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. 1988 Mar;85(5):1503–1507. doi: 10.1073/pnas.85.5.1503

Diffusion models of ion-channel gating and the origin of power-law distributions from single-channel recording.

G L Millhauser 1, E E Salpeter 1, R E Oswald 1
PMCID: PMC279800  PMID: 2449693

Abstract

The lifetimes of the unitary currents from ion channels, as revealed from single-channel recording, are traditionally thought to follow exponential or multiexponential distributions. The interpretation of these event-time distributions is that the gating process follows Markov kinetics among a small number of states. There is recent evidence, however, that certain systems exhibit distributions that follow power laws or functions related to power laws. Likewise, it has been suggested that data sets that appear to be multiexponential may be fit to simple power laws as well. In this paper we propose a different view of ion-channel-gating kinetics that is consistent with these recent experimental observations. We retain the Markovian nature of the kinetics, but, in contrast to the traditional models, we suggest that ion-channel proteins have a very large number of states all of similar energy. Gating, therefore, resembles a diffusion process. We show that our simplest one-dimensional model exhibits single-channel distributions that follow power laws of the form t-a, where 1/2 less than or equal to a less than or equal to 3/2. Exponents determined from recent experiments approximately fall within this range. We believe that this model is consistent with modern views of protein dynamics and, thus, may provide a key to the molecular details of the gating process.

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Selected References

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

  1. Aldrich R. W., Corey D. P., Stevens C. F. A reinterpretation of mammalian sodium channel gating based on single channel recording. Nature. 1983 Dec 1;306(5942):436–441. doi: 10.1038/306436a0. [DOI] [PubMed] [Google Scholar]
  2. 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]
  3. Brisson A., Unwin P. N. Quaternary structure of the acetylcholine receptor. Nature. 1985 Jun 6;315(6019):474–477. doi: 10.1038/315474a0. [DOI] [PubMed] [Google Scholar]
  4. Campbell I. D., Dobson C. M., Williams R. J. The study of conformational states of proteins by nuclear magnetic resonance. Biochem J. 1985 Oct 1;231(1):1–10. doi: 10.1042/bj2310001. [DOI] [PMC free article] [PubMed] [Google Scholar]
  5. Elber R., Karplus M. Multiple conformational states of proteins: a molecular dynamics analysis of myoglobin. Science. 1987 Jan 16;235(4786):318–321. doi: 10.1126/science.3798113. [DOI] [PubMed] [Google Scholar]
  6. Frauenfelder H., Petsko G. A., Tsernoglou D. Temperature-dependent X-ray diffraction as a probe of protein structural dynamics. Nature. 1979 Aug 16;280(5723):558–563. doi: 10.1038/280558a0. [DOI] [PubMed] [Google Scholar]
  7. 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]
  8. Labarca P., Montal M. S., Lindstrom J. M., Montal M. The occurrence of long openings in the purified cholinergic receptor channel increases with acetylcholine concentration. J Neurosci. 1985 Dec;5(12):3409–3413. doi: 10.1523/JNEUROSCI.05-12-03409.1985. [DOI] [PMC free article] [PubMed] [Google Scholar]
  9. 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]
  10. Ring A. Brief closures of gramicidin A channels in lipid bilayer membranes. Biochim Biophys Acta. 1986 Apr 25;856(3):646–653. doi: 10.1016/0005-2736(86)90160-4. [DOI] [PubMed] [Google Scholar]
  11. Rudnick J., Gaspari G. The shapes of random walks. Science. 1987 Jul 24;237(4813):384–389. doi: 10.1126/science.237.4813.384. [DOI] [PubMed] [Google Scholar]
  12. Sakmann B., Patlak J., Neher E. Single acetylcholine-activated channels show burst-kinetics in presence of desensitizing concentrations of agonist. Nature. 1980 Jul 3;286(5768):71–73. doi: 10.1038/286071a0. [DOI] [PubMed] [Google Scholar]

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