A detailed shape characterization of regular polypeptide conformations

Regular polypeptide conformations include secondary structural motifs such as α-helices and β-strands. The occurrence of some regular conformation is usually deduced from a local analysis of dihedral angles. However, the value of a dihedral angle in itself does not provide any information on the conformation's "shape." This drawback can be circumvented with global, rather than local, macromolecular shape descriptors. Recently, fractal exponents have been proposed as a source of such descriptors. Yet, this approach does not fully capture all essential shape features, since protein backbones are not fractal. In this work, we deal instead with a more "natural" characterization of the polymer's global shape that uses both the chain's geometry and "topology." For the geometry, we study the behaviour of molecular size and anisometry. For the chain's folding features, we study the self-entanglements in a polymer fold. We compute these descriptors for all relevant secondary structural motifs. By using self-entaglements and molecular geometry, we provide a view of secondary structure that is both conceptually appealing and also more discriminating than previous ones in the literature. Keywords: molecular shape analysis, protein secondary structure, self-entanglements.