Determination of the backbone dihedral angles phi in human ubiquitin from reparametrized empirical Karplus equations

The backbone dihedral angle phi in polypeptides is characterized by four different J couplings: (3)J(HNH alpha), (3)J(HNC'), (3)J(HNC beta), and (3)J(H alpha C'). E.COSY and quantitative J correlation techniques have been used to measure these couplings in the protein human ubiquitin, uniformly enriched in C-13 and N-15. Assuming that the dihedral backbone angles in solution are identical to those in the X-ray structure of this protein and that H-N is located in the C'-N-C-alpha plane, Karplus relations for (3)J(HNH alpha), (3)J(H alpha C'), and (3)J(HNC beta), have been reparametrized. The root-mean-square (rms) difference between measured values of (3)J(HNH alpha), (3)J(H alpha C beta), (3)J(HNC') and their corresponding Karplus curves are 0.53, 0.25, 0.24, and 0.36 Hz, respectively, whereas the precision of these measurements is considerably better. For any given residue, the differences between the four measured J couplings and values predicted by their Karplus curves on the basis of the X-ray structure-derived phi angle are highly correlated with one another. On average, a root-mean-square change of 5.7 degrees in the X-ray derived phi angles is needed to obtain optimal agreement with all four measured J couplings. There is no clear correlation between the phi angle correction needed and the out-of-plane position of the amide proton predicted by ab initio calculations. The small differences in phi angles therefore presumably result from small uncertainties in the atomic positions of the 1.8 Angstrom X-ray structure. However, they may also be caused by genuine differences between the structure of the protein in solution and in the crystalline state or contain a contribution resulting from deviations from the assumption that the H-N-N-C-alpha-H-alpha dihedral angle equals phi - 60 degrees.