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

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 N-15-H-1 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 C-13'-H-N and N-15-H-N residual dipolar couplings, measured under five different alignment orientations, permits modelfree determination of the average equilibrium N-H bond length in GB3, yielding r(NH)(eq) = 1.008 +/- 0.006 angstrom. Anharmonicity of the bond stretching results in a slightly longer time-averaged bond length < r(NH)> = 1.015 +/- 0.006 angstrom, and an effective bond Length r(eff) = < r(NH)(-3)>(-1/3) = 1.023 +/- 0.006 angstrom 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 C degrees-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.