. Phys., 122 (2005), article 014116.
7. Y. CAO, D. T. GILLESPIE, AND L. PETZOLD, Efficient stepsize selection for the Tau-leaping method, J. Chem. Phys., 124 (2006), article 044109.
8. COPASI DEVELOPMENT TEAM, COPASI Documentation, http:// www.copasi.org/tiki-index.php (September 2007).
9. D. COX AND H. MILLER, The Theory of Stochastic Processes, Methuen, London, 1965.
10. E. J. CRAMPIN AND S. SCHNELL, New approaches to modelling and analysis of biochemical reactions, pathways and networks, Progr. Biophys. Molecular Biol., 86 (2004), pp. 1-4.
11. W. E, D. Liu, AND E. VANDEN-EIJNDEN, Nested stochastic simulation algorithm for chemical kinetic systems with disparate rates, J. Chem. Phys., 123 (2005), article 194107.
12. W. E, D. Liu, AND E. VANDEN-EIJNDEN, Nested stochastic simulation algorithm for chemical kinetic systems with multiple time scales, J. Comput. Phys., 221 (2007), pp. 158-180.
13. C. W. GARDINER, Handbook of Stochastic Methods, for Physics, Chemistry and the Natural Sciences, 3rd ed., Springer-Verlag, Berlin, 2004.
14. M. GIBSON AND J. BRUCK, Efficient exact stochastic simulation of chemical systems with many species and many channels, J. Phys. Chem. A, 104 (2000), pp. 1876-1889.
15. D. T. GILLESPIE, A general method for numerically simulating the stochastic time evolution of coupled chemical reactions, J. Comput. Phys., 22 (1976), pp. 403-434.
16. D. T. GILLESPIE, Exact stochastic simulation of coupled chemical reactions, J. Phys. Chem., 81 (1977), pp. 2340-2361.
17. D. T. GILLESPIE, The chemical Langevin equation, J. Chem. Phys., 113 (2000), pp. 297-306.
18. D. T. GILLESPIE, Approximate accelerated stochastic simulation of chemically reacting systems, J. Chem. Phys., 115 (2001), pp. 1716-1733.
19. D. T. GILLESPIE AND L. PETZOLD, Numerical simulation for biochemical kinetics, in System Modelling in Cellular Biology, Z. Szallasi, J. Stelling, and V. Periwal, eds., MIT Press, Cambridge, MA, 2006, pp. 331-354.
20. D. T. GILLESPIE, L. PETZOLD, AND Y. CAO, Comment on "Nested stochastic simulation algorithm for chemical kinetic systems with disparate rates" [J. Chem. Phys., 123 (2005), article 194107], J. Chem. Phys., 126 (2007), article 137101.
21. D. J. HIGHAM, An algorithmic introduction to numerical simulation of stochastic differential equations, SIAM Rev., 43 (2001), pp. 525-546.
22. D. J. HIGHAM AND N. J. HIGHAM, MATLAB Guide, 2nd ed., SIAM, Philadelphia, 2005.
23. T. G. KURTZ, Approximation of Population Processes, SIAM, Philadelphia, 1981.
24. N. LE NOVÉRE AND T. S. SHIMIZU, StochSim: Modelling of stochastic biomolecular processes, Bioinform., 17 (2001), pp. 575-576.
25. B. LEIMKUHLER AND S. REICH, Simulating Hamiltonian Dynamics, Cambridge University Press, Cambridge, UK, 2005.
26. H. LI, Y. CAO, L. PETZOLD, AND D. GILLESPIE, Algorithms and software for stochastic simulation of biochemical reacting systems, Biotechnology Progr., to appear.
27. T. LU, D. VOLFSON, L. TSIMRING, AND J. HASTY, Cellular growth and division in the Gillespie algorithm, IEE Proc. Systems Biol., 1 (2004), pp. 121-128.
28. J. MARTÍNEZ-URREAGA, J. MIRA, AND C. GONZÀLEZ-FERNÁNDEZ, Introducing the stochastic simulation of chemical reactions. Using the Gillespie algorithm and MATLAB, Chem. Engrg. Educ., 37 (2003), pp. 14-19.
29. C. V. RAO AND A. P. ARKIN, Stochastic chemical kinetics and the quasi-steady-state assumption: Application to the Gillespie algorithm, J. Chem. Phys., 118 (2003), pp. 4999-5010.
30. C. V. RAO, D. M. WOLF, AND A. P. ARKIN, Control, exploitation and tolerance of intracellular noise, Nature, 420 (2002), pp. 231-237.
31. E. RENSHAW, Modelling Biological Populations in Space and Time, Cambridge University Press, Cambridge, UK, 1991.
32. H. SALIS AND Y. KAZNESSIS, Accurate hybrid stochastic simulation of coupled chemical or biochemical reactions, J. Chem. Phys., 122 (2005), article 0541031-13.
33. H. SALIS, V. SOTIROPOULOS, AND Y. N. KAZNESSIS, Multiscale Hy3S: Hybrid stochastic simulation for supercomputers, BMC Bioinform., 7 (2006), p. 93.
34. H. E. SAMAD, M. KHAMMASH, L. PETZOLD, AND D. T. GILLESPIE, Stochastic modeling of gene regulatory networks, Internat. J. Robust Nonlinear Control, 15 (2005), pp. 691-711.
35. T. SCHLICK, Molecular Modeling and Simulation, Springer-Verlag, Berlin, 2002.
36. S. SCHNELL AND T. E. TURNER, Reaction kinetics in intracellular environments with macro-molecular crowding: Simulations and rate laws, Progr. Biophys. Molecular Biol., 85 (2004), pp. 235-260.
37. T. E. TURNER, S. SCHNELL, AND K. BURRAGE, Stochastic approaches for modelling in vivo reactions, Comput. Biol. Chem., 28 (2004), pp. 165-178.
38. M. ULLAH, H. SCHMIDT, K.-H. CHO, AND O. WOLKENHAUER, Deterministic modelling and stochastic simulation of pathways using MATLAB, IEE Proc. Systems Biol., 153 (2006), pp. 53-60.
39. N. VAN KAMPEN, Stochastic Processes in Physics and Chemistry, 3rd ed., North-Holland, Amsterdam, New York, 2001.
40. D. J. WILKINSON, Stochastic Modelling for Systems Biology, Chapman & Hall/CRC, Boca Raton, FL, 2006.
41. W. M. YOUNG AND E. W. ELCOCK, Monte Carlo studies of vacancy migration in binary ordered alloys: I, Proc. Phys. Sec., 89 (1966), pp. 735-746.