Abstract
This paper describes a global analysis of macromolecular B values. It is shown that the distribution of B values generally follows the shifted inverse-gamma distribution (SIGD). The parameters of the SIGD are estimated using the Fisher scoring technique with the expected Fisher information matrix. It is demonstrated that a contour plot based on the parameters of the SIGD can play a role in the validation of macromolecular structures. The dependence of the peak-height distribution on resolution and atomic B values is also analysed. It is demonstrated that the B-value distribution can have a dramatically different effect on peak heights at different resolutions. Consequently, a comparative analysis of the B values of neighbouring atoms must account for resolution. A combination of the SIGD, peak-height distribution and outlier detection was used to identify a number of entries from the PDB that require attention. It is also shown that the presence of a multimodal B-value distribution often indicates that some loops or parts of the molecule have either been mismodelled or have dramatically different mobility, depending on their environment within the crystal. These distributions can also indicate the level of sharpening/blurring used before atomic structure refinement. It is recommended that procedures such as sharpening/blurring should be avoided during refinement, although they can play important roles in map visualization and model building.