The joint probability distribution, $Px(Us-m,εm),$ of the interaction of the ion with the representative protein medium ε_m versus the interaction of the site with the bulk protein medium, U_s−m. We regard the water molecules in S₁ and S₃ sites as the protein medium (Table I). ε_m and U_s−m are nearly independent of each other and similar for Na⁺ and K⁺ in KcsA (left), whereas they are inversely correlated in KcsA-G77A_D (right). Figure reprinted from Dixit and Asthagiri (2011) with permission from Elsevier.