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. 1990 Apr;57(4):857–864. doi: 10.1016/S0006-3495(90)82605-9

Reptation theory of ion channel gating.

G L Millhauser 1
PMCID: PMC1280786  PMID: 1693091

Abstract

Reptation theory is a highly successful approach for describing polymer dynamics in entangled systems. In turn, this molecular process is the basis of viscoelasticity. We apply a modified version of reptation dynamics to develop an actual physical model of ion channel gating. We show that at times longer than microseconds these dynamics predict an alpha-helix-screw motion for the amphipathic protein segment that partially lines the channel pore. Such motion has been implicated in several molecular mechanics studies of both voltage-gated and transmitter-gated channels. The experimental probability density function (pdf) for this process follows t-3/2 which has been observed in several experimental systems. Reptation theory predicts that channel gating will occur on the millisecond time scale and this is consistent with experimental results from single-channel recording. We examine the consequences of reptation over random barriers and we show that, to first order, the pdf remains unchanged. In the case of a charged helix undergoing reptation in the presence of a transmembrane potential we show that the tail of the pdf will be exponential. We provide a list of practical experimental predictions to test the validity of this physical theory.

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Selected References

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

  1. Ansari A., Berendzen J., Bowne S. F., Frauenfelder H., Iben I. E., Sauke T. B., Shyamsunder E., Young R. D. Protein states and proteinquakes. Proc Natl Acad Sci U S A. 1985 Aug;82(15):5000–5004. doi: 10.1073/pnas.82.15.5000. [DOI] [PMC free article] [PubMed] [Google Scholar]
  2. Armstrong C. M. Sodium channels and gating currents. Physiol Rev. 1981 Jul;61(3):644–683. doi: 10.1152/physrev.1981.61.3.644. [DOI] [PubMed] [Google Scholar]
  3. Boulter J., Connolly J., Deneris E., Goldman D., Heinemann S., Patrick J. Functional expression of two neuronal nicotinic acetylcholine receptors from cDNA clones identifies a gene family. Proc Natl Acad Sci U S A. 1987 Nov;84(21):7763–7767. doi: 10.1073/pnas.84.21.7763. [DOI] [PMC free article] [PubMed] [Google Scholar]
  4. Catterall W. A. Structure and function of voltage-sensitive ion channels. Science. 1988 Oct 7;242(4875):50–61. doi: 10.1126/science.2459775. [DOI] [PubMed] [Google Scholar]
  5. Condat C. A., Jäckle J. Closed-time distribution of ionic channels. Analytical solution to a one-dimensional defect-diffusion model. Biophys J. 1989 May;55(5):915–925. doi: 10.1016/S0006-3495(89)82890-5. [DOI] [PMC free article] [PubMed] [Google Scholar]
  6. Grenningloh G., Rienitz A., Schmitt B., Methfessel C., Zensen M., Beyreuther K., Gundelfinger E. D., Betz H. The strychnine-binding subunit of the glycine receptor shows homology with nicotinic acetylcholine receptors. Nature. 1987 Jul 16;328(6127):215–220. doi: 10.1038/328215a0. [DOI] [PubMed] [Google Scholar]
  7. Guy H. R., Seetharamulu P. Molecular model of the action potential sodium channel. Proc Natl Acad Sci U S A. 1986 Jan;83(2):508–512. doi: 10.1073/pnas.83.2.508. [DOI] [PMC free article] [PubMed] [Google Scholar]
  8. Levitt D. G. Continuum model of voltage-dependent gating. Macroscopic conductance, gating current, and single-channel behavior. Biophys J. 1989 Mar;55(3):489–498. doi: 10.1016/S0006-3495(89)82842-5. [DOI] [PMC free article] [PubMed] [Google Scholar]
  9. Läuger P. Internal motions in proteins and gating kinetics of ionic channels. Biophys J. 1988 Jun;53(6):877–884. doi: 10.1016/S0006-3495(88)83168-0. [DOI] [PMC free article] [PubMed] [Google Scholar]
  10. Millhauser G. L., Salpeter E. E., Oswald R. E. Diffusion models of ion-channel gating and the origin of power-law distributions from single-channel recording. Proc Natl Acad Sci U S A. 1988 Mar;85(5):1503–1507. doi: 10.1073/pnas.85.5.1503. [DOI] [PMC free article] [PubMed] [Google Scholar]
  11. Millhauser G. L., Salpeter E. E., Oswald R. E. Rate-amplitude correlation from single-channel records. A hidden structure in ion channel gating kinetics? Biophys J. 1988 Dec;54(6):1165–1168. doi: 10.1016/S0006-3495(88)83051-0. [DOI] [PMC free article] [PubMed] [Google Scholar]
  12. Oiki S., Danho W., Montal M. Channel protein engineering: synthetic 22-mer peptide from the primary structure of the voltage-sensitive sodium channel forms ionic channels in lipid bilayers. Proc Natl Acad Sci U S A. 1988 Apr;85(7):2393–2397. doi: 10.1073/pnas.85.7.2393. [DOI] [PMC free article] [PubMed] [Google Scholar]
  13. Rousselet A., Cartaud J., Devaux P. F., Changeux J. P. The rotational diffusion of the acetylcholine receptor in Torpeda marmorata membrane fragments studied with a spin-labelled alpha-toxin: importance of the 43 000 protein(s). EMBO J. 1982;1(4):439–445. doi: 10.1002/j.1460-2075.1982.tb01188.x. [DOI] [PMC free article] [PubMed] [Google Scholar]
  14. 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]
  15. Stühmer W., Conti F., Suzuki H., Wang X. D., Noda M., Yahagi N., Kubo H., Numa S. Structural parts involved in activation and inactivation of the sodium channel. Nature. 1989 Jun 22;339(6226):597–603. doi: 10.1038/339597a0. [DOI] [PubMed] [Google Scholar]
  16. Unwin N. Is there a common design for cell membrane channels? Nature. 1986 Sep 4;323(6083):12–13. doi: 10.1038/323012a0. [DOI] [PubMed] [Google Scholar]

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