Efficient, accurate calculation of rotational diffusion and NMR relaxation of globular proteins from atomic-level structures and approximate hydrodynamic calculations

The calculation of the rotational diffusion tensor and NMR relaxation times of quasi-rigid macromolecular structures with atomic detail can be made by means of bead/shell models. The computing time required for calculation of these properties for a single structure using rigorous hydrodynamic methods requires a moderate computing time. In possible applications of the methodology in which such a calculation had to be repeated for many structures, a faster method would be welcome. We have studied the effect of introducing a simplifying approximation in the treatment of hydrodynamic interaction, comparing the rigorous and approximate results for a set of 30 globular proteins. When the NMR relaxation times are combined in some relative form, the rigorous and approximate results are practically coincident. For absolute quantities, such as the correlation time, we find that the bias introduced by the approximation can be closely predicted and corrected. The differences between the results of the approximate-corrected and rigorous procedures are not greater than usual experimental errors, and the typical computing time is reduced from 5 min to 1 s.