Binding of Phosphate Species to Ca2+ and Mg2+ in Aqueous Solution

Phosphate derivatives and their interaction with metal cations are involved in many important biological phenomena, so an accurate characterization of the phosphate-metal interaction is necessary to properly understand the role of phosphate-metal contacts in mediating biological function. Herein, we improved the standard 12-6 Lennard-Jones (LJ) potential via the usage of the 12-6-4 LJ model, which incorporates ion-induced dipole interactions. Via parameter scanning, we fine-tuned the 12-6-4 LJ polarizability values to obtain accurate absolute binding free energies for the phosphate anions H2PO4-, HPO42-, PO43- coordinating with Ca2+ and Mg2+. First, we modified the phosphate 12-6-4 LJ parameters to reproduce the solvation free energies of the series of phosphate anions using the thermodynamic integration (TI) method. Then, using the potential mean force (PMF) method, the polarizability of the metal-phosphate interaction was obtained. We show that the free energy profiles of phosphate ions coordinated to Ca2+ and Mg2+ generally show similar trends at longer metal-phosphate distances, while the absolute binding energy values increased with deprotonation. The resulting parameters demonstrate the flexibility of the 12-6-4 LJ-type nonbonded model and its usefulness in accurately describing cation-anion interactions.