A Comparison of Bimolecular Reaction Models for Stochastic Reaction-Diffusion Systems

Bulletin of Mathematical Biology

Volumn 76, Issue 4, 2014, Pages 922-946

  Agbanusi, I C ^a   Isaacson, S A ^a  

^a USA   (United States)

Author keywords

Diffusion limited reaction; Stochastic reaction diffusion

Indexed keywords

DNA; PROTEIN;

BIOLOGICAL MODEL; CHEMISTRY; COMPARATIVE STUDY; COMPUTER SIMULATION; KINETICS; STATISTICS;

COMPUTER SIMULATION; DNA; KINETICS; MODELS, BIOLOGICAL; PROTEINS; STOCHASTIC PROCESSES;

EID: 84899509008     PISSN: 00928240     EISSN: 15229602     Source Type: Journal    
DOI: 10.1007/s11538-013-9833-6     Document Type: Article

References (39)

1. Andrews, S. S., & Bray, D. (2004). Stochastic simulation of chemical reactions with spatial resolution and single molecule detail. Phys. Biol., 1, 137-151.
2. BelHadjAli, H., Amor, A. B., & Brasche, J. F. (2011). Large coupling convergence: overview and new results. In M. Demuth, B. W. Schulze, & I. Witt (Eds.), Operator theory: advances and applications: Vol. 211. Partial differential equations and spectral theory (pp. 73-117). Basel: Springer.
3. Demuth, M. (1980). On scattering of diffusion process generators. Lett. Math. Phys., 4(5), 417-424.
4. Demuth, M., Jeske, F., & Kirsch, W. (1993). Rate of convergence for large coupling limits by Brownian motion. Ann. Inst. Henri Poincaré, a Phys. Théor., 59(3), 327-355.
5. Doi, M. (1976a). Second quantization representation for classical many-particle system. J. Phys. A, Math. Gen., 9(9), 1465-1477.
6. Doi, M. (1976b). Stochastic theory of diffusion-controlled reaction. J. Phys. A, Math. Gen., 9(9), 1479-1495.
7. Donev, A., Bulatov, V. V., Oppelstrup, T., Gilmer, G. H., Sadigh, B., & Kalos, M. H. (2010). A first-passage kinetic Monte Carlo algorithm for complex diffusion-reaction systems. J. Comp. Physiol., 229(9), 3214-3236.
8. Drawert, B., Engblom, S., & Hellander, A. (2012). URDME: a modular framework for stochastic simulation of reaction-transport processes in complex geometries. BMC Syst. Biol., 6(1), 76.
9. Dushek, O., van der Merwe, P. A., & Shahrezaei, V. (2011). Ultrasensitivity in multisite phosphorylation of membrane-anchored proteins. Biophys. J., 100(5), 1189-1197.
10. Elf, J., & Ehrenberg, M. (2004). Spontaneous separation of bi-stable biochemical systems into spatial domains of opposite phases. IET Syst. Biol., 1(2), 230-236.
11. Erban, R., & Chapman, S. J. (2009). Stochastic modelling of reaction-diffusion processes: algorithms for bimolecular reactions. Phys. Biol., 6(4), 046001.
12. Erban, R., Chapman, S. J., & Maini, P. K. (2007). A practical guide to stochastic simulations of reaction-diffusion processes. arXiv: 0704. 1908 [q-bio. SC].
13. Fange, D., Berg, O. G., Sjöberg, P., & Elf, J. (2010). Stochastic reaction-diffusion kinetics in the microscopic limit. Proc. Natl. Acad. Sci. USA, 107(46), 19820-19825.
14. Fange, D., Mahmutovic, A., & Elf, J. (2012). MesoRD 1. 0: stochastic reaction-diffusion simulations in the microscopic limit. Bioinformatics, 28(23), 3155-3157.
15. Gardiner, C. W. (1996). Springer series in synergetics: Vol. 13. Handbook of stochastic methods: for physics, chemistry, and the natural sciences (2nd ed.). New York: Springer.
16. Gardiner, C. W., McNeil, K. J., Walls, D. F., & Matheson, I. S. (1976). Correlations in stochastic models of chemical reactions. J. Stat. Phys., 14, 307.
17. Gesztesy, F., Gurarie, D., Holder, H., Klaus, M., Sadun, L., Simon, B., & Vogl, P. (1988). Trapping and cascading of eigenvalues in the large coupling limit. Commun. Math. Phys., 118(4), 597-634.
