Determination of phi and chi(1) angles in proteins from C-13-C-13 three-bond J couplings measured by three-dimensional heteronuclear NMR. How planar is the peptide bond?

A new pulse scheme, HN(CO)C, is described for simultaneous measurement of three-bond 3J(C'C beta) and 3J(C'C gamma) couplings in proteins uniformly enriched with C-13 and N-15. The experiment is demonstrated for human ubiquitin and apo-calmodulin, which have rotational correlation times of 4 and 8 ns, respectively. A Karplus relation, 3J(C'C beta) = 1.59 cos(2)(phi-120 degrees) - 0.67 cos(phi-120 degrees) + 0.27 Hz, is obtained by correlating the ubiquitin 3J(C'C beta) values with backbone phi angles from its crystal structure. Using these crystal structure phi angles, the root-mean-square difference (rmsd) between experimental 3J(C'C beta) values and those predicted from the Karplus relation is 0.24 Hz. When using phi angles derived from 3J(HNH alpha), 3J(HNC beta), 3(JHC), 3(JH alpha C'), and 3J(C'C'), this rmsd decreases to 0.17 Hz. Peptide backbone phi angles can be derived from J couplings between either C'i-1 or H-i(N) and the three C-i(alpha) substituents, C'(i), C-i(beta), H-i(alpha). For 45 residues in ubiquitin in all six couplings have been measured, the phi angles derived from these residues from couplings involving H-i(N) agree to within experimental error (rmsd = 7.7 degrees) with phi angles derived from the three J couplings to C'(i-1). This confirms that, on average, the angle between the C'(i-1)-N-i-C-i(alpha) and H-i(N)-N-i-C-i(alpha) planes is considerably less than 7.7 degrees and excludes the possibility of large deviations from peptide bond planarity in alpha-helices. Intraresidue (3)J(C'C gamma), couplings for aliphatic residues are found to range form 0.7 Hz for a gauche conformation to ca 4 Hz for a trans conformation.