Ion selectivity in the KcsA potassium channel from the perspective of the ion binding site

To understand the thermodynamic exclusion of Na⁺ relative to K⁺ from the S₂ site of the selectivity filter, the distribution PX(ε) (X = K⁺ or Na⁺) of the binding energy (ε) of the ion with the channel is analyzed using the potential distribution theorem. By expressing the excess chemical potential of the ion as a sum of mean-field 〈ε〉 and fluctuation μ_flux,X ^ex contributions, we find that selectivity arises from a higher value of μ_flux;Na+^ex relative to μ_flux;K+ ^ex . To understand the role of site-site interactions on μ_flux,X^ex, we decompose PX(ε) into n-dependent distributions, where n is the number of ion-coordinating ligands within a distance λ from the ion. For λ comparable to typical ion-oxygen bond distances, investigations building on this multistate model reveal an inverse correlation between favorable ion-site and site-site interactions: the ion-coordination states that most influence the thermodynamics of the ion are also those for which the binding site is energetically less strained and vice versa. This correlation motivates understanding entropic effects in ion binding to the site and leads to the finding that μ_flux,X^ex is directly proportional to the average site-site interaction energy, a quantity that is sensitive to the chemical type of the ligand coordinating the ion. Increasing the coordination number around Na⁺ only partially accounts for the observed magnitude of selectivity; acknowledging the chemical type of the ion-coordinating ligand is essential.