  The KcsA potassium channel belongs to a class of K+ channels that is
selective for K+ over Na+ at rates of K+ transport approaching the diffusion
limit. This selectivity is explained thermodynamically in terms of favorable
partitioning of K+ relative to Na+ in a narrow selectivity filter in the
channel. One mechanism for selectivity based on the atomic structure of the
KcsA channel invokes the size difference between K+ and Na+, and the molecular
complementarity of the selectivity filter with the larger K+ ion. An
alternative view holds that size-based selectivity is precluded because atomic
structural fluctuations are greater than the size difference between these two
ions. We examine these hypotheses by calculating the distribution of binding
energies for Na+ and K+ in a simplified model of the selectivity filter of the
KcsA channel. We find that Na+ binds strongly to the selectivity filter with a
mean binding energy substantially lower than that for K+. The difference is
comparable to the difference in hydration free energies of Na+ and K+ in bulk
aqueous solution. Thus, the average filter binding energies do not discriminate
Na+ from K+ when measured from the baseline of the difference in bulk hydration
free energies. Instead, Na+/K+ discrimination can be attributed to scarcity of
good binding configurations for Na+ compared to K+. That relative scarcity is
quantified as enhanced binding energy fluctuations, and is consistent with
predicted relative constriction of the filter by Na+.
