Using fractals and nonlinear dynamics to determine the physical properties of ion channel proteins

Critical Reviews in Neurobiology

Volumn 10, Issue 2, 1996, Pages 169-187

  Liebovitch, Larry S ^a   Todorov, Angelo T ^a  

^a FLORIDA ATLANTIC UNIVERSITY   (United States)

Author keywords

Fractals; Ion channels; Nonlinear dynamics; Rescaled range analysis; Whole cell recording

Indexed keywords

ION CHANNEL;

ELECTRIC POTENTIAL; ION CURRENT; MODEL; NONLINEAR SYSTEM; PATCH CLAMP; PHYSICAL CHEMISTRY; PROTEIN ANALYSIS; PROTEIN CONFORMATION; REVIEW;

EID: 0030467115     PISSN: 08920915     EISSN: None     Source Type: Journal    
DOI: 10.1615/critrevneurobiol.v10.i2.20     Document Type: Review

References (53)

1. Bassingthwaighte, J. B., Liebovitch, L. S., and West, B. J., Fractal Physiology, Oxford University Press, New York, 1994.
2. Feder, J., Fractals, Plenum, New York, 1988.
3. Mandelbrot, B. B., The Fractal Geometry of Nature, W. H. Freeman and Company, New York, 1983.
4. Peters, E. E., Chaos and Order in the Capital Markets, John Wiley & Sons, New York, 1991.
5. Gleick, J., Chaos: Making a New Science, Viking, New York, 1987.
6. Hille, B., Ionic Channels of Excitable Membranes, Sinauer Associates, Sunderland, MA, 1984.
7. Sakmann, B. and Neher, E., Eds., Single-Channel Recording, Plenum, New York, 1983.
8. Liebovitch, L. S., Fischbarg, J., and Koniarek, J., Ion channel kinetics: a model based on fractal scaling rather than multistate Markov processes, Math. Biosci., 84, 37, 1987.
9. Catterall, W. A., Structure and function of voltage-sensitive ion channels, Science, 242, 50, 1988.
10. Miller, C., Annus mirabilis of potassium channels, Science, 252, 1092, 1990.
11. Karplus, M. and Petsko, G. A., Molecular dynamics simulations in biology, Nature, 347, 631, 1990.
12. McCammon, J. A. and Harvey, S. C., Dynamics of Proteins and Nucleic Acids, Cambridge University Press, New York, 1987.
13. Elber, R. and Karplus, M., Multiple conformational states of proteins: a molecular dynamics analysis of myoglobin, Science, 235, 318, 1987.
14. Karplus, M. and McCammon, J. A., Dynamics of proteins: elements and function, Ann. Rev. Biochem., 52, 263, 1983.
15. Austin, R. H., Beeson, K. W., Eisenstein, L., Frauenfelder, H., and Gunsalus, I. C., Dynamics of ligand binding to myoglobin, Biochem., 14, 5355, 1975.
16. Liebovitch, L. S. and Tóth, T. I., Distributions of activation energy barriers that produce stretched exponential probability distributions for the time spent in each state of the two state reaction A ⇔ B, Bull. Math. Biol., 53, 443, 1991.
17. Saviotti, M. L. and Galley, W. C., Room temperature phosphorescence and the dynamic aspects of protein structure, Proc. Natl. Acad. Sci. U.S.A., 71, 4154, 1974.
18. Alcala, J. R., Gratton, E., and Prendergast, F. G., Interpretation of fluorescence decays in proteins using continuous lifetime distributions, Biophys. J., 51, 925, 1987.
19. Welch, G. R., Ed., The Fluctuating Enzyme, John Wiley & Sons, New York, 1986.
20. Englander, S. W., Englander, J. J., McKinnie, R. E., Ackers, G. K., Turner, G. J., Westrick, J. A., and Gill, S. J., Hydrogen exchange measurement of the free energy of structural and allosteric change in hemoglobin, Science, 256, 1684, 1992.
21. Frauenfelder, H., Parak, F., and Young, R. D., Conformational substates in proteins, Ann. Rev. Biophys. Biochem., 17, 451, 1988.
22. Ringe, D. and Petsko, G. A., Mapping protein dynamics by X-ray diffraction, Prog. Biophys. Molec. Biol., 45, 197, 1984.
23. Gurd, F. R. N. and Rothgeb, T. M., Motions in proteins, Adv. Protein Chem., 33, 73, 1979.
24. Jorgensen, W. L., Rusting of the lock and key model for protein-ligand binding, Science, 254, 954, 1991.
25. Rini, J. M., Schulze-Gahmen, U., and Wilson, I. A., Structural evidence for induced fit as a mechanism for antibody-antigen recognition, Science, 255, 959, 1992.
26. Beece, D. Eisenstein, L., Frauenfelder, H., Good, D., Marden, M. C., Reinisch, L., Reynolds, A. H., Sorensen, L. B., and Yue, K. T., Solvent viscosity and protein dynamics. Biochem., 19, 5147, 1980.
27. Weber, G., Energetics of ligand binding to proteins, Adv. Protein Chem., 29, 1, 1975.
28. Sansom, M. S. P., Ball, F. G., Kerry, C. J., McGee, R., Ramsey, R. L., and Usherwood, P. N. R., Markov, fractal, diffusion, and related models of ion channel gating. Biophys. J., 56, 1229, 1989.
