A consistent picture of phosphate–divalent cation binding from models with implicit and explicit electronic polarization

The binding of divalent cations to the ubiquitous phosphate group is essential for a number of key biological processes, such as DNA compaction, RNA folding or interaction of some proteins with membranes. Yet, probing their binding sites, modes and associated binding free energy is a challenge for both experiments and simulations. In simulations, standard force fields strongly overestimate the interaction between phosphate groups and divalent cations. Here, we examine how different strategies to include electronic polarization effects in force fields—implicitly through the use of scaled charges or pair-specific Lennard-Jones parameters, or explicitly with the polarizable force fields Drude and AMOEBA—capture the interaction of a model phosphate compound, dimethylphosphate, with calcium and magnesium divalent cations. We show that both implicit and explicit approaches, when carefully parametrized, are successful in capturing the overall binding free energy, and that common trends emerge from the comparison of different simulation approaches. Overall, the binding is very moderate, slightly weaker for Ca2+ than Mg2+, and the solvent-shared ion pair is the most stable. Our results thus suggest practical ways to capture the divalent cations with biomolecular phosphate groups in complex biochemical systems. In particular, the computational efficiency of implicit models makes them ideally suited for large-scale simulations of biological assemblies, with improved accuracy compared to state-of-the-art fixed-charge force fields.