Motivation: A common practice in X-ray crystallographic structure refinement has been to model atomic displacements or thermal fluctuations as isotropic motions. Recent high-resolution data reveal, however, significant departures from isotropy, described by anisotropic displacement parameters (ADPs) modeled for individual atoms. Yet, ADPs are currently reported for a limited set of structures, only.
Results: We present a comparative analysis of the experimentally reported ADPs and those theoretically predicted by the anisotropic network model (ANM) for a representative set of structures. The relative sizes of fluctuations along different directions are shown to agree well between experiments and theory, while the cross-correlations between the (x-, y- and z-) components of the fluctuations show considerable deviations. Secondary structure elements and protein cores exhibit more robust anisotropic characteristics compared to disordered or flexible regions. The deviations between experimental and theoretical data are comparable to those between sets of experimental ADPs reported for the same protein in different crystal forms. These results draw attention to the effects of crystal form and refinement procedure on experimental ADPs and highlight the potential utility of ANM calculations for consolidating experimental data or assessing ADPs in the absence of experimental data.
Availability: The ANM server at http://www.ccbb.pitt.edu/anm is upgraded to permit users to compute and visualize the theoretical ADPs for any PDB structure, thus providing insights into the anisotropic motions intrinsically preferred by equilibrium structures.
Supplementary information: Two Supplementary Material files can be accessed at the journal website. The first presents the tabulated results from computations (Pearson correlations and KL distances with respect to experimental ADPs) reported for each of the 93 proteins in Set I (the averages over all proteins are presented above in Table 3). The second file consists of three sections: (A) detailed derivation of Equation (7), (B) analysis of the effect of ANM parameters on computed ADPs and identification of parameters that achieve optimal correlation with experiments and (C) description of the method for computing the tangential and radial components of equilibrium fluctuations.