Abstract:

A theoretical framework is elaborated to account for the effect of a transmembrane potential in explicit solvent computer simulations of membrane proteins [1]. The framework relies on a modified Poisson-Boltzmann equation previously developed from statistical mechanical considerations [2]. 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 a voltage difference via ion-exchanging electrodes connected to an electromotive force. 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 electromotive force 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 constructed from the variations in the voltage-dependent potential of mean force along a reaction path connecting two conformations of the protein, the Q-route based on the average displacement charge as a function of the conformation of the protein, and the G-route based on the relative charging free energy of specific residues, with and without applied membrane potentials. The theory is applied to examine atomic models of the Kv1.2 potassium channel in the active and resting state [2]. Methodologies to treat asymmetric membrane conditions have also been developed [3]. Calculations of the fractional transmembrane potential, acting upon key charged residues of the voltage sensing domain of the Kv1.2 potassium channel, reveals that the applied field varies rapidly over a narrow region of 10 to 15 Angstroms, corresponding to the outer leaflet of the bilayer [4]. The focused field allows the transfer of a large gating charge without translocation of S4 across the membrane. The theory is also applied to examine the binding of sodium and potassium ions to the Na,K ATPase membrane pump. 

1. B. Roux. Influence of the membrane potential on the free energy of an intrinsic protein. Biophysical Journal. 1997;73(6):2980-9. 

2. B. Roux. The membrane potential and its representation by a constant electric field in computer simulations. Biophys J. 2008;95(9):4205-16. 

3. F. Khalili-Araghi, B. Ziervogel, J.C. Gumbart, B. Roux. Molecular dynamics simulations of membrane proteins under asymmetric ionic concentrations. J Gen Physiol. 2013;142(4):465-75. 

4. F. Khalili-Araghi, V. Jogini, V. Yarov-Yarovoy, E. Tajkhorshid, B. Roux, K. Schulten. Calculation of the gating charge for the Kv1.2 voltage-activated potassium channel. Biophys J. 2010;98(10):2189-98.