Analysis of Brownian dynamics simulations of reversible bimolecular reactions

SIAM Journal on Applied Mathematics

Volumn 71, Issue 3, 2011, Pages 714-730

  Lipková, Jana ^a   Zygalakis, Konstantinos C ^b   Jonathan Chapman, S ^b   Erban, Radek ^b  

^a CHARLES UNIVERSITY   (Czech Republic)

^b UNIVERSITY OF OXFORD   (United Kingdom)

Author keywords

Brownian dynamics; Reaction diffusion problems; Reversible bimolecular reactions; Stochastic simulation algorithms

Indexed keywords

ALGORITHM PARAMETERS; BIMOLECULAR REACTION; BROWNIAN DYNAMICS; BROWNIAN DYNAMICS SIMULATIONS; DIFFUSION CONSTANT; GEMINATE RECOMBINATION; REACTION DIFFUSION PROBLEMS; REACTION-DIFFUSION MODELS; STOCHASTIC SIMULATION ALGORITHMS;

ALGORITHMS; COMPUTER SIMULATION; DIFFUSION IN LIQUIDS; RATE CONSTANTS; STOCHASTIC MODELS; STOCHASTIC SYSTEMS;

BROWNIAN MOVEMENT;

EID: 79960351109     PISSN: 00361399     EISSN: None     Source Type: Journal    
DOI: 10.1137/100794213     Document Type: Article

References (35)

