Bumps on the Road: The Way to Clean Relaxation Dispersion Magic-Angle Spinning NMR

Abstract

Microsecond-to-millisecond motions are instrumental for many biomolecular functions, including enzymatic activity and ligand binding. Bloch-McConnell Relaxation Dispersion (BMRD) Nuclear Magnetic Resonance (NMR) spectroscopy is a key technique for studying these dynamic processes. While BMRD experiments are routinely used to probe protein motions in solution, the experiment is more demanding in the solid state, where dipolar couplings complicate the spin dynamics. It is believed that high deuteration levels are required and sufficient to obtain accurate and quantitative data. Here we show that even under fast magic-angle spinning and high levels of deuteration artifactual "bumps" in ¹⁵N R_1ρ BMRD profiles are common. The origin of these artifacts is identified as a second-order three-spin Mixed Rotational and Rotary Resonance (MIRROR) recoupling condition. These artifacts are found to be a significant confounding factor for the accurate quantification of microsecond protein dynamics using BMRD in the solid state. We show that the application of low-power continuous wave (CW) decoupling simultaneously with the ¹⁵N spin-lock leads to the suppression of these conditions and enables quantitative measurements of microsecond exchange in the solid state. Remarkably, the application of decoupling allows the measurement of accurate BMRD even in fully protonated proteins at 100 kHz MAS, thus extending the scope of μs dynamics measurements in MAS NMR.

1

Several examples of artifacts observed in solid-state NMR ¹⁵N Bloch-McConnell relaxation dispersion curves. The residue number is given in square brackets. Gray lines show fits of a two-site exchange model to the data, while blue lines show a two-site exchange model with the addition of a phenomenological model of the artifacts as a visual guide. In all cases, the protein samples were perdeuterated and back-exchanged with ¹H₂O. (a) ubiquitin crystallized in MPD. (b) TET2 (this work). (c) Microcrystalline GB1 with 2 mM Gd­(DTPA-BMA). (d) huPrP23-144 A117 V mutant (this work).

2

Variation of the observed artifacts under different experimental conditions. (a, b) Measurements made at 55.56 kHz MAS on perdeuterated ubiquitin (with ¹³C_δ/²H _βγ /¹⁵N_ϵ labeled arginine) at two magnetic fields (note that owing to probe head limitations, the 600 MHz measurements were made at a higher temperature than those at 700 MHz). Inset axes show the same data, only with the frequency axis in units of ¹H ppm (that is, divided by the ¹H Larmor frequency). (c, d) Dispersion curves at 700 MHz (¹H Larmor frequency) on perdeuterated ubiquitin at 55.56 and 100.0 kHz MAS. (e, f) Dispersion curves at 100.0 kHz MAS, 700 MHz, on protonated and perdeuterated ubiquitin (both with ¹³C_δ/²H _βγ /¹⁵N_ϵ labeled arginine). Uncertainty bars are illustrated at ±1 standard deviation. The SI contains a full set of dispersion curves for each condition given here.

3

Simulations of the bump artifact. (a) Illustrative spin system. The chemical shifts of the ¹H spins were set at −700 and +700 Hz, and 30 s^–1 of random field relaxation was applied to them to represent the effect of the bulk proton spin bath (note that in the absence of this random field relaxation, there is insignificant contribution to the dispersion). Simulations are shown both under irradiation at the MIRROR condition (1270 Hz (shifted from 1400 Hz owing to the MAS dependence), solid red) and not at the MIRROR condition (100 Hz, dashed gray). These simulations were performed at 55.56 kHz MAS. (ai) evolution of the transverse ¹⁵N magnetization. (aii,aiii) evolution of the longitudinal magnetization on the two protons. (b) effective R _1ρ measured under irradiation of the ¹⁵N at frequency ν₁. (c) Frequency at which the bump artifact occurs as a function of spinning frequency, ν _r . (d) Maximum R _1ρ rate constant as a function of spinning frequency.

4

Dispersion profiles for sites in close proximity to serines and threonines. Left: The local structure surrounding S20, T22, T55, S57 (PDB: 3ONS ). Right: Selected dispersion profiles (measured at a ¹H Larmor frequency of 700 MHz and under 55.56 kHz MAS) in close proximity to this region. The difference in chemical shift between the adjacent amide ¹H and 5 ppm, a frequency typical of Thr/Ser OH groups, is indicated by a dashed red line. Uncertainty bars are illustrated at ±1 standard deviation.

5

Application of decoupling to remove the bump artifact. (a) GAMMA simulations of the effect of low power CW decoupling on the bump artifact. (b–d) Comparison of dispersion curves measured in protonated and perdeuterated ubiquitin, with or without 16 kHz CW ¹H decoupling at 100.0 kHz MAS. (e–g) Comparison of dispersion curves measured in perdeuterated TET2 at 55.56 kHz with and without 16 kHz CW decoupling (note that only 48 frequencies were recorded for nondecoupled TET2). Uncertainty bars are illustrated at ±1 standard deviation.

6

Modeling of the artifactual bump residual, Δ_1ρ, according to the local chemical environment of the nuclear spin. (a) Assuming that one of the protons involved in the three-spin MIRROR recoupling is the directly bound amide proton, the spin-lock RF frequency can be related to a ¹H chemical shift of the other spin involved. Subtracting the decoupled BMRD profile from the nondecoupled profile (in this case, for ¹H ubiquitin at 100.0 kHz MAS) gives a “bump residual”. (b–d) Comparison of experimental “bump residuals” (¹H (purple) and ²H (green) ubiquitin (with arginine labeling, see Methods) at 100.0 kHz MAS) with a four parameter model based on a structural model of ubiquitin (PDB: 3ONS). Uncertainty bars are illustrated at ±1 standard deviation.

7

Consideration of the impact of not accounting for the bump artifact. Relaxation dispersion profiles measured at 100.0 kHz MAS in perdeuterated and protonated ubiquitin with and without decoupling were analyzed separately. For each case, all well-resolved sites were fit with a single k _ex value. A two-site exchange model was used for all sites in a two step fitting process; first, all residues were included. Then, any residues for which ϕ_ex < 10⁵ (rad s^–1)² had ϕ_ex set to 0. The results of the second fitting step are shown. (a–c) Relaxation dispersion profiles with fit models shown as dashed lines. (d) The resulting global fit k _ex values for each experimental setup. (e) The resulting ϕ_ex values for a selection of residues.