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

Abstract

N CSA-15 N-1 H 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 15 N 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. 15 N 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 M X 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 R -C i R 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.

Structural dynamics of bio-macromolecules by NMR: The slowly relaxing local structure approach

“…There is compelling evidence within the scope of NMR spin relaxation in proteins for motion about the ${\text{C}}_{\text{i}-1}^{\alpha }-{\text{C}}_{\text{i}}^{\alpha }$ axis, which is tilted from the N–H bond direction [20,46–50,65,66], which thus represents non-trivial geometry, and for asymmetric motions [20,34,35,46,48–50,67–71]. The current MD-based picture visualizes that short-range correlations between dihedral-angles dominate protein dynamics, with information propagating through the protein in a diffusion-like manner via local interaction networks [72].…”

An Improved Picture of Methyl Dynamics in Proteins from Slowly Relaxing Local Structure Analysis of 2H Spin Relaxation

“…[16][17][18][19][20][21][22][23] Two rotators, representing the global motion of the protein, R C , and the local motion of the probe (C-D bond in this case), R L , are treated. The motions of the protein and the probe are coupled by a local potential, U(Ω C'M ), where C' denotes the local director fixed in the protein, and M the local ordering/local diffusion frame fixed in the probe.…”

“…[16][17][18][19][20][21][22][23] This has been accomplished by applying to NMR spin relaxation in proteins 16 the Slowly Relaxing Local Structure (SRLS) approach of Freed and co-workers. [24][25][26] SRLS can be considered the generalization of MF, yielding the latter in asymptotic limits.…”

“…It features explicitly local motional modes parallel and perpendicular to the methyl rotation axis. [16][17][18][19][20][21][22][23]25,26 and accounts rigorously for the tilt between a rhombic local ordering frame, M, and the magnetic frame, Q. The Euler angles Ω C'M , which relate the M frame to a local director frame, C' (e.g., the equilibrium C-CH 3 orientation), are governed by the coupling/ ordering potential.…”

A Multifrequency Electron Spin Resonance Study of T4 Lysozyme Dynamics Using the Slowly Relaxing Local Structure Model

“…17,18 It has also been used in the analysis of protein NMR relaxation data. [19][20][21][22] Compared with the MOMD model, more experimental data are needed to determine the larger number of fitting parameters associated with the SRLS model. One approach is to use the global diffusion constant estimated from independent experiments or from hydrodynamic theory.…”