Fixed point theory of iterative excitation schemes in NMR

SORDOR pulses: expansion of the Böhlen-Bodenhausen scheme for low-power broadband magnetic resonance

A novel type of efficient broadband pulse, called second-order phase dispersion by optimised rotation (SORDOR), has recently been introduced. In contrast to adiabatic excitation, SORDOR-90 pulses provide effective transverse 90∘ rotations throughout their bandwidth, with a quadratic offset dependence of the phase in the x , y plane. Together with phase-matched SORDOR-180 pulses, this enables the Böhlen-Bodenhausen broadband refocusing approach for linearly frequency-swept pulses to be extended to any type of 90∘ /180∘ pulse-delay sequence. Example pulse shapes are characterised in theory and experiment, and an example application is given with a 19 F -PROJECT experiment for measuring relaxation times with reduced distortions due to J -coupling evolution.

Broadband measurement of true transverse relaxation rates in systems with coupled protons: application to the study of conformational exchange

Accurate measurement of transverse relaxation rates in coupled spin systems is important in the study of molecular dynamics, but is severely complicated by the signal modulations caused by scalar couplings in spin echo experiments. The most widely used experiments for measuring transverse relaxation in coupled systems, CPMG and PROJECT, can suppress such modulations, but they also both suppress some relaxation contributions, and average relaxation rates between coupled spins. Here we introduce a new experiment which for the first time allows accurate broadband measurement of transverse relaxation rates of coupled protons, and hence the determination of exchange rate constants in slow exchange from relaxation measurements. The problems encountered with existing methods are illustrated, and the use of the new method is demonstrated for the classic case of hindered amide rotation and for the more challenging problem of exchange between helical enantiomers of a gold(i) complex.

Constraints on the Structure of Fibrils Formed by a Racemic Mixture of Amyloid-β Peptides from Solid-State NMR, Electron Microscopy, and Theory

Previous studies have shown that racemic mixtures of 40- and 42-residue amyloid-β peptides (d,l-Aβ40 and d,l-Aβ42) form amyloid fibrils with accelerated kinetics and enhanced stability relative to their homochiral counterparts (l-Aβ40 and l-Aβ42), suggesting a "chiral inactivation" approach to abrogating the neurotoxicity of Aβ oligomers (Aβ-CI). Here we report a structural study of d,l-Aβ40 fibrils, using electron microscopy, solid-state nuclear magnetic resonance (NMR), and density functional theory (DFT) calculations. Two- and three-dimensional solid-state NMR spectra indicate molecular conformations in d,l-Aβ40 fibrils that resemble those in known l-Aβ40 fibril structures. However, quantitative measurements of 13C-13C and 15N-13C distances in selectively labeled d,l-Aβ40 fibril samples indicate a qualitatively different supramolecular structure. While cross-β structures in mature l-Aβ40 fibrils are comprised of in-register, parallel β-sheets, our data indicate antiparallel β-sheets in d,l-Aβ40 fibrils, with alternation of d and l molecules along the fibril growth direction, i.e., antiparallel "rippled sheet" structures. The solid-state NMR data suggest the coexistence of d,l-Aβ40 fibril polymorphs with three different registries of intermolecular hydrogen bonds within the antiparallel rippled sheets. DFT calculations support an energetic preference for antiparallel alignments of the β-strand segments identified by solid-state NMR. These results provide insight into the structural basis for Aβ-CI and establish the importance of rippled sheets in self-assembly of full-length, naturally occurring amyloidogenic peptides.

Transiently structured head domains control intermediate filament assembly

Assembly of intermediate filaments (IFs) is reliant upon amino-terminal head domains. These head domains are of low sequence complexity and are assumed to function in the absence of structural order. Herein, we provide evidence that the head domains of the desmin and neurofilament light (NFL) IF proteins self-associate via the formation of labile but structurally specific cross-β interaction. Disease-causing mutations in the head domains of both proteins cause enhanced cross-β interactions. By assembling desmin and NFL IFs bearing isotopically labeled head domains, we provide evidence of structural order in properly assembled biological filaments. We propose that these observations on IF head domains may be instructive to the function of low complexity domains operative in other aspects of cell biology.

