Accurate pKa Calculations in Proteins with Reactive Molecular Dynamics Provide Physical Insight Into the Electrostatic Origins of Their Values

Classical molecular dynamics simulations are a versatile tool in the study of biomolecular systems, but they usually rely on a fixed bonding topology, precluding the explicit simulation of chemical reactivity. Certain modifications can permit the modeling of reactions. One such method, multiscale reactive molecular dynamics, makes use of a linear combination approach to describe condensed-phase free energy surfaces of reactive processes of biological interest. Before these simulations can be performed, models of the reactive moieties must first be parametrized using electronic structure data. A recent study demonstrated that gas-phase electronic structure data can be used to derive parameters for glutamate and lysine which reproduce experimental pK_a values in both bulk water and the staphylococcal nuclease protein with remarkable accuracy and transferability between the water and protein environments. In this work, we first present a new model for aspartate derived in similar fashion and demonstrate that it too produces accurate pK_a values in both bulk and protein contexts. We also describe a modification to the prior methodology, involving refitting some of the classical force field parameters to density functional theory calculations, which improves the transferability of the existing glutamate model. Finally and most importantly, this reactive molecular dynamics approach, based on rigorous statistical mechanics, allows one to specifically analyze the fundamental physical causes for the marked pK_a shift of both aspartate and glutamate between bulk water and protein and also to demonstrate that local steric and electrostatic effects largely explain the observed differences.