An accelerated algorithm for discrete stochastic simulation of reaction-diffusion systems using gradient-based diffusion and tau-leaping

Journal of Chemical Physics

Volumn 134, Issue 15, 2011, Pages

  Koh, Wonryull ^a   Blackwell, Kim T ^a  

^a GEORGE MASON UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BIOLOGICAL CELLS; CONCENTRATION GRADIENTS; DIFFUSION PROCESS; DIFFUSIVE TRANSFER; DISCRETE STOCHASTIC SIMULATION; GRADIENT BASED; HETEROGENEOUS DISTRIBUTIONS; MICRO-DOMAINS; MOLECULAR POPULATION; MOLECULAR SPECIES; NEW STRATEGY; NUMERICAL RESULTS; REACTION DIFFUSION SYSTEMS; SIMULATION SPEED; SPATIAL STOCHASTIC; SPATIOTEMPORAL ACTIVITY; STOCHASTIC EVENTS; STOCHASTIC SIMULATION ALGORITHMS; STOCHASTIC SIMULATIONS; STOCHASTIC VARIATION; SUBVOLUMES; TAU-LEAPING;

ALGORITHMS; DIFFUSION IN LIQUIDS; DYNAMIC MODELS; STOCHASTIC MODELS; SYSTEMS ANALYSIS;

STOCHASTIC SYSTEMS;

CYCLIC AMP; PROTEIN KINASE;

ALGORITHM; ARTICLE; CHEMICAL MODEL; CHEMISTRY; DIFFUSION; DRUG EFFECT; ENZYME ACTIVATION; METABOLISM; POISSON DISTRIBUTION; STATISTICS;

ALGORITHMS; CYCLIC AMP; DIFFUSION; ENZYME ACTIVATION; MODELS, CHEMICAL; POISSON DISTRIBUTION; PROTEIN KINASES; STOCHASTIC PROCESSES;

EID: 79955434615     PISSN: 00219606     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.3572335     Document Type: Article

References (84)

