IMR Press / FBL / Volume 8 / Issue 6 / DOI: 10.2741/1177

Frontiers in Bioscience-Landmark (FBL) is published by IMR Press from Volume 26 Issue 5 (2021). Previous articles were published by another publisher on a subscription basis, and they are hosted by IMR Press on as a courtesy and upon agreement with Frontiers in Bioscience.

Open Access Article
Numerical framework models of single proton conduction through gramicidin
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1 Department of Mathematics and Center for Integrated Biotechnology, Washington State University, Pullman WA 99164-3113, USA

Academic Editor: Michael Green

Front. Biosci. (Landmark Ed) 2003, 8(6), 982–991;
Published: 1 September 2003
(This article belongs to the Special Issue Proton transport in biological systems)

A framework model of single-proton conduction through gramicidin was previously designed to incorporate potentials of mean force and diffusion coefficients computed by the molecular dynamics simulations of Pom s and Roux (1). The resulting diffusion model was solved analytically using the lumped state approximation (LSA), allowing a detailed comparison to be made with conductance data from gramicidin A and two Trp→ Phe analogs (2). The comparison included a sensitivity analysis which required over 1 million current evaluations. A numerical method for constructing framework models is now introduced which involves finding the steady states of random walks using a trapezoid rule closely related to the rule for numerical integration. The method is described and then applied directly to the LSA. Convergence of the results to the analytical solution is seen as the number of random walk sites increase. The numerical method is then used to construct a more elaborate framework model which avoids the LSA. This is also in very good agreement with the analytical solution under the experimental conditions, confirming the accuracy of the LSA. The numerical method remains fast enough to allow an extensive comparison with conductance data.

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