The Ordered Water Ion Channel Model

  • Donald T. Edmonds


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.


Sodium Channel Membrane Voltage Root Mean Square Amplitude Continuous Fluid Water Ring 
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Copyright information

© Springer Science+Business Media New York 1985

Authors and Affiliations

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

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