Low complexity (LC) head domains 92 and 108 residues in length are, respectively, required for assembly of neurofilament light (NFL) and desmin intermediate filaments (IFs). As studied in isolation, these IF head domains interconvert between states of conformational disorder and labile, β-strand–enriched polymers. Solid-state NMR (ss-NMR) spectroscopic studies of NFL and desmin head domain polymers reveal spectral patterns consistent with structural order. A combination of intein chemistry and segmental isotope labeling allowed preparation of fully assembled NFL and desmin IFs that could also be studied by ss-NMR. Assembled IFs revealed spectra overlapping with those observed for β-strand–enriched polymers formed from the isolated NFL and desmin head domains. Phosphorylation and disease-causing mutations reciprocally alter NFL and desmin head domain self-association yet commonly impede IF assembly. These observations show how facultative structural assembly of LC domains via labile, β-strand–enriched self-interactions may broadly influence cell morphology.

Combined multi-band decoupling in biomolecular NMR spectroscopy

Multi-resonance NMR experiments are powerful analytical and structural tools. Their conceptualization assumes that RF fields may be combined independently to manipulate spin interactions. However, practical implementation can compromise performance. One limitation is the generation of combination bands when two or more RF fields are applied simultaneously within the NMR probe. The combination bands can lead to significant interference with the detection circuitry. A facile approach to combined multi-band decoupling can resolve these problems and increase sensitivity two-fold (or more), by time sharing the application of the individual frequencies rather than time sharing decoupling and data acquisition.

13C-Satellite Decoupling Strategies for Improving Accuracy in Quantitative Nuclear Magnetic Resonance

Quantitative ¹H nuclear magnetic resonance (qHNMR) with an appropriate internal standard is a well-established quantitation method for assigning purity to organic molecules. For accurate measurements, the premise of qHNMR relies on the careful selection of integrals, for both the analyte and the standard, in such a way that the selected integrals are free from interferences. The ¹³C-satellite signals of adjacent integrals, low-level impurities, and tautomer signals are among the common integral interferences that are typically encountered. One of the simplest ways to identify and avoid these interferences is to decouple the ¹³C-satellites. Two decoupling schemes were explored to illustrate the benefits of ¹³C-decoupling for qHNMR or qH{¹³C}NMR: GARP and bilevel adiabatic broadband decoupling. Unwanted sample heating and nuclear Overhauser effect (NOE) enhancements are the two main drawbacks of decoupling schemes. We show that with careful optimization of acquisition parameters and decoupling power, no excessive sample heating occurred during acquisition at 400 MHz. At 900 MHz, only bilevel adiabatic decoupling could be safely implemented. Furthermore, any undesirable NOE enhancements were completely avoided if acquisition was executed with an inverse-gated pulse sequence. We explored and confirmed the benefits of qH{¹³C}NMR through the quantitation of a diverse set of compounds, namely, small molecules (dimethyl terephthalate and zearalenone), a ¹³C-labeled compound (¹³C₆-ochratoxin A), and an octapeptide (angiotensin II). Statistical comparisons confirmed that qH{¹³C}NMR produced comparable data to qHNMR. However, with qH{¹³C}NMR data providing added clarity about the presence of overlapping ¹³C-satellites, impurities, and tautomers, it has an edge over qHNMR for accurate measurements.

Molecular structure and interactions within amyloid-like fibrils formed by a low-complexity protein sequence from FUS

Protein domains without the usual distribution of amino acids, called low complexity (LC) domains, can be prone to self-assembly into amyloid-like fibrils. Self-assembly of LC domains that are nearly devoid of hydrophobic residues, such as the 214-residue LC domain of the RNA-binding protein FUS, is particularly intriguing from the biophysical perspective and is biomedically relevant due to its occurrence within neurons in amyotrophic lateral sclerosis, frontotemporal dementia, and other neurodegenerative diseases. We report a high-resolution molecular structural model for fibrils formed by the C-terminal half of the FUS LC domain (FUS-LC-C, residues 111-214), based on a density map with 2.62 Å resolution from cryo-electron microscopy (cryo-EM). In the FUS-LC-C fibril core, residues 112-150 adopt U-shaped conformations and form two subunits with in-register, parallel cross-β structures, arranged with quasi-21 symmetry. All-atom molecular dynamics simulations indicate that the FUS-LC-C fibril core is stabilized by a plethora of hydrogen bonds involving sidechains of Gln, Asn, Ser, and Tyr residues, both along and transverse to the fibril growth direction, including diverse sidechain-to-backbone, sidechain-to-sidechain, and sidechain-to-water interactions. Nuclear magnetic resonance measurements additionally show that portions of disordered residues 151-214 remain highly dynamic in FUS-LC-C fibrils and that fibrils formed by the N-terminal half of the FUS LC domain (FUS-LC-N, residues 2-108) have the same core structure as fibrils formed by the full-length LC domain. These results contribute to our understanding of the molecular structural basis for amyloid formation by FUS and by LC domains in general.

