Determination of φ and χ1 Angles in Proteins from 13C−13C Three-Bond J Couplings Measured by Three-Dimensional Heteronuclear NMR. How Planar Is the Peptide Bond?

Abstract

A new pulse scheme, HN(CO)C, is described for simultaneous measurement of three-bond 3JC‘Cβ and 3JC‘Cγ couplings in proteins uniformly enriched with 13C and 15N. The experiment is demonstrated for human ubiquitin and apo-calmodulin, which have rotational correlation times of 4 and 8 ns, respectively. A Karplus relation, 3JC‘Cβ = 1.59 cos2(φ − 120°) − 0.67 cos(φ − 120°) + 0.27 Hz, is obtained by correlating the ubiquitin 3JC‘Cβ values with backbone φ angles from its crystal structure. Using these crystal structure φ angles, the root-mean-square difference (rmsd) between experimental 3JC‘Cβ values and those predicted from the Karplus relation is 0.24 Hz. When using φ angles derived from 3JHNHα, 3JHNCβ, 3JHNC‘, 3JHαC‘, and 3JC‘C‘, this rmsd decreases to 0.17 Hz. Peptide backbone φ angles can be derived from J couplings between either C‘i-1 or HNi and the three Cαi substituents, C‘i, Cβi, Hαi. For 45 residues in ubiquitin all six couplings have been measured, and the φ angles derived for these residues from couplings involving HNi agree to within experimental error (rmsd = 7.7°) with φ angles derived from the three J couplings to C‘i-1. This confirms that, on average, the angle between the C‘i-1− Ni − Cαi and HNi− Ni − Cαi planes is considerably less than 7.7° and excludes the possibility of large deviations from peptide bond planarity in α-helices. Intraresidue 3JC‘Cγ couplings for aliphatic residues are found to range from 0.7 Hz for a gauche conformation to ca. 4 Hz for a trans conformation.