NMR Determination of Amide N−H Equilibrium Bond Length from Concerted Dipolar Coupling Measurements

Abstract

The N-H bond length in backbone peptide groups of the protein GB3 has been studied by liquid crystal NMR, using five structurally conserved mutants of this protein. In the absence of additional information, the impact of dynamic fluctuations of the N-H vector orientation on the 15N-1H dipolar interaction cannot be separated from a change in N-H bond length. However, a change in N-H bond length directly impacts the orientation of C′-H vectors in the peptide group, and simultaneous analysis of 13C′-HN and 15N-HN residual dipolar couplings, measured under five different alignment orientations, permits modelfree determination of the average equilibrium N-H bond length in GB3, yielding rNHeq = 1.008 ± 0.006 A. Anharmonicity of the bond stretching results in a slightly longer time-averaged bond length = 1.015 ± 0.006 A, and an effective bond length reff = -1/3 = 1.023 ± 0.006 A pertinent for NMR relaxation analysis, not including the impact of zero-point or other angular fluctuations in N-H orientation. Using a reference frame defined by the backbone Cα-C′ vectors of the protein, angular fluctuations for N-H vectors in elements of secondary structure are approximately 1.5 fold larger for out-of-plane fluctuations than motions within the peptide plane and not much larger than anticipated on the basis of quantum mechanical analysis of their zero-point librations.