18. Girsanov, I. V. (1960). The solution of certain boundary problems for parabolic and elliptic equations with discontinuous coefficients. Sov. Math. Dokl., 1, 1373-1375.
19. Glimm, J., & Jaffe, A. (1987). Quantum physics; a functional integral point of view (2nd ed.). New York: Springer.
20. Hellander, S., Hellander, A., & Petzold, L. (2012). Reaction-diffusion master equation in the microscopic limit. Phys. Rev. E, 85(4), 042901.
21. Hepburn, I., Chen, W., Wils, S., & De Schutter, E. (2012). STEPS: efficient simulation of stochastic reaction-diffusion models in realistic morphologies. BMC Syst. Biol., 6(1), 36.
22. Isaacson, S. A. (2008). Relationship between the reaction-diffusion master equation and particle tracking models. J. Phys. A, Math. Theor., 41(6), 065003.
23. Isaacson, S. A. (2009). The reaction-diffusion master equation as an asymptotic approximation of diffusion to a small target. SIAM J. Appl. Math., 70(1), 77-111.
24. Isaacson, S. A. (2012, submitted). A convergent reaction-diffusion master equation. Preprint. arXiv: 1211. 6772.
25. Isaacson, S. A., & Isaacson, D. (2009). Reaction-diffusion master equation, diffusion-limited reactions, and singular potentials. Phys. Rev. E, 80(6), 066106.
26. Isaacson, S. A., McQueen, D. M., & Peskin, C. S. (2011). The influence of volume exclusion by chromatin on the time required to find specific DNA binding sites by diffusion. Proc. Natl. Acad. Sci. USA, 108(9), 3815-3820.
27. Kang, H.-W., Zheng, L., & Othmer, H. G. (2012). A new method for choosing the computational cell in stochastic reaction-diffusion systems. J. Math. Biol., 65(6-7), 1017-1099.
28. Keizer, J. (1982). Nonequilibrium statistical thermodynamics and the effect of diffusion on chemical reaction rates. J. Phys. Chem., 86, 5052-5067.
29. Kerr, R. A., et al. (2008). Fast Monte Carlo simulation methods for biological reaction-diffusion systems in solution and on surfaces. SIAM J. Sci. Comput., 30(6), 3126-3149.
30. Kühner, F., Costa, L. T., Bisch, P. M., Thalhammer, S., Heckl, W. M., & Gaub, H. E. (2004). LexA-DNA bond strength by single molecule force spectroscopy. Biophys. J., 87, 2683-2690.
31. Lipkova, J., Zygalakis, K. C., Chapman, S. J., & Erban, R. (2011). Analysis of Brownian Dynamics simulations of reversible bimolecular reactions. SIAM J. Appl. Math., 71(3), 714.
32. McQuarrie, D. A. (1967). Stochastic approach to chemical kinetics. J. Appl. Probab., 4, 413-478.
33. Nadkarni, S., Bartol, T. M., Stevens, C. F., Sejnowski, T. J., & Levine, H. (2012). Short-term plasticity constrains spatial organization of a hippocampal presynaptic terminal. Proc. Natl. Acad. Sci. USA, 109(36), 14657-14662.
34. Olenik, O. A. (1961). Boundary-value problems for linear elliptic and parabolic equations with discontinuous coefficients. Izv. Akad. Nauk SSSR, Ser. Mat., 25(1), 3-20.
35. Smoluchowski, M. V. (1917). Mathematical theory of the kinetics of the coagulation of colloidal solutions. Z. Phys. Chem., 92, 129-168.
36. Takahashi, K., Tanase-Nicola, S., & ten Wolde, P. R. (2010). Spatio-temporal correlations can drastically change the response of a MAPK pathway. Proc. Natl. Acad. Sci. USA, 107(6), 2473-2478.
37. Taylor, M. E. (1996). Applied mathematical sciences: Vol. 116. Partial differential equations II: qualitative studies of linear equations. New York: Springer.
38. Teramoto, E., & Shigesada, N. (1967). Theory of bimolecular reaction processes in liquids. Prog. Theor. Phys., 37(1), 29-51.
39. van Kampen, N. G. (2001). Stochastic processes in physics and chemistry. Amsterdam: North-Holland.