Figure 1.

a) ATP·Mg²⁺ in tridentate (triple Mg²⁺–phosphate coordination, C3) and bidentate (double, C2) configurations. b) Free energy calculation scheme. Conversion between coordination modes (black arrows) is prohibitively slow in unbiased molecular dynamics simulation of this strongly charged complex. We therefore devised an alchemical thermodynamic cycle that couples an artificial state (dashed box) to the unmodified (‘native’) physical ensemble. The nonphysical analogue ATP^2.5–·Mg^0.5+ defined therein, with cation charge reduced to +0.5 and a compensating +1.5 charge spread uniformly over the atoms of the triphosphate, rapidly samples diverse Mg²⁺–phosphate configurations. By means of alchemical charge-scaling free energy calculations, we obtained the respective free energy differences (along green arrows) between multiple native subensembles, each restrained to a defined coordination mode, and this rapidly exchanging common reference state. These calculated free energy differences also define the relative free energies (along black arrows) between coordination modes in the unmodified force field.