Mode-Coupling Analysis of ¹⁵N CSA-¹⁵N-¹H Dipolar Cross-Correlation in Proteins. Rhombic Potentials at the N-H Bond

¹⁵N CSA-¹⁵N-¹H dipolar cross-correlation (η_xy) in proteins has been treated thus far with the model-free (MF) approach, where the global (R^C) and local (R^L) motions are assumed to be decoupled as a consequence of R^L ≫ R^C. In the context of η_xy, it is additionally assumed that the local motion is very fast and highly symmetrical. We have recently applied to auto-correlated ¹⁵N spin relaxation the slowly relaxing local structure (SRLS) approach, which accounts rigorously for mode-coupling. SRLS can analyze η_xy, for arbitrary time scale separations between R^L and R^C. Simulations of η_xy, for slow local motions are presented herein for the first time. Experimental η_xy, values of RNase and AKeco could not be reproduced from best-fit parameters generated by data fitting that used axial potentials. Calculations showed they are reproducible using rhombic coupling/ordering potentials. The conformational exchange term, R_ex, "absorbs" potential rhombicity when axial potentials are used to fit the data. ¹⁵N CSA variability and R^C anisotropy are shown to have a small effect on the analysis. The shape of the rhombic potentials detected corresponds to nearly "planar Y_MX_M ordering" (M denotes the local ordering frame). This potential form is consistent with the known geometry of the peptide plane, the SRLS dynamic model in the R_⊥^L ≈ R^C regime, and makes possible associating the local director with the C_i-1 ^α-C_i^α axis. It is shown that back-calculation of NMR variables from the best-fit parameters and comparison with the experimental counterparts is an effective tool for identifying inappropriate elements of the dynamic model and can thereby help improve it.