The role of bulk protein in local models of ion-binding to proteins: Comparative study of KcsA, its semisynthetic analog with a locked-in binding site, and valinomycin

In studying ion-selectivity in biomaterials, it is common to study ion-protein interactions within a local neighborhood around the ion. This local system analysis for the S₂ site of KcsA, its semisynthetic analog, and valinomycin yields the free energy change in exchanging K⁺ with Na⁺ in quantitative agreement with the value obtained by considering ion-interactions with the entire system. But the energetics of ion binding in the local system and in the entire system differ significantly and lead to different conclusions regarding the physical basis of ion selectivity. For configurations sampled from an all-atom simulation, we show that the selectivity free energy can be decomposed into a contribution arising from interactions of the ion with its local neighborhood, δW_local, and a term arising from the field imposed on the ion and the binding site by the rest of the medium, δW_φ. The local contribution δW _local is numerically close to the actual free energy difference because the field contribution is small. The field contribution is small because of cancellation of inversely related ion-medium and site-medium interactions. Our analysis presents a rigorous foundation for the numerical success of the local system analysis and shows that its implications do not always hold for the entire protein.