Quantitative organization of the known protein x-ray structures. I. Methods and short-length-scale results

We address herein the problem of delineating the relationships between the known protein structures. In order to study this problem, methods have been developed to represent arbitrarily sized fragments of biopolymer backbone, and to compare distributions of such fragments. These methods are applied to a classification of 123 structures representing the entire set of known x-ray structures. The resulting data are analyzed (on the four-C alpha length scale) to determine both the large-scale organization of the set of known structures (i.e., the relationships between large groups of structures, each comprised of proteins that are structurally related) and its local structure (i.e., the quantitative degree of similarity between any two specific structures). It is shown that the set of structures forms a continuum of structural types, ranging from all-helical to all-sheet/barrel proteins. It is further demonstrated that the density of protein structures is not uniform across this continuum, but rather that structures cluster in certain regions, separated by regions of lower population. The properties of the various regions of the structural space are determined. The existence is demonstrated of strong quantitative correlations between the contents of different types of four-C alpha fragments within protein structures, which imply significant constraints on the types of architecture that can occur in proteins. Analysis of the distribution of structures demonstrates some hitherto unsuspected similarities and suggests that, in some circumstances, neither structural similarity nor sequence homology may be necessary conditions for evolutionary relationship between proteins. It is also suggested that these unsuspected similarities may imply similar folding mechanisms for structures of apparently different global architecture. Cases are also noted in which apparently similar structures may fold by different mechanisms. The connection between structure and dynamic properties is discussed, and a possible role of dynamics in the evolution of protein structures is suggested. The sensitivity of the methods presented herein to anomalies of structure refinement is demonstrated. It is suggested that the present results provide a framework for analyzing experimental results on structural similarity obtained using vibrational circular dichroism spectra, which are sensitive to local backbone structure.