Perspectives of adiabatic decoupling in liquids

It is shown that adiabatic decoupling is extremely flexible and achieves very high figure of merit (decoupling bandwidth to RF amplitude ratio) exceeding that of the conventional composite pulse decoupling (CPD) methods by more than an order of magnitude. This comes at a price of increasingly intrusive cycling sidebands when the decoupling bandwidth exceeds that of the CPD methods. Following a brief review of the decoupling theory and modes of adiabatic sweeps a particular attention is focused on decoupling sideband suppression techniques. The close to perfect inversion profiles of adiabatic pulses ensure by far fewer cyclic sidebands as compared to the typically complex sideband patterns observed in CPD applications. The coherent sideband suppression techniques eliminate the cycling sidebands by altering their phase in successive scans thus achieving sideband reduction levels by up to four orders of magnitude and leaving a clean baseline. We show that adiabatic decoupling is highly adaptive offering significant power savings in spin systems with smaller J-couplings while in the other extreme enabling ¹³C decoupling of up to a 1 MHz wide bandwidth potentially satisfying the needs of ultra-high-field NMR for the foreseeable future.

Concatenated Composite Pulses Applied to Liquid-State Nuclear Magnetic Resonance Spectroscopy

The error-robust and short composite operations named ConCatenated Composite Pulses (CCCPs), developed as high-precision unitary operations in quantum information processing (QIP), are derived from composite pulses widely employed in nuclear magnetic resonance (NMR). CCCPs simultaneously compensate for two types of systematic errors, which was not possible with the known composite pulses in NMR. Our experiments demonstrate that CCCPs are powerful and versatile tools not only in QIP but also in NMR.

Practical aspects of real-time pure shift HSQC experiments

Pure shift NMR spectroscopy has become an efficient tool for improving resolution in proton NMR spectra by removing the effect of homonuclear couplings. The introduction of real-time acquisition methods has allowed the main drawback of pure shift NMR, the long experiment times needed, to be circumvented. Real-time methods use periodic application of J-refocusing pulse sequence elements, acquiring a single free induction decay, in contrast to previous methods that construct a pure shift interferogram by concatenating excerpts from multiple free induction decays. In the important heteronuclear single-quantum correlation experiment, implementing real-time pure shift data acquisition typically leads to the simultaneous improvement of both resolution and sensitivity. The current limitations of and problems with real-time pure shift acquisition methods are discussed here in the context of heteronuclear single-quantum correlation experiments. We aim to provide a detailed account of the technical challenges, together with a practical guide to exploiting the full potential of such methods.

Suppression of 13C satellites in 1H DOSY spectra

Diffusion-ordered spectroscopy (DOSY) is a valuable tool for the analysis of intact mixtures, since it can separate the signals of components according to their apparent diffusion coefficients. However, DOSY experiments are acutely sensitive to spectral quality, and especially to signal overlap, which can lead to misleading apparent diffusion coefficients. Here, we introduce a new NMR experiment to reduce signal overlap in mixtures with a wide range of concentrations, by removing one-bond ¹³C satellites. In such high dynamic range mixtures, ¹³C isotopomer signals from major components can overlap with signals from minor components, causing problematic distortions in the diffusion domain of a DOSY spectrum. The new method, Oneshot-iDISPEL, is a combination of the Oneshot and DISPEL experiments, and its performance has been demonstrated on a Greek alcoholic beverage, ouzo, which contains small amounts of anise flavour components and sucrose. Ethanol is a major component, and the suppression of its ¹³C satellites reduces signal overlap with minor components, offering significant improvement in DOSY spectra.

Semi-real-time acquisition for fast pure shift NMR at maximum resolution

Homonuclear decoupling can give impressive improvements in spectral resolution when overlapping multiplet structures limit the interpretability of NMR spectra. General homodecoupling methods ("pure shift NMR") typically use either interferogram-style acquisition, which is slow but gives optimum resolution, or real-time acquisition, which is fast but gives broader lines. Here we describe an alternative data acquisition strategy that allows rapid acquisition without resolution loss, illustrating the method with band-selective homodecoupling experiments and demonstrating its advantages over competing methods.

