Empirical force fields for biologically active divalent metal cations in water

We have presented a strategy for deriving ion-water van der Waals (vdW) parameters that implicitly include the microscopic solvent molecular effects around the ion. The strategy can be used to obtain vdW parameters for metal cations of the same formal charge and known experimental hydration free energies. In this work, it was applied to derive the vdW parameters for 24 divalent metal ions with measured hydration free energies ranging from -300 to -572 kcal/mol, coordination numbers (CNs) from 4 to 15, and ion-O (water) distances from 1.67 to 2.90 angstroms. The strategy used to derive the vdW parameters employs (1) a numerical procedure that links the coupling parameter used in free energy simulations with the experimental hydration free energies and (2) the first-shell CNs and structure for the entire series of divalent cations. One of the parameter sets obtained (referred to as MWc) simultaneously reproduces the observed (i) relative hydration free energies, (ii) first-shell CNs, and (iii) average ion-water distances of all the dications studied. In particular, the MWc parameters reproduce the observed (i) decrease in the CN from 6 for Cu2+ to 4 for Be2+, (ii) no change in the CN of 6 for dications with hydration free energies between those of Cu2+ and Cd2+, and (iii) an expansion of the CN from 6 for Cd2+ to 9.5 for Ba2+. The ion-water parameters derived herein represent a first step in the simulations of metalloproteins, which will also require potential energy functions incorporating polarizability, charge transfer, and other electronic effects to accurately model the protein-metal interactions in aqueous solution.