Dihedral-angle Gaussian distribution driving protein folding

The proposal of this paper is to provide a simple angular random-walk model to build up polypeptide structures, which encompass properties of dihedral angles of folded proteins. From this model, structures will be built with lengths ranging from 125 up to 400 amino acids for the different fractions of secondary structure motifs, in which dihedral angles were randomly chosen according to narrow Gaussian probability distributions. In order to measure the fractal dimension of proteins three different cases were analyzed. The first contained α-helix structures only, the second β-strands structures and the third a mix of α-helices and β-sheets. The behavior of proteins with α-helix motifs are more compact than in other situations. The findings herein indicate that this model describes some structural properties of a protein and suggest that randomness is an essential ingredient but proteins are driven by narrow angular Gaussian probability distributions and not by random-walk processes.