Comparing anisotropic displacement parameters in protein structures

The increasingly widespread use of synchrotron-radiation sources and cryo-preparation of samples in macromolecular crystallography has led to a dramatic increase in the number of macromolecular structures determined at atomic or near-atomic resolution. This permits expansion of the structural model to include anisotropic displacement parameters U^ij for individual atoms. In order to explore the physical significance of these parameters in protein structures, it is useful to be able to compare quantitatively the electron-density distribution described by the refined U^ij values associated with corresponding crystallographically independent atoms. This paper presents the derivation of an easily calculated correlation coefficient in real space between two atoms modeled with anisotropic displacement parameters. This measure is used to investigate the degree of similarity between chemically equivalent but crystallographically independent atoms in the set of protein structural models currently available from the Protein Data Bank.