The geometrical analysis of peptide backbone structure and its local deformations.

A proposal to use a unified description of protein structures is presented, assuming that all peptide chain conformations (including beta-structure) may be considered as helix-derived. In this understanding the beta-conformation of the peptide chain may be obtained by extending or unwinding the helical form. A unified description could be based on a commonly defined internal axis (Z-axis) determined by the averaged direction of the CO bonds in a pentapeptide analytical unit. Five parameters were proposed to describe the peptide conformation: i) radius of curvature (R), calculated from the position of five consecutive peptide bond planes; ii) horizontal angular displacement (H) of the neighboring (i+1-th) versus the central amino acid residue (i-th) in the pentapeptide fragment; iii) vertical angular displacement (Vi) of the peptide bond plane of the i-th residue versus the Z-axis; iv) vertical angular displacement (Vi+1) of the i+1-th peptide plane measured versus the Z-axis; and v) vertical rise (VR) defined for the i+2-th residue versus the i-th residue. This geometrical analysis was used to study the mechanism of a possible transition from alpha R to beta and to alpha L transition, based on data taken from the known Phi, Psi distribution in proteins. This analysis was also designed and preliminarily used to reveal local peptide backbone distortions and their distributions in proteins for structure-function relation studies.