Fractional diffusion modeling of ion channel gating

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

Volumn 70, Issue 5, 2004, Pages 9-

  Goychuk, Igor ^a   Hänggi, Peter ^a  

^a UNIVERSITY OF AUGSBURG   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; DIFFUSION; IONS; MARKOV PROCESSES; PHYSIOLOGY; POTASSIUM;

CONFORMATIONAL DIFFUSION; ION CHANNEL GATING; MEMBRANE PROTEINS; RESIDENCE TIME DISTRIBUTION (RTD);

PROTEINS;

ION CHANNEL; POTASSIUM; POTASSIUM CHANNEL;

ANIMAL; ARTICLE; BIOLOGICAL MODEL; CELL MEMBRANE; CELL MEMBRANE POTENTIAL; CHANNEL GATING; CHEMICAL MODEL; CHEMISTRY; COMPARATIVE STUDY; COMPUTER SIMULATION; DIFFUSION; EVALUATION; GRASSHOPPER; HUMAN; METABOLISM; PHYSIOLOGY; STATISTICAL MODEL; VALIDATION STUDY;

ANIMALS; CELL MEMBRANE; COMPUTER SIMULATION; DIFFUSION; GRASSHOPPERS; HUMANS; ION CHANNEL GATING; ION CHANNELS; MEMBRANE POTENTIALS; MODELS, BIOLOGICAL; MODELS, CHEMICAL; MODELS, STATISTICAL; POTASSIUM; POTASSIUM CHANNELS;

EID: 41349096645     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.70.051915     Document Type: Article

References (75)

