Tuning the Van Der Waals Forces between Cations and Proteins in Polarizable and Non-polarizable Force Fields

Abstract

Molecular dynamics (MD) is a set of computational methods widely used in various disciplines to simulate the motion of various molecular structures. In this work, MD refers particularly to their application to the study of biomolecular systems like proteins. Despite constant refinement and progress, there remain shortcomings in the ability of MD in several cases, such as in accurately capturing the interactions between metals and proteins. This work evaluates some widely used molecular dynamics force-fields such as CHARMM and OPLS-AA. Evaluations are also performed on existing extensions of these force-fields that include polarization or charge transfer effects, which are known to be crucial to metal-protein interactions. Preliminary studies show that while polarizable force-fields may better reproduce some QM energies of representative molecules in vacuum, there still remains a need to further optimize them, particularly the van der Waals interactions described by the Lennard-Jones potential, which is challenging due to the additional parameters involved. This is evident from the benchmarking study performed with Ca2+, with calmodulin as the protein used for experimental verification. A follow-up study implements a charge transfer and polarization (CTPOL) extension of OPLS-AA for a specific Zn-finger system and evaluates the extension with a variety of coordination metrics extracted from experimental data. The results show significant improvement over the original OPLS-AA, particularly when the Lennard-Jones parameters are re-optimized, with some caveats which are discussed in the study. The Drude polarizable force-field, which extends CHARMM by adding Drude particles to capture atomic polarization, is evaluated against osmotic pressure data for monovalent cations in acetate solutions, representing M+COO- interactions common in proteins with a number of exposed ASP and GLU residues. Quantum mechanical (QM) data of acetate-M+ in vacuum in various conformations is used as a reference to perform optimization of the Lennard-Jones and Coulomb screening parameters of specific cation-oxygen pairs in the Drude polarizable force-field. Different criteria are explored to perform these optimizations, with interestingly very different results. The most effective predictor of osmotic pressure is a criterion that compares local variations, or “shape” of energy minima rather than absolute differences. This criterion provides parameters that reproduce experimental osmotic pressure quite accurately for a full range of concentrations and three different ions (K+, Li+, Na+), without the need for further refinement. Future direction for parametrization in general is suggested, which includes exploring objective functions as a high priority, as well as deviating from the standard Lennard-Jones potential as a representation of van der Waals forces.