Theory of stochastic dipolar recoupling in solid-state nuclear magnetic resonance

Short and long range 2D 15N-15N NMR correlations among peptide groups by novel solid state dipolar mixing schemes

A recently developed homonuclear dipolar recoupling scheme, Adiabatic Linearly FREquency Swept reCOupling (AL FRESCO), was applied to record two-dimensional (2D) 15N-15N correlations on uniformly 15N-labeled GB1 powders. A major feature exploited in these 15N-15N correlations was AL FRESCO's remarkably low RF power demands, which enabled seconds-long mixing schemes when establishing direct correlations. These 15N-15N mixing schemes proved efficient regardless of the magic-angle spinning (MAS) rate and, being nearly free from dipolar truncation effects, they enabled the detection of long-range, weak dipolar couplings, even in the presence of strong short-range dipolar couplings. This led to a connectivity information that was significantly better than that obtained with spontaneously proton-driven, 15N spin-diffusion experiments. An indirect approach producing long-range 15N-15N correlations was also tested, relying on short (ms-long) 1HN-1HN mixings schemes while applying AL FRESCO chirped pulses along the 15N channel. These indirect mixing schemes produced numerous long-distance Ni-Ni±n (n = 2 - 5) correlations, that might be useful for characterizing three-dimensional arrangements in proteins. Once again, these AL FRESCO mediated experiments proved more informative than variants based on spin-diffusion-based 1HN-1HN counterparts.

Solid-State NMR: Methods for Biological Solids

In the last two decades, solid-state nuclear magnetic resonance (ssNMR) spectroscopy has transformed from a spectroscopic technique investigating small molecules and industrial polymers to a potent tool decrypting structure and underlying dynamics of complex biological systems, such as membrane proteins, fibrils, and assemblies, in near-physiological environments and temperatures. This transformation can be ascribed to improvements in hardware design, sample preparation, pulsed methods, isotope labeling strategies, resolution, and sensitivity. The fundamental engagement between nuclear spins and radio-frequency pulses in the presence of a strong static magnetic field is identical between solution and ssNMR, but the experimental procedures vastly differ because of the absence of molecular tumbling in solids. This review discusses routinely employed state-of-the-art static and MAS pulsed NMR methods relevant for biological samples with rotational correlation times exceeding 100's of nanoseconds. Recent developments in signal filtering approaches, proton methodologies, and multiple acquisition techniques to boost sensitivity and speed up data acquisition at fast MAS are also discussed. Several examples of protein structures (globular, membrane, fibrils, and assemblies) solved with ssNMR spectroscopy have been considered. We also discuss integrated approaches to structurally characterize challenging biological systems and some newly emanating subdisciplines in ssNMR spectroscopy.

Solid-State NMR Dipolar and Chemical Shift Anisotropy Recoupling Techniques for Structural and Dynamical Studies in Biological Systems

With the development of NMR methodology and technology during the past decades, solid-state NMR (ssNMR) has become a particularly important tool for investigating structure and dynamics at atomic scale in biological systems, where the recoupling techniques play pivotal roles in modern high-resolution MAS NMR. In this review, following a brief introduction on the basic theory of recoupling in ssNMR, we highlight the recent advances in dipolar and chemical shift anisotropy recoupling methods, as well as their applications in structural determination and dynamical characterization at multiple time scales (i.e., fast-, intermediate-, and slow-motion). The performances of these prevalent recoupling techniques are compared and discussed in multiple aspects, together with the representative applications in biomolecules. Given the recent emerging advances in NMR technology, new challenges for recoupling methodology development and potential opportunities for biological systems are also discussed.

Recent progress in dipolar recoupling techniques under fast MAS in solid-state NMR spectroscopy

With the recent advances in NMR hardware and probe design technology, magic-angle spinning (MAS) rates over 100 ​kHz are accessible now, even on commercial solid NMR probes. Under such fast MAS conditions, excellent spectral resolution has been achieved by efficient suppression of anisotropic interactions, which also opens an avenue to the proton-detected NMR experiments in solids. Numerous methods have been developed to take full advantage of fast MAS during the last decades. Among them, dipolar recoupling techniques under fast MAS play vital roles in the determination of the molecular structure and dynamics, and are also key elements in multi-dimensional correlation NMR experiments. Herein, we review the dipolar recoupling techniques, especially those developed in the past two decades for fast-to-ultrafast MAS conditions. A major focus for our discussion is the ratio of RF field strength (in frequency) to MAS frequency, ν₁/ν_r, in different pulse sequences, which determines whether these dipolar recoupling techniques are suitable for NMR experiments under fast MAS conditions. Systematic comparisons are made among both heteronuclear and homonuclear dipolar recoupling schemes. In addition, the schemes developed specially for proton-detection NMR experiments under ultrafast MAS conditions are highlighted as well.

