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 orientati on and the magnitude of the chemical shift anisotropy (CSA) tensor in molec ules with a pair of spin 1/2 nuclei, typically C-13-H-1 or N-15-H-1. The me thod relies on the fact that the longitudinal cross-correlation rate as wel l as a linear combination of the autorelaxation rates of longitudinal heter ospin magnetization, longitudinal two-spin order and longitudinal proton ma gnetization are proportional to the spectral density at the Larmor frequenc y 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 sl ow tumbling, nor is it sensitive to chemical exchange broadening. It is tes ted on the 22 amino acid residue peptide motilin, selectively C-13 labeled in the ortho positions in the ring of the single tyrosine residue. In the a pproximation of an axially symmetric C-13 CSA tensor, the symmetry axis of the CSA tensor makes an angle of 23 degrees +/- 1 degrees to the C-13-H-1 b ond vector, and has a magnitude of 156 +/- 5 ppm. This is in close agreemen t with solid-state NMR data on tyrosine powder [Frydman et al. (1992) Isr. J. Chem., 32, 161-164].