Transferable interactions of Li+ and Mg2+ ions in polarizable models

Abstract

Therapeutic implications of Li⁺, in many cases, stem from its ability to inhibit certain Mg²⁺-dependent enzymes, where it interacts with or substitutes for Mg²⁺. The underlying details of its action are, however, unknown. Molecular simulations can provide insights, but their reliability depends on how well they describe relative interactions of Li⁺ and Mg²⁺ with water and other biochemical groups. Here, we explore, benchmark, and recommend improvements to two simulation approaches: the one that employs an all-atom polarizable molecular mechanics (MM) model and the other that uses a hybrid quantum and MM implementation of the quasi-chemical theory (QCT). The strength of the former is that it describes thermal motions explicitly and that of the latter is that it derives local contributions from electron densities. Reference data are taken from the experiment, and also obtained systematically from CCSD(T) theory, followed by a benchmarked vdW-inclusive density functional theory. We find that the QCT model predicts relative hydration energies and structures in agreement with the experiment and without the need for additional parameterization. This implies that accurate descriptions of local interactions are essential. Consistent with this observation, recalibration of local interactions in the MM model, which reduces errors from 10.0 kcal/mol to 1.4 kcal/mol, also fixes aqueous phase properties. Finally, we show that ion-ligand transferability errors in the MM model can be reduced significantly from 10.3 kcal/mol to 1.2 kcal/mol by correcting the ligand's polarization term and by introducing Lennard-Jones cross-terms. In general, this work sets up systematic approaches to evaluate and improve molecular models of ions binding to proteins.

FIG. 1.

Radial distribution functions g(r) and running integrations n(r) of the water oxygens around ions determined from all-atom MM models. The standard deviation represented as a gray shade on the Pol^* model is computed from block averaging.

FIG. 2.

Quasi-chemical components in the calculation of the hydration free energies of Li⁺ and Mg²⁺ ions.

FIG. 3.

Water → methanol and water → NMA substitution energies (ΔE_sub) obtained before and after recalibration. Pol^* refers to our recalibrated model of ligands corrected for their dipolar field response, and Pol^*+NB-fix refers to the model in which the remaining error in the Pol^* model is corrected for by ignoring Lorentz–Berthelot type ion–ligand LJ combination rules and introducing specific ion–ligand cross-terms.