Electrostatics of ions inside the nanopores and trans-membrane channelsY. Levin
Instituto de Física, Universidade Federal do Rio Grande do Sul Caixa Postal 15051, CEP 91501-970, Porto Alegre, RS, Brazil
received 3 May 2006; accepted in final form 11 August 2006
published online 1 September 2006
A model of a finite cylindrical ion channel through a phospholipid membrane of width L separating two electrolyte reservoirs is studied. Analytical solution of the Poisson equation is obtained for an arbitrary distribution of ions inside the trans-membrane pore. The solution is asymptotically exact in the limit of large ionic strength of electrolyte on the two sides of membrane. However, even for physiological concentrations of electrolyte, the electrostatic barrier sizes found using the theory are in excellent agreement with the numerical solution of the Poisson equation. The analytical solution is used to calculate the electrostatic potential energy profiles for pores containing charged protein residues. Availability of a semi-exact interionic potential should greatly facilitate the study of ionic transport through nanopores and ion channels.
87.16.Uv - Active transport processes; ion channels.
87.10.+e - Biological and medical physics: General theory and mathematical aspects.
41.20.Cv - Electrostatics; Poisson and Laplace equations, boundary-value problems.
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