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The Membrane Potential and its Representation by a Constant Electric Field in Computer Simulations.

by: Benoit Roux
Biophysical journal (18 July 2008)


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A theoretical framework is elaborated to account for the effect of a transmembrane potential in computer dynamics simulations. It is shown that a simulation with a constant external electric field applied in the direction normal to the membrane is equivalent to the influence of surrounding infinite baths maintained to voltage difference via ion-exchanging electrodes connected to an electromotive force (EMF). It is also shown that the linearly-weighted displacement charge within the simulation system tracks the net flow of charge through the external circuit comprising the EMF and the electrodes. Using a statistical mechanical reduction of the degrees of freedom of the external system, three distinct theoretical routes are formulated and examined for the purpose of characterizing the free energy of a protein embedded in a membrane that is submitted to a voltage difference. The W-route is constructed from the variations in the voltage-dependent potential of mean force (PMF) along a reaction path connecting two conformations of the protein. The Q-route is based on the average displacement charge as a function of the conformation of the protein. Finally, the G-route considers the relative charging free energy of specific residues, with and without applied membrane potentials. The theoretical formulation is illustrated with a simple model of an ion crossing a vacuum slab surrounding by two aqueous bulk phases and with a fragment of the voltage-sensor of the KvAP potassium channel.


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