1. B. Hille, Ionic Channels of Excitable Membranes, 3rd ed. (Sinauer Associates, Sunderland, 2001).
2. Single-Channel Recording, 2nd ed., edited by B. Sakmann and N. Neher (Plenum, New York, 1995).
3. D. Colquhoun and A. G. Hawkes, Philos. Trans. R. Soc. London, Ser. BPTRBAE0962-8436 300, 1 (1982).10.1098/rstb.1982.0156
4. F. Bezanilla, E. Perozo, and E. Stefani, Biophys. J.BIOJAU0006-3495 66, 1011 (1994).10.1016/S0006-3495(94)80882-3
5. B. M. Rodriguez, D. Sigg, and F. Bezanilla, J. Gen. Physiol.JGPLAD0022-129510.1085/jgp.112.2.223 112, 223 (1998).
6. L. S. Liebovitch and J. M. Sullivan, Biophys. J.BIOJAU0006-3495 52, 979 (1987);10.1016/S0006-3495(87)83290-3
7. L. S. Liebovitch, J. Fishbarg, and J. P. Koniarek, Math. Biosci.MABIAR0025-556410.1016/0025-5564(87)90042-3 84, 37 (1987).
8. G. L. Millhauser, E. E. Salpeter, and R. E. Oswald, Proc. Natl. Acad. Sci. U.S.A.PNASA60027-8424 85, 1503 (1988).10.1073/pnas.85.5.1503
9. M. S. P. Sansom, F. G. Ball, C. J. Kerry, R. McGee, R. L. Ramsey, and P. N. R. Usherwood, Biophys. J.BIOJAU0006-3495 56, 1229 (1989).10.1016/S0006-3495(89)82770-5
10. C. A. Condat and J. Jäckle, Biophys. J.BIOJAU0006-3495 55, 915 (1989).10.1016/S0006-3495(89)82890-5
11. W. Nadler and D. L. Stein, Proc. Natl. Acad. Sci. U.S.A.PNASA60027-8424 88, 6750 (1991).10.1073/pnas.88.15.6750
12. I. Goychuk and P. Hänggi, Proc. Natl. Acad. Sci. U.S.A.PNASA60027-842410.1073/pnas.052015699, 99, 3552 (2002).
13. I. Goychuk and P. Hänggi, Physica APHYADX0378-437110.1016/S0378-4371(03)00177-8 325, 9 (2003).
14. P. Läuger, Biophys. J.BIOJAU0006-3495 53, 877 (1988).10.1016/S0006-3495(88)83168-0
15. D. G. Levitt, Biophys. J.BIOJAU0006-3495 55, 489 (1989).10.1016/S0006-3495(89)82842-5
16. R. Shirokov, G. Ferreira, J. Yi, and E. Rios, J. Gen. Physiol.JGPLAD0022-129510.1085/jgp.111.6.807 111, 807 (1998).
17. D. Sigg, H. Qian, and F. Bezanilla, Biophys. J.BIOJAU0006-3495 76, 782 (1999).10.1016/S0006-3495(99)77243-7
18. A. Ring, Biochim. Biophys. ActaBBACAQ0006-3002 856, 646 (1986).10.1016/0005-2736(86)90160-4
19. E. Gorczynska, P. L. Huddie, B. A. Miller, I. R. Mellor, H. Vais, R. K. Ramsey, and P. N. R. Usherwood, Pfluegers Arch.PFLABK0031-676810.1007/s004240050175 432, 597 (1996).
20. S. Mercik and K. Weron, Phys. Rev. EPLEEE81063-651X10.1103/PhysRevE.63.051910 63, 051910 (2001).
21. H. Frauenfelder, S. G. Sligar, and P. G. Wolynes, ScienceSCIEAS0036-8075 254, 1598 (1991).10.1126/science.1749933
22. H. Frauenfelder and B. H. McMahon, Ann. Phys. (Leipzig)ANPYA20003-380410.1002/1521-3889(200010)9:9/10<655::AID-ANDP655>3.0.CO;2-Z 9, 655 (2000).
23. F. G. Parak and G. U. Nienhaus, ChemPhysChemCPCHFT1439-423510.1002/1439-7641(20020315)3:3<249::AID-CPHC249>3.0.CO;2-A 3, 249 (2002).
24. E. W. Montroll and G. H. Weiss, J. Math. Phys.JMAPAQ0022-248810.1063/1.1704269 6, 167 (1965).
25. M. Lax and H. Scher, Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.39.781 39, 781 (1977).
26. B. D. Hughes, Random Walks and Random Environments, Volume 1: Random Walks (Clarendon Press, Oxford, 1995).
27. M. F. Shlesinger, Random Processes, in Encyclopedia of Applied Physics Vol. 16 (VCH, New York, 1996), pp. 45–70.
28. G. H. Weiss, Aspects and Applications of the Random Walk (North-Holland, Amsterdam, 1994).
29. V. M. Kenkre, E. W. Montroll, and M. F. Shlesinger, J. Stat. Phys.JSTPBS0022-4715 9, 45 (1973).10.1007/BF01016796
30. G. H. Weiss and R. J. Rubin, Adv. Chem. Phys.ADCPAA0065-2385 52, 363 (1983).
31. A. I. Burshtein, A. A. Zharikov, and S.I. Temkin, Theor. Math. Phys.TMPHAH0040-5779 66, 166 (1986).10.1007/BF01017769
32. See also, where the GME of Ref. and its generalization by Burshtein, Zharikov, and Temkin (used here) are reproduced from the most general GME of CTRW with uncorrelated jumps, see Eq. (A8) in.
33. I. Goychuk, Phys. Rev. EPLEEE81063-651X10.1103/PhysRevE.70.016109 70, 016109 (2004).
34. N. G. van Kampen, Stochastic Processes in Physics and Chemistry, revised and enlarged edition (North-Holland, Amsterdam, 1992);
35. P. Hänggi and H. Thomas, Phys. Rep.PRPLCM0370-157310.1016/0370-1573(82)90045-X88, 207 (1982).
36. N. W. Goel and N. Richter-Dyn, Stochastic Models in Biology (Academic Press, New York, 1974).
37. K. Cole and R. Cole, J. Chem. Phys.JCPSA60021-960610.1063/1.1750906 9, 341 (1941).
