13C−13C Rotational Resonance Width Distance Measurements in Uniformly 13C-Labeled Peptides

Pulse induced resonance with angular dependent total enhancement of multi-dimensional solid-state NMR correlation spectra

We demonstrate a new resonance condition that obeys the relation Δδ=nν_R/2, where Δδ is the chemical shift difference between two homonuclear-coupled spins, ν_R is the magic-angle spinning speed and n is an integer. This modulation on the rotational resonance recoupling condition is obtained by the application of rotor-synchronous ¹H pulses when at least one proton is dipolar-coupled to one of the homonuclear spins. We suggest a new experimental scheme entitled 'pulse induced resonance with angular dependent total enhancement' (PIRATE) that can enhance proton-driven spin diffusion by the application of a single ¹H pulse every rotor period. Experimental evidence is demonstrated on the two carbon spins of glycine and on the Y21M mutant of fd bacteriophage virus. Numerical simulations reveal the existence of the resonances and report on the important interactions governing these phenomena.

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.

Application of solid-state NMR techniques for structural characterization of metal-organic frameworks

Solid-state NMR can afford the structural information about the chemical composition, local environment, and spatial coordination at the atomic level, which has been extensively applied to characterize the detailed structure and host-guest interactions in metal-organic frameworks (MOFs). In this review, recent advances for the structural characterizations of MOFs using versatile solid-state NMR techniques were briefly introduced. High-field sensitivity-enhanced solid-state NMR method enabled the direct observation of metal centers in MOFs containing low-γ nuclei. Two-dimensional (2D) homo- and hetero-nuclear correlation MAS NMR experiments provided the spatial proximity among linkers, metal clusters and the introduced guest molecules. Moreover, quantitative measurement of inter-nuclear distances using solid-state NMR provided valuable structural information about the connectivity geometry as well as the host-guest interactions within MOFs. Furthermore, solid-state NMR has exhibited great potential for unraveling the structure property of MOFs containing paramagnetic metal centers.

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.

Structural characterization of bacteriophage viruses by NMR

Magic-angle spinning (MAS) solid-state NMR has provided structural insights into various bacteriophage systems including filamentous, spherical, and tailed bacteriophage viruses. A variety of methodologies have been utilized including elementary two and three-dimensional assignment experiments, proton-detection techniques at fast spinning speeds, non-uniform sampling, structure determination protocols, conformational dynamics revealed by recoupling of anisotropic interactions, and enhancement by dynamic nuclear polarization. This review summarizes most of the studies performed during the last decade by MAS techniques and makes comparisons with prior knowledge obtained from static and solution NMR techniques. Chemical shifts for the capsids of the various systems are reported and analyzed, and DNA shifts are reported and discussed in the context of general high molecular-weight DNA molecules. Chemical shift and torsion angle prediction techniques are compared and applied to the various phage systems. The structures of the intact M13 filamentous bacteriophage and that of the Acinetobacter phage AP205 capsid, determined using MAS-based experimental data, are presented. Finally, filamentous phages, which are highly rigid systems, show interesting dynamics at the interface of the capsid and DNA, and their mutual electrostatic interactions are shown to be mediated by highly mobile positively charged residues. Novel results obtained from recoupling the chemical shift anisotropy of a single arginine in IKe phage, which is in contact with its DNA, further demonstrate this point. MAS NMR thus provides many new insights into phage structure, and on the other hand the richness, complexity and variety of bacteriophage systems provide opportunities for new NMR methodologies and technique developments.

A Structural Model for a Self-Assembled Nanotube Provides Insight into Its Exciton Dynamics

The design and synthesis of functional self-assembled nanostructures is frequently an empirical process fraught with critical knowledge gaps about atomic-level structure in these noncovalent systems. Here, we report a structural model for a semiconductor nanotube formed via the self-assembly of naphthalenediimide-lysine (NDI-Lys) building blocks determined using experimental 13C-13C and 13C-15N distance restraints from solid-state nuclear magnetic resonance supplemented by electron microscopy and X-ray powder diffraction data. The structural model reveals a two-dimensional-crystal-like architecture of stacked monolayer rings each containing ∼50 NDI-Lys molecules, with significant π-stacking interactions occurring both within the confines of the ring and along the long axis of the tube. Excited-state delocalization and energy transfer are simulated for the nanotube based on time-dependent density functional theory and an incoherent hopping model. Remarkably, these calculations reveal efficient energy migration from the excitonic bright state, which is in agreement with the rapid energy transfer within NDI-Lys nanotubes observed previously using fluorescence spectroscopy.

