Rational Design of Particle Mesh Ewald Compatible Lennard-Jones Parameters for +2 Metal Cations in Explicit Solvent

Abstract

Metal ions play significant roles in biological systems. Accurate molecular dynamics (MD) simulations on these systems require a validated set of parameters. Although there are more detailed ways to model metal ions, the nonbonded model, which employs a 12–6 Lennard-Jones (LJ) term plus an electrostatic potential, is still widely used in MD simulations today due to its simple form. However, LJ parameters have limited transferability due to different combining rules, various water models, and diverse simulation methods. Recently, simulations employing a Particle Mesh Ewald (PME) treatment for long-range electrostatics have become more and more popular owing to their speed and accuracy. In the present work, we have systematically designed LJ parameters for 24 +2 metal (M(II)) cations to reproduce different experimental properties appropriate for the Lorentz–Berthelot combining rules and PME simulations. We began by testing the transferability of currently available M(II) ion LJ parameters. The results showed that there are differences between simulations employing Ewald summation with other simulation methods and that it was necessary to design new parameters specific for PME based simulations. Employing the thermodynamic integration (TI) method and performing periodic boundary MD simulations employing PME, allowed for a systematic investigation of the LJ parameter space. Hydration free energies (HFEs), the ion–oxygen distance in the first solvation shell (IOD), and coordination numbers (CNs) were obtained for various combinations of the parameters of the LJ potential for four widely used water models (TIP3P, SPC/E, TIP4P, and TIP4P EW ). Results showed that the three simulated properties were highly correlated. Meanwhile, M(II) ions with the same parameters in different water models produce remarkably different HFEs but similar structural properties. It is difficult to reproduce various experimental values simultaneously because the nonbonded model underestimates the interaction between the metal ions and water molecules at short-range. Moreover, the extent of underestimation increases successively for the TIP3P, SPC/E, TIP4P EW, and TIP4P water models. Nonetheless, we fitted a curve to describe the relationship between ε (the well depth) and radius ( R min /2) from experimental data on noble gases to facilitate the generation of the best possible compromise models. Hence, by targeting different experimental values, we developed three sets of parameters for M(II) cations for three different water models (TIP3P, SPC/E, and TIP4P EW ). These parameters we feel represent the best possible compromise that can be achieved using the nonbonded model for the ions in combination with simple water models. From a computational uncertainty analysis we estimate that the uncertainty in our computed HFEs is on the order of ±1 kcal/mol. Further improvements will require more advanced nonbonded models likely with inclusion of polarization.