Refocused linewidths less than 10 Hz in 1H solid-state NMR

Coherence lifetimes in homonuclear dipolar decoupled ¹H solid-state NMR experiments are usually on the order of a few ms. We discover an oscillation that limits the lifetime of the coherences by recording spin-echo dephasing curves. We find that this oscillation can be removed by the application of a double spin-echo experiment, leading to coherence lifetimes of more than 45 ms in adamantane and more that 22 ms in β-AspAla, corresponding to refocused linewidths of less than 7 and 14 Hz respectively.

Advanced solvent signal suppression for the acquisition of 1D and 2D NMR spectra of Scotch Whisky

A simple and robust solvent suppression technique that enables acquisition of high-quality 1D 1 H nuclear magnetic resonance (NMR) spectra of alcoholic beverages on cryoprobe instruments was developed and applied to acquire NMR spectra of Scotch Whisky. The method uses 3 channels to suppress signals of water and ethanol, including those of 13 C satellites of ethanol. It is executed in automation allowing high throughput investigations of alcoholic beverages. On the basis of the well-established 1D nuclear Overhauser spectroscopy (NOESY) solvent suppression technique, this method suppresses the solvent at the beginning of the pulse sequence, producing pure phase signals minimally affected by the relaxation. The developed solvent suppression procedure was integrated into several homocorrelated and heterocorrelated 2D NMR experiments, including 2D correlation spectroscopy (COSY), 2D total correlation spectroscopy (TOCSY), 2D band-selective TOCSY, 2D J-resolved spectroscopy, 2D 1 H, 13 C heteronuclear single-quantum correlation spectroscopy (HSQC), 2D 1 H, 13 C HSQC-TOCSY, and 2D 1 H, 13 C heteronuclear multiple-bond correlation spectroscopy (HMBC). A 1D chemical-shift-selective TOCSY experiments was also modified. The wealth of information obtained by these experiments will assist in NMR structure elucidation of Scotch Whisky congeners and generally the composition of alcoholic beverages at the molecular level.

The use of composite pulses for improving DEER signal at 94GHz

The sensitivity of pulsed electron paramagnetic resonance (EPR) measurements on broad-line paramagnetic centers is often limited by the available excitation bandwidth. One way to increase excitation bandwidth is through the use of chirp or composite pulses. However, performance can be limited by cavity or detection bandwidth, which in commercial systems is typically 100-200MHz. Here we demonstrate in a 94GHz spectrometer, with >800MHz system bandwidth, an increase in signal and modulation depth in a 4-pulse DEER experiment through use of composite rather than rectangular π pulses. We show that this leads to an increase in sensitivity by a factor of 3, in line with theoretical predictions, although gains are more limited in nitroxide-nitroxide DEER measurements.

Rf-inhomogeneity compensation using method of Fourier synthesis

In this paper, we propose a new method for design of composite pulses that are robust to rf-amplitude (rf-inhomogeneity). We call this, the method of Fourier synthesis. The method is general enough to design excitation, inversion, refocusing or arbitary flip angle pulses that are robust to rf-amplitude. The method can be tailored to have amplitude selective excitation. We experimentally show rf-compensation over a order of magnitude (20db) variation in rf-amplitude. The method is expected to find use in invivo NMR studies using surface coils, where there is large dispersion in rf-amplitude over the sample.

Towards a protocol for solution structure determination of copper(II) proteins: the case of Cu(II)Zn(II) superoxide dismutase

We have developed an optimized protocol to solve the solution structure of copper(II) proteins. After assignment, proton-proton NOEs are used for the shell where 1H spectra are conveniently observed. In a shell closer to the metal ion, 13C NMR spectra with band-selective homonuclear decoupling provide the assignment of all nuclei except for those of the metal ligands. A convenient method for the measurement of 13C longitudinal-relaxation rates (R1) of carbonyls and carboxylate moieties is proposed. 1H NOEs and 1H and 13C R1 data are sufficient to produce a good/reasonable solution structure, as demonstrated for a monomeric species of superoxide dismutase, a 153-residue protein.