1. L. Shapiro and R. Losick, Cell 100, 89 (2000). 10.1016/S0092-8674(00) 81686-4
2. F. M. Harold, Microbiol. Mol. Biol. Rev. 69, 544 (2005). 10.1128/MMBR.69.4.544-564.2005 (Pubitemid 41798462)
3. A. M. Turing, Philos. Trans. R. Soc. London, Ser. B 237, 37 (1952). 10.1098/rstb.1952.0012
4. N. Rashevsky, Bull. Math. Biol. 2, 15 (1940).
5. G. Nicolis and I. Prigogine, Proc. Natl. Acad. Sci. U.S.A. 68, 2102 (1971). 10.1073/pnas.68.9.2102
6. N. Glade, J. Demongeot, and J. Tabony, BMC Cell Biology 5, 23 (2004).
7. M. Howard and A. D. Rutenberg, Phys. Rev. Lett. 90, 128102 (2003). 10.1103/PhysRevLett.90.128102
8. M. Mayford, Curr. Opin. Neurobiol. 17, 313 (2007). 10.1016/j.conb.2007. 05.001 (Pubitemid 46880332)
9. B. L. Bloodgood, A. J. Giessel, and B. L. Sabatini, PLoS Biol. 7, e 1000190 (2009). 10.1371/journal.pbio.1000190
10. S. Gasparini, A. Losonczy, X. Chen, D. Johnston, and J. C. Magee, J. Physiol. (London) 580, 787 (2007). 10.1113/jphysiol.2006.121343 (Pubitemid 46909035)
11. A. Majewska, E. Brown, J. Ross, and R. Yuste, J. Neurosci. 20, 1722 (2000). 10.1038/76609 (Pubitemid 30437199)
12. H. Zhong, G.-M. Sia, T. R. Sato, N. W. Gray, T. Mao, Z. Khuchua, R. L. Huganir, and K. Svoboda, Neuron 62, 363 (2009). 10.1016/j.neuron.2009.03.013
13. C. D. Harvey, R. Yasuda, H. Zhong, and K. Svoboda, Science 321, 136 (2008). 10.1126/science.1159675 (Pubitemid 351956251)
14. S.-J. R. Lee, Y. Escobedo-Lozoya, E. M. Szatmari, and R. Yasuda, Nature (London) 458, 299 (2009). 10.1038/nature07842
15. D. Longo and J. Hasty, Mol. Syst. Biol. 2 (2006). 10.1038/msb4100110 (Pubitemid 46061085)
16. H. H. McAdams and A. Arkin, Trends Genet. 15, 65 (1999). 10.1016/S0168-9525(98)01659-X (Pubitemid 29136643)
17. J. Paulsson, Phys. Life. Rev. 2, 157 (2005). 10.1016/j.plrev.2005.03.003 (Pubitemid 40792434)
18. J. M. Raser and E. K. O'Shea, Science 309, 2010 (2005). 10.1126/science.1105891 (Pubitemid 41362308)
19. W. J. Blake, M. Kaern, C. R. Cantor, and J. J. Collins, Nature (London) 422, 633 (2003). 10.1038/nature01546 (Pubitemid 36460419)
20. M. B. Elowitz, A. J. Levine, E. D. Siggia, and P. S. Swain, Science 297, 1183 (2002). 10.1126/science.1070919 (Pubitemid 36193353)
21. E. M. Ozbudak, M. Thattai, I. Kurtser, A. D. Grossman, and A. van Oudenaarden, Nat. Genet. 31, 69 (2002). 10.1038/ng869
22. D. A. McQuarrie, J. Appl. Probab. 4, 413 (1967). 10.2307/3212214
23. D. T. Gillespie, J. Comput. Phys. 22, 403 (1976). 10.1016/0021-9991(76) 90041-3 (Pubitemid 8008311)
24. D. T. Gillespie, J. Phys. Chem. 81, 2340 (1977). 10.1021/j100540a008
25. D. T. Gillespie, Physica A 188, 404 (1992). 10.1016/0378-4371(92)90283-V
26. S. S. Andrews and D. Bray, Phys. Biol. 1, 137 (2004). 10.1088/1478-3967/1/3/001 (Pubitemid 44362291)
27. R. A. Kerr, T. M. Bartol, B. Kaminsky, M. Dittrich, J.-C. J. Chang, S. B. Baden, T. J. Sejnowski, and J. R. Stiles, SIAM J. Sci. Comput. (USA) 30, 3126 (2008). 10.1137/070692017
28. C. J. Morton-Firth, T. S. Shimizu, and D. Bray, J. Mol. Biol. 286, 1059 (1999). 10.1006/jmbi.1999.2535 (Pubitemid 29116676)
29. M. Byrne, M. Waxham, and Y. Kubota, Neuroinformatics 8, 63 (2010). 10.1007/s12021-010-9066-x
