Liquid-like and rigid-body motions in molecular-dynamics simulations of a crystalline protein

Abstract

To gain insight into crystalline protein dynamics, we performed molecular-dynamics (MD) simulations of a periodic 2×2×2 supercell of staphylococcal nuclease. We used the resulting MD trajectories to simulate X-ray diffraction and to study collective motions. The agreement of simulated X-ray diffraction with the data is comparable to previous MD simulation studies. We studied collective motions by analyzing statistically the covariance of alpha-carbon position displacements. The covariance decreases exponentially with the distance between atoms, which is consistent with a liquid-like motions (LLM) model, in which the protein behaves like a soft material. To gain finer insight into the collective motions, we examined the covariance behavior within a protein molecule (intra-protein) and between different protein molecules (inter-protein). The inter-protein atom pairs, which dominate the overall statistics, exhibit LLM behavior; however, the intra-protein pairs exhibit behavior that is consistent with a superposition of LLM and rigid-body motions (RBM). Our results indicate that LLM behavior of global dynamics is present in MD simulations of a protein crystal. They also show that RBM behavior is detectable in the simulations but that it is subsumed by the LLM behavior. Finally the results provide clues about how correlated motions of atom pairs both within and across proteins might manifest in diffraction data. Overall our findings increase our understanding of the connection between molecular motions and diffraction data, and therefore advance efforts to extract information about functionally important motions from crystallography experiments.