Protein flexibility: coordinate uncertainties and interpretation of structural differences.

Valid interpretations of conformational movements in protein structures determined by X-ray crystallography require that the movement magnitudes exceed their uncertainty threshold. Here, it is shown that such thresholds can be obtained from the distance difference matrices (DDMs) of 1014 pairs of independently determined structures of bovine ribonuclease A and sperm whale myoglobin, with no explanations provided for reportedly minor coordinate differences. The smallest magnitudes of reportedly functional motions are just above these thresholds. Uncertainty thresholds can provide objective criteria that distinguish between true conformational changes and apparent 'noise', showing that some previous interpretations of protein coordinate changes attributed to external conditions or mutations may be doubtful or erroneous. The use of uncertainty thresholds, DDMs, the newly introduced CDDMs (contact distance difference matrices) and a novel simple rotation algorithm allows a more meaningful classification and description of protein motions, distinguishing between various rigid-fragment motions and nonrigid conformational deformations. It is also shown that half of 75 pairs of identical molecules, each from the same asymmetric crystallographic cell, exhibit coordinate differences that range from just outside the coordinate uncertainty threshold to the full magnitude of large functional movements. Thus, crystallization might often induce protein conformational changes that are comparable to those related to or induced by the protein function.