Stochastic modelling of reaction-diffusion processes: Algorithms for bimolecular reactions

Physical Biology

Volumn 6, Issue 4, 2009, Pages

  Erban, Radek ^a   Chapman, S Jonathan ^a  

^a UNIVERSITY OF OXFORD   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHM; ARTICLE; CHEMICAL REACTION; MATHEMATICAL ANALYSIS; MONTE CARLO METHOD; PRIORITY JOURNAL; STOCHASTIC MODEL; BIOCHEMISTRY; CHEMICAL MODEL; DIFFUSION; MOLECULAR BIOLOGY; STATISTICAL MODEL;

ALGORITHMS; BIOCHEMISTRY; DIFFUSION; MODELS, CHEMICAL; MODELS, STATISTICAL; MOLECULAR BIOLOGY;

EID: 70350729439     PISSN: 14783967     EISSN: 14783975     Source Type: Journal    
DOI: 10.1088/1478-3975/6/4/046001     Document Type: Article

References (40)

1. Alberts B, Johnson A, Lewis J, Raff M, Roberts K and Walter P 2002 Molecular Biology of the Cell (New York: Garland Science)
2. Andrews S 2005 Serial rebinding of ligands to clustered receptors as exemplified by bacterial chemotaxis Phys. Biol. 2 111-22
3. Andrews S and Bray D 2004 Stochastic simulation of chemical reactions with spatial resolution and single molecule detail Phys. Biol. 1 137-51
4. Berg H 1983 Random Walks in Biology (Princeton, NJ: Princeton University Press)
5. Berg H and Purcell E 1977 Physics of chemoreception Biophys. J. 20 193-219
6. Chandrasekhar S 1943 Stochastic problems in physics and astronomy Rev. Mod. Phys. 15 2-89
7. DeVille R, Muratov C and Vanden-Eijnden E 2006 Non-meanfield deterministic limits in chemical reaction kinetics J. Chem. Phys. 124 231102
8. Dix J and Verkman A 2008 Crowding effects on diffusion in solutions and cells Annu. Rev. Biophys. 37 247-63
9. Doi M 1976 Stochastic theory of diffusion-controlled reaction J. Phys. A: Math. Gen. 9 1479-95
10. Einstein A 1905 ber die von der molekularkinetischen Theorie der Wärme geforderte Bewegung von in ruhenden Flüssigkeiten suspendierten Teilchen Ann. Phys., Lpz. 17 549-60
11. Engblom S 2006 Computing the moments of high dimensional solutions of the master equation Appl. Math. Comput. 180 498-515
12. Engblom S, Ferm L, Hellander A and Lötstedt P 2008 Simulation of stochastic reaction-diffusion processes on unstructured meshes Technical Report 2008-012 Dept. of Information Technology, Uppsala University, Sweden
13. Erban R and Chapman S J 2007 Reactive boundary conditions for stochastic simulations of reaction-diffusion processes Phys. Biol. 4 16-28
14. Erban R, Chapman S J, Fisher K, Kevrekidis I and Seymour L 2007 Dynamics of polydisperse irreversible adsorption: a pharmacological example Math. Models Methods Appl. Sci. (M3AS) 17 759-81
15. Erban R, Chapman S J, Kevrekidis I and Vejchodsky T 2009 Analysis of a stochastic chemical system close to a sniper bifurcation of its mean-field model SIAM J. Appl. Math. arXiv:0807.4498 at press
16. Erban R, Chapman S J and Maini P 2007 A practical guide to stochastic simulations of reaction-diffusion processes arXiv:0704.1908
17. Erban R and Othmer H 2004 From individual to collective behaviour in bacterial chemotaxis SIAM J. Appl. Math. 65 361-91
18. Erban R and Othmer H 2005 From signal transduction to spatial pattern formation in E coli: a paradigm for multi-scale modeling in biology Multiscale Model. Simul. 3 362-94
19. Erban R and Othmer H 2007 Taxis equations for amoeboid cells J. Math. Biol. 54 847-85
20. Fushimi K and Verkman A 1991 Low viscosity in the aqueous domain of cell cytoplasm measured by picosecond polarization microfluorimetry J. Cell Biol. 112 719-25
21. Gillespie D 1977 Exact stochastic simulation of coupled chemical reactions J. Phys. Chem. 81 2340-61
22. Gillespie D 1992 Markov Processes, An Introduction for Physical Scientists (New York: Academic)
23. Gillespie D 2000 The chemical Langevin equation J. Chem. Phys. 113 297-306
24. Hattne J, Fange D and Elf J 2005 Stochastic reaction-diffusion simulation with MesoRD Bioinformatics 21 2923-4
25. Higham D J 2001 An algorithmic introduction to numerical simulation of stochastic differential equations SIAM Rev. 43 525-46
26. Isaacson S 2009 The reaction-diffusion master equation as an asymptotic approximation of diffusion to a small target SIAM J. Appl. Math. 70 77-111
27. Isaacson S and Peskin C 2006 Incorporating diffusion in complex geometries into stochastic chemical kinetics simulations SIAM J. Sci. Comput. 28 47-74
28. McKane A and Newman T 2004 Stochastic models in population biology and their deterministic analogs Phys. Rev. E 70 041902
29. Murray J 2002 Mathematical Biology (Berlin: Springer)
30. Northrup S and Erickson H 1992 Kinetics of protein-protein association explained by Brownian dynamics computer simulation Proc. Natl Acad. Sci. 89 3338-42
31. Paulsson J, Berg O and Ehrenberg M 2000 Stochastic focusing: fluctuation-enhanced sensitivity of intracellular regulation Proc. Natl Acad. Sci. 97 7148-53
32. Singer A, Schuss Z, Osipov A and Holcman D 2008 Partially reflected diffusion SIAM J. Appl. Math. 68 844-68
33. Smoluchowski M 1917 Versuch einer mathematischen Theorie der Koagulationskinetik kolloider Lösungen Z. Phys. Chem. 92 129-68
34. Stiles J and Bartol T 2001 Monte Carlo methods for simulating realistic synaptic microphysiology using MCell Computational Neuroscience: Realistic Modeling for Experimentalists ed E Schutter (Boca Raton, FL: CRC Press) pp 87-127
35. Thomas J 1995 Numerical Partial Differential Equations vol 22 (Berlin: Springer)
36. Tournier A, Fitzjohn P and Bates P 2006 Probability-based model of protein-protein interactions on biological timescales Algorithms Mol. Biol. 1 1-11
37. Twomey A 2007 On the stochastic modelling of reaction-diffusion processes MSc Thesis University of Oxford
38. van Kampen N 2007 Stochastic Processes in Physics and Chemistry 3rd edn (Amsterdam: North-Holland)
39. van Zon J and ten Wolde P 2005 Green's-function reaction dynamics: a particle-based approach for simulating biochemical networks in time and space J. Chem. Phys. 123 234910
40. Zauderer E 1983 Partial Differential Equations of Applied Mathematics (New York: Wiley)