Frequency-selective homonuclear dipolar recoupling in solid state NMR

Great Offset Difference Internuclear Selective Transfer

Carbon-carbon dipolar recoupling sequences are frequently used building blocks in routine magic-angle spinning NMR experiments. While broadband homonuclear first-order dipolar recoupling sequences mainly excite intra-residue correlations, selective methods can detect inter-residue transfers and long-range correlations. Here, we present the great offset difference internuclear selective transfer (GODIST) pulse sequence optimized for selective carbonyl or aliphatic recoupling at fast magic-angle spinning, here, 55 kHz. We observe a 3- to 5-fold increase in intensities compared with broadband RFDR recoupling for perdeuterated microcrystalline SH3 and for the membrane protein influenza A M2 in lipid bilayers. In 3D (H)COCO(N)H and (H)CO(CO)NH spectra, inter-residue carbonyl-carbonyl correlations up to about 5 Å are observed in uniformly ¹³C-labeled proteins.

Quantum computation of molecular structure using data from challenging-to-classically-simulate nuclear magnetic resonance experiments

We propose a quantum algorithm for inferring the molecular nuclear spin Hamiltonian from time-resolved measurements of spin-spin correlators, which can be obtained via nuclear magnetic resonance (NMR). We focus on learning the anisotropic dipolar term of the Hamiltonian, which generates dynamics that are challenging to classically simulate in some contexts. We demonstrate the ability to directly estimate the Jacobian and Hessian of the corresponding learning problem on a quantum computer, allowing us to learn the Hamiltonian parameters. We develop algorithms for performing this computation on both noisy near-term and future fault-tolerant quantum computers. We argue that the former is promising as an early beyond-classical quantum application since it only requires evolution of a local spin Hamiltonian. We investigate the example of a protein (ubiquitin) confined on a membrane as a benchmark of our method. We isolate small spin clusters, demonstrate the convergence of our learning algorithm on one such example, and then investigate the learnability of these clusters as we cross the ergodic to non-ergodic phase transition by suppressing the dipolar interaction. We see a clear correspondence between a drop in the multifractal dimension measured across many-body eigenstates of these clusters, and a transition in the structure of the Hessian of the learning cost function (from degenerate to learnable). Our hope is that such quantum computations might enable the interpretation and development of new NMR techniques for analyzing molecular structure.

Selective Nuclear Magnetic Resonance Method for Enhancing Long-Range Heteronuclear Correlations in Solids

The long-range heteronuclear correlation remains a significant challenge in solid-state nuclear magnetic resonance (NMR), which is critical in the structural elucidation of biomolecular, material, and pharmaceutical solids. We propose a selective NMR method, heteronuclear selective phase-optimized recoupling (hetSPR), to selectively enhance long-range correlations of interest by utilizing characteristic chemical shifts. Compared to conventional methods, hetSPR can selectively enhance desired heteronuclear correlations (e.g., ¹H-¹³C and ¹H-¹⁹F) by factors up to 5 and largely suppress the unwanted ones. The method proves useful by enhancing the long-range correlation from an intermolecular ¹H-¹⁹F distance of 4.8 Å by a factor of 2.4 in a fluorinated pharmaceutical drug, bicalutamide, under fast magic-angle spinning. It does not use selective pulses and is thus user-friendly even for nonexperts. The new method is expected to boost solid-state NMR to elucidate the structures of various solids.

1H-Detected Biomolecular NMR under Fast Magic-Angle Spinning

Since the first pioneering studies on small deuterated peptides dating more than 20 years ago, 1H detection has evolved into the most efficient approach for investigation of biomolecular structure, dynamics, and interactions by solid-state NMR. The development of faster and faster magic-angle spinning (MAS) rates (up to 150 kHz today) at ultrahigh magnetic fields has triggered a real revolution in the field. This new spinning regime reduces the 1H-1H dipolar couplings, so that a direct detection of 1H signals, for long impossible without proton dilution, has become possible at high resolution. The switch from the traditional MAS NMR approaches with 13C and 15N detection to 1H boosts the signal by more than an order of magnitude, accelerating the site-specific analysis and opening the way to more complex immobilized biological systems of higher molecular weight and available in limited amounts. This paper reviews the concepts underlying this recent leap forward in sensitivity and resolution, presents a detailed description of the experimental aspects of acquisition of multidimensional correlation spectra with fast MAS, and summarizes the most successful strategies for the assignment of the resonances and for the elucidation of protein structure and conformational dynamics. It finally outlines the many examples where 1H-detected MAS NMR has contributed to the detailed characterization of a variety of crystalline and noncrystalline biomolecular targets involved in biological processes ranging from catalysis through drug binding, viral infectivity, amyloid fibril formation, to transport across lipid membranes.

