Abstract
A quantitative expression key to evaluating significant structural differences or induced shifts between any two protein structures is derived. Because crystallography leads to reports of a single (or sometimes dual) position for each atom, the significance of any structural change based on comparison of two structures depends critically on knowing the expected precision of each median atomic position reported, and on extracting it for each atom, from the information provided in the Protein Data Bank and in the publication. The differences between structures of protein molecules that should be identical, and that are normally distributed, indicating that they are not affected by crystal contacts, were analyzed with respect to many potential indicators of structure precision, so as to extract, essentially by "machine learning" principles, a generally applicable expression involving the highest correlates. Eighteen refined crystal structures from the Protein Data Bank, in which there are multiple molecules in the crystallographic asymmetric unit, were selected and compared. The thermal B factor, the connectivity of the atom, and the ratio of the number of reflections to the number of atoms used in refinement correlate best with the magnitude of the positional differences between regions of the structures that otherwise would be expected to be the same. These results are embodied in a six-parameter equation that can be applied to any crystallographically refined structure to estimate the expected uncertainty in position of each atom. Structure change in a macromolecule can thus be referenced to the expected uncertainty in atomic position as reflected in the variance between otherwise identical structures with the observed values of correlated parameters.