30. S. S. Andrews, N. J. Addy, R. Brent, and A. P. Arkin, PLOS Comput. Biol. 6, e1000705 (2010). 10.1371/journal.pcbi.1000705
31. M. Ander, P. Beltrao, B. Di Ventura, J. A. F.-B. J. Ferkinghoff-Borg, M. A. F. M. Foglierini, A. A. K. A. Kaplan, C. A. L. C. Lemerle, I. A. T. -O. I. Tomas-Oliveira, and L. A. S. L. Serrano, IET Systems Biology 1, 129 (2004). 10.1049/sb:20045017
32. A. Chatterjee and D. Vlachos, J. Comput.-Aided Mater. Des. 14, 253 (2007). 10.1007/s10820-006-9042-9 (Pubitemid 46433463)
33. T. Oppelstrup, V. V. Bulatov, A. Donev, M. H. Kalos, G. H. Gilmer, and B. Sadigh, Phys. Rev. E 80, 066701 (2009). 10.1103/PhysRevE.80.066701
34. A. Donev, V. V. Bulatov, T. Oppelstrup, G. H. Gilmer, B. Sadigh, and M. H. Kalos, J. Comput. Phys. 229, 3214 (2010). 10.1016/j.jcp.2009.12.038
35. J. Elf and M. Ehrenberg, Syst. Biol. 1, 230 (2004). 10.1049/sb:20045021
36. R. Erban and S. J. Chapman, Phys. Biol. 4, 16 (2007). 10.1088/1478-3975/4/1/003 (Pubitemid 46553674)
37. S. A. Isaacson and C. S. Peskin, SIAM J. Sci. Comput.(USA) 28, 47 (2006). 10.1137/040605060
38. F. Baras and M. M. Mansour, Phys. Rev. E 54, 6139 (1996). 10.1103/PhysRevE.54.6139
39. C. W. Gardiner, Stochastic Methods: A Handbook for the Natural and Social Sciences, 4th ed. (Springer-Verlag, Berlin, 2009).
40. N. G. van Kampen, Stochastic Processes in Physics and Chemistry, 3rd ed. (Elsevier, Amsterdam, 2007).
41. R. Erban and S. J. Chapman, Phys. Biol. 6, 046001 (2009). 10.1088/1478-3975/6/4/046001
42. S. Isaacson, SIAM J. Appl. Math. 70, 77 (2009). 10.1137/070705039
43. S. A. Isaacson and D. Isaacson, Phys. Rev. E 80, 066106 (2009). 10.1103/PhysRevE.80.066106
44. P. Sjoberg, O. G. Berg, and J. Elf, e-print arXiv:0905.4629v1 q-bio.QM.
45. Y. Cao, H. Li, and L. Petzold, J. Chem. Phys. 121, 4059 (2004). 10.1063/1.1778376
46. M. A. Gibson and J. Bruck, J. Phys. Chem. A 104, 1876 (2000). 10.1021/jp993732q
47. D. T. Gillespie, Annu Rev. Phys. Chem. 58, 35 (2007). 10.1146/annurev.physchem.58.032806.104637 (Pubitemid 46877584)
48. L. Lok and R. Brent, Nat. Biotechnol. 23, 131 (2005). 10.1038/nbt1054 (Pubitemid 41724639)
49. J. M. McCollum, G. D. Peterson, C. D. Cox, M. L. Simpson, and N. F. Samatova, Comput. Biol. Chem. 30, 39 (2006). 10.1016/j.compbiolchem.2005.10.007 (Pubitemid 43144430)
50. B. Bayati, P. Chatelain, and P. Koumoutsakos, J. Comput. Phys. 228, 5908 (2009). 10.1016/j.jcp.2009.05.004
51. Y. Cao, D. T. Gillespie, and L. R. Petzold, J. Chem. Phys. 124, 044109 (2006). 10.1063/1.2159468 (Pubitemid 43166307)
52. A. Chatterjee, K. Mayawala, J. S. Edwards, and D. G. Vlachos, Bioinformatics 21, 2136 (2005). 10.1093/bioinformatics/bti308 (Pubitemid 40668069)
53. D. T. Gillespie, J. Chem. Phys. 115, 1716 (2001). 10.1063/1.1378322 (Pubitemid 32715518)
54. D. T. Gillespie and L. R. Petzold, J. Chem. Phys. 119, 8229 (2003). 10.1063/1.1613254
55. E. L. Haseltine and J. B. Rawlings, J. Chem. Phys. 117, 6959 (2002). 10.1063/1.1505860 (Pubitemid 35354142)
56. C. V. Rao and A. P. Arkin, J. Chem. Phys. 118, 4999 (2003). 10.1063/1.1545446
57. M. Rathinam and H. El Samad, J. Comput. Phys. 224, 897 (2007). 10.1016/j.jcp.2006.10.034
