Binding and selectivity in L-type calcium channels: a mean spherical approximation

L-type calcium channels are Ca(2+) binding proteins of great biological importance. They generate an essential intracellular signal of living cells by allowing Ca(2+) ions to move across the lipid membrane into the cell, thereby selecting an ion that is in low extracellular abundance. Their mechanism of selection involves four carboxylate groups, containing eight oxygen ions, that belong to the side chains of the "EEEE" locus of the channel protein, a setting similar to that found in many Ca(2+)-chelating molecules. This study examines the hypothesis that selectivity in this locus is determined by mutual electrostatic screening and volume exclusion between ions and carboxylate oxygens of finite diameters. In this model, the eight half-charged oxygens of the tethered carboxylate groups of the protein are confined to a subvolume of the pore (the "filter"), but interact spontaneously with their mobile counterions as ions interact in concentrated bulk solutions. The mean spherical approximation (MSA) is used to predict ion-specific excess chemical potentials in the filter and baths. The theory is calibrated using a single experimental observation, concerning the apparent dissociation constant of Ca(2+) in the presence of a physiological concentration of NaCl. When ions are assigned their independently known crystal diameters and the carboxylate oxygens are constrained, e.g., to a volume of 0.375 nm(3) in an environment with an effective dielectric coefficient of 63.5, the hypothesized selectivity filter produces the shape of the calcium binding curves observed in experiment, and it predicts Ba(2+)/Ca(2+) and Na(+)/Li(+) competition, and Cl(-) exclusion as observed. The selectivities for Na(+), Ca(2+), Ba(2+), other alkali metal ions, and Cl(-) thus can be predicted by volume exclusion and electrostatic screening alone. Spontaneous coordination of ions and carboxylates can produce a wide range of Ca(2+) selectivities, depending on the volume density of carboxylate groups and the permittivity in the locus. A specific three-dimensional structure of atoms at the binding site is not needed to explain Ca(2+) selectivity.