The Ordered Water Ion Channel Model

  • Donald T. Edmonds

Abstract

A lipid bilayer presents a formidable energy barrier to the passage of ions which is largely electrostatic. The electrostatic self-energy in joules of an ion of charge Q coulombs and radius R metres immersed in a continuous fluid of relative dielectric constant e is given by
$$ U = \left( {{1 \mathord{\left/ {\vphantom {1 {4\pi \varepsilon \varepsilon _0 }}} \right. \kern-\nulldelimiterspace} {4\pi \varepsilon \varepsilon _0 }}} \right)\left( {{{Q^2 } \mathord{\left/ {\vphantom {{Q^2 } {2R}}} \right. \kern-\nulldelimiterspace} {2R}}} \right) $$
where e = 8.85 x 10−12Fm. From this formula one would calculate that a sodium ion needs to surmount an energy barrier of 6 x 10-19J (144 kBT) to leave water with e = 80 and enter a lipid layer with e = 2. To treat water and lipid as continuous fluids with their bulk dielectric constant is clearly a poor approximation in these circumstances but more realistic calculation’ and experiment still predict that the barrier is so large as to completely preclude thermally activated transit at normal temperatures.

Keywords

Sodium Channel Membrane Voltage Root Mean Square Amplitude Continuous Fluid Water Ring 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    A.D. Buckingham, Discuss. Faraday Soc. 24: 151 (1957).CrossRefGoogle Scholar
  2. 2.
    L.G. Palmer, J. Membrane Biol., 67: 91 (1982).CrossRefGoogle Scholar
  3. 3.
    C. Edwards, Neuroscience, 7: 1335 (1982).PubMedCrossRefGoogle Scholar
  4. 4.
    B. Hille, in: “Membranes”, Vol 3, G. Eisenman, ed., (1975).Google Scholar
  5. 5.
    G. Eisenman, Biophys. J., 2: 259 (1962).CrossRefGoogle Scholar
  6. 6.
    H. Frauenfelder, G.A. Petsko and D. Tsernoglu, Nature 280: 558 (1979).CrossRefGoogle Scholar
  7. 7.
    P.J. Artymink, C.C.F. Blake, D.E.D. Grace, S.J. Oatley, D.C. Phillips and M.J.E. Sternberg, Nature, 280: 563 (1979).CrossRefGoogle Scholar
  8. 8.
    D.T. Edmonds, in: “Biological Membranes”, Vol. 5, D. Chapman, ed., Academic Press, London (1983).Google Scholar
  9. 9.
    D.T. Edmonds, Proc. R. Soc., B211: 51 (1980).CrossRefGoogle Scholar
  10. 10.
    D.T. Edmonds, Chem. Phys. Lett., 65: 429 (1979).CrossRefGoogle Scholar
  11. 11.
    D.T. Edmonds, Proc. R. Soc., B214: 125 (1981).CrossRefGoogle Scholar
  12. 12.
    C.M. Armstrong, F. Bezanilla and E. Rojas, J. Gen. Physiol. 62: 375 (1973).PubMedCrossRefGoogle Scholar
  13. 13.
    R. Horn, J. Patlak and C.F. Stevens, Nature 291: 426 (1981).CrossRefGoogle Scholar
  14. 14.
    W.G.J. Hol, P.T. van Duijnen and H.J.C. Berendsen, Nature 273: 443 (1978).PubMedCrossRefGoogle Scholar
  15. 15.
    D.T. Edmonds, Trends in Biochem. Sci., 6: 92 (1981).CrossRefGoogle Scholar
  16. 16.
    C.M. Armstrong and W.F. Gilly, J. Gen. Physiol. 74: 691 (1979).PubMedCrossRefGoogle Scholar
  17. 17.
    K.R. Courtney, J. Phar. Exp. Ther., 195: 225 (1975).Google Scholar
  18. 18.
    C.M. Armstrong, J. Gen. Physiol. 58: 413 (1971).CrossRefGoogle Scholar
  19. 19.
    C.M. Armstrong and B. Hille, J. Gen. Physiol. 59: 388 (1972).PubMedCrossRefGoogle Scholar
  20. 20.
    D.T. Edmonds, Proc. R. Soc., B217: 111 (1982).CrossRefGoogle Scholar
  21. D.T. Edmonds, Biochem. Soc. Symp. 46: 91 (1980).Google Scholar
  22. 22.
    R.C. Thomas and R.W. Meech, Nature 299: 826 (1982).PubMedCrossRefGoogle Scholar
  23. R.D. Keynes, N.G. Greeff and D.T. van Helden, Proc. R. Soc. 215: 391 (1982).CrossRefGoogle Scholar
  24. 24.
    D.W. Davidson, in: “Water a Comprehensive Treatise”, Vol. 2, Chap. 4., F. Franks, ed., Plenum Press, London (1973).Google Scholar

Copyright information

© Springer Science+Business Media New York 1985

Authors and Affiliations

  • Donald T. Edmonds
    • 1
  1. 1.The Clarendon LaboratoryOxfordUK

Personalised recommendations