58. T. Tian and K. Burrage, J. Chem. Phys. 121, 10356 (2004). 10.1063/1.1810475 (Pubitemid 40001577)
59. L. A. Harris and P. Clancy, J. Chem. Phys. 125, 144107 (2006). 10.1063/1.2354085 (Pubitemid 44570773)
60. D. Bernstein, Phys. Rev. E 71, 041103 (2005). 10.1103/PhysRevE.71.041103 (Pubitemid 40629670)
61. S. Engblom, L. Ferm, A. Hellander, and P. Lotstedt, SIAM J. Sci. Comput. (USA) 31, 1774 (2009). 10.1137/080721388
62. D. Rossinelli, B. Bayati, and P. Koumoutsakos, Chem. Phys. Lett. 451, 136 (2008). 10.1016/j.cplett.2007.11.055
63. S. Lampoudi, D. T. Gillespie, and L. R. Petzold, J. Chem. Phys. 130, 094104 (2009). 10.1063/1.3074302
64. J. V. Rodriguez, J. A. Kaandorp, M. Dobrzynski, and J. G. Blom, Bioinformatics 22, 1895 (2006). 10.1093/bioinformatics/btl271 (Pubitemid 44283035)
65. R. F. Oliveira, A. Terrin, G. Di Benedetto, R. C. Cannon, W. Koh, M. Kim, M. Zaccolo, and K. T. Blackwell, PLoS ONE 5, e11725 (2010). 10.1371/journal.pone.0011725
66. Y. Cao, D. T. Gillespie, and L. R. Petzold, J. Chem. Phys. 123, 054104 (2005). 10.1063/1.1992473 (Pubitemid 41203876)
67. P. Hanusse and A. Blanche, J. Chem. Phys. 74, 6148 (1981). 10.1063/1.441005
68. A. B. Stundzia and C. J. Lumsden, J. Comput. Phys. 127, 196 (1996). 10.1006/jcph.1996.0168 (Pubitemid 126168728)
69. K. T. Blackwell, J. Neurosci. Methods 157, 142 (2006). 10.1016/j.jneumeth.2006.04.003 (Pubitemid 44287073)
70. R. Das, V. Esposito, M. Abu-Abed, G. S. Anand, S. S. Taylor, and G. Melacini, Proc. Natl. Acad. Sci. U.S.A. 104, 93 (2007). 10.1073/pnas.0609033103 (Pubitemid 46067990)
71. C. Kim, C. Y. Cheng, S. A. Saldanha, and S. S. Taylor, Cell 130, 1032 (2007). 10.1016/j.cell.2007.07.018 (Pubitemid 47410267)
72. Y. Cao and L. Petzold, J. Comput. Phys. 212, 6 (2006). 10.1016/j.jcp.2005.06.012
73. M. Rathinam, L. R. Petzold, Y. Cao, and D. T. Gillespie, J. Chem. Phys. 119, 12784 (2003). 10.1063/1.1627296
74. P. M. Burrage and K. Burrage, SIAM J. Sci. Comput. (USA) 24, 848 (2003). 10.1137/S1064827500376922
75. D. T. Gillespie, J. Chem. Phys. 113, 297 (2000). 10.1063/1.481811
76. J. Goutsias, J. Chem. Phys. 122, 184102 (2005). 10.1063/1.1889434 (Pubitemid 40682792)
77. E. L. Haseltine and J. B. Rawlings, J. Chem. Phys. 123, 164115 (2005). 10.1063/1.2062048 (Pubitemid 41527637)
78. Y. Cao, D. T. Gillespie, and L. R. Petzold, J. Chem. Phys. 122, 014116 (2005). 10.1063/1.1824902 (Pubitemid 41047759)
79. D. F. Anderson, J. Chem. Phys. 128, 054103 (2008). 10.1063/1.2819665 (Pubitemid 351598437)
80. M. F. Pettigrew and H. Resat, J. Chem. Phys. 126, 084101 (2007). 10.1063/1.2432326 (Pubitemid 46355598)
81. A. Auger, P. Chatelain and P. Koumoutsakos, J. Chem. Phys. 125, 084103 (2006). 10.1063/1.2218339 (Pubitemid 44320037)
82. K. H. Chiam, C. M. Tan, V. Bhargava, and G. Rajagopal, Phys. Rev. E 74, 051910 (2006). 10.1103/PhysRevE.74.051910 (Pubitemid 44770583)
83. K. A. Iyengar, L. A. Harris, and P. Clancy, J. Chem. Phys. 132, 094101 (2010). 10.1063/1.3310808
84. B. N. G. Giepmans, S. R. Adams, M. H. Ellisman and R. Y. Tsien, Science 312, 217 (2006). 10.1126/science.1124618