Consistent Picture of Phosphate–Divalent Cation Binding from Models with Implicit and Explicit Electronic Polarization

Abstract

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 interactions 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 interactions of a model phosphate compound, dimethyl phosphate, with calcium and magnesium divalent cations. We show that both implicit and explicit approaches, when carefully parameterized, 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 slightly more stable than the contact monodentate ion pair. The bidentate ion pair is higher in energy (or even fully unstable for Mg2+). 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.