Limited Variations in <sup>15</sup>N CSA Magnitudes and Orientations in Ubiquitin Are Revealed by Joint Analysis of Longitudinal and Transverse NMR Relaxation

The site-specific magnitudes and orientations of the chemical shift tensors have been estimated for 70 backbone <sup>15</sup>N-nuclei in human ubiquitin from the field dependence of dynamic independent ratios between relaxation rates, both longitudinal and transverse, measured at 9.4, 11.7, 14.1, and 18.8 T. The results were jointly analyzed with previously published relaxation data [Fushman; Tjandra; Cowburn. <i>J. </i><i>Am. Chem. Soc.</i> <b>1998</b>, <i>120</i>, 10947−10952] [Kövér; Batta. <i>J. Mag. </i><i>Reson</i>. <b>2001</b>, <i>150</i>, 137−146]. The effective magnitudes of the anisotropies distribute around 169 ppm with a variability of 5 ppm. The orientation factors, reflecting the orientation of the CSA relative to the NH bond, distribute around −0.80 with a variability of 0.04, which corresponds to an angle between the symmetry axis of an assumed axially symmetric shielding tensor and the NH bond of 21.4°, and a variability of 2.3°. Correlations with the isotropic <sup>15</sup>N-chemical shifts are observed. Variations in the shielding anisotropies add uncertainty to the obtained order parameters proportional to the square of the magnetic field, when data are analyzed using an assumed invariant CSA tensor for all sites. Around 3% additional uncertainty in the order parameters for 800 MHz data is expected. The optimal TROSY field for amide nitrogen TROSY is estimated, with only marginal variations due to site-to-site variations. Variations in the shielding tensors add uncertainty to the exchange terms calculated from cross-correlation rates. An approach for estimating the exchange terms is suggested, where the uncertainty due to CSA-variations is minimized.