Determination of dihedral angles in peptides through experimental and theoretical studies of alpha-carbon chemical shielding tensors

A simple method for the determination of backbone dihedral angles in peptides and proteins is presented. The chemical-shift anisotropies (CSA) of the central alanine alpha-carbon in powdered crystalline tripeptides, whose structures have been determined previously by X-ray crystallography, were measured by cross-polarization magic-angle-spinning nuclear magnetic resonance. The experimental CSA values were correlated with ab initio chemical-shielding calculations over Ramanchandran phi/psi space on an N-formyl-L-alanine amide fragment. Using this correlation, phi/psi probability surfaces for one of the tripeptides were calculated based only on the alpha-carbon CSA, allowing a prediction of backbone angles. Dihedral angles predicted by these calculations fall within +/-12 degrees of the values determined by crystallography. This approach should be useful in the determination of solid-slate protein structure.