Recent advances in magic angle spinning solid state NMR of membrane proteins

Membrane proteins mediate many critical functions in cells. Determining their three-dimensional structures in the native lipid environment has been one of the main objectives in structural biology. There are two major NMR methodologies that allow this objective to be accomplished. Oriented sample NMR, which can be applied to membrane proteins that are uniformly aligned in the magnetic field, has been successful in determining the backbone structures of a handful of membrane proteins. Owing to methodological and technological developments, Magic Angle Spinning (MAS) solid-state NMR (ssNMR) spectroscopy has emerged as another major technique for the complete characterization of the structure and dynamics of membrane proteins. First developed on peptides and small microcrystalline proteins, MAS ssNMR has recently been successfully applied to large membrane proteins. In this review we describe recent progress in MAS ssNMR methodologies, which are now available for studies of membrane protein structure determination, and outline a few examples, which highlight the broad capability of ssNMR spectroscopy.

Selective inversion of 1H resonances in solid-state nuclear magnetic resonance: Use of double-DANTE pulse sequence

We here present a method based on DANTE pulses and homonuclear dipolar decoupling scheme to invert selectively any desired resonance in a proton spin system under magic-angle spinning. Experimental results are reported on a sample of L-histidine·HCl·H2O at magic-angle spinning frequencies of 15 and 60kHz. The results are also substantiated numerically.

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.

(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.

Intramolecular 1H-13C distance measurement in uniformly 13C, 15N labeled peptides by solid-state NMR

A (1)H-(13)C frequency-selective REDOR (FS-REDOR) experiment is developed for measuring intramolecular (1)H-(13)C distances in uniformly (13)C, (15)N-labeled molecules. Theory and simulations show that the experiment removes the interfering homonuclear (1)H-(1)H, (13)C-(13)C and heteronuclear (1)H-(15)N, (13)C-(15)N dipolar interactions while retaining the desired heteronuclear (1)H-(13)C dipolar interaction. Our results indicate that this technique, combined with the numerical fitting, can be used to measure a (1)H-(13)C distance up to 5Å. We also demonstrate that the measured intramolecular (1)H-(13)C distances are useful to determine dihedral angles in proteins.

Compensated second-order recoupling: application to third spin assisted recoupling

We consider the effect of phase shifts in the context of second-order recoupling techniques in solid-state NMR. Notably we highlight conditions leading to significant improvements for the Third Spin Assisted Recoupling (TSAR) mechanism and demonstrate the benefits of resulting techniques for detecting long-distance transfer in biomolecular systems. The modified pulse sequences of PAR and PAIN-CP, Phase-Shifted Proton Assisted Recoupling (AH-PS-PAR) and Phase-Shifted Proton-Assisted Insensitive Nuclei Cross Polarization (ABH-PS-PAIN-CP), still rely on cross terms between heteronuclear dipolar couplings involving assisting protons that mediate zero-quantum polarization transfer between low-γ nuclei ((13)C-(13)C, (15)N-(15)N, (15)N-(13)C polarization transfer). Using Average Hamiltonian Theory we show that phase inversion compensates off-resonance contributions and yields improved polarization transfer as well as substantial broadening of the matching conditions. PS-TSAR greatly improves on the standard TSAR based methods because it alleviates their sensitivity to precise RF settings which significantly enhances robustness of the experiments. We demonstrate these new methods on a 19.6 kDa protein (U-[(15)N, (13)C]-YajG) at high magnetic fields (up to 900 MHz (1)H frequency) and fast sample spinning (up to 65 kHz MAS frequency).

Fractional deuteration applied to biomolecular solid-state NMR spectroscopy

Solid-state Nuclear Magnetic Resonance can provide detailed insight into structural and dynamical aspects of complex biomolecules. With increasing molecular size, advanced approaches for spectral simplification and the detection of medium to long-range contacts become of critical relevance. We have analyzed the protonation pattern of a membrane-embedded ion channel that was obtained from bacterial expression using protonated precursors and D(2)O medium. We find an overall reduction of 50% in protein protonation. High levels of deuteration at H(α) and H(β) positions reduce spectral congestion in ((1)H,(13)C,(15)N) correlation experiments and generate a transfer profile in longitudinal mixing schemes that can be tuned to specific resonance frequencies. At the same time, residual protons are predominantly found at amino-acid side-chain positions enhancing the prospects for obtaining side-chain resonance assignments and for detecting medium to long-range contacts. Fractional deuteration thus provides a powerful means to aid the structural analysis of complex biomolecules by solid-state NMR.

