Anisotropic fluctuations of amino acids in protein structures: Insights from X-ray crystallography and elastic network models

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.