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.

Modest Offset Difference Internuclear Selective Transfer via Homonuclear Dipolar Coupling

Homonuclear dipolar recoupling is routinely used for magic-angle spinning NMR-based structure determination. In fully protonated samples, only short proton-proton distances are accessible to broadband recoupling approaches because of high proton density. Selective methods allow detection of longer distances by directing polarization to a subset of spins. Here we introduce the selective pulse sequence MODIST, which recouples spins that have a modest chemical shift offset difference, and demonstrate it to selectively record correlations between amide protons. The sequence was selected for good retention of total signal, leading to up to twice the intensity for proton-proton correlations compared with other selective methods. The sequence is effective across a range of spinning conditions and magnetic fields, here tested at 55.555 and 100 kHz magic-angle spinning and at proton Larmor frequencies from 600 to 1200 MHz. For influenza A M2 in lipid bilayers, cross-peaks characteristic of a helical conformation are observed.

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.

Theory of frequency-selective homonuclear dipolar recoupling in solid-state NMR

In solid-state nuclear magnetic resonance, frequency-selective homonuclear dipolar recoupling is key to quantitative distance measurement or selective enhancement of correlations between atoms of interest in multiple-spin systems, which are not amenable to band-selective or broadband recoupling. Previous frequency-selective recoupling is mostly based on the so-called rotational resonance (R²) condition that restricts the application to spin pairs with resonance frequencies differing in integral multiples of the magic-angle spinning (MAS) frequency. Recently, we have proposed a series of frequency-selective homonuclear recoupling sequences called SPR (short for Selective Phase-optimized Recoupling), which have been successfully applied for selective ¹H-¹H or ¹³C-¹³C recoupling under from moderate (∼10 kHz) to ultra-fast (150 kHz) MAS frequencies. In this study, we fully analyze the average Hamiltonian theory of SPR sequences and reveal the origin of frequency selectivity in recoupling. The theoretical description, as well as numerical simulations and experiments, demonstrates that the frequency selectivity can be easily controlled by the flip angle (p) in the (p)_ϕk(p)_ϕk+π unit in the pSPR-N_n sequences. Small flip angles lead to frequency-selective recoupling, while large flip angles may lead to broadband recoupling in principle. The result shall shed new light on the design of homonuclear recoupling sequences with arbitrary frequency bandwidths.

Selective 1H-1H recoupling via symmetry sequences in fully protonated samples at fast magic angle spinning

Proton-detected solid-state NMR at fast Magic Angle Spinning (MAS) is becoming the norm to characterize molecules. Routinely ¹H-¹H and ¹H-X dipolar couplings are used to characterize the structure and dynamics of molecules. Selective proton recoupling techniques are emerging as a method for structural characterization via estimation of qualitative and quantitative distances. In the present study, we demonstrate through numerical simulations and experiments that the well-characterized CN^v_n sequences can also be tailored for selective recoupling of proton spins by employing C elements of the type (β)_Φ(4β)_Φ+π(3β)_Φ. Herein, several CN^v_n sequences were examined through numerical simulations and experiments. C6¹₄ recoupling sequence with a modified POST-element ((β)_Φ(4β)_Φ+π(3β)_Φ) shows selective polarization transfer efficiencies on the order of 40-50% between various proton spin pairs in fully protonated samples at rf amplitudes ranging from 0.3 to 0.8 times the MAS frequency. These selective recoupling sequences have been labeled as frequency-selective-CN^v_n sequences. The extent of selectivity, polarization transfer efficiency and the feasibility of experimentally measuring proton-proton distances in fully protonated samples are explored here. The development of efficient and robust selective ¹H-¹H recoupling experiments is required to structurally characterize molecules without artificial isotope enrichment or the need for diffracting crystals.

