Deterministic Model of Ion Channel Flipping with Fractal Scaling of Kinetic Rates

Annals of Biomedical Engineering

Volumn 27, Issue 5, 1999, Pages 682-695

  Cavalcanti, Silvio ^a   Fontanazzi, Francesco ^a  

^a NONE

Author keywords

Channel gating; Chaos; Complex dynamics; Fractal; Ion channel

Indexed keywords

ION CHANNEL;

ARTICLE; BIOLOGICAL MODEL; CHANNEL GATING; ELECTRIC CONDUCTIVITY; FRACTAL ANALYSIS; KINETICS; METABOLISM; NONLINEAR SYSTEM; PATCH CLAMP; PHYSIOLOGY; PROBABILITY; PROTEIN CONFORMATION;

ELECTRIC CONDUCTIVITY; FRACTALS; ION CHANNEL GATING; ION CHANNELS; KINETICS; MARKOV CHAINS; MODELS, BIOLOGICAL; NONLINEAR DYNAMICS; PATCH-CLAMP TECHNIQUES; PROTEIN CONFORMATION;

EID: 0033197272     PISSN: 00906964     EISSN: None     Source Type: Journal    
DOI: 10.1114/1.212     Document Type: Article

References (47)

1. Armstrong, C. M., and F. Bezanilla. Currents related to movement of the gating particles of the sodium channels. Nature (London) 242:459-461, 1973.
2. Austin, R. H., K. W. Beeson, L. Eisenstein, H. Frauenfelder, and I. C. Gunsalus. Dynamics of ligand binding to myoglobin. Biochemistry 14:5355-5373, 1975.
3. Bassingthwaighte, J. B., L. S. Liebovitch, and B. J. West. Fractal Physiology. New York: Oxford University Press, 1994.
4. Blatz, A. L., Properties of single fast chloride channels from rat cerebral cortex neurons. J. Physiol. (London) 441:1-21, 1991.
5. Braxenthaler, M., R. Unger, D. Auerbach, J. A. Given, and J. Moult. Chaos in protein dynamics. Proteins: Struct., Funct., Genet. 29:417-425, 1997.
6. Chinarov, V. A., Y. B. Gaididei, V. N. Kharkyanen, and S. P. Sit'ko. Ion pores in biological membranes as self-organized bistable systems. Phys. Rev. A 46:5232-5241, 1992.
7. Cole, K. S., and J. W. Moore. Potassium ion current in the squid giant axon: Dynamic characteristic. Biophys. J. 1:1-14, 1960.
8. Colquhoun, D., and A. G. Hawkes. Relaxation and fluctuations of membrane currents that flow through drug-operated channels. Proc. R. Soc. London, Ser. B 199:231-262, 1977.
9. Croxton, T. L. A model of the gating of ion channels. Biochim. Biophys. Acta 946:19-24, 1988.
10. Dempster, J. Computer Analysis of Electrophysiological Signals. London: Hacourt Brace Jovanovich, 1993.
11. Edmonds, D. T. A physical model of sodium channel gating. Eur. Biophys. J. 14:195-201, 1987.
12. Frauenfelder, H., F. Parak, and R. D. Young. Conformational substrates in proteins. Annu. Rev. Biophys. Biophys. Chem. 17:451-479, 1988.
13. Fulinski, A., Z. Grzywna, I. Mellor, Z. Siwy, and P. N. R. Usherwood. Non-Markovian character of ionic current fluctuations in membrane channels. Phys. Rev. E 58:919-924, 1998.
14. Gibb, A. J., and D. Colquhoun. Activation of N-methyl-D-aspartate receptors by L-glutamate in cells dissociated from adult rat hippocampus. J. Physiol. (London) 456:143-179, 1992.
15. Glass, L., P. Hunter, and M. C. MacKey. From Clocks to Chaos: the Rhythm of Life. Princeton, NJ: Princeton University Press, 1988.
16. Hille, B. Ionic Channels of Excitable Membrane. Sunderland, MA: Sinauer, 1992.
17. Horn, R. Statistical methods for model discrimination. Applications to gating kinetics and permeation of the acetylcholine receptor channel. Biophys. J. 51:255-263, 1987.
18. Horn, R., and K. Lange. Estimating kinetic constants from single channel data. Biophys. J. 43:207-223, 1983.
19. Hoshi, T., W. N. Zagotta, and R. W. Aldrich. Shaker potassium channel gating. I: Transitions near the open state. J. Gen. Physiol. 103:249-278, 1994.
20. Jackson, M. B. Inversion of Markov processes to determine rate constants from single-channel data. Biophys. J. 73:1382-1394, 1997.
21. Karplus, M., and J. A. McCammon. The internal dynamics of globular proteins. CRC Crit. Rev. Biochem. 9:293-349, 1981.
22. Keynes, R. D., and J. E. Kimura. Kinetics of the sodium conductance in the squid giant axon. J. Physiol. (London) 336:621-634, 1983.
