The selectivity filter of the L-type calcium channel works as a Ca2 +binding site with a very large affinity for Ca2 + versus Na+. Ca2 + replaces half of the Na+ ions in the filter even when these ions are present in 1 μM and 30 mM concentrations in the bath, respectively. The energetics of this strong selectivity is analyzed in this paper. We use Widom's particle insertion method to compute the space-dependent profiles of excess chemical potential in our grand canonical Monte Carlo simulations. These profiles define the free-energy landscape for the various ions. Following Gillespie [Biophys. J. 94, 1169 (2008)], the difference of the excess chemical potentials for the two competing ions defines the advantage that one of the ions has over the other in the competition for space in the crowded selectivity filter. These advantages depend on ionic bath concentrations: the ion that is present in the bath in larger quantity (Na+) has the “number” advantage which is balanced by the free-energy advantage of the other ion (Ca2 +). The excess chemical potentials are decomposed into hard sphere exclusion and electrostatic components. The electrostatic terms correspond to interactions with the mean electric field produced by ions and induced charges as well to ionic correlations beyond the mean field description. Dielectrics are needed to produce micromolar Ca2 + versus Na+ selectivity in the L-type channel. We study the behavior of these terms with changes in bath concentrations of ions, charges, and diameters of ions, as well as geometrical parameters such as radius of the pore and the dielectric constant of the protein. Ion selectivity in calcium binding proteins probably has a similar mechanism.
This work was supported by the Hungarian National Research Fund (OTKA K75132) and in part by NIH Grant No. GM076013. We are grateful for a generous allotment of computing time at the MARYLOU supercomputing facility of Brigham Young University.
I. INTRODUCTION II. MODEL III. COMPUTATION OF THE CHEMICAL POTENTIAL TERMS A. Energy terms B. The components of the excess chemical potential C. Energetics of ion selectivity IV. METHODS A. Grand canonical Monte Carlo simulations B. Numerical implementation of the Widom sampling V. RESULTS VI. SUMMARY