Understanding molecular mechanisms of biologics drug delivery and stability from NMR spectroscopy

Protein therapeutics carry inherent limitations of membrane impermeability and structural instability, despite their predominant role in the modern pharmaceutical market. Effective formulations are needed to overcome physiological and physicochemical barriers, respectively, for improving bioavailability and stability. Knowledge of membrane affinity, cellular internalization, encapsulation, and release of drug-loaded carrier vehicles uncover the structural basis for designing and optimizing biopharmaceuticals with enhanced delivery efficiency and therapeutic efficacy. Understanding stabilizing and destabilizing interactions between protein drugs and formulation excipients provide fundamental mechanisms for ensuring the stability and quality of biological products. This article reviews the molecular studies of biologics using solution and solid-state NMR spectroscopy on structural attributes pivotal to drug delivery and stability. In-depth investigation of the structure-function relationship of drug delivery systems based on cell-penetrating peptides, lipid nanoparticles and polymeric colloidal, and biophysical and biochemical stability of peptide, protein, monoclonal antibody, and vaccine, as the integrative efforts on drug product design, will be elaborated.

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.

Selectively Enhanced 1H-1H Correlations in Proton-Detected Solid-State NMR under Ultrafast MAS Conditions

Proton-detected solid-state NMR has emerged as a powerful analytical technique in structural elucidation via ¹H-¹H correlations, which are mostly established by broadband methods. We propose a new class of frequency-selective homonuclear recoupling methods to selectively enhance ¹H-¹H correlations of interest under ultrafast magic-angle spinning (MAS). These methods, dubbed as selective phase-optimized recoupling (SPR), can provide a sensitivity enhancement by a factor of ∼3 over the widely used radio-frequency-driven recoupling (RFDR) to observe ¹H_N-¹H_N contacts in a protonated tripeptide N-formyl-Met-Leu-Phe (fMLF) under 150 kHz MAS and are successfully utilized to probe a long-range ¹H-¹H contact in a pharmaceutical molecule, the hydrochloride form of pioglitazone (PIO-HCl). SPR is not only highly efficient in frequency-selective recoupling but also easy to implement, imparting to it great potential to probe ¹H-¹H contacts for the structural elucidation of organic solids such as proteins and pharmaceuticals under ultrafast MAS conditions.

Accuracy of 1H-1H distances measured using frequency selective recoupling and fast magic-angle spinning

Selective recoupling of protons (SERP) is a method to selectively and quantitatively measure magnetic dipole-dipole interaction between protons and, in turn, the proton-proton distance in solid-state samples at fast magic-angle spinning. We present a bimodal operator-based Floquet approach to describe the numerically optimized SERP recoupling sequence. The description calculates the allowed terms in the first-order effective Hamiltonian, explains the origin of selectivity during recoupling, and shows how different terms are modulated as a function of the radio frequency amplitude and the phase of the sequence. Analytical and numerical simulations have been used to evaluate the effect of higher-order terms and offsets on the polarization transfer efficiency and quantitative distance measurement. The experimentally measured ¹H-¹H distances on a fully protonated thymol sample are ∼10%-15% shorter than those reported from diffraction studies. A semi-quantitative model combined with extensive numerical simulations is used to rationalize the effect of the third-spin and the role of different parameters in the experimentally observed shorter distances. Measurements at high magnetic fields improve the match between experimental and diffraction distances. The measurement of ¹H-¹H couplings at offsets different from the SERP-offset has also been explored. Experiments were also performed on a perdeuterated ubiquitin sample to demonstrate the feasibility of simultaneously measuring multiple quantitative distances and to evaluate the accuracy of the measured distance in the absence of multispin effects. The estimation of proton-proton distances provides a boost to structural characterization of small pharmaceuticals and biomolecules, given that the positions of protons are generally not well defined in x-ray structures.

Can proton-proton recoupling in fully protonated solids provide quantitative, selective and efficient polarization transfer?

Dipolar recoupling sequences have been used to probe spatial proximity of nuclear spins and were traditionally designed to probe rare spins such as ¹³C and/or ¹⁵N nuclei. The multi-spin dipolar-coupling network of the rare spins is weak due to smaller couplings and large chemical shift dispersion. Therefore, the recoupling approaches were tailored to design offset compensated or broadband sequences. In contrast, protons have a substantially stronger dipolar-coupling network and much narrower chemical shift range. Broadband recoupling sequences such as radio-frequency driven recoupling (RFDR), back-to-back (BABA), and lab frame proton-proton spin diffusion have been routinely used to characterize the structures of protein/macromolecules and small molecules. Recently selective ¹H-¹H recoupling sequences have been proposed that combine chemical shift offset of the resolved proton spectrum (at fast MAS) with first- and second-order dipolar recoupling Hamiltonians to obtain quantitative and qualitative proton distances, respectively. Herein, we evaluate the performances of broadband and selective proton recoupling sequences such as finite pulse RFDR (fp-RFDR), band-selective spectral spin diffusion (BASS-SD), second-order cross-polarization (SOCP), and selective recoupling of proton (SERP) in terms of the selectivity and efficiency of ¹H-¹H polarization transfers in a dense network of proton spins and explore the possibility of measuring ¹H-¹H distances. We use theoretical considerations, numerical simulations, and experiments to support the distinct advantages and disadvantages of each recoupling sequence. Experiments were performed on L-histidine.HCl.H₂O at a MAS frequency of 71.43 kHz. This study rationalizes the proper selection of ¹H-¹H recoupling sequences when working with fully protonated solids.

