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

Abstract

15N CSA−15N-1H dipolar cross-correlation (ηxy) in proteins has been treated thus far with the model-free (MF) approach, where the global (RC) and local (RL) motions are assumed to be decoupled as a consequence of RL ≫ RC. In the context of ηxy, 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 ηxy for arbitrary time scale separations between RL and RC. Simulations of ηxy for slow local motions are presented herein for the first time. Experimental ηxy 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, Rex, “absorbs” potential rhombicity when axial potentials are used to fit the data. 15N CSA variability and RC anisotropy are shown to have a small effect on the analysis. The shape of the rhombic potentials detected corresponds to nearly “planar YMXM 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 ≈ RC regime, and makes possible associating the local director with the − 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.