Characterization of fold diversity among proteins with the same number of amino acid residues

Chain entanglements provide a simple and global measure of folding in a macromolecule. The complexity of these entanglements can be expressed by the pattern of projected bond-bond crossings, or "overcrossings", associated with the molecular backbone. In this work, we use this approach to characterize quantitatively the range of tertiary folds observed in proteins with a given chain length. To discriminate among folding features, we use two shape descriptors derived from the probability distribution of overcrossings: the mean overcrossing number, (N) over bar, and the most probable overcrossing number, N*. The values of (N) over bar and N* relate to the content of secondary structure in a protein as well as its global three-dimensional organization. We propose a measure of folding diversity based on the properties of these descriptors. In addition, we discuss the application of our method to study how tertiary folds evolve during protein dynamics.