Homonuclear dipolar recoupling of arbitrary pairs in multi-spin systems under magic angle spinning: A double-frequency-selective ZQ-SEASHORE experiment

We describe a useful method for measuring the internuclear distances within arbitrarily selected pairs of like nuclei in dipolar-coupled multi-spin systems. The method uses a combination of the zero-quantum shift-evolution-assisted selective homonuclear recoupling (ZQ-SEASHORE) technique developed by Hu and Tycko [J. Chem. Phys. 2009, 131, 045101] and double-frequency-selective radio-frequency pulse. The double-frequency-selective pulse inverts polarizations of two spins simultaneously, and thus applications of the method presented here are only limited by the spectral resolution, and not by the number of interacting spins. Our experiments demonstrate the validity of the method and present analytical expressions for the dephasing curve.

Quantitative 1H-1H Distances in Protonated Solids by Frequency-Selective Recoupling at Fast Magic Angle Spinning NMR

Nuclear magnetic resonance (NMR) spectroscopy of protons in protonated solids is challenging. Fast magic angle spinning (MAS) and homonuclear decoupling schemes, in conjunction, with high magnetic fields have improved the proton resolution. However, experiments to quantitatively measure ¹H-¹H distances still remain elusive due to the dense proton-proton dipolar coupling network. A novel MAS solid-state NMR pulse sequence is proposed to selectively recouple and measure interproton distances in protonated samples. The phase-modulated sequence combined with a judicious choice of transmitter frequency is used to measure quantitative ¹H-¹H distances on the order of 3 Å in l-histidine·HCl·H₂O, despite the presence of other strongly coupled protons. This method provides a major boost to NMR crystallography approaches for structural determination of pharmaceutical molecules by directly measuring ¹H-¹H distances. The band-selective nature of the sequence also enables observation of selective ¹H-¹H correlations (e.g., H^N-H^N/H^N-H^α/Η^Ν-Η^Methyl) in peptides and proteins, which should serve as useful restraints in structure determination.

Selective measurements of long-range homonuclear J-couplings in solid-state NMR

We demonstrate here that the principle of frequency-selective spin-echoes can be extended to the measurements of long-range homonuclear scalar J-couplings in the solid-state. Singly or doubly frequency-selective pulses were used to generate either a J-modulated experiment (S) or a reference experiment (S0). The combination of these two distinct experiments provides experimental data that, in favorable cases, are insensitive to incoherent relaxation effects, and which can be used to estimate long-range homonuclear J-couplings in multiple spin-systems. The concept is illustrated in the case of a uniformly (13)C and (15)N labeled sample of L-histidine, where the absolute value of homonuclear J-couplings between two spins separated by one, two or three covalent bonds are measured. Moreover, we show that a (2)J((15)N-C-(15)N) coupling as small as 0.9 Hz can be precisely measured with the method presented here.

Quantum simulation via filtered Hamiltonian engineering: application to perfect quantum transport in spin networks

We propose a method for Hamiltonian engineering that requires no local control but only relies on collective qubit rotations and field gradients. The technique achieves a spatial modulation of the coupling strengths via a dynamical construction of a weighting function combined with a Bragg grating. As an example, we demonstrate how to generate the ideal Hamiltonian for perfect quantum information transport between two separated nodes of a large spin network. We engineer a spin chain with optimal couplings starting from a large spin network, such as one naturally occurring in crystals, while decoupling all unwanted interactions. For realistic experimental parameters, our method can be used to drive almost perfect quantum information transport at room temperature. The Hamiltonian engineering method can be made more robust under decoherence and coupling disorder by a novel apodization scheme. Thus, the method is quite general and can be used to engineer the Hamiltonian of many complex spin lattices with different topologies and interactions.

