Protein dynamics from X-ray crystallography: anisotropic, global motion in diffuse scattering patterns

Understanding X-ray crystallographic diffuse scattering is likely to improve our comprehension of equilibrium collective protein dynamics. Here, using molecular dynamics (MD) simulation, a detailed analysis is performed of the origins of diffuse scattering in crystalline Staphylococcal nuclease, for which the complete diffuse scattering pattern has been determined experimentally. The hydrogen-atom contribution and the scattering range over which the scattering can be considered to be a sum of solvent and protein scattering are determined. Two models of correlated protein motion are investigated by calculating the model-derived diffuse scattering and comparing with the scattering calculated directly from MD trajectories. In one model, previously used in diffuse scattering interpretation, the atomic displacement correlations decay isotropically with increasing separation. Model correlation lengths are obtained by refining the model scattering against the simulation-derived scattering pattern, and are found to be significantly different from those correlation lengths derived directly from the MD trajectories. Furthermore, the convergence between the model-derived and MD-derived scattering is poor. The second model, in which the displacement correlations are calculated from the principal components of the MD trajectories, is capable of fully reproducing the MD-derived diffuse scattering if the approximately 50% lowest-frequency modes are included. However, a small number ( approximately 10) of lowest-frequency and largest-amplitude modes dominates the diffuse scattering and thus the correlated protein motions. A detailed analysis of the principal components is performed. In particular, the effective free energy profile associated with each principle mode is analyzed and the eigenfrequency and damping coefficient computed using a model of Brownian dynamics. Those collective modes with effective frequencies below approximately 0.5 THz, including those that determine the diffuse scattering, are overdamped.