Skip to main content
PMC home page
Biophysical Journal logoLink to Biophysical Journal
. 1988 Nov;54(5):871–877. doi: 10.1016/S0006-3495(88)83023-6

Statistical discrimination of fractal and Markov models of single-channel gating.

S J Korn 1, R Horn 1
PMCID: PMC1330395  PMID: 2468367

Abstract

A statistical comparison is presented of Markov and fractal models of ion channel gating. The analysis is based on single-channel data from two types of ion channels: open times from a 90 pS Ca-activated K channel from GH3 pituitary cells, and closed times from a nonselective channel from rabbit corneal endothelium (Liebovitch et al., 1987a). Maximum likelihood methods were used to fit the data. For both data sets the best Markov model had three exponential components. The best Markov model had a higher likelihood than the fractal model, and the Asymptotic Information Criterion favored the Markov model for each data set. A more detailed analysis, using the Monte Carlo methods described in Horn (1987), showed that the Markov model was not significantly better than the fractal model for the corneal endothelium channels. The inability to discriminate the models definitively in this case was shown to be due in part to the small size of the data set.

Full text

PDF
871

Images in this article

875FIGURE 5
on p.875

Selected References

These references are in PubMed. This may not be the complete list of references from this article.

  1. Blatz A. L., Magleby K. L. Quantitative description of three modes of activity of fast chloride channels from rat skeletal muscle. J Physiol. 1986 Sep;378:141–174. doi: 10.1113/jphysiol.1986.sp016212. [DOI] [PMC free article] [PubMed] [Google Scholar]
  2. Colquhoun D., Hawkes A. G. On the stochastic properties of single ion channels. Proc R Soc Lond B Biol Sci. 1981 Mar 6;211(1183):205–235. doi: 10.1098/rspb.1981.0003. [DOI] [PubMed] [Google Scholar]
  3. Fishman H. M. Relaxations, fluctuations and ion transfer across membranes. Prog Biophys Mol Biol. 1985;46(2):127–162. doi: 10.1016/0079-6107(85)90007-0. [DOI] [PubMed] [Google Scholar]
  4. HODGKIN A. L., HUXLEY A. F. A quantitative description of membrane current and its application to conduction and excitation in nerve. J Physiol. 1952 Aug;117(4):500–544. doi: 10.1113/jphysiol.1952.sp004764. [DOI] [PMC free article] [PubMed] [Google Scholar]
  5. Hamill O. P., Marty A., Neher E., Sakmann B., Sigworth F. J. Improved patch-clamp techniques for high-resolution current recording from cells and cell-free membrane patches. Pflugers Arch. 1981 Aug;391(2):85–100. doi: 10.1007/BF00656997. [DOI] [PubMed] [Google Scholar]
  6. Hestrin S., Korenbrot J. I., Maricq A. V. Kinetics of activation of acetylcholine receptors in a mouse muscle cell line under a range of acetylcholine concentrations. Biophys J. 1987 Mar;51(3):449–455. doi: 10.1016/S0006-3495(87)83366-0. [DOI] [PMC free article] [PubMed] [Google Scholar]
  7. Horn R. Statistical methods for model discrimination. Applications to gating kinetics and permeation of the acetylcholine receptor channel. Biophys J. 1987 Feb;51(2):255–263. doi: 10.1016/S0006-3495(87)83331-3. [DOI] [PMC free article] [PubMed] [Google Scholar]
  8. Liebovitch L. S., Fischbarg J., Koniarek J. P., Todorova I., Wang M. Fractal model of ion-channel kinetics. Biochim Biophys Acta. 1987 Jan 26;896(2):173–180. doi: 10.1016/0005-2736(87)90177-5. [DOI] [PubMed] [Google Scholar]
  9. Liebovitch L. S., Sullivan J. M. Fractal analysis of a voltage-dependent potassium channel from cultured mouse hippocampal neurons. Biophys J. 1987 Dec;52(6):979–988. doi: 10.1016/S0006-3495(87)83290-3. [DOI] [PMC free article] [PubMed] [Google Scholar]
  10. Magleby K. L., Pallotta B. S. Burst kinetics of single calcium-activated potassium channels in cultured rat muscle. J Physiol. 1983 Nov;344:605–623. doi: 10.1113/jphysiol.1983.sp014958. [DOI] [PMC free article] [PubMed] [Google Scholar]
  11. Magleby K. L., Pallotta B. S. Calcium dependence of open and shut interval distributions from calcium-activated potassium channels in cultured rat muscle. J Physiol. 1983 Nov;344:585–604. doi: 10.1113/jphysiol.1983.sp014957. [DOI] [PMC free article] [PubMed] [Google Scholar]
  12. McManus O. B., Blatz A. L., Magleby K. L. Sampling, log binning, fitting, and plotting durations of open and shut intervals from single channels and the effects of noise. Pflugers Arch. 1987 Nov;410(4-5):530–553. doi: 10.1007/BF00586537. [DOI] [PubMed] [Google Scholar]
  13. McManus O. B., Magleby K. L. Kinetic states and modes of single large-conductance calcium-activated potassium channels in cultured rat skeletal muscle. J Physiol. 1988 Aug;402:79–120. doi: 10.1113/jphysiol.1988.sp017195. [DOI] [PMC free article] [PubMed] [Google Scholar]
  14. McManus O. B., Weiss D. S., Spivak C. E., Blatz A. L., Magleby K. L. Fractal models are inadequate for the kinetics of four different ion channels. Biophys J. 1988 Nov;54(5):859–870. doi: 10.1016/S0006-3495(88)83022-4. [DOI] [PMC free article] [PubMed] [Google Scholar]
  15. Pallotta B. S. Calcium-activated potassium channels in rat muscle inactivate from a short-duration open state. J Physiol. 1985 Jun;363:501–516. doi: 10.1113/jphysiol.1985.sp015724. [DOI] [PMC free article] [PubMed] [Google Scholar]
  16. Papke R. L., Millhauser G., Lieberman Z., Oswald R. E. Relationships of agonist properties to the single channel kinetics of nicotinic acetylcholine receptors. Biophys J. 1988 Jan;53(1):1–10. doi: 10.1016/S0006-3495(88)83059-5. [DOI] [PMC free article] [PubMed] [Google Scholar]
  17. Rubinson K. A. The sodium currents of nerve under voltage clamp as heterogeneous kinetics. A model that is consistent with possible kinetic behavior. Biophys Chem. 1982 Jun;15(3):245–262. doi: 10.1016/0301-4622(82)80008-2. [DOI] [PubMed] [Google Scholar]
  18. Sigworth F. J., Sine S. M. Data transformations for improved display and fitting of single-channel dwell time histograms. Biophys J. 1987 Dec;52(6):1047–1054. doi: 10.1016/S0006-3495(87)83298-8. [DOI] [PMC free article] [PubMed] [Google Scholar]
  19. Sine S. M., Steinbach J. H. Activation of acetylcholine receptors on clonal mammalian BC3H-1 cells by low concentrations of agonist. J Physiol. 1986 Apr;373:129–162. doi: 10.1113/jphysiol.1986.sp016039. [DOI] [PMC free article] [PubMed] [Google Scholar]

Articles from Biophysical Journal are provided here courtesy of The Biophysical Society

RESOURCES