Spinning-rate encoded chemical shift correlations from rotational resonance solid-state NMR experiments

Structural measurements in magic-angle-spinning (MAS) solid-state NMR rely heavily on (13)C-(13)C distance measurements. Broadbanded recoupling methods are used to generate many cross-peaks, but have complex polarization transfer mechanisms that limit the precision of distance constraints and can suffer from weak intensities for distant peaks due to relaxation, the broad distribution of polarization, as well as dipolar truncation. Frequency-selective methods that feature narrow-banded recoupling can reduce these effects. Indeed, rotational resonance (R(2)) experiments have found application in many different biological systems, where they have afforded improved precision and accuracy. Unfortunately, a highly selective transfer mechanism also leads to few cross-peaks in the resulting spectra, which complicates the extraction of multiple constraints. R(2)-width (R(2)W) measurements that scan a range of MAS rates to probe the R(2) matching conditions of one or more sites can improve precision, and also permit multiple simultaneous distance measurements. However, multidimensional R(2)W can be very time-consuming. Here, we present an approach that facilitates the acquisition of 2D-like spectra based on a series of 1D R(2)W experiments, by taking advantage of the chemical shift information encoded in the MAS rates where matching occurs. This yields a more time-efficient experiment with many of the benefits of more conventional multidimensional R(2)W measurements. The obtained spectra reveal long-distance (13)C-(13)C cross-peaks resulting from R(2)-mediated polarization transfer. This experiment also enables the efficient setup and targeted implementation of traditional R(2) or R(2)W experiments. Analogous applications may extend to other variable-MAS and frequency-selective solid-state NMR experiments.

Utilizing NMR and EPR spectroscopy to probe the role of copper in prion diseases

Copper is an essential nutrient for the normal development of the brain and nervous system, although the hallmark of several neurological diseases is a change in copper concentrations in the brain and central nervous system. Prion protein (PrP) is a copper-binding, cell-surface glycoprotein that exists in two alternatively folded conformations: a normal isoform (PrP(C)) and a disease-associated isoform (PrP(Sc)). Prion diseases are a group of lethal neurodegenerative disorders that develop as a result of conformational conversion of PrP(C) into PrP(Sc). The pathogenic mechanism that triggers this conformational transformation with the subsequent development of prion diseases remains unclear. It has, however, been shown repeatedly that copper plays a significant functional role in the conformational conversion of prion proteins. In this review, we focus on current research that seeks to clarify the conformational changes associated with prion diseases and the role of copper in this mechanism, with emphasis on the latest applications of NMR and EPR spectroscopy to probe the interactions of copper with prion proteins.

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.

(13)C-(13)c homonuclear recoupling in solid-state nuclear magnetic resonance at a moderately high magic-angle-spinning frequency

Two-dimensional (13)C-(13)C correlation experiments are widely employed in structure determination of protein assemblies using solid-state nuclear magnetic resonance. Here, we investigate the process of (13)C-(13)C magnetisation transfer at a moderate magic-angle-spinning frequency of 30 kHz using some of the prominent second-order dipolar recoupling schemes. The effect of isotropic chemical-shift difference and spatial distance between two carbons and amplitude of radio frequency on (1)H channel on the magnetisation transfer efficiency of these schemes is discussed in detail.

Restraints on backbone conformations in solid state NMR studies of uniformly labeled proteins from quantitative amide 15N-15N and carbonyl 13C-13C dipolar recoupling data

Recent structural studies of uniformly (15)N, (13)C-labeled proteins by solid state nuclear magnetic resonance (NMR) rely principally on two sources of structural restraints: (i) restraints on backbone conformation from isotropic (15)N and (13)C chemical shifts, based on empirical correlations between chemical shifts and backbone torsion angles; (ii) restraints on inter-residue proximities from qualitative measurements of internuclear dipole-dipole couplings, detected as the presence or absence of inter-residue crosspeaks in multidimensional spectra. We show that site-specific dipole-dipole couplings among (15)N-labeled backbone amide sites and among (13)C-labeled backbone carbonyl sites can be measured quantitatively in uniformly-labeled proteins, using dipolar recoupling techniques that we call (15)N-BARE and (13)C-BARE (BAckbone REcoupling), and that the resulting data represent a new source of restraints on backbone conformation. (15)N-BARE and (13)C-BARE data can be incorporated into structural modeling calculations as potential energy surfaces, which are derived from comparisons between experimental (15)N and (13)C signal decay curves, extracted from crosspeak intensities in series of two-dimensional spectra, with numerical simulations of the (15)N-BARE and (13)C-BARE measurements. We demonstrate this approach through experiments on microcrystalline, uniformly (15)N, (13)C-labeled protein GB1. Results for GB1 show that (15)N-BARE and (13)C-BARE restraints are complementary to restraints from chemical shifts and inter-residue crosspeaks, improving both the precision and the accuracy of calculated structures.

