Improved Molecular Model of a Peptide Unit for Proteins

Pauling et al. (1951, “The Structure of Proteins: Two Hydrogen-Bonded Helical Configurations of the Polypeptide Chain,” Proc. Natl. Acad. Sci. U.S.A., 37(4), pp. 205–211) in their seminal paper in 1951 reported numerical values for the bond lengths and bond angles for a peptide unit in proteins. These values became the standard model for several decades after that. In this paper, we have made an attempt to calibrate the values of these bond lengths and bond angles based on a systematic approach applied to a collection of proteins defined structurally in the protein data bank (PDB). Our method is based on the assumption that a peptide chain is a serial chain of identical rigid bodies connected by revolute joints (i.e., dihedral angles). Through an optimization process, the structural error (root mean square deviation of all atoms) between the resultant conformation and the PDB data is minimized to yield the best values for the bond length and bond angles in the calibrated peptide unit. Our numerical experiments indicate that by making small changes in the Pauling-Corey peptide model parameters (0.15–8.7%), the structural error is reduced significantly (3.0–57.4%). The optimum values for the bond angles and bond lengths are as follow; bond lengths: N–C(A): $1.4721Å$⁠, C(A)–C: $1.6167Å$⁠, C–N: $1.2047Å$⁠, $CO$⁠: $1.1913Å$ and N–H: $0.9621Å$⁠. Bond bending angles: N–C(A)–C: $109.6823deg$⁠, $C(A)–CO$⁠: $119.518deg$⁠, C(A)–C–N: $114.5553deg$⁠, $OC–N$⁠: $125.9233deg$⁠, C–N–H: $123.5155deg$⁠, C–N–C(A): $121.5756deg$⁠, C(A)–N–H: $114.901deg$ peptide bond torsion angle: $ω$⁠: $179.4432deg$⁠.