23. Keynes, R. D., and E. Rojas. The temporal and steady-state relationships between activation of the sodium conductance and movement of the gating particles in the squid giant axon. J. Physiol. (London) 255:157-189, 1976.
24. Kuznetosv, Y. A. Elements of Applied Bifucation Theory. New York: Springer, 1995.
25. Lauger, P. Internal motions in proteins and gating kinetics of ionic channels. Biophys. J. 53:877-884, 1988.
26. Liebovitch, L. S., J. Fischbarg, J. P. Koniarek, I. Todorova, and M. Wang. Fractal model of ion-channel kinetics. Biochim. Biophys. Acta 896:173-180, 1987.
27. Liebovitch, L. S. Analysis of fractal ion channel gating kinetics: Kinetic rates, energy levels, and activation energies. Math. Biosci. 93:97-115, 1989.
28. Liebovitch, L. S., and F. P. Czegledy. A model of ion channel kinetics based on deterministic, chaotic motion in a potential with two local minima. Ann. Biomed. Eng. 20:517-531, 1992.
29. Liebovitch, L. S., J. Fischbarg, and J. P. Koniarek. Ion channel kinetics: A model based on fractal scaling rather than multistate Markov processes. Math. Biosci. 84:37-68, 1987.
30. Liebovitch, L. S., and T. I. Toth. A model of ion channel kinetics using deterministic chaotic rather than stochastic processes. J. Theor. Biol. 148:243-267, 1991.
31. McCammon, J. A., and S. C. Harvey. Dynamics of Proteins and Nucleic Acids. New York: Cambridge University Press, 1987.
32. McManus, O. B., D. S. Weiss, C. E. Spivak, A. L. Blatz, and K. L. Magleby. Fractal models are inadequate for the kinetics of four different ion channels. Biophys. J. 54:859-870, 1988.
33. Millhauser, D. L., E. E. Salpeter, and R. E. Oswald. Diffusion models of ion channel gating and the origin of power-law distributions from single channel recording. Proc. Natl. Acad. Sci. USA 85:1503-1507, 1988.
34. Neher, E., and B. Sakmann. Single-Channel Recording. New York: Plenum, 1983.
35. Oswald, R. E., G. L. Millhauser, and A. A. Carter. Diffusion model in ion channel gating. Extension to agonist-activated ion channels. Biophys. J. 59:1136-1142, 1991.
36. Petracchi, D., M. Barbi, M. Pellegrini, M. Pellegrino, and A. Simoni. Use of conditioned distributions in the analysis of ion channel recordings. Eur. Biophys. J. 20:31-39, 1991.
37. Pietronero, L., and E. Tosatti. Fractals in Physics. Amsterdam, The Netherlands: North-Holland Physics, 1986.
38. Ring, A. Brief closures of gramicidin A channels in lipid bilayer membranes. Biochim. Biophys. Acta 856:646-653, 1986.
39. Sansom, M. S., F. G. Ball, C. J. Kerry, R. McGee, R. L. Ramsey, and P. N. Usherwood. Markov, fractal, diffusion, and related models of ion channel gating. A comparison with experimental data from two ion channels. Biophys. J. 56:1229-1243, 1989.
40. Schoppa, N. E., and F. J. Sigworth. Activation of shaker potassium channels. I. Characterization of voltage-dependent transitions. J. Gen. Physiol. 111:271-294, 1998.
41. Schoppa, N. E., and F. J. Sigworth. Activation of Shaker potassium channels. II. Kinetics of the V2 mutant channel. J. Gen. Physiol. 111:295-311, 1998.
42. Schoppa, N. E., and F. J. Sigworth. Activation of Shaker potassium channels. III. An activation gating model for wildtype and V2 mutant channels. J. Gen. Physiol. 111:313-342, 1998.
43. Sigworth, F. J., and S. M. Sine. Data transformations for improved display and fitting of single-channel dwell time histograms. Biophys. J. 52:1047-1054, 1987.
44. Vandenberg, C. A., and F. Bezanilla. A sodium channel gating model based on single channel, macroscopic ionic, and gating currents in the squid giant axon. Biophys. J. 60:1511-1533, 1991.
45. Zagotta, W. N., T. Hoshi, and R. W. Aldrich. Shaker potassium channel gating. III: Evaluation of kinetic models for activation. J. Gen. Physiol. 103:321-362, 1994.
46. Zagotta, W. N., T. Hoshi, J. Dittman, and R. W. Aldrich. Shaker potassium channel gating. II: Transitions in the activation pathway. J. Gen. Physiol. 103:279-319, 1994.
47. Zizi, M., C. Byrd, R. Boxus, and M. Colombini. The voltage-gating process of the voltage-dependent anion channel is sensitive to ion flow. Biophys. J. 75:704-713, 1998.