Selectivity in K+ channels is due to topological control of the permeant ion's coordinated state

The selectivity filter of K+ channels provides specific coordinative interactions between dipolar carbonyl ligands, water, and the permeant cation, which allow for selective flow of K+ over (most importantly) Na+ across the cell membrane. Although a structural viewpoint attributes K+ selectivity to coordination geometry provided by the filter, recent molecular dynamics simulation studies attribute it to dynamic and unique chemical/electrostatic properties of the filter's carbonyl ligands. Here we provide a simple theoretical analysis of K+ and Na+ complexation with water in the context of simplified binding site models and bulk solution. Our analysis reveals that water molecules and carbonyl groups can both provide K+ selective environments if equivalent constraints are imposed on the coordination number of the complex. Absence of such constraints annihilates selectivity, demonstrating that whether a coordinating ligand is a water molecule or a carbonyl group, "external" or "topological" constraints/forces must be imposed on an ion-coordinated complex to elicit selective binding. These forces must inevitably originate from the channel protein, because in bulk water, which, by definition, presents a nonselective medium, the coordination number is allowed to relax to suit the ion. We show that the coordination geometry of K+ channel binding sites is replicated by 8-fold complexation of K+ in both water and simplified binding site models due to dominance of local interactions within a complex and is thus a requirement for topologically constraining the coordination number to a specific value.