PREDICTIONS OF PROTEIN BACKBONE STRUCTURAL PARAMETERS FROM FIRST PRINCIPLES - SYSTEMATIC COMPARISONS OF CALCULATED N-C(ALPHA)-C' ANGLES WITH HIGH-RESOLUTION PROTEIN CRYSTALLOGRAPHIC RESULTS

The performance of an algorithm was tested which uses spline-function representations of ab initio peptide conformational geometry maps to predict backbone bond lengths and angles in proteins as functions of the phi[N-C(alpha)]/psi[C(alpha)-C'] torsions. For the ith residues of some 40 protein crystal structures the observed N-C(alpha)-C' angles, (cryst)alpha(i), were compared with values calculated ((calc)alpha(i)) at the crystallographic phi/psi(i)-torsions. The average root mean square (rms) deviation between the two sets of angles for all proteins included in the test is 2.9 degrees, which compares to angle variations exceeding 10 degrees. When the (calc)alpha(i) are empirically corrected, the average rms deviations drops to 2.6 degrees. When the (cryst)alpha(i) and (calc)alpha(i) are ordered by regions in phi/psi-space defined by a 30 degrees grid and region-average values calculated, the average rms deviation between the two sets in the most populated regions is 1.2 degrees. In the alpha-helical region the dipeptide-based angle predictions are on the average 1.5 degrees too high compared to experimental values, indicating helix compression in proteins: Similarly, in the beta-region the calculated angles are an average 2.1 degrees too low, indicating beta-expansion in extended sheets. The analysis demonstrates that a definite correlation exists between the phi/psi-torsions and the extension of N-C(alpha)-C' in protein crystal structures and that the deviations from ideal geometry derived from fitting models to the crystallographic data are similar to the ab initio results. We expect the procedure to be generally important for establishing detailed dictionaries of flexible geometry functions for use in empirical peptide and protein modeling.