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Biophys J. 1978 May; 22(2): 209–219.
PMCID: PMC1473444

Electrostatic calculations for an ion channel. I. Energy and potential profiles and interactions between ions.


The electrostatic energy profile of one, two, or three ions in an aqueous channel through a lipid membrane is calculated. It is shown that the previous solution to this problem (based on the assumption that the channel is infinitely long) significantly overestimates the electrostatic energy barrier. For example, for a 3-A radius pore, the energy is 16 kT for the infinite channel and 6.7 kT for an ion in the center of a channel 25 A long. The energy as a function of the position of the ion is also determined. With this energy profile, the rate of crossing the membrane (using the Nernst-Planck equation) was estimated and found to be compatible with the maximum conductance observed for the gramicidin A channel. The total electrostatic energy (as a function of position) required to place two or three ions in the channel is also calculated. The electrostatic interaction is small for two ions at opposite ends of the channel and large for any positioning of the three ions. Finally, the gradient through the channel of an applied potential is calculated. The solution to these problems is based on solving an equivalent problem in which an appropriate surface charge is placed on the boundary between the lipid and aqueous regions. The magnitude of the surface charge is obtained from the numerical solution for a system of coupled integral equations.

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Selected References

These references are in PubMed. This may not be the complete list of references from this article.
  • Finkelstein A. Membrane channels and conductance. Discussion paper. Ann N Y Acad Sci. 1975 Dec 30;264:244–246. [PubMed]
  • Levitt DG. Electrostatic calculations for an ion channel. II. Kinetic behavior of the gramicidin A channel. Biophys J. 1978 May;22(2):221–248. [PMC free article] [PubMed]
  • Parsegian A. Energy of an ion crossing a low dielectric membrane: solutions to four relevant electrostatic problems. Nature. 1969 Mar 1;221(5183):844–846. [PubMed]
  • Parsegian VA. Ion-membrane interactions as structural forces. Ann N Y Acad Sci. 1975 Dec 30;264:161–171. [PubMed]
  • Tredgold RH, Hole PN. Dielectric behaviour of dry synthetic polypeptides. Biochim Biophys Acta. 1976 Aug 4;443(1):137–142. [PubMed]

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