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The S$_2$ site of the KcsA K$^+$ channel has eight carbonyl ligands in theion-binding site. A recent study suggests that the K$^+$-over-Na$^+$selectivity of the S$_2$ site can be understood by noting the larger freeenergy change involved in enforcing an eight water coordination state aroundNa$^+$ relative to K$^+$. The free energies were obtained from theprobabilities of observing eight water molecules within a coordination spherewhose radius ($\lambda_{\rm Na^+} \approx 3.1$ {\AA} and $\lambda_{\rm K^+}\approx 3.5$ {\AA}) extends to the first minimum of the ion-water oxygen paircorrelation function. Curiously, using the same coordination radius led toresults that question the very idea of using coordination states in water tounderstand selectivity in the channel. We show that density fluctuations inneat water at the length scale of the coordination volume enter the descriptionof the hydration thermodynamics of the ion expressed in terms of itscoordination states. Density fluctuations explain the sensitivity to the choiceof radius. After accounting for this effect, the results lead to the conclusionthat free energy changes involved in the transition between coordination statesin water are inadequate to explain selectivity in the ion-channel.

On inferring the ion selectivity of the KcsA potassium channel using the distribution of coordination states of the aqueous ions