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.

Solid-state NMR techniques for the structural determination of amyloid fibrils

This review discusses the solid-state NMR techniques developed for the study of amyloid fibrils. Literature up to the end of 2010 has been surveyed and the materials are organized according to five categories, viz. homonuclear dipolar recoupling and polarization transfer via J-coupling, heteronuclear dipolar recoupling, correlation spectroscopy, recoupling of chemical shift anisotropy, and tensor correlation. Our emphasis is on the NMR techniques and their practical aspects. The biological implications of the results obtained for amyloid fibrils are only briefly discussed. Our main objective is to showcase the power of NMR in the study of biological unoriented solids.

Dipolar-coupling-mediated total correlation spectroscopy in solid-state 13C NMR: selection of individual 13C-13C dipolar interactions

Herein is described a useful approach in solid-state NMR, for selecting homonuclear (13)C-(13)C spin pairs in a multiple-(13)C homonuclear dipolar coupled spin system. This method builds upon the zero-quantum (ZQ) dipolar recoupling method introduced by Levitt and coworkers (Marin-Montesinos et al., 2006) by extending the originally introduced one-dimensional (1D) experiment into a two-dimensional (2D) method with selective irradiation scheme, while moving the (13)C-(13)C mixing scheme from the transverse to the longitudinal mode, together with a dramatic improvement in the proton decoupling efficiency. Selective spin-pair recoupling experiments incorporating Gaussian and cosine-modulated Gaussian pulses for inverting specific spins were performed, demonstrating the ability to detect informative, simplified/individualized, long-range (13)C-(13)C homonuclear dipolar coupling interactions more accurately by removing less informative, stronger, short-range (13)C-(13)C interactions from 2D correlation spectra. The capability of this new approach was demonstrated experimentally on uniformly (13)C-labeled Glutamine and a tripeptide sample, GAL.

Homonuclear dipolar recoupling under ultra-fast magic-angle spinning: probing 19F-19F proximities by solid-state NMR

We describe dipolar recoupling methods that accomplish, at high magic-angle spinning (MAS) frequencies, the excitation of double-quantum (DQ) coherences between spin-1/2 nuclei. We employ rotor-synchronized symmetry-based pulse sequences which are either gamma-encoded or non-gamma-encoded. The sensitivity and the robustness to both chemical-shift anisotropy and offset are examined. We also compare different techniques to avoid signal folding in the indirect dimension of two-dimensional double-quantum<-->single-quantum (DQ-SQ) spectra. This comprehensive analysis results in the identification of satisfactory conditions for dipolar (19)F-(19)F recoupling at high magnetic fields and high MAS frequencies. The utility of these recoupling methods is demonstrated with high-resolution DQ-SQ NMR spectra, which allow probing (19)F-(19)F proximities in powered fluoroaluminates.

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.

Zero-quantum frequency-selective recoupling of homonuclear dipole-dipole interactions in solid state nuclear magnetic resonance

We describe a method for measuring magnetic dipole-dipole interactions, and hence distances, between pairs of like nuclear spins in a many-spin system under magic-angle spinning (MAS). This method employs a homonuclear dipolar recoupling sequence that creates an average dipole-dipole coupling Hamiltonian under MAS with full zero-quantum symmetry, including both secular and flip-flop terms. Flip-flop terms are then attenuated by inserting rotor-synchronized periods of chemical shift evolution between recoupling blocks, leaving an effective Hamiltonian that contains only secular terms to a good approximation. Couplings between specific pairs of nuclear spins can then be selected with frequency-selective pi pulses. We demonstrate this technique, which we call zero-quantum shift evolution assisted homonuclear recoupling, in a series of one-dimensional and two-dimensional (13)C NMR experiments at 17.6 T and 40.00 kHz MAS frequency on uniformly (13)C-labeled L-threonine powder and on the helix-forming peptide MB(i+4)EK, synthesized with a pair of uniformly (13)C-labeled L-alanine residues. Experimental demonstrations include measurements of distances between (13)C sites that are separated by three bonds, placing quantitative constraints on both sidechain and backbone torsion angles in polypeptides.