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.

Heteronuclear proton assisted recoupling

We describe a theoretical framework for understanding the heteronuclear version of the third spin assisted recoupling polarization transfer mechanism and demonstrate its potential for detecting long-distance intramolecular and intermolecular (15)N-(13)C contacts in biomolecular systems. The pulse sequence, proton assisted insensitive nuclei cross polarization (PAIN-CP) relies on a cross term between (1)H-(15)N and (1)H-(13)C dipolar couplings to mediate zero- and∕or double-quantum (15)N-(13)C recoupling. In particular, using average Hamiltonian theory we derive effective Hamiltonians for PAIN-CP and show that the transfer is mediated by trilinear terms of the form N(±)C(∓)H(z) (ZQ) or N(±)C(±)H(z) (DQ) depending on the rf field strengths employed. We use analytical and numerical simulations to explain the structure of the PAIN-CP optimization maps and to delineate the appropriate matching conditions. We also detail the dependence of the PAIN-CP polarization transfer with respect to local molecular geometry and explain the observed reduction in dipolar truncation. In addition, we demonstrate the utility of PAIN-CP in structural studies with (15)N-(13)C spectra of two uniformly (13)C,(15)N labeled model microcrystalline proteins-GB1, a 56 amino acid peptide, and Crh, a 85 amino acid domain swapped dimer (MW=2×10.4 kDa). The spectra acquired at high magic angle spinning frequencies (ω(r)∕2π>20 kHz) and magnetic fields (ω(0H)∕2π=700-900 MHz) using moderate rf fields, yield multiple long-distance intramonomer and intermonomer (15)N-(13)C contacts. We use these distance restraints, in combination with the available x-ray structure as a homology model, to perform a calculation of the monomer subunit of the Crh protein.

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.

Structural characterization of GNNQQNY amyloid fibrils by magic angle spinning NMR

Several human diseases are associated with the formation of amyloid aggregates, but experimental characterization of these amyloid fibrils and their oligomeric precursors has remained challenging. Experimental and computational analysis of simpler model systems has therefore been necessary, for instance, on the peptide fragment GNNQQNY7−13 of yeast prion protein Sup35p. Expanding on a previous publication, we report here a detailed structural characterization of GNNQQNY fibrils using magic angle spinning (MAS) NMR. On the basis of additional chemical shift assignments we confirm the coexistence of three distinct peptide conformations within the fibrillar samples, as reflected in substantial chemical shift differences. Backbone torsion angle measurements indicate that the basic structure of these coexisting conformers is an extended β-sheet. We structurally characterize a previously identified localized distortion of the β-strand backbone specific to one of the conformers. Intermolecular contacts are consistent with each of the conformers being present in its own parallel and in-register sheet. Overall the MAS NMR data indicate a substantial difference between the structure of the fibrillar and crystalline forms of these peptides, with a clearly increased complexity in the GNNQQNY fibril structure. These experimental data can provide guidance for future work, both experimental and theoretical, and provide insights into the distinction between fibril growth and crystal formation.

Accurate determination of interstrand distances and alignment in amyloid fibrils by magic angle spinning NMR

Amyloid fibrils are structurally ordered aggregates of proteins whose formation is associated with many neurodegenerative and other diseases. For that reason, their high-resolution structures are of considerable interest and have been studied using a wide range of techniques, notably electron microscopy, X-ray diffraction, and magic angle spinning (MAS) NMR. Because of the excellent resolution in the spectra, MAS NMR is uniquely capable of delivering site-specific, atomic resolution information about all levels of amyloid structure: (1) the monomer, which packs into several (2) protofilaments that in turn associate to form a (3) fibril. Building upon our high-resolution structure of the monomer of an amyloid-forming peptide from transthyretin (TTR(105-115)), we introduce single 1-(13)C labeled amino acids at seven different sites in the peptide and measure intermolecular carbonyl-carbonyl distances with an accuracy of ~0.11 A. Our results conclusively establish a parallel, in register, topology for the packing of this peptide into a β-sheet and provide constraints essential for the determination of an atomic resolution structure of the fibril. Furthermore, the approach we employ, based on a combination of a double-quantum filtered variant of the DRAWS recoupling sequence and multispin numerical simulations in SPINEVOLUTION, is general and should be applicable to a wide range of systems.

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 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.