Real-time pure shift ¹⁵N HSQC of proteins: a real improvement in resolution and sensitivity

Spectral resolution in proton NMR spectroscopy is reduced by the splitting of resonances into multiplets due to the effect of homonuclear scalar couplings. Although these effects are often hidden in protein NMR spectroscopy by low digital resolution and routine apodization, behind the scenes homonuclear scalar couplings increase spectral overcrowding. The possibilities for biomolecular NMR offered by new pure shift NMR methods are illustrated here. Both resolution and sensitivity are improved, without any increase in experiment time. In these experiments, free induction decays are collected in short bursts of data acquisition, with durations short on the timescale of J-evolution, interspersed with suitable refocusing elements. The net effect is real-time (t 2) broadband homodecoupling, suppressing the multiplet structure caused by proton-proton interactions. The key feature of the refocusing elements is that they discriminate between the resonances of active (observed) and passive (coupling partner) spins. This can be achieved either by using band-selective refocusing or by the BIRD element, in both cases accompanied by a nonselective 180° proton pulse. The latter method selects the active spins based on their one-bond heteronuclear J-coupling to (15)N, while the former selects a region of the (1)H spectrum. Several novel pure shift experiments are presented, and the improvements in resolution and sensitivity they provide are evaluated for representative samples: the N-terminal domain of PGK; ubiquitin; and two mutants of the small antifungal protein PAF. These new experiments, delivering improved sensitivity and resolution, have the potential to replace the current standard HSQC experiments.

Pure shift NMR

Although scalar-coupling provides important structural information, the resulting signal splittings significantly reduce the resolution of NMR spectra. Limited resolution is a particular problem in proton NMR experiments, resulting in part from the limited proton chemical shift range (∼10 ppm) but even more from the splittings due to scalar coupling to nearby protons. "Pure shift" NMR spectroscopy (also known as broadband homonuclear decoupling) has been developed for disentangling overlapped proton NMR spectra. The resulting spectra are considerably simplified as they consist of single lines, reminiscent of proton-decoupled C-13 spectra at natural abundance, with no multiplet structure. The different approaches to obtaining pure shift spectra are reviewed here and several applications presented. Pure shift spectra are especially useful for highly overlapped proton spectra, as found for example in reaction mixtures, natural products and biomacromolecules.

Further perspective on the theory of heteronuclear decoupling

An exact general theory of heteronuclear decoupling is presented for spin-1/2 IS systems. RF irradiation applied to the I spins both modifies and generates additional couplings between states of the system. The recently derived equivalence between the dynamics of any N-level quantum system and a system of classical coupled harmonic oscillators makes explicit the exact physical couplings between states. Decoupling is thus more properly viewed as a complex intercoupling. The sign of antiphase magnetization plays a fundamental role in decoupling. A one-to-one correspondence is demonstrated between ±2SyIz and the sense of the S-spin coupling evolution. Magnetization Sx is refocused to obtain the desired decoupled state when ∫2SyIzdt=0. The exact instantaneous coupling at any time during the decoupling sequence is readily obtained in terms of the system states, showing that the creation of two-spin coherence is crucial for reducing the effective scalar coupling, as required for refocusing to occur. Representative examples from new aperiodic sequences as well as standard cyclic, periodic composite-pulse and adiabatic decoupling sequences illustrate the decoupling mechanism. The more general aperiodic sequences, obtained using optimal control, realize the potential inherent in the theory for significantly improved decoupling.

Controlling the dipole-dipole interaction using NMR composite rf pulses

New composite rf pulses are proposed during which the average dipole-dipole interactions within a spin ensemble are controlled, while a global rotation is achieved. The method used to tailor the pulses is based on the average Hamiltonian theory and relies on the geometrical properties of the spin-spin dipolar interaction. I describe several such composite pulses and analyze quantitatively the improvement brought on the control of the NMR dynamics. Numerical simulations show that the magic sandwich pulse sequence, during which the average dipolar field is effectively reversed, is plagued by defects originating from the finite initial and final π/2 rf pulses. A numerical test based on a classical description of nuclear magnetic resonance is used to check that, when these pulses are replaced by magic composite pulses, the efficiency of the magic sandwich is improved.