Proton assisted recoupling and protein structure determination

We introduce a homonuclear version of third spin assisted recoupling, a second-order mechanism that can be used for polarization transfer between (13)C or (15)N spins in magic angle spinning (MAS) NMR experiments, particularly at high spinning frequencies employed in contemporary high field MAS experiments. The resulting sequence, which we refer to as proton assisted recoupling (PAR), relies on a cross-term between (1)H-(13)C (or (1)H-(15)N) couplings to mediate zero quantum (13)C-(13)C (or (15)N-(15)N recoupling). In particular, using average Hamiltonian theory we derive an effective Hamiltonian for PAR and show that the transfer is mediated by trilinear terms of the form C(1) (+/-)C(2) (-/+)H(Z) for (13)C-(13)C recoupling experiments (or N(1) (+/-)N(2) (-/+)H(Z) for (15)N-(15)N). We use analytical and numerical simulations to explain the structure of the PAR optimization maps and to delineate the PAR matching conditions. We also detail the PAR polarization transfer dependence with respect to the local molecular geometry and explain the observed reduction in dipolar truncation. Finally, we demonstrate the utility of PAR in structural studies of proteins with (13)C-(13)C spectra of uniformly (13)C, (15)N labeled microcrystalline Crh, a 85 amino acid model protein that forms a domain swapped dimer (MW=2 x 10.4 kDa). The spectra, which were acquired at high MAS frequencies (omega(r)2pi>20 kHz) and magnetic fields (750-900 MHz (1)H frequencies) using moderate rf fields, exhibit numerous cross peaks corresponding to long (up to 6-7 A) (13)C-(13)C distances which are particularly useful in protein structure determination. Using results from PAR spectra we calculate the structure of the Crh protein.

Biomolecular solid state NMR with magic-angle spinning at 25K

A magic-angle spinning (MAS) probe has been constructed which allows the sample to be cooled with helium, while the MAS bearing and drive gases are nitrogen. The sample can be cooled to 25K using roughly 3 L/h of liquid helium, while the 4-mm diameter rotor spins at 6.7 kHz with good stability (+/-5 Hz) for many hours. Proton decoupling fields up to at least 130 kHz can be applied. This helium-cooled MAS probe enables a variety of one-dimensional and two-dimensional NMR experiments on biomolecular solids and other materials at low temperatures, with signal-to-noise proportional to 1/T. We show examples of low-temperature (13)C NMR data for two biomolecular samples, namely the peptide Abeta(14-23) in the form of amyloid fibrils and the protein HP35 in frozen glycerol/water solution. Issues related to temperature calibration, spin-lattice relaxation at low temperatures, paramagnetic doping of frozen solutions, and (13)C MAS NMR linewidths are discussed.

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

Dipolar recoupling techniques in solid-state nuclear magnetic resonance (NMR) consist of radio frequency (rf) pulse sequences applied in synchrony with magic-angle spinning (MAS) that create nonzero average magnetic dipole-dipole couplings under MAS. Stochastic dipolar recoupling (SDR) is a variant in which randomly chosen rf carrier frequency offsets are introduced to cause random phase modulations of individual pairwise couplings in the dipolar spin Hamiltonian. Several aspects of SDR are investigated through analytical theory and numerical simulations: (1) An analytical expression for the evolution of nuclear spin polarization under SDR in a two-spin system is derived and verified through simulations, which show a continuous evolution from coherent, oscillatory polarization exchange to incoherent, exponential approach to equilibrium as the range of random carrier offsets (controlled by a parameter f(max)) increases; (2) in a many-spin system, polarization transfers under SDR are shown to be described accurately by a rate matrix in the limit of large f(max), with pairwise transfer rates that are proportional to the inverse sixth power of pairwise internuclear distances; (3) quantum mechanical interferences among noncommuting pairwise dipole-dipole couplings, which are a complicating factor in solid-state NMR studies of molecular structures by traditional dipolar recoupling methods, are shown to be absent from SDR data in the limit of large f(max), provided that coupled nuclei have distinct NMR chemical shifts.

Determination of methyl 13C-15N dipolar couplings in peptides and proteins by three-dimensional and four-dimensional magic-angle spinning solid-state NMR spectroscopy

