Quantitative estimation of magnitude and orientation of the CSA tensor from field dependence of longitudinal NMR relaxation rates

A method is presented that makes it possible to estimate both the orientation and the magnitude of the chemical shift anisotropy (CSA) tensor in molecules with a pair of spin 1/2 nuclei, typically ¹³C-¹H or ¹⁵ N-¹H. The method relies on the fact that the longitudinal cross-correlation rate as well as a linear combination of the autorelaxation rates of longitudinal heterospin magnetization, longitudinal two-spin order and longitudinal proton magnetization are proportional to the spectral density at the Larmor frequency of the heterospin. Therefore the ratio between the cross-correlation rate and the above linear combination is independent of the dynamics. From the field dependence of the ratio both the magnitude and the orientation of the CSA tensor can be estimated. The method is applicable to molecules in all motional regimes and is not limited to molecules in extreme narrowing or slow tumbling, nor is it sensitive to chemical exchange broadening. It is tested on the 22 amino acid residue peptide motilin, selectively ¹³ C labeled in the ortho positions in the ring of the single tyrosine residue. In the approximation of an axially symmetric ¹³C CSA tensor, the symmetry axis of the CSA tensor makes an angle of 23° ± 1° to the ¹³ C-¹H bond vector, and has a magnitude of 156 ± 5 ppm. This is in close agreement with solid-state NMR data on tyrosine powder Frydman et al. (1992) Isr. J. Chem., 32, 161–164].