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Application of the Poisson-Nernst-Planck Theory with Space-Dependent Diffusion Coefficients to KcsA

Simone Furini ^*, Francesco Zerbetto  and Silvio Cavalcanti ^*

^* Department of Electronics, Computer Science and Systems; and Department of Chemistry "G. Ciamician", University of Bologna, Bologna, Italy

Correspondence: Address reprint requests to Simone Furini, Dept. of Electronics, Computer Science and Systems, University of Bologna, viale Risorgimento 2, 40126 Bologna, Italy. Tel.: 39-05-1209-3067; Fax: 39-05-1209-3540; E-mail: sfurini{at}deis.unibo.it.

The Poisson-Nernst-Planck electrodiffusion theory serves to compute charge fluxes and is here applied to the ion current through a protein channel. KcsA was selected as an example because of the abundance of experimental and theoretical data. The potassium channels MthK and KvAP were used as templates to define two open channel models for KcsA. Channel boundary surfaces and protein charge distributions were defined according to atomic radii and partial atomic charges. To establish the sensitivity of the results to these parameters, two different sets were used. Assigning the potassium diffusion coefficients equal to the value for free-diffusion in water (1.96 x 10^–9 m²/s), the computed currents overestimated the experimental data. Ion distributions inside the channel suggest that the overestimate is not due to an excess of charge shielding. A good agreement with the experimental data was achieved by reducing the potassium diffusion coefficient inside the channel to 1.96 x 10^–10 m²/s, a value of substantial motility but nonetheless in accord with the intuitive notion that the channel has a high affinity for the ions and therefore slows them down. These results are independent of the open channel model and the parameterization adopted for atomic radii and partial atomic charges. The method offers a reliable estimate of the channel current with low computational effort.

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