Rigid Protein Motion as a Model for Crystallographic Temperature Factors

The extent to which the librations of rigid molecules can model the crystallographic temperature factor profiles of proteins has been examined. For all proteins considered, including influenza virus hemagglutinin, glutathione reductase, myohemerythrin, myoglobin, and streptavidin, a simple 10-parameter model [V. Schomaker and K. N. Trueblood (1968) Acta Crystallogr. Sect. B 24, 63-76] is found to reproduce qualitatively the patterns of maxima and minima in the isotropic backbone meansquare displacements. Large deviations between the rigid molecule and individual atomic temperature factors are found to be correlated with a region in hemagglutinin for which the refined structural model is unsatisfactory and with errors in the structure in a partially incorrect model of myohemerythrin. For the high-resolution glutathione reductase structure, better results are obtained on treating each of the compact domains in the structure as independent rigid bodies. The method allows for the refinement of reliable temperature factors with the introduction of minimal parameters and may prove useful for the evaluation of models in the early stages of x-ray structure refinement. While these results by themselves do not establish the nature of the underlying displacements, the success of the rigid protein model in reproducing qualitative features of temperature factor profiles suggests that rigid body refinement results should be considered in any interpretation of crystallographic thermal parameters.