The effect of noncollinearity of ¹⁵N-¹H dipolar and ¹⁵N CSA tensors and rotational anisotropy on ¹⁵N relaxation, CSA/dipolar cross correlation, and TROSY

Current approaches to ¹⁵N relaxation in proteins assume that the ¹⁵N-¹H dipolar and ¹⁵N CSA tensors are collinear. We show theoretically that, when there is significant anisotropy of molecular rotation, different orientations of the two tensors, experimentally observed in proteins, nucleic acids, and small peptides, will result in differences in site-specific correlation functions and spectral densities. The standard treatments of the rates of longitudinal and transverse relaxation of amide ¹⁵N nuclei, of the ¹⁵N CSA/¹⁵N-¹H dipolar cross correlation, and of the TROSY experiment are extended to account for the effect of noncollinearity of the ¹⁵N-¹H dipolar and ¹⁵N CSA (chemical shift anisotropy) tensors. This effect, proportional to the degree of anisotropy of the overall motion, (D is parallel with/D is perpendicular to - 1), is sensitive to the relative orientation of the two tensors and to the orientation of the peptide plane with respect to the diffusion coordinate frame. The effect is negligible at small degrees of anisotropy, but is predicted to become significant for D is parallel with/D is perpendicular to ≥ 1.5, and at high magnetic fields. The effect of noncollinearity of ¹⁵N CSA and ¹⁵N-¹H dipolar interaction is sensitive to both gross (hydrodynamic) properties and atomic-level details of protein structure. Incorporation of this effect into relaxation data analysis is likely to improve both precision and accuracy of the derived characteristics of protein dynamics, especially at high magnetic fields and for molecules with a high degree of anisotropy of the overall motion. The effect will also make TROSY efficiency dependent on local orientation in moderately anisotropic systems.