Role of fluctuations in a snug-fit mechanism of KcsA channel selectivity

The thermodynamic exclusion of Na ⁺ relative to K ⁺ in potassium channels is examined by calculating the distribution of binding energies for Na ⁺ and K ⁺ in a model of the selectivity filter of the KcsA potassium channel. These distributions are observed to take a surprisingly simple form: Gaussian with a slight positive skewness that is insignificant in the present context. Complications that might be anticipated from these distributions are not problematic here. Na ⁺ occupies the filter with a mean binding energy substantially lower than that of K ⁺. The difference is comparable to the difference in hydration free energies of Na ⁺ and K ⁺ in bulk aqueous solution. Thus, the average energies of binding to the filter do not discriminate Na ⁺ from K ⁺ when measured from a baseline of the difference in bulk hydration free energies. The strong binding of Na ⁺ constricts the filter, consistent with a negative partial molar volume of Na ⁺ in water in contrast with a positive partial molar volume of K ⁺ in water. Discrimination in favor of K ⁺ can be attributed to the scarcity of favorable binding configurations for Na ⁺ compared to K ⁺. That relative scarcity is quantified as enhanced binding energy fluctuations, which reflects both the energetically stronger binding of Na ⁺ and the constriction of the filter induced by Na ⁺ binding.