K⁺ and Na⁺ concentration profiles and isocontour surfaces of ion distributions. K⁺, green; Na⁺, yellow. (A) top, K⁺; middle, Na⁺; bottom, superposition of ion concentration profiles. (A and B) Results at uu infinite dilution conditions (A) and at uv finite bulk concentration (B) are depicted. (B) Profiles and their axial integral functions are shown for pure 0.1 M KCl (water density of 0.03324 Å⁻³) and 0.1 M NaCl (0.03327 Å⁻³) solutions (left) and mixed 0.05:0.05 M K/NaCl solution (middle). (right) Depictions of the corresponding structures and isocontour surfaces in mixed solution. Calculations were performed at 298.15 K on 64 × 64 × 64 grids with 0.6-Å spacing according to protocols that were described previously (Tayefeh et al., 2007). Integrals were computed over the volume generated by HOLE software (Smart et al., 1996) of 91.8 ų. The uu results in A and the uv data in the top row of B have been computed for the truncated high K⁺ structure (ATTVGYGDL), which is followed in B from the second row to the bottom by results for carbonyl groups enclosing binding sites S0–S4 (TTVGYG), for carbonyl groups enclosing binding sites S1–S3 (TVGY), and for carbonyl groups enclosing binding site S2 only (VG). The largest values of the integral functions reflect the equilibrium binding constants K (A) and partitioning constants K_c (B), the ratios of which can be assigned to the equilibrium constant (A) and mass action constants (B) for the reaction Na⁺–Ch_aq + K⁺_aq→K⁺–Ch_aq + Na⁺_aq. The infinite dilution result (A) is K = 186.4. The finite concentration results (B) are K_c = 2.1 (pure) and 9.5 (mixed) for the atomically detailed model (top), K_c = 2.8 (pure) and 8.8 (mixed) for the S0–S4 carbonyl group model (second row), K_c = 2.7 (pure) and 8.6 (mixed) for the S1–S3 model (third row), and K_c = 2.5 (pure) and 6.5 (mixed) for the S2 model (bottom row). Isocontour values were chosen as (uu) g_K+ = g_Na+ = 800 (A) and (uv) g_K+ = g_Na+ = 80 (B). Throughout, only two opposing subunits are shown. Structural images were created with MOLCAD software (MOLCAD GmbH).