Stereochemical criteria for polypeptide and protein chain conformations. Part I. Evaluation of helical parameters

Abstract

A large number of configurations are possible for a polypeptide structure depending upon the relative orientations of the two peptide groups linked at an α-carbon atom. If the linkages at the α-carbon atoms are identical, then the structure assumes a regular helical form. Such a regular helical structure can be specified by two parameters φ, φ' which are the angles of rotation of the two groups about the N−αC and αC−C' bonds meeting at an α-carbon atom. In this paper, a method of evaluating the helical parameters of a structure, namely, the number of residues per turn n, the unit translation along the axis of the helix h and the direction cosines of the helical axis with respect to a suitably chosen co-ordinate system, is described making use of rotation matrices. The evaluation has been done for three different values of the angle NαCC at the α-carbon atom, namely, 105°, 110° and 115°. The results are shown graphically in the form of curves for constant n and constant h in the φ-φ' plane.