Lifting Constraints in Protein Molecular Dynamics Simulations

Abstract

Protein dynamics involve both slow conformational as well as fast bond vibrational degrees of freedom. The slow conformational degrees of freedom can safely and efficiently be described using classical nuclei in molecular dynamics simulations. However, this description breaks down for the faster bond motions as quantum effects begin to dominate. To overcome this shortcoming of the classical propagation, fast protein degrees of freedom are routinely removed and replaced by constraints.In this study, we lifted the constraints from individual protein atoms and investigated the differences between classical, constraint, semi-classical and quantum nuclear motion. To this end, we chose atoms across the high, mid and low frequency regimes of a protein: a light Hydrogen, a tightly bound Oxygen and a low frequency Carbon atom. Nuclear quantum effects were reintroduced to the time dependent potential generated by the protein and the surrounding solvent. Classical and constraint trajectories were generated using a molecular dynamics integrator. The semi-classical solution was obtained by solving the nuclear Schrodinger Equation using coupled coherent state basis sets of varying sizes and the fully quantum solution was calculated on a numerical grid.The effects of introducing quantum degrees of freedom in protein molecular dynamics simulations were investigated. Position distributions for the different approaches are presented which illustrate the effect of approximating the quantum distributions by constraints and classical particles.