A method is presented to mathematically extract concerted structural transitions in proteins from collections of crystal structures. The "essential dynamics" procedure is used to filter out small-amplitude fluctuations from such a set of structures; the remaining large conformational changes describe motions such as those important for the uptake/release of substrate/ligand and in catalytic reactions. The method is applied to sets of x-ray structures for a number of proteins, and the results are compared with the results from essential dynamics as applied to molecular dynamics simulations of those proteins. A significant degree of similarity is found, thereby providing a direct experimental basis for the application of such simulations to the description of large concerted motions in proteins.