38. R. Hilfer, J. Non-Cryst. SolidsJNCSBJ0022-309310.1016/S0022-3093(02)01088-8 305, 122 (2002).
39. I. Y. Wong, M. L. Gardel, D. R. Reichman, E. R. Weeks, M. T. Valentine, A. R. Bausch, and D. A. Weitz, Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.92.178101 92, 178101 (2004).
40. I. M. Tolić-Nørrelykke, E.-L. Munteanu, G. Thon, L. Oddershede, and K. Berg-Sørensen, Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.93.078102 93, 078102 (2004).
41. G. Seisenberger, M. U. Ried, T. Endreß, H. Büning, M. Hallek, and C. Bräuchle, ScienceSCIEAS0036-807510.1126/science.1064103 294, 1929 (2001);
42. C. Bräuchle, G. Seisenberger, Thomas Endreß, M. U. Ried, H. Büning, and M. Hallek, ChemPhysChemCPCHFT1439-4235 3, 299 (2002).10.1002/1439-7641(20020315)3:3<299::AID-CPHC299>3.0.CO;2-R
43. D. R. Cox, Renewal Theory (Methuen, London, 1962).
44. R. Gorenflo and F. Mainardi, in Fractals and Fractional Calculus in Continuum Mechanics, edited by A. Carpinteri and F. Mainardi (Springer, Vienna, 1997), pp. 223–276.
45. R. Metzler and J. Klafter, Phys. Rep.PRPLCM0370-157310.1016/S0370-1573(00)00070-3 339, 1 (2000).
46. I. M. Sokolov, J. Klafter, and A. Blumen, Phys. TodayPHTOAD0031-9228 55(11), 48 (2002).10.1063/1.1535007
47. I. M. Sokolov and R. Metzler, Phys. Rev. EPLEEE81063-651X10.1103/PhysRevE.67.010101 67, 010101 (2003).
48. A. A. Stanislavsky, Phys. Rev. EPLEEE81063-651X10.1103/PhysRevE.67.021111 67, 021111 (2003).
49. Fractional Calculus in Physics, edited by R. Hilfer (World Scientific, Singapore, 2000).
50. R. Metzler, E. Barkai, and J. Klafter, Europhys. Lett.EULEEJ0295-5075 46, 431 (1999);10.1209/epl/i1999-00279-7
51. E. Barkai, R. Metzler and J. Klafter, Phys. Rev. EPLEEE81063-651X10.1103/PhysRevE.61.132 61, 132 (2000).
52. R. Hilfer and L. Anton, Phys. Rev. EPLEEE81063-651X10.1103/PhysRevE.51.R848 51, R848 (1995).
53. C. Van den Broeck and P. Hänggi, Phys. Rev. APLRAAN1050-294710.1103/PhysRevA.30.2730 30, 2730 (1984).
54. V. Balakrishnan, C. Van den Broeck, and P. Hänggi, Phys. Rev. APLRAAN1050-294710.1103/PhysRevA.38.4213 38, 4213 (1988).
55. P. Hänggi, P. Talkner, and M. Borkovec, Rev. Mod. Phys.RMPHAT0034-686110.1103/RevModPhys.62.251 62, 251 (1990);
56. P. Hänggi, J. Stat. Phys.JSTPBS0022-4715 42, 105 (1986);10.1007/BF01010843
57. P. Hänggi, J. Stat. Phys.JSTPBS0022-471544, 1003(E) (1986).10.1007/BF01011919
58. A. L. Hodgkin and A. F. Huxley, J. Physiol. (London)JPHYA70022-3751 117, 500 (1952).
59. N. G. van Kampen, Physica APHYADX0378-437110.1016/0378-4371(79)90005-0 96, 435 (1979).
60. A. Toib, V. Lyakhov, and S. Marom, J. Neurosci.JNRSDS0270-6474 18, 1893 (1998).
61. M. A. Lavrentiev and B. V. Shabat, The Methods of Theory of Functions of Complex Variable, 5th ed. (Nauka, Moscow, 1987) (in Russian), theorem on p. 491.
62. R. L. Stratonovich, Topics in the Theory of Random Noise (Gordon and Breach, New York, 1963), Vol. 1, p. 176.
63. I. Goychuk and P. Hänggi, Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.91.070601 91, 070601 (2003);
64. I. Goychuk and P. Hänggi, Phys. Rev. EPLEEE81063-651X10.1103/PhysRevE.69.021104 69, 021104 (2004).
65. G. Doetsch, Theorie und Anwendungen der Laplace-Transformation (Dover, New York, 1943).
66. S. B. Lowen and M. C. Teich, Phys. Rev. EPLEEE81063-651X10.1103/PhysRevE.47.992 47, 992 (1993).
67. H. Stehfest, Commun. ACMCACMA20001-078210.1145/361953.361969 13, 47 (1970);
68. H. Stehfest, Commun. ACMCACMA20001-078210.1145/355598.36278713, 624 (1970);
69. P.P. Valko and S. Vajda, Inverse Probl. Eng.IPENEK1068-2767 10, 467 (2002).10.1080/10682760290004294
70. Z. Siwy and A. Fulinski, Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.89.158101 89, 158101 (2002).
71. R. E. Oswald, G. L. Millhauser, and A. A. Carter, Biophys. J.BIOJAU0006-3495 59, 1136 (1991).10.1016/S0006-3495(91)82328-1
72. S. M. Bezrukov and M. Winterhalter, Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.85.202 85, 202 (2000);
73. S. M. Bezrukov, Fluct. Noise Lett.0219-4775 4, L23 (2004).10.1142/S0219477504001641
74. B. J. West and W. Deering, Phys. Rep.PRPLCM0370-157310.1016/0370-1573(94)00055-7 246, 1 (1994).
75. A. Fulinski, Z. Grzywna, I. Mellor, Z. Siwy, and P. N. R. Usherwood, Phys. Rev. EPLEEE81063-651X10.1103/PhysRevE.58.919 58, 919 (1998).