The role of stochasticity on compactness of the native state of protein peptide backbone

A restricted angular random-walk model to build up polypeptide structures, which encompasses properties of the dihedral-angle Ramachandran map of folded proteins, is proposed to study the role of stochasticity on the compactness of the native state of proteins. Sample structures will be built with lengths ranging from 125 up to 400 amino acids for the different fractions of secondary structure motifs, from which dihedral angles were randomly chosen according to narrow Gaussian probability distributions. Physical properties of these polypeptide protein backbones such as the radius of gyration, the compactness parameter, the number of contacts, and the associated energy were computed and analyzed from an ensemble of thousands of realizations of protein peptide chains built with different rates of alpha-helix or beta-strand motifs. Such geometric and physical parameters are compared to data from several globular proteins extracted from the Protein Data Bank indicating that a certain (small fraction) randomness is an essential ingredient for achieving the folded state of proteins, suggesting that they are neither driven by deterministic nor random-walk processes.