1. B. ALBERTS, A. JOHNSON, J. LEWIS, M. RAFF, K. ROBERTS, AND P. WALTER, Molecular Biology of the Cell, Garland Science, New York, 2002.
2. S. ANDREWS, Serial rebinding of ligands to clustered receptors as exemplified by bacterial chemotaxis, Phys. Biol., 2(2005), pp. 111-122. (Pubitemid 40991713)
3. S. ANDREWS, Accurate particle-based simulation of adsorption, desorption and partial transmission, Phys. Biol., 6(2009), 046015.
4. S. ANDREWS, N. ADDY, R. BRENT, AND A. ARKIN, Detailed simulations of cell biology with Smoldyn 2.1, PLoS Comput. Biol., 6(2010), e1000705.
5. S. ANDREWS AND D. BRAY, Stochastic simulation of chemical reactions with spatial resolution and single molecule detail, Phys. Biol., 1(2004), pp. 137-151. (Pubitemid 44362291)
6. H. BERG, Random Walks in Biology, Princeton University Press, Princeton, NJ, 1983.
7. D. BRUNE AND S. KIM, Predicting protein diffusion coefficients, Proc. Natl. Acad. Sci. USA, 90(1993), pp. 3835-3839. (Pubitemid 23134120)
8. B. CORRY, S. KUYUCAK, AND S. CHUNG, Test of continuum theories as models of ion channels. II. Poisson-Nernst-Planck theory versus Brownian dynamics, Biophys. J., 78(2000), pp. 2364-2381. (Pubitemid 30313795)
9. M. DOI, Stochastic theory of diffusion-controlled reaction, J. Phys. A, 9(1976), pp. 1479-1495.
10. B. DRAWERT, M. LAWSON, L. PETZOLD, AND M. KHAMMASH, The diffusive finite state projection algorithm for efficient simulation of the stochastic reaction-diffusion master equation, J. Chem. Phys., 132(2010), 074101.
11. S. ENGBLOM, L. FERM, A. HELLANDER, AND P. LÖTSTEDT, Simulation of stochastic reactiondiffusion processes on unstructured meshes, SIAM J. Sci. Comput., 31(2009), pp. 1774-1797.
12. R. ERBAN AND S. J. CHAPMAN, Reactive boundary conditions for stochastic simulations of reaction-diffusion processes, Phys. Biol., 4(2007), pp. 16-28. (Pubitemid 46553674)
13. R. ERBAN AND S. J. CHAPMAN, Stochastic modelling of reaction-diffusion processes: Algorithms for bimolecular reactions, Phys. Biol., 6(2009), 046001.
14. R. ERBAN, S. J. CHAPMAN, AND P. MAINI, A Practical Guide to Stochastic Simulations of Reaction-Diffusion Processes, http://arxiv.org/abs/0704.1908 (2007).
15. D. ERMAK AND J. MCCAMMON, Brownian dynamics with hydrodynamic interactions, J. Chem. Phys., 69(1978), pp. 1352-1360.
16. L. FERM, A. HELLANDER, AND P. LÖTSTEDT, An adaptive algorithm for simulation of stochastic reaction-diffusion processes, J. Comput. Phys., 229(2010), pp. 343-360.
17. D. GILLESPIE, Exact stochastic simulation of coupled chemical reactions, J. Phys. Chem., 81(1977), pp. 2340-2361.
18. J. HATTNE, D. FANGE, AND J. ELF, Stochastic reaction-diffusion simulation with MesoRD, Bioinformatics, 21(2005), pp. 2923-2924. (Pubitemid 40862297)
19. S. A. ISAACSON, The reaction-diffusion master equation as an asymptotic approximation of diffusion to a small target, SIAM J. Appl. Math., 70(2009), pp. 77-111.
20. S. A. ISAACSON AND C. S. PESKIN, Incorporating diffusion in complex geometries into stochastic chemical kinetics simulations, SIAM J. Sci. Comput., 28(2006), pp. 47-74.
21. H. KIM AND K. J. SHIN, Exact solution of the reversible diffusion-influenced reaction for an isolated pair in three dimensions, Phys. Rev. Lett., 82(1999), pp. 1578-1581. (Pubitemid 129646678)
22. H. KIM, M. YANG, AND K. J. SHIN, Dynamic correlation effect in reversible diffusion-influenced reactions: Brownian dynamics simulation in three dimensions, J. Chem. Phys., 111(1999), pp. 1068-1075. (Pubitemid 129308212)
23. R. LARSON, H. HU, D. SMITH, AND S. CHU, Brownian dynamics simulations of a DNA molecule in an extensional flow field, J. Rheology, 43(1999), pp. 267-303.
24. K. LIPKOW, S. ANDREWS, AND D. BRAY, Simulated diffusion of phosphorylated CheY through the cytoplasm of Escherichia coli, J. Bacteriology, 187(2005), pp. 45-53. (Pubitemid 40024179)
25. H. MARIANAYAGAM, M. SUNDE, AND J. MATTHEWS, The power of two: Protein dimerization in biology, Trends Biochem. Sci., 29(2004), pp. 618-625. (Pubitemid 39389082)
26. S. NORTHRUP AND H. ERICKSON, Kinetics of protein-protein association explained by Brownian dynamics computer simulation, Proc. Natl. Acad. Sci. USA, 89(1992), pp. 3338-3342.
27. E. PLATEN, An introduction to numerical methods for stochastic differential equations, in Acta Numerica 1999, Acta Numer. 8, Cambridge University Press, Cambridge, UK, 1999, pp. 197-246.
28. A. V. POPOV AND N. AGMON, Three-dimensional simulations of reversible bimolecular reactions: The simple target problem, J. Chem. Phys., 115(2001), pp. 8921-8932. (Pubitemid 33099593)
29. L. QIAO, R. ERBAN, C. KELLEY, AND I. KEVREKIDIS, Spatially distributed stochastic systems: Equation-free and equation-assisted preconditioned computation, J. Chem. Phys., 125(2006), 204108.
30. C. SIETTOS, M. GRAHAM, AND I. KEVREKIDIS, Coarse Brownian dynamics for nematic liquid crystals: Bifurcation, projective integration, and control via stochastic simulation, J. Chem. Phys., 118(2003), pp. 10149-10156.
31. M. SMOLUCHOWSKI, Versuch einer mathematischen Theorie der Koagulationskinetik kolloider Lösungen, Z. Physikalische Chemie, 92(1917), pp. 129-168.
32. E. TERAMOTO AND N. SHIGESADA, Theory of bimolecular reaction processes in liquids, Progr. Theoret. Phys., 37(1967), pp. 29-51.
33. F. TOSTEVIN, P. TEN WOLDE, AND M. HOWARD, Fundamental limits to position determination by concentration gradients, PLoS Comput. Biol., 3(2007), pp. 763-771. (Pubitemid 46683458)
34. N. VAN KAMPEN, Stochastic Processes in Physics and Chemistry, 3rd ed., North-Holland, Amsterdam, 2007.
35. J. VAN ZON AND P. TEN WOLDE, Green's-function reaction dynamics: A particle-based approach for simulating biochemical networks in time and space, J. Chem. Phys., 123(2005), 234910.