We describe three- and four-dimensional semiconstant-time transferred echo double resonance (SCT-TEDOR) magic-angle spinning solid-state nuclear magnetic resonance (NMR) experiments for the simultaneous measurement of multiple long-range (15)N-(13)C(methyl) dipolar couplings in uniformly (13)C, (15)N-enriched peptides and proteins with high resolution and sensitivity. The methods take advantage of (13)C spin topologies characteristic of the side-chain methyl groups in amino acids alanine, isoleucine, leucine, methionine, threonine, and valine to encode up to three distinct frequencies ((15)N-(13)C(methyl) dipolar coupling, (15)N chemical shift, and (13)C(methyl) chemical shift) within a single SCT evolution period of initial duration approximately 1(1)J(CC) (where (1)J(CC) approximately 35 Hz, is the one-bond (13)C(methyl)-(13)C J-coupling) while concurrently suppressing the modulation of NMR coherences due to (13)C-(13)C and (15)N-(13)C J-couplings and transverse relaxation. The SCT-TEDOR schemes offer several important advantages over previous methods of this type. First, significant (approximately twofold to threefold) gains in experimental sensitivity can be realized for weak (15)N-(13)C(methyl) dipolar couplings (corresponding to structurally interesting, approximately 3.5 A or longer, distances) and typical (13)C(methyl) transverse relaxation rates. Second, the entire SCT evolution period can be used for (13)C(methyl) and/or (15)N frequency encoding, leading to increased spectral resolution with minimal additional coherence decay. Third, the experiments are inherently "methyl selective," which results in simplified NMR spectra and obviates the use of frequency-selective pulses or other spectral filtering techniques. Finally, the (15)N-(13)C cross-peak buildup trajectories are purely dipolar in nature (i.e., not influenced by J-couplings or relaxation), which enables the straightforward extraction of (15)N-(13)C(methyl) distances using an analytical model. The SCT-TEDOR experiments are demonstrated on a uniformly (13)C, (15)N-labeled peptide, N-acetyl-valine, and a 56 amino acid protein, B1 immunoglobulin-binding domain of protein G (GB1), where the measured (15)N-(13)C(methyl) dipolar couplings provide site-specific information about side-chain dihedral angles and the packing of protein molecules in the crystal lattice.

Stochastic dipolar recoupling in nuclear magnetic resonance of solids

I describe a nuclear magnetic resonance (NMR) technique, called stochastic dipolar recoupling (SDR), that permits continuous experimental control of the character of spin dynamics between coherent and incoherent limits in a system of magnetic dipole-coupled nuclei. In the fully incoherent limit of SDR, spin polarization transfers occur at distance-dependent rates without the quantum mechanical interferences among pairwise dipole-dipole couplings that often limit the feasibility or precision of structural studies of solids by NMR. In addition to facilitating structural studies, SDR represents a possible route to experimental studies of effects of decoherence on the dynamics of quantum many-body systems.

(13)C-(13)C distance measurements in U-(13)C, (15)N-labeled peptides using rotational resonance width experiment with a homogeneously broadened matching condition

In this publication, we introduce a version of the rotational resonance width experiment with a homogeneously broadened matching condition. The increase in the bandwidth is achieved by the reduction of the proton decoupling power during mixing, which results in the reduction of zero-quantum relaxation, and broadens the rotational resonance condition. We show that one can achieve recoupling of the carbonyl-aliphatic side chain dipolar interactions band selectively, while avoiding the recoupling of strongly interacting C'-Calpha and C'-Cbeta spin pairs. The attenuation of the multi-spin effects in the presence of short zero-quantum relaxation enables a two-spin approximation to be employed for the analysis of the experimental data. The systematic error introduced by this approximation is estimated by comparing the results with a three-spin simulation. The experiment is demonstrated in [U-(13)C,(15)N]N-acetyl-L-Val-L-Leu dipeptide, where 11 distances, ranging from 2.5 to 6 A, were measured.

Symmetry-based constant-time homonuclear dipolar recoupling in solid state NMR

Constant-time dipolar recoupling pulse sequences are advantageous in structural studies by solid state nuclear magnetic resonance (NMR) with magic-angle spinning (MAS) because they yield experimental data that are relatively insensitive to radio-frequency pulse imperfections and nuclear spin relaxation processes. A new approach to the construction of constant-time homonuclear dipolar recoupling sequences is described, based on symmetry properties of the recoupled dipole-dipole interaction Hamiltonian under cyclic displacements in time with respect to the MAS sample rotation period. A specific symmetry-based pulse sequence called PITHIRDS-CT is introduced and demonstrated experimentally. (13)C NMR data for singly-(13)C-labeled amino acid powders and amyloid fibrils indicate the effectiveness of PITHIRDS-CT in measurements of intermolecular distances in solids. (15)N-detected and (13)C-detected measurements of intramolecular (15)N-(15)N distances in peptides with alpha-helical and beta-sheet structures indicate the utility of PITHIRDS-CT in studies of molecular conformations, especially measurements of backbone psi torsion angles in peptides containing uniformly (15)N- and (13)C-labeled amino acids.