The logarithm of the distribution of binding energies, $Px(ε),$ of K⁺ (blue) and Na⁺ (red) with the entire protein. The ions are in the S₂ site. (Inset) Binding energy distribution considering only interactions with the eight carbonyls of the S₂ site. (The eight-carbonyl site is extracted from simulations of the entire system.) Note that the local component more acutely highlights the larger range of energies sampled by Na⁺. The dashed blue curve is the K⁺ binding energy distribution translated along the energy axis to match the mean binding energy of the Na⁺ distribution.