29. McManus, O. B., Spivak, C. E., Blatz, A. L., Weiss, D. S., and Magelby, K. L., Fractal models, Markov models, and channel kinetics, Biophys. J., 55, 383, 1989.
30. Blatz, A. L. and Magleby, K. L., Quantitative description of three modes of activity of fast chloride channels from rat skeletal muscle, J. Physiol. (Lond.), 378, 141, 1986.
31. + channel in NG108-15 neuroblastoma x glioma cells: gating kinetics and the effects of enrichment of membrane phospholipids with arachidonic acid, J. Memb. Biol., 102, 21, 1988.
32. Liebovitch, L. S., Single channels: from Markovian to fractal models, in Cardiac Electrophysiology: From Cell to Bedside, Zipes, D. P. and Jalife, J., Eds., W. B. Saunders, Philadelphia, 1994.
33. Tian, W. D., Sage, J. T., Srajer, V., and Champion, P. M., Relaxation dynamics of myoglobin in solution, Phys. Rev. Lett., 68, 408, 1992.
34. Liebovitch, L. S. and Sullivan, J. M., Fractal analysis of a voltage-dependent potassium channel from cultured mouse hippocampal neurons. Biophys. J., 52, 979, 1987.
35. Korn, S. J. and Horn, R., Statistical discrimination of fractal and Markov models of single-channel gating, Biophys. J., 54, 871, 1988.
36. Horn, R. and Korn, S. J., Model selection: reliability and bias. Biophys. J., 55, 379, 1989.
37. McManus, O. B., Weiss, D. S., Spivak, C. E., Blatz, A. L., and Magleby, K. L., Fractal models are inadequate for the kinetics of four different ion channels, Biophys. J., 54, 859, 1988.
38. Liebovitch, L. S., Testing fractal and Markov models of ion channel kinetics, Biophys. J., 55, 373, 1989.
39. Liebovitch, L. S. and Tóth, T. I., The Akaike Information Criterion (AIC) is not a sufficient condition to determine the number of ion channel states from single channel recordings, Synapse, 5, 134, 1990.
40. Liebovitch, L. S. and Tóth, T. I., A model of ion channel kinetics using deterministic chaotic rather than stochastic processes, J. Theoret. Biol., 148, 243, 1991.
41. Liebovitch, L. S. and Czegledy, F. P., A model of ion channel kinetics based on deterministic motion in a potential with two local minima, Ann. Biomed. Eng., 20, 517, 1992.
42. Billah, K. Y. and Scanlan, R. H., Tacoma Narrows bridge failure and undergraduate physics textbook, Am. J. Phys., 59, 118, 1991.
43. Feller, W., An Introduction to Probability Theory and Its Applications, Vol 2, 2nd ed., John Wiley & Sons, New York, 1971.
44. Churilla, A. M., Gottschalk, W. A., Liebovitch, L. S., Selector, L. Y., Todorov, A. T., and Yeandle. S., Membrane potential fluctuations of human T-lymphocytes have fractal characteristics of fractional Brownian motion, Ann. Biomed. Eng., 24, 99, 1996.
45. Peng, C.-K., Buldyrev, S. V., Goldberger, A. L., Havlin, S., Simons, M., and Stanley, H. E., Finite-size effects on long-range correlations: implications for analyzing DNA sequences, Phys. Rev., E47, 3730, 1993.
46. Peng, C.-K., Mietus, J., Hausdorff, J. M., Havlin, S., Stanley, H. E., and Goldberger, A. L., Long-range anticorrelations and non-Gaussian behavior of the heartbeat, Phys. Rev. Lett., 70, 1343, 1993.
47. Schepers, H. E., van Beek, J. H. G. M., and Bassingthwaighte, J. B., Four methods to estimate the fractal dimension from self-affine signals, IEEE Eng. Med. Biol. Mag., 11(2), 57, 1992.
48. Teich, M. C., Fractal neuronal firing patterns, in Single Neuron Computation, McKenna, T., Davis, J., and Zornetzer, S., Eds., Academic Press, Boston, 1992, 589.
49. Nogueira, R. A., Varanda, W. A., and Liebovitch, L. S., Hurst analysis in the study of ion channel kinetics, Brazilian J. Med. Biol. Res., 28, 491, 1995.
50. Flandrin, P., On the spectrum of fractional Brownian motions, IEEE Trans. Infor. Theor., 35, 197, 1988.
51. Lowen, S. B. and Teich, M. C., Fractal auditory nerve firing patterns may derive from fractal switching in sensory hair-cell ion channels, in Noise in Physical Systems and 1/f Fluctuations (AIP Conf. Proc. 285), Handel, P. H. and Chung, A. L., Eds., Amer. Inst. Phys, New York, 1993.
52. Lowen, S. B. and Teich, M. C., Fractal renewal processes, IEEE Trans. Info. Theory, 39, 1669, 1993.
53. Roncaglia, R., Mannell, R., and Grigolini, P., Fractal properties of ionic channels and diffusion, Math. Biosci., 123, 77, 1994.