The Application of Simple and Easy to Implement Decoupling Pulse Scheme Combinations to Effect Decoupling of Large J Values with Reduced Artifacts

Of the various problems in decoupling one nucleus type from another using standard decoupling pulse schemes for broadband decoupling, a particular challenge is to effect full, artifact-free decoupling when the size of the coupling constant is very large. Herein it is demonstrated that 1H decoupling of the 31P NMR spectrum of diethyl phosphonate {HP(=O)(OCH2CH3)2} can be accomplished with reduced artifacts despite the large JH,P1 value of 693 Hz by using a combination of decoupling pulse schemes involving continuous-wave (CW) irradiation and either adiabatic-pulse decoupling (APD), MPF decoupling, or traditional composite-pulse decoupling (CPD) schemes such as WALTZ or GARP. The considered strategy is simple, efficient, and easy to implement on most instruments. The best result was attained for a combination of CW and CPD using GARP with a standard pulse width of 60 μs. Altogether, the advantages of the methodology include low power requirements, complete decoupling, tolerance of a range of large J values, large bandwidth for normal-sized J values, and the suppression of sidebands.

The nuclear Overhauser effect from a quantitative perspective

The nuclear Overhauser enhancement or effect (NOE) is the most important measure in liquid-state NMR with macromolecules. Thus, the NOE is the subject of numerous reviews and books. Here, the NOE is revisited in light of our recently introduced measurements of exact nuclear Overhauser enhancements (eNOEs), which enabled the determination of multiple-state 3D protein structures. This review encompasses all relevant facets from the theoretical considerations to the use of eNOEs in multiple-state structure calculation. Important aspects include a detailed presentation of the relaxation theory relevant for the nuclear Overhauser effect, the estimation of the correction for spin diffusion, the experimental determination of the eNOEs, the conversion of eNOE rates into distances and validation of their quality, the distance-restraint classification and the protocols for calculation of structures and ensembles.

Further analysis of some symmetric and antisymmetric composite pulses for tackling pulse strength errors

Composite pulses have found widespread use in both conventional Nuclear Magnetic Resonance experiments and in experimental quantum information processing to reduce the effects of systematic errors. Here we describe several families of time symmetric and antisymmetric fully compensating composite pulses, inspired by the previous Fn, Gn and BB1 families family developed by Wimperis. We describe families of composite 180° pulses (not gates) which exhibit unprecedented tolerance of pulse strength errors without unreasonable sensitivity to off-resonance errors, and related families with more exotic tailored responses. Next we address the problem of extending these methods to other rotation angles, and discuss numerical results for 90° pulses. Finally we demonstrate the performance of some 90° and 180° pulses in NMR experiments.

Dual-compensated antisymmetric composite refocusing pulses for NMR

Novel antisymmetric composite 180° pulses are designed for use in nuclear magnetic resonance (NMR) and verified experimentally. The pulses are simultaneously broadband with respect to both inhomogeneity of the radiofrequency (B(1)) field and resonance offset and, as a result of their antisymmetric phase schemes, can be used to form spin echoes without the introduction of a phase error. The new dual-compensated pulses are designed analytically, using symmetry arguments and a graphical interpretation of average Hamiltonian theory. Two families of composite refocusing pulses are presented, one (ASBO-9) consisting of sequences made up of 9 simple 180° pulses and one (ASBO-11) of sequences made up of 11 simple 180° pulses. There are an infinite number of composite pulses in each family owing to a free phase variable in the solution to the average Hamiltonian equations and this allows selection of individual composite pulses with particular properties. Finally, a comparison is made between composite pulses designed using average Hamiltonian theory and those proposed for use in quantum computing by NMR.

Exploring the limits of broadband 90° and 180° universal rotation pulses

90° and 180° universal rotation (UR) pulses are two of the most important classes of pulses in modern NMR spectroscopy. This article presents a systematic study characterizing the achievable performance of these pulses as functions of bandwidth, pulse length, and tolerance to B(1)-field inhomogeneity/miscalibration. After an evaluation of different quality factors employed in pulse design algorithms based on optimal control theory, resulting pulses are discussed in detail with a special focus on pulse symmetry. The vast majority of resulting BURBOP (broadband universal rotations by optimal control) pulses are either fully symmetric or have one symmetric and one antisymmetric Cartesian rf component, where the importance of the first symmetry has not been demonstrated yet and the latter one matches the symmetry that results from a previously derived construction principle of universal rotation pulses out of point-to-point pulses [3]. Optimized BURBOP pulses are shown to perform better than previously reