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.
ASJC Scopus subject areas
- Physics and Astronomy(all)
- Physical and Theoretical Chemistry