Determination of Relative N−HN, N−C‘, Cα−C‘, and Cα−Hα Effective Bond Lengths in a Protein by NMR in a Dilute Liquid Crystalline Phase

Abstract

Weak alignment of solute macromolecules with the magnetic field can be achieved in a dilute, aqueous liquid crystalline phase of planar phospholipid micelles, consisting of mixtures of dimyristoylphosphatidylcholine (DMPC) and dihexanoylphosphatidylcholine (DHPC). Alignment of proteins in such a medium is sufficiently weak to retain the simplicity of the isotropic solution NMR spectrum but strong enough to permit accurate measurement of residual one-bond dipolar couplings. Highly accurate one-bond N−H N, C α −H α, C α −C‘, and C‘−N and two-bond C‘−H N dipolar couplings were measured in 13 C/ 15 N-enriched ubiquitin. Together with knowledge of the protein's three-dimensional structure, the dipolar couplings permit calculation of the relative, vibrationally corrected average bond lengths for these interactions. Assuming a C‘−N bond length of 1.329 Å (Engh, R. A.; Huber, R. Acta Crystallogr. 1992, A47, 392−400), the relative C α −C‘ distance of 1.526 Å is found to be in excellent agreement with results from Engh and Huber (1.525 Å). Using a C‘−N bond length of 1.329 Å as a reference, N−H N (1.041 ± 0.006 Å) and C α −H α (1.117 ± 0.007 Å) are considerably longer than equilibrium or average internuclear distances derived from ab initio calculations, electron diffraction, neutron diffraction, or microwave spectroscopy. The increase in effective N−H N and C α −H α bond lengths is attributed to a decrease in the corresponding dipolar couplings resulting from fast librations, which must be of considerably larger amplitude than the C α −C‘ and C‘−N angular fluctuations. Accurate knowledge of the relative effective N−H N, C α −H α, C α −C‘, C‘−N, and two-bond C‘−H N effective internuclear distances is essential for determining the magnitude of the molecular alignment tensor, for using the dipolar couplings in macromolecular structure determination, and for extracting angular information from recently described cross correlation experiments.