J. Am. Chem. Soc., 2008, 130 (49), pp 16518–16520

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

Lishan Yao, Beat Vögeli, Jinfa Ying and Ad Bax

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 Å. Anharmonicity of the bond stretching results in a slightly longer time-averaged bond length = 1.015 ± 0.006 Å, and an effective bond length reff = −1/3 = 1.023 ± 0.006 Å 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.