Principles that rule the calculation of dihedral angles in secondary structures: the cases of an α-helix and a β-sheet

The folding process has been described as the output of main mechanical forces which generate from the specific chemical interplay among residues of an amino acid chain. Recently, we have reported that dihedral angle values in (poly)peptides can be calculated by means of a newly defined parameter referred as folding factor. This physical measure is directly linked to the determination of the degrees of freedom (η), namely the number of possible interactions that can occur between atoms (on the base of changes in interatomic distances). Precise rules to accurately define the degrees of freedom and, in turn, the related folding factors, have not been reported to date. We propose here an empirical analysis of possible physico-chemical principles for a careful evaluation of the degrees of freedom, as well as the threshold distances for the chemical interactions to occur. To validate our systematic approach, we have applied these rules to the calculation of dihedral angles of the α-helix Vps27p and the beta-sheet U(1–17)T9D, highlighting wide agreement between predicted and experimental values.