Fig. 3.

Thermodynamic analysis of the three ion occupancy configurations with best structural consistency with the NCX_Mj crystal structure. (A) Thermodynamic cycles used to deduce the alchemical transformations (ΔG_sim) that are required to evaluate the relative free energies of the three ion configurations considered. (B) Calculated free-energy differences between configurations a and c, and between configurations c and b. The sum of these is the free-energy difference between a and b. It was assumed that pH = 7, [Na⁺] = [K⁺] = 100 mM, [W] = 55 M, and pK_a^s = 3.86. The last two terms in the expression of the free-energy difference between a and c are thus -4.28 and 3.73 kcal/mol, respectively; and the last term in the expression of the free-energy difference between c and b is zero. Note that the volumes occupied by Na⁺, K⁺, or water at the S_mid site are approximately equivalent, and thus the related entropic contributions are omitted. Free-energy values are reported for the standard CHARMM27 force field, as well as for a modified version in which the Lennard–Jones R_min parameter for the Na⁺–carboxylate and K⁺–carboxylate interactions are optimized so as to reproduce osmotic pressure and binding affinity measurements (SI Methods and Figs. S3 and S4). The values shown are means of two independent free-energy calculations carried out in opposite directions, e.g., a to c and c to a. The differences between the calculated values in each direction are shown as error bars.