How accurate are the nonlinear chemical Fokker-Planck and chemical Langevin equations?

Journal of Chemical Physics

Volumn 135, Issue 8, 2011, Pages

  Grima, Ramon ^a   Thomas, Philipp ^a,b   Straube, Arthur V ^b  

^a UNIVERSITY OF EDINBURGH   (United Kingdom)

^b HUMBOLDT UNIVERSITY   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

BIOCHEMICAL REACTIONS; CHARACTERISTIC SIZE; CHEMICAL LANGEVIN EQUATION; CHEMICAL MASTER EQUATION; CHEMICAL SYSTEMS; CONCENTRATION FLUCTUATION; DETAILED BALANCE; ENZYME-CATALYZED REACTIONS; FOKKER PLANCK; KRAMERS-MOYAL EXPANSION; MASTER EQUATIONS; MEAN CONCENTRATIONS; REACTION SYSTEM; RELATIVE ERRORS; SECOND ORDERS; VARIANCE ESTIMATE;

DIFFERENTIAL EQUATIONS; ERRORS; ESTIMATION; FORECASTING; NONLINEAR EQUATIONS; TIMING JITTER;

FOKKER PLANCK EQUATION;

ARTICLE; CHEMICAL MODEL; MULTIVARIATE ANALYSIS; REPRODUCIBILITY;

MODELS, CHEMICAL; MULTIVARIATE ANALYSIS; REPRODUCIBILITY OF RESULTS;

EID: 80052396994     PISSN: 00219606     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.3625958     Document Type: Review

References (41)

1. D. T. Gillespie, Annu. Rev. Phys. Chem. 58, 35 (2007). 10.1146/annurev.physchem.58.032806.104637
2. D. T. Gillespie, Physica A 188, 404 (1992). 10.1016/0378-4371(92)90283-V
3. D. T. Gillespie, J. Chem. Phys. 131, 164109 (2009). 10.1063/1.3253798
4. D. A. McQuarrie, J. Appl. Prob. 4, 413 (1967). 10.2307/3212214
5. N. G. van Kampen, Stochastic Processes in Physics and Chemistry (Elsevier, New York, 2007).
6. H. Kramers, Physica 7, 284 (1940). 10.1016/S0031-8914(40)90098-2
7. J. E. Moyal, J. R. Stat. Soc. 11, 150 (1949).
8. C. W. Gardiner, Handbook of Stochastic Methods for Physics, Chemistry and the Natural Sciences (Springer, New York, 2004).
9. N. G. van Kampen, Can. J. Phys. 39, 551 (1961). 10.1139/p61-056
10. N. G. van Kampen, Adv. Chem. Phys. 34, 245 (1976). 10.1002/SERIES2007
11. N. G. van Kampen, The diffusion approximation for Markov process., in Thermodynamics and Kinetics of Biological Processes, edited by, I. Lamprecht, and, A. I. Zotin, (Walter de Gruyter and Co., New York, 1982), pp. 185-195.
12. T. G. Kurtz, J. Chem. Phys. 50, 460 (1969). 10.1063/1.1670820
13. W. Horsthemke and L. Brenig, Z. Phys. B 27, 341 (1977). 10.1007/BF01320526
14. D. T. Gillespie, J. Chem. Phys. 113, 297 (2000). 10.1063/1.481811
15. T. E. Turner, S. Schnell, and K. Burrage, Comput. Biol. Chem. 28, 165 (2004). 10.1016/j.compbiolchem.2004.05.001
16. R. Grima and S. Schnell, Essays Biochem. 45, 41 (2008). 10.1042/BSE0450041
17. J. Paulsson, Phys. Life. Rev. 2, 157 (2005). 10.1016/j.plrev.2005.03.003
18. T. C. Meng, S. Somani, and P. Dhar, In Silico Biol. 4, 293 (2004).
19. D. T. Gillespie, J. Phys. Chem. 81, 2340 (1977). 10.1021/j100540a008
20. Z. Hou and H. Xin, J. Chem. Phys. 119, 11508 (2003). 10.1063/1.1624053
21. M. L. Simpson, C. D. Cox, and G. S. Sayler, J. Theor. Biol. 229, 383 (2004). 10.1016/j.jtbi.2004.04.017
22. T. Xiao, J. Ma, Z. Hou, and H. Xin, New J. Phys. 9, 403 (2007). 10.1088/1367-2630/9/11/403
23. J. Wilkie and Y. M. Wong, Chem. Phys. 353, 132 (2008). 10.1016/j.chemphys.2008.08.001
24. V. Sotiropoulos, M.-N. Contou-Carrere, P. Daoutidis, and Y. N. Kaznessis, IEEE/ACM Trans. Comput. Biol. Bioinf. 6, 470 (2009). 10.1109/TCBB.2009.23
25. Y. Ishihama, T. Schmidt, J. Rappsilber, M. Mann, F. U. Hart, M. J. Kerner, and D. Frishman, BMC Genomics 9, 102 (2008). 10.1186/1471-2164-9-102
26. S. Ghaemmaghami, W.-K. Huh, K. Bower, R. W. Howson, A. Belle, N. Dephoure, E. K. OShea, and J. S. Weissman, Nature (London) 425, 737 (2003). 10.1038/nature02046
27. J. Elf and M. Ehrenberg, Genome Res. 13, 2475 (2003). 10.1101/gr.1196503
28. R. Grima, J. Chem. Phys. 133, 035101 (2010). 10.1063/1.3454685
29. D. T. Gillespie, J. Chem. Phys. 72, 5363 (1980). 10.1063/1.439029
30. J. Keizer, Statistical Thermodynamics of Nonequilibrium Processes (Springer, New York, 1987).
31. R. M. Mazo, J. Chem. Phys. 62, 4244 (1975). 10.1063/1.430277
32. H. Grabert, P. Haenggi, and I. Oppenheim, Physica 117A, 300 (1983). 10.1016/0378-4371(83)90119-X
33. H. Risken, The Fokker-Planck Equation: Methods of Solution and Applications (Springer, New York, 1996).
34. A. Cornish-Bowden, Fundamentals of Enzyme Kinetics (Portland Press, London, 1995).
35. R. Grima, BMC Sys. Biol. 3, 101 (2009). 10.1186/1752-0509-3-101
36. D. T. Gillespie, J. Phys. Chem. A 106, 5063 (2002). 10.1021/jp0128832
37. D. J. Higham and R. Khanin, Open Appl. Math. J 2, 59 (2008). 10.2174/1874114200802010059
38. R. F. Pawula, Phys. Rev. 162, 186 (1967). 10.1103/PhysRev.162.186
39. H. Risken and H. D. Vollmer, Z. Phys. B 35, 313 (1979). 10.1007/BF01319854
40. R. Grima, Phys. Rev. Lett. 102, 218103 (2009). 10.1103/PhysRevLett.102. 218103
41. P. Thomas, A. V. Straube, and R. Grima, J. Chem. Phys. 133, 195101 (2010). 10.1063/1.3505552