Zero-quantum stochastic dipolar recoupling in solid state nuclear magnetic resonance

We present the theoretical description and experimental demonstration of a zero-quantum stochastic dipolar recoupling (ZQ-SDR) technique for solid state nuclear magnetic resonance (NMR) studies of (13)C-labeled molecules, including proteins, under magic-angle spinning (MAS). The ZQ-SDR technique combines zero-quantum recoupling pulse sequence blocks with randomly varying chemical shift precession periods to create randomly amplitude- and phase-modulated effective homonuclear magnetic dipole-dipole couplings. To a good approximation, couplings between different (13)C spin pairs become uncorrelated under ZQ-SDR, leading to spin dynamics (averaged over many repetitions of the ZQ-SDR sequence) that are fully described by an orientation-dependent N × N polarization transfer rate matrix for an N-spin system, with rates that are inversely proportional to the sixth power of internuclear distances. Suppression of polarization transfers due to non-commutivity of pairwise couplings (i.e., dipolar truncation) does not occur under ZQ-SDR, as we show both analytically and numerically. Experimental demonstrations are reported for uniformly (13)C-labeled L-valine powder (at 14.1 T and 28.00 kHz MAS), uniformly (13)C-labeled protein GB1 in microcrystalline form (at 17.6 T and 40.00 kHz MAS), and partially labeled (13)C-labeled protein GB1 (at 14.1 T and 40.00 kHz MAS). The experimental results verify that spin dynamics under ZQ-SDR are described accurately by rate matrices and suggest the utility of ZQ-SDR in structural studies of (13)C-labeled solids.

Controlling spin-spin network dynamics by repeated projective measurements

We show that coupled-spin network manipulations can be made highly effective by repeated projections of the evolving quantum states onto diagonal density-matrix states (populations). As opposed to the intricately crafted pulse trains that are often used to fine-tune a complex network's evolution, the strategy hereby presented derives from the "quantum Zeno effect" and provides a highly robust route to guide the evolution by destroying all unwanted correlations (coherences). We exploit these effects by showing that a relaxationlike behavior is endowed to polarization transfers occurring within a N-spin coupled network. Experimental implementations yield coupling constant determinations for complex spin-coupling topologies, as demonstrated within the field of liquid-state nuclear magnetic resonance.

Broad-band homo-nuclear correlations assisted by 1H irradiation for bio-molecules in very high magnetic field at fast and ultra-fast MAS frequencies

We propose a new broadband second-order proton-assisted (13)C-(13)C correlation experiment, SHANGHAI. The (13)C-(13)C magnetization transfer is promoted by (1)H irradiation with interspersed four phases super-cycling. This through-space homo-nuclear sequence only irradiates on the proton channel during the mixing time. SHANGHAI benefits from a large number of modulation sidebands, hence leading to a large robustness with respect to chemical shift differences, which permits its use in a broad MAS frequency range. At ultra-fast MAS (ν(R) 60 kHz), SHANGHAI is only efficient when the amplitude of (1)H recoupling rf-field is close to half the spinning speed (ν(1) ≈ ν(R)/2). However, at moderate to fast MAS (ν(R)=20-35 kHz), SHANGHAI is efficient at any rf-power level larger than ν(1) ≈ 10 kHz, which simultaneously permits avoiding excessive heating of bio-molecules, and using large sample volumes. We show that SHANGHAI can be employed at the very high magnetic field of 23.5 T and then allows the observation of correlation between (13)C nuclei, even if their resonance frequencies differ by more than 38 kHz.

Solid-state NMR studies of amyloid fibril structure

Current interest in amyloid fibrils stems from their involvement in neurodegenerative and other diseases and from their role as an alternative structural state for many peptides and proteins. Solid-state nuclear magnetic resonance (NMR) methods have the unique capability of providing detailed structural constraints for amyloid fibrils, sufficient for the development of full molecular models. In this article, recent progress in the application of solid-state NMR to fibrils associated with Alzheimer's disease, prion fibrils, and related systems is reviewed, along with relevant developments in solid-state NMR techniques and technology.

A Monte Carlo/simulated annealing algorithm for sequential resonance assignment in solid state NMR of uniformly labeled proteins with magic-angle spinning

We describe a computational approach to sequential resonance assignment in solid state NMR studies of uniformly (15)N,(13)C-labeled proteins with magic-angle spinning. As input, the algorithm uses only the protein sequence and lists of (15)N/(13)C(alpha) crosspeaks from 2D NCACX and NCOCX spectra that include possible residue-type assignments of each crosspeak. Assignment of crosspeaks to specific residues is carried out by a Monte Carlo/simulated annealing algorithm, implemented in the program MC_ASSIGN1. The algorithm tolerates substantial ambiguity in residue-type assignments and coexistence of visible and invisible segments in the protein sequence. We use MC_ASSIGN1 and our own 2D spectra to replicate and extend the sequential assignments for uniformly-labeled HET-s(218-289) fibrils previously determined manually by Siemer et al. (J. Biomol. NMR, 34 (2006) 75-87) from a more extensive set of 2D and 3D spectra. Accurate assignments by MC_ASSIGN1 do not require data that are of exceptionally high quality. Use of MC_ASSIGN1 (and its extensions to other types of 2D and 3D data) is likely to alleviate many of the difficulties and uncertainties associated with manual resonance assignments in solid state NMR studies of uniformly labeled proteins, where spectral resolution and signal-to-noise are often sub-optimal.

Homonuclear dipolar recoupling techniques for structure determination in uniformly 13C-labeled proteins

In solid-state NMR magic angle spinning is often used to remove line broadening associated with anisotropic interactions, such as chemical shift anisotropy and dipolar couplings. Dipolar recoupling refers to sequences of pulses designed to reintroduce dipolar interactions that are otherwise averaged by magic angle spinning. One of the key applications of homonuclear (and heteronuclear) dipolar recoupling is for the purpose of protein structure determination. Recoupling experiments, originally designed for applications in spin-pair labeled samples, have been revised in recent years for applications in samples with extensive or uniform incorporation of isotopic labels. In these samples multiple internuclear distances can in principle be probed simultaneously, but the dipolar truncation effects (i.e. attenuation of the effects of weak couplings by strong ones) circumvent such measurements. In this article we review some of the recent developments in homonuclear recoupling methods that allow overcoming this problem.