Targeted 13C-13C distance measurements in a microcrystalline protein via J-decoupled rotational resonance width measurements

Rotational resonance width (R(2)W) magic-angle spinning (MAS) NMR experiments are performed to measure (13)C-(13)C distances in the hydrophobic core of the microcrystalline model protein G(Beta1). Such inter-residue distances are of particular value in NMR structure determinations. The experiments are done at a Larmor frequency of 750 MHz (1)H where the contribution of (13)C chemical shift anisotropy (CSA) to the R(2) transfer mechanism is significant. To minimize line broadening in the 2D spectra, we employ a combination of even/odd isotopic labeling with [1,3-(13)C] glycerol, and J-decoupling in the indirect dimension. This results in high-precision distance measurements between aromatic side chains of three tyrosine residues and distant methyl groups in the hydrophobic core of the protein. Even in the absence of information on the relative orientation of the shift tensors, we obtain relatively high precision data, which can be further improved by additional constraints on the tensor orientations.

High-resolution solid-state NMR structure of alanyl-prolyl-glycine

We present a de novo high-resolution structure of the peptide Alanyl-Prolyl-Glycine using a combination of sensitive solid-state NMR techniques that each yield precise structural constraints. High-quality (13)C-(13)C distance constraints are extracted by fitting rotational resonance width (R(2)W) experiments using Multimode Multipole Floquet Theory and experimental chemical shift anisotropy (CSA) orientations. In this strategy, a structure is first calculated using DANTE-REDOR and torsion angle measurements and the resulting relative CSA orientations are used as an input parameter in the (13)C-(13)C distance calculations. Finally, a refined structure is calculated using all the constraints. We investigate the effect of different structural constraints on structure quality, as determined by comparison to the crystal structure and also self-consistency of the calculated structures. Inclusion of all or subsets of these constraints into CNS calculations resulted in high-quality structures (0.02A backbone RMSD using all 11 constraints).

Dipolar truncation in magic-angle spinning NMR recoupling experiments

Quantitative solid-state NMR distance measurements in strongly coupled spin systems are often complicated due to the simultaneous presence of multiple noncommuting spin interactions. In the case of zeroth-order homonuclear dipolar recoupling experiments, the recoupled dipolar interaction between distant spins is attenuated by the presence of stronger couplings to nearby spins, an effect known as dipolar truncation. In this article, we quantitatively investigate the effect of dipolar truncation on the polarization-transfer efficiency of various homonuclear recoupling experiments with analytical theory, numerical simulations, and experiments. In particular, using selectively (13)C-labeled tripeptides, we compare the extent of dipolar truncation in model three-spin systems encountered in protein samples produced with uniform and alternating labeling. Our observations indicate that while the extent of dipolar truncation decreases in the absence of directly bonded nuclei, two-bond dipolar couplings can generate significant dipolar truncation of small, long-range couplings. Therefore, while alternating labeling alleviates the effects of dipolar truncation, and thus facilitates the application of recoupling experiments to large spin systems, it does not represent a complete solution to this outstanding problem.

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.

Paramagnetic shifts in solid-state NMR of proteins to elicit structural information

The recent observation of pseudocontact shifts (pcs) in (13)C high-resolution solid-state NMR of paramagnetic proteins opens the way to their application as structural restraints. Here, by investigating a microcrystalline sample of cobalt(II)-substituted matrix metalloproteinase 12 [CoMMP-12 (159 AA, 17.5 kDa)], it is shown that a combined strategy of protein labeling and dilution of the paramagnetic species (i.e., (13)C-,(15)N-labeled CoMMP-12 diluted in unlabeled ZnMMP-12, and (13)C-,(15)N-labeled ZnMMP-12 diluted in unlabeled CoMMP-12) allows one to easily separate the pcs contributions originated from the protein internal metal (intramolecular pcs) from those due to the metals in neighboring proteins in the crystal lattice (intermolecular pcs) and that both can be used for structural purposes. It is demonstrated that intramolecular pcs are significant structural restraints helpful in increasing both precision and accuracy of the structure, which is a need in solid-state structural biology nowadays. Furthermore, intermolecular pcs provide unique information on positions and orientations of neighboring protein molecules in the solid phase.

High-frequency dynamic nuclear polarization using biradicals: a multifrequency EPR lineshape analysis

To date, the cross effect (CE) and thermal mixing (TM) mechanisms have consistently provided the largest enhancements in dynamic nuclear polarization (DNP) experiments performed at high magnetic fields. Both involve a three-spin electron-electron-nucleus process whose efficiency depends primarily on two electron-electron interactions--the interelectron distance R and the correct electron paramagnetic resonance (EPR) frequency separation that matches the nuclear Larmor frequency, /omega(e2)-omega(e1)/ = omega(n). Biradicals, for example, two 2,2,6,6-tetramethyl-piperidine-1-oxyls (TEMPOs) tethered with a molecular linker, can in principle constrain both the distance and relative g-tensor orientation between two unpaired electrons, allowing these two spectral parameters to be optimized for the CE and TM. To verify this hypothesis, we synthesized a series of biradicals--bis-TEMPO tethered by n ethylene glycol units (a.k.a. BTnE)--that show an increasing DNP enhancement with a decreasing tether length. Specifically at 90 K and 5 T, the enhancement grew from approximately 40 observed with 10 mM monomeric TEMPO, where the average R approximately 56 A corresponding to electron-electron dipolar coupling constant omega(d)2 pi = 0.3 MHz, to approximately 175 with 5 mM BT2E (10 mM electrons) which has R approximately 13 A with omega(d)2 pi = 24 MHz. In addition, we compared these DNP enhancements with those from three biradicals having shorter and more rigid tethers-bis-TEMPO tethered by oxalyl amide, bis-TEMPO tethered by the urea structure, and 1-(TEMPO-4-oxyl)-3-(TEMPO-4-amino)-propan-2-ol (TOTAPOL) TOTAPOL is of particular interest since it is soluble in aqueous media and compatible with DNP experiments on biological systems such as membrane and amyloid proteins. The interelectron distances and relative g-tensor orientations of all of these biradicals were characterized with an analysis of their 9 and 140 GHz continuous-wave EPR lineshapes. The results show that the largest DNP enhancements are observed with BT2E and TOTAPOL that have shorter tethers and the two TEMPO moieties are oriented so as to satisfy the matching condition for the CE.

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.

Isotropic chemical shifts in magic-angle spinning NMR spectra of proteins

Here we examine the effect of magic-angle spinning (MAS) rate upon lineshape and observed peak position for backbone carbonyl (C') peaks in NMR spectra of uniformly-(13)C,15N-labeled (U-(13)C,15N) solid proteins. 2D N-C' spectra of U-(13)C,15N microcrystalline protein GB1 were acquired at six MAS rates, and the site-resolved C' lineshapes were analyzed by numerical simulations and comparison to spectra from a sparsely labeled sample (derived from 1,3-(13)C-glycerol). Spectra of the U-(13)C,15N sample demonstrate large variations in the signal-to-noise ratio and peak positions, which are absent in spectra of the sparsely labeled sample, in which most 13C' sites do not possess a directly bonded 13CA. These effects therefore are a consequence of rotational resonance, which is a well-known phenomenon. Yet the magnitude of this effect pertaining to chemical shift assignment has not previously been examined. To quantify these effects in high-resolution protein spectra, we performed exact numerical two- and four-spin simulations of the C' lineshapes, which reproduced the experimentally observed features. Observed peak positions differ from the isotropic shift by up to 1.0 ppm, even for MAS rates relatively far (a few ppm) from rotational resonance. Although under these circumstances the correct isotropic chemical shift values may be determined through simulation, systematic errors are minimized when the MAS rate is equivalent to approximately 85 ppm for 13C. This moderate MAS condition simplifies spectral assignment and enables data sets from different labeling patterns and spinning rates to be used most efficiently for structure determination.

(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.

Description of depolarization effects in double-quantum solid state nuclear magnetic resonance experiments using multipole-multimode Floquet theory

Using an analytical model based on multipole-multimode Floquet theory (MMFT), we describe the polarization loss (or depolarization) observed in double-quantum (DQ) dipolar recoupling magic angle spinning (MAS) experiments. Specifically, the factors responsible for depolarization are analyzed in terms of higher order corrections to the spin Hamiltonian in addition to the usual phenomenological decay rate constant. From the MMFT model and the effective Hamiltonians, we elucidate the rationale behind the inclusion of a phenomenological damping term in DQ recoupling experiments. As a test of this theoretical approach, the recoupling efficiency of one class of (13)C-(13)C and (13)C-(15)N resonance width dipolar recoupling experiments are investigated at different magnetic field strengths and compared with the more exact numerical simulations. In contrast to existing analytical treatments, the role of higher order corrections is clearly explained in the context of the MMFT approach leading to a better understanding of the underlying spin physics. Furthermore, the analytical model presented herein provides a general framework for describing coherent and incoherent effects in homonuclear and heteronuclear DQ MAS recoupling experiments.

Multipole-multimode Floquet theory of rotational resonance width experiments: C13–C13 distance measurements in uniformly labeled solids

A formal description of zero-quantum (ZQ) NMR processes using multipole-multimode Floquet theory is proposed for studying polarization transfer in magic angle spinning experiments. Specifically, we investigate the factors affecting the accuracy and precision of 13C-13C distance measurements that are based on ZQ-magnetization exchange processes in rotational resonance width experiments. With suitable examples drawn from measurements in N-acetyl-[U-13C,15N]-L-valine-L-leucine, we substantiate our approach and propose methods for improving the accuracy and reliability of such 13C-13C distance measurements in uniformly 13C, 15N-labeled solids. In addition, the theoretical model presented in this article provides a more general framework for describing relaxation phenomena involving multiple decay rate constants in zero-quantum processes.

Broadband homonuclear correlation spectroscopy at high magnetic fields and MAS frequencies

We present a new homonuclear recoupling sequence, CMAR, that allows observation of 2D 13C-13C correlation spectra at high magnetic fields and MAS frequencies (10-30 kHz). The main advantages of the sequence are that it provides efficient, broadband dipolar recoupling and concurrently decouples the 1H spins from the 13C's. Thus, no additional 1H decoupling is required during the mixing period, thereby significantly reducing the radio frequency power requirements for the experiment. Thus, CMAR significantly extends the range of applicability of the usual homonuclear recoupling techniques and should be of major interest for structure determinations of biomolecules at high magnetic fields.

Structural and dynamic studies of proteins by solid-state NMR spectroscopy: rapid movement forward

Starting only a few years ago, many solid-state NMR spectroscopy laboratories have become engaged in solving the complete structures of biological macromolecules using high-resolution methods based on magic angle spinning. These efforts typically involve structurally homogeneous samples, and utilize recently developed pulse sequences for the sequential correlation of resonances, the detection of tertiary contacts and the characterization of torsion angles. Thereby, systems have been studied that evaded other, more established, structure determination methods.

3D NMR spectroscopy for resonance assignment and structure elucidation of proteins under MAS: novel pulse schemes and sensitivity considerations

Two types of 3D MAS NMR experiments are introduced, which combine standard (NC,CC) transfer schemes with (1H,1H) mixing to simultaneously detect connectivities and structural constraints of uniformly 15N,13C-labeled proteins with high spectral resolution. The homonuclear CCHHC and CCC experiments are recorded with one double-quantum evolution dimension in order to avoid a cubic diagonal in the spectrum. Depending on the second transfer step, spin systems or proton-proton contacts can be determined with reduced spectral overlap. The heteronuclear NHHCC experiment encodes NH-HC proton-proton interactions, which are indicative for the backbone conformation of the protein. The third dimension facilitates the identification of the amino acid spin system. Experimental results on U-[15N,13C]valine and U-[15N,13C]ubiquitin demonstrate their usefulness for resonance assignments and for the determination of structural constraints. Furthermore, we give a detailed analysis of alternative multidimensional sampling schemes and their effect on sensitivity and resolution.

Myelin basic protein-diverse conformational states of an intrinsically unstructured protein and its roles in myelin assembly and multiple sclerosis

The 18.5 kDa isoform of myelin basic protein (MBP) is a major component of the myelin sheath in the central nervous system of higher vertebrates, and a member of a larger family of proteins with a multiplicity of forms and post-translational modifications (PTMs). The 18.5 kDa protein is the exemplar of the family, being most abundant in adult myelin, and thus the most-studied. It is peripherally membrane-associated, but has generally been investigated in isolated form. MBP is an 'intrinsically unstructured' protein with a high proportion (approximately 75%) of random coil, but postulated to have core elements of beta-sheet and alpha-helix. We review here the properties of the MBP family, especially of the 18.5 kDa isoform, and discuss how its three-dimensional (3D) structure may be resolved by direct techniques available to us, viz., X-ray and electron crystallography, and solution and solid-state NMR spectrometry. In particular, we emphasise that creating an appropriate environment in which the protein can adopt a physiologically relevant fold is crucial to such endeavours. By solving the 3D structure of 18.5 kDa MBP and the effects of PTMs, we will attain a better understanding of myelin architecture, and of the molecular mechanisms that transpire in demyelinating diseases such as multiple sclerosis.