On inferring the ion selectivity of the KcsA potassium channel using the distribution of coordination states of the aqueous ions
The S$_2$ site of the KcsA K$^+$ channel has eight carbonyl ligands in the ion-binding site. A recent study suggests that the K$^+$-over-Na$^+$ selectivity of the S$_2$ site can be understood by noting the larger free energy change involved in enforcing an eight water coordination state around Na$^+$ relative to K$^+$. The free energies were obtained from the probabilities of observing eight water molecules within a coordination sphere whose radius ($λ_{\rm Na^+} \approx 3.1$ Å and $λ_{\rm K^+} \approx 3.5$ Å) extends to the first minimum of the ion-water oxygen pair correlation function. Curiously, using the same coordination radius led to results that question the very idea of using coordination states in water to understand selectivity in the channel. We show that density fluctuations in neat water at the length scale of the coordination volume enter the description of the hydration thermodynamics of the ion expressed in terms of its coordination states. Density fluctuations explain the sensitivity to the choice of radius. After accounting for this effect, the results lead to the conclusion that free energy changes involved in the transition between coordination states in water are inadequate to explain selectivity in the ion-channel.