SMALL-SCALE AND LARGE-SCALE GLOBAL SHAPE-FEATURES IN MACROMOLECULAR BACKBONES

A methodology to analyze and characterize small- and large-scale shape and structural features in a macromolecule is presented. The procedure involves the construction of a continuum of spherical shape maps. This continuum is built by analyzing the overcrossing pattern of a molecular space curve from every direction in 3-space as seen by a viewer with a reduced vision field. The method derives global shape descriptors (shape maps) that characterize the backbone as a whole (large-scale structure), but also allows one to focus the analysis on details of the backbone's small-scale structure. A continuous function is proposed as a simplified descriptor derived from the shape maps. This function discriminates reasonably well among elements of secondary structure and supersecondary structural motifs in proteins. The procedure is applied to alpha-helices, beta-sheets, and models of alpha-helical packing.