Fractal ion-channel behavior generates fractal firing patterns in neuronal models

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

Volumn 59, Issue 5, 1999, Pages 5970-5980

  Lowen, Steven B ^a   Liebovitch, Larry S ^b   White, John A ^a  

^a Boston University   (United States)

^b FLORIDA ATLANTIC UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ION CHANNEL;

ACTION POTENTIAL; BIOLOGICAL MODEL; BIOPHYSICS; CHANNEL GATING; FRACTAL ANALYSIS; NERVE CELL; PHYSIOLOGY; PROBABILITY;

ACTION POTENTIALS; BIOPHYSICAL PHENOMENA; BIOPHYSICS; FRACTALS; ION CHANNEL GATING; ION CHANNELS; MARKOV CHAINS; MODELS, NEUROLOGICAL; NEURONS;

EID: 0033134427     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.59.5970     Document Type: Article

References (49)

1. A. L. Hodgkin and A. F. Huxley, J. Physiol. (London) 117, 500 (1952).
2. B. Hille, Ionic Channels of Excitable Membranes, 2nd ed. (Sinauer Associates, Sunderland, MA, 1992).
3. B. Sakmann and E. Neher, Single-Channel Recording, 2nd ed. (Plenum, New York, 1995).
4. R. H. Austin, Biochemistry 14, 5355 (1975).
5. M. L. Saviotti and W. C. Galley, Proc. Natl. Acad. Sci. USA 71, 4154 (1974).
6. F. R. N. Gurd and T. M. Rothgeb, Adv. Protein Chem. 33, 73 (1979).
7. D. Ringe and G. A. Petski, Prog. Biophys. Mol. Biol. 45, 197 (1984).
8. G. R. Welch, The Fluctuating Enzyme (John Wiley and Sons, New York, 1986).
9. J. R. Alcala, E. Gratton, and F. G. Prendergast, Biophys. J. 51, 925 (1987).
10. S. W. Englander, Science 256, 1684 (1992).
11. J. A. McCammon and S. C. Harvey, Dynamics of Proteins and Nucleic Acids (Cambridge University Press, New York, 1987).
12. M. Karplus and G. A. Petsko, Nature (London) 347, 631 (1990).
13. A. Fuliński, Phys. Rev. E 58, 919 (1998).
14. B. B. Mandelbrot, The Fractal Geometry of Nature, 2nd ed. (W. H. Freeman, New York, 1983).
15. J. B. Bassingthwaighte, L. S. Liebovitch, and B. J. West, Fractal Physiology (Oxford, New York, 1994).
16. L. S. Liebovitch, J. Fischbarg, and J. P. Koniarek, Math. Biosci. 84, 37 (1987).
17. L. S. Liebovitch and J. M. Sullivan, Biophys. J. 52, 979 (1987).
18. A. Toib, V. Lyakhov, and S. Marom, J. Neurosci. 18, 1893 (1998).
19. N. L. Powers, R. J. Salvi, and S. S. Saunders, in Abstracts of the XIV Midwinter Research Meeting, Association for Research in Otolaryngology, edited by D. J. Lim (Association for Research in Otolaryngology, Des Moines, IA, 1991), p. 129, abstract 411.
20. N. L. Powers and R. J. Salvi, in Abstracts of the XV Midwinter Research Meeting, Association for Research in Otolaryngology, edited by D. J. Lim (Association for Research in Otolaryngology, Des Moines, IA, 1992), p. 101, abstract 292.
21. O. E. Kelly, D. H. Johnson, B. Delgutte, and P. Cariani, J. Acoust. Soc. Am. 99, 2210 (1996).
22. M. C. Teich, J. Opt. Soc. Am. A 14, 529 (1997).
23. R. G. Turcott, P. D. R. Barker, and M. C. Teich, J. Stat. Comput. Simul. 52, 253 (1995).
24. M. E. Wise, in Statistical Distributions in Scientific Work, edited by C. E. A. Taillie, G. P. Patil, and B. A. Baldessari (D. Reidel, Boston, 1981), Vol. 6, pp. 211–231.
25. F. Grüneis, Biol. Cybern. 68, 193 (1993).
26. S. B. Lowen and M. C. Teich, J. Acoust. Soc. Am. 99, 3585 (1996).
27. Data collected at the Eaton-Peabody Laboratory and provided by Don Johnson.
28. M. C. Teich, IEEE Trans. Biomed. Eng. 36, 150 (1989).
29. M. C. Teich, R. G. Turcott, and S. B. Lowen, in The Mechanics and Biophysics of Hearing, edited by P. Dallos, Lecture Notes in Biomathematics Vol. 87 (Springer-Verlag, New York, 1990), pp. 354–361.
30. S. B. Lowen, S. S. Cash, M.-m. Poo, and M. C. Teich, J. Neurosci. 17, 5666 (1997).
31. S. B. Lowen, S. S. Cash, M.-m. Poo, and M. C. Teich, in Computational Neuroscience: Trends in Research 1997, edited by J. M. Bower (Plenum Press, New York, 1997).
32. A. S. French and L. L. Stockbridge, Can. J. Physiol. Pharmacol. 66, 967 (1988).
33. S. B. Lowen and M. C. Teich, Fractals 3, 183 (1995).
34. C. C. Chow and J. A. White, Biophys. J. 71, 3013 (1996).
35. D. T. Gillespie, J. Phys. Chem. 81, 2340 (1977).
36. E. Skaugen and L. Walløe, Acta Physiol. Scand. 107, 343 (1979).
37. L. S. Liebovitch, Math. Biosci. 93, 97 (1989).
38. D. R. Cox and V. Isham, Point Processes (Chapman and Hall, London, 1980).
39. S. Thurner, Fractals 5, 565 (1997).
40. M. C. Teich, in Single Neuron Computation, edited by T. McKenna, J. Davis, and S. Zornetzer (Academic Press, Boston, 1992), pp. 589–625.
41. K. Matsuo, B. E. A. Saleh, and M. C. Teich, J. Math. Phys. 23, 2353 (1982).
42. M. C. Teich, C. Heneghan, S. B. Lowen, and R. G. Turcott, in Wavelets in Medicine and Biology, edited by A. Aldroubi and M. Unser (CRC Press, Boca Raton, FL, 1996), Chap. 14, pp. 383–412.
43. D. W. Allan, Proc. IEEE 54, 221 (1966).
44. J. A. Barnes and D. W. Allan, Proc. IEEE 54, 176 (1966).
45. R. P. Gaumond, Ph.D. thesis, Washington University, St. Louis, MO, 1980.
46. S. M. Bezrukov and I. Vodyanoy, Nature (London) 385, 319 (1997).
47. S. M. Bezrukov and I. Vodyanoy, Biophys. J. 73, 2456 (1997).
48. S. M. Bezrukov, Phys. Lett. A 248, 29 (1998).
49. B. Rudy, Neuroscience (Oxford) 25, 729 (1988).