Phi/Psi-Torsional dependence of peptide backbone bond-lengths and bond-angles: Comparison of crystallographic and calculated parameters

The crystallographic N-C(alpha), C(alpha)-C' and N-C(alpha)-C' backbone parameters of 43 oligopeptides and the N-C(alpha)-C' angles of 37 proteins were compared with peptide conformational geometry surfaces derived from ab initio calculations of N-acetyl N'-methyl alanine amide. The calculated values were obtained by spline-function representations of ab initio dipeptide conformational geometry maps which allow one to predict backbone bond lengths and angles in peptides and proteins as functions of the phi[N-C(alpha)]/psi[C(alpha)-C']-torsions. When the parameters are ordered by regions in phi/psi-space defined by a 30 degrees grid and region-average values calculated, the rms deviations between the crystallographic and calculated parameters in the most populated regions of the oligopeptides are 0.009 Angstrom, 0.013 Angstrom and 1.2 degrees, for N-C(alpha), C(alpha)-C' and N-C(alpha)-C' respectively; and 1.2 degrees for the N-C(alpha)-C' angles in proteins. The flexibility in phi psi-space is significant for the N-C(alpha)-C' angles (observed variations of > 8 degrees), but of lesser importance for the bond lengths (conformational variations of similar to 0.02 Angstrom). Thus, torsion dependent ideal geometry functions are recommended for the former, but not necessarily the latter, for use in various areas of protein study, such as protein crystallography and empirical molecular modelling procedures.