Modeling ion channel dynamics through reflected stochastic differential equations

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 85, Issue 5, 2012, Pages

  Dangerfield, Ciara E ^a   Kay, David ^a   Burrage, Kevin ^a,b  

^a UNIVERSITY OF OXFORD   (United Kingdom)

^b QUEENSLAND UNIVERSITY OF TECHNOLOGY   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

ACTION POTENTIALS; BIOCHEMICAL REACTION NETWORK; COMPUTATIONALLY EFFICIENT; CONFORMATIONAL CHANGE; DISTRIBUTIONAL PROPERTY; EXCITABLE CELLS; GOLD STANDARDS; ION CHANNEL; MARKOV CHAIN METHOD; MARKOV CHAIN MODELS; MEMBRANE PROTEINS; OPEN CHANNELS; REALISTIC SIMULATION; SINGLE-CELL LEVEL; STOCHASTIC DIFFERENTIAL EQUATIONS; STOCHASTIC EFFECTS; STOCHASTIC METHODS; STOCHASTIC MODELING; STOCHASTIC NATURE;

BIOLOGICAL MEMBRANES; DIFFERENTIAL EQUATIONS; DYNAMICS; IONS; MARKOV PROCESSES; PROTEINS; STOCHASTIC MODELS; STOCHASTIC SYSTEMS;

COMPUTER SIMULATION;

EID: 84861852648     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.85.051907     Document Type: Article

References (64)

1. F. Bezanilla, Physiol. Rev. 80, 555 (2000).
2. B. Hille, Ionic Channels of Excitable Membranes, 3rd ed. (Sinauer Associates, Sunderland, USA, 1991).
3. B. Sakmann and E. Neher, Single-Channel Recording (Plenum, New York, 1995).
4. J. A. White, J. T. Rubinstein, and A. R. Kay, Trends Neurosci. TNSCDR 0166-2236 10.1016/S0166-2236(99)01521-0 23, 131 (2000). (Pubitemid 30110629)
5. E. Pueyo, A. Corrias, L. Virág, N. Jost, T. Szél, A. Varró, N. Szentandrássy, P. P. Nánási, K. Burrage, and B. Rodríguez, Biophys. J. BIOJAU 0006-3495 10.1016/j.bpj.2011.09.060 12, 2892 (2011).
6. M. Lemay, E. de Lange, and J. P. Kucera, J. Theor. Biol. JTBIAP 0022-5193 10.1016/j.jtbi.2011.04.019 281, 84 (2011).
7. G. De Vries and A. Sherman, J. Theor. Biol. JTBIAP 0022-5193 10.1006/jtbi.2000.2193 207, 513 (2000).
8. J. R. Clay and L. J. DeFelice, Biophys. J. BIOJAU 0006-3495 10.1016/S0006-3495(83)84381-1 42, 151 (1983).
9. E. Schneidman, B. Freedman, and I. Segev, Neural Comput. NEUCEB 0899-7667 10.1162/089976698300017089 10, 1679 (1998), URL http://neco.mitpress.org/cgi/ content/abstract/10/7/1679.
10. P. Oosterhoff, A. Oros, and M. A. Vos, Anadolu Kardiyoloji Dergisi 7 (Suppl 1), 73 (2007).
11. M. L. Martins, S. C. Ferreira, and M. J. Vilela, Current Opinion in Colloid & Interface Science COCSFL 1359-0294 10.1016/j.cocis.2009.04.004 15, 18 (2010).
12. J. R. Groff, H. DeRemigio, and G. D. Smith, in Markov Chain Models of Ion Channels and The Collective Gating of Ca2+ Release Sites (Oxford University Press, Oxford, 2010), pp. 29-64.
13. D. T. Gillespie, Physica A PHYADX 0378-4371 10.1016/0378-4371(92)90283-V 188, 404 (1992).
14. N. G. Van Kampen, Stochastic Processes in Physics and Chemistry, 3rd ed. (North Holland, 2007).
15. R. N. Bhattacharya and E. C. Waymire, Stochastic Processes with Applications, 2nd ed. (SIAM, 2009).
16. A. L. Hodgkin and A. F. Huxley, J. Physiol. 117, 500 (1952).
17. T. Austin, Ann. Appl. Probab. 1050-5164 10.1214/07-AAP494 18, 1279 (2008).
18. D. T. Gillespie, Annu. Rev. Phys. Chem. ARPLAP 0066-426X 10.1146/annurev.physchem.58.032806.104637 58, 35 (2007). (Pubitemid 46877584)
19. T. Jahnke and W. Huisinga, J. Math. Biol. JMBLAJ 0303-6812 10.1007/s00285-006-0034-x 54, 1 (2007). (Pubitemid 44951311)
20. S. MacNamara and K. Burrage, Numerical Algorithms NUALEG 1017-1398 10.1007/s11075-008-9239-y 51, 281 (2009).
21. C. Chow and J. White, Biophys. J. BIOJAU 0006-3495 10.1016/S0006-3495(96) 79494-8 71, 3013 (1996).
22. D. T. Gillespie, J. Phys. Chem. JPCHAX 0022-3654 10.1021/j100540a008 81, 2340 (1977).
23. H. Mino, J. T. Rubinstein, and J. A. White, Ann. Biomed. Eng. ABMECF 0090-6964 10.1114/1.1475343 30, 578 (2002). (Pubitemid 34726344)
24. R. Fox, Biophys. J. BIOJAU 0006-3495 10.1016/S0006-3495(97)78850-7 72, 2068 (1997).
25. X. J. Sun, J. Z. Lei, M. Perc, Q. S. Lu, and S. J. Lv, Eur. Phys. J. B EPJBFY 1434-6028 10.1140/epjb/e2010-10031-3 79, 61 (2011).
26. R. F. Fox and Y. N. Lu, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.49.3421 49, 3421 (1994).
27. I. C. Bruce, Ann. Biomed. Eng. ABMECF 0090-6964 10.1007/s10439-009-9635-z 37, 824 (2009).
28. B. Sengupta, S. B. Laughlin, and J. E. Niven, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.81.011918 81, 011918 (2010).
29. J. H. Goldwyn, N. S. Imennov, M. Famulare, and E. Shea-Brown, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.83.041908 83, 041908 (2011).
30. J. H. Goldwyn and E. Shea-Brown, PLoS Comput. Biol. 1553-734X 10.1371/journal.pcbi.1002247 7, e1002247 (2011).
31. C. E. Dangerfield, D. Kay, and K. Burrage, Procedia Computer Science 1877-0509 10.1016/j.procs.2010.04.178 1, 1581 (2010).
32. C. E. Dangerfield, D. Kay, S. MacNamara, and K. Burrage, BIT Numerical Mathematics doi: 10.1007/s10543-011-0351-3 (2011).
33. R. Lord, R. Koekkoek, and D. V. Dijk, Quantitative Finance 1469-7688 10.1080/14697680802392496 10, 177 (2010).
34. D. R. Brillinger, Lecture Notes-Monograph Series 41 (2003).
35. T. Kawamura and Y. Saisho, Stochastic Models 1532-6349 10.1080/15326340600649037 22, 273 (2006).
36. D. Riley, X. Koutsoukos, and K. Riley, Simulation Conference, 2008, WSC pp. 804-812.
37. K. Pakdaman, M. Thieullen, and G. Wainrib, Adv. Appl. Probab. AAPBBD 0001-8678 10.1239/aap/1282924062 42, 761 (2010).
38. I. I. Gihman and A. V. Skorokhod, Stochastic Differential Equations (Springer-Verlag, Berlin, 1972).
39. D. T. Gillespie, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.481811 113, 297 (2000).
40. D. T. Gillespie, J. Phys. Chem. A JPCAFH 1089-5639 10.1021/jp0128832 106, 5063 (2002). (Pubitemid 35289985)
41. P. E. Kloeden and E. Platen, Numerical Solution of Stochastic Differential Equations, corrected ed. (Springer, Berlin, 2011).
42. J. C. Cox, J. E. Ingersoll, and S. A. Ross, Econometrica 0012-9682 10.2307/1911242 53, 385 (1985).
43. W. Feller, The Annals of Mathematics ANMAAH 0003-486X 10.2307/1969318 54, 173 (1951).
44. C. Bayer, A. Szepessy, and R. Tempone, Monte Carlo Methods and Applications 0929-9629 10.1515/mcma.2010.001 16, 1 (2010).
45. M. Bossy, E. Gobet, and D. Talay, J. Appl. Probab. JPRBAM 0021-9002 10.1239/jap/1091543431 41, 877 (2004). (Pubitemid 39620520)
46. A. V. Skorokhod, Theory Probab. Appl. TPRBAU 0040-585X 10.1137/1106035 6, 264 (1961).
47. A. V. Skorokhod, Theory Probab. Appl. TPRBAU 0040-585X 10.1137/1107002 7, 3 (1962).
48. Y. Rudy and J. R. Silva, Q. Rev. Biophys. QURBAW 0033-5835 10.1017/S0033583506004227 39, 57 (2006). (Pubitemid 44566374)
49. B. Mélykúti, K. Burrage, and K. C. Zygalakis, J. Chem. Phys. 0021-9606 10.1063/1.3380661 132, 164109 (2010).
50. R. Pettersson, Stochastic Processes and their Applications STOPB7 0304-4149 10.1016/0304-4149(95)00040-E 59, 295 (1995).
51. S. Wantanebe, J. Math. Kyoto Univ. 11, 169 (1971).
52. H. Tanaka, Hiroshima Math. J. 9, 162 (1979).
53. P. L. Lions and A. S. Sznitman, Commun. Pure Appl. Math. 0010-3640 10.1002/cpa.3160370408 37, 511 (1984).
54. Y. Liu, Mathematics and Computers in Simulation MCSIDR 0378-4754 10.1016/0378-4754(93)E0072-D 38, 103 (1995).
55. R. Pettersson, Bernoulli 1350-7265 10.2307/3318456 3, 403 (1997).
56. D. Ding, Comput. Math. Appl. CMAPDK 0898-1221 10.1016/j.camwa.2007.08.043 55, 2413 (2008). (Pubitemid 351508387)
57. L. Slominski, Stochastic Processes and their Applications STOPB7 0304-4149 10.1016/0304-4149(94)90118-X 50, 197 (1994).
58. D. Lépingle, Mathematics and Computers in Simulation MCSIDR 0378-4754 10.1016/0378-4754(93)E0074-F 38, 119 (1995).
59. Y. Chen and X. Ye, e-print arXiv: 1101.6081.
60. P. L. Combettes and V. R. Wajs, Multiscale Modeling Simulation 1540-3459 10.1137/050626090 4, 1168 (2005). (Pubitemid 44932287)
61. A. A. Verveen and H. E. Derksen, Proc. IEEE IEEPAD 0018-9219 10.1109/PROC.1968.6443 56, 906 (1968).
62. I. C. Bruce, Ann. Biomed. Eng. ABMECF 0090-6964 10.1007/s10439-006-9174-9 35, 315 (2007). (Pubitemid 46122186)
63. J. Rubinstein, Biophys. J. BIOJAU 0006-3495 10.1016/S0006-3495(95)80252-3 68, 779 (1995).
64. D. Higham, IMA J. Appl. Math. IJAMDM 0272-4960 10.1093/imamat/hxr016 76, 449 (2011).