Abstract

Solid-state near-rotary-resonance measurements of the spin–lattice relaxation rate in the rotating frame (R1ρ) is a powerful NMR technique for studying molecular dynamics in the microsecond time scale. The small difference between the spin-lock (SL) and magic-angle-spinning (MAS) frequencies allows sampling very slow motions, at the same time it brings up some methodological challenges. In this work, several issues affecting correct measurements and analysis of 15N R1ρ data are considered in detail. Among them are signal amplitude as a function of the difference between SL and MAS frequencies, “dead time” in the initial part of the relaxation decay caused by transient spin-dynamic oscillations, measurements under HORROR condition and proper treatment of the multi-exponential relaxation decays. The multiple 15N R1ρ measurements at different SL fields and temperatures have been conducted in 1D mode (i.e. without site-specific resolution) for a set of four different microcrystalline protein samples (GB1, SH3, MPD-ubiquitin and cubic-PEG-ubiquitin) to study the overall protein rocking in a crystal. While the amplitude of this motion varies very significantly, its correlation time for all four sample is practically the same, 30–50 μs. The amplitude of the rocking motion correlates with the packing density of a protein crystal. It has been suggested that the rocking motion is not diffusive but likely a jump-like dynamic process.

Highlights

  • Spin–lattice relaxation in the rotating frame is a powerful NMR method used to obtain quantitative information on molecular dynamics in the microsecond timescale

  • The SH3 domain and the GB1 protein were measured at Halle University, while the two ubiquitin samples were measured at the Institut de Biologie Structurale (IBS) Grenoble

  • A small difference between the spin-lock and magic angle spinning (MAS) frequencies allows expanding the frequency range of the sampled molecular motions towards rather low frequencies

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Summary

Introduction

Spin–lattice relaxation in the rotating frame is a powerful NMR method used to obtain quantitative information on molecular dynamics in the microsecond timescale. Measurements of the 15N rotating-frame relaxation rate (R1ρ = 1/T1ρ) have been widely applied in the solid-state NMR studies of protein dynamics. The ability to vary the spinlock field strength from < 1 to 40–50 kHz enables covering a wide frequency range of dynamics, and the simultaneous analysis of both the chemical-exchange contribution to R1ρ and the dipole/CSA relaxation mechanisms (Ma et al 2014; Lamley et al 2015b) provides abundant data that characterize protein dynamics in much detail. When measured under MAS, R1ρ due to the heteronuclear dipolar and CSA relaxation mechanisms is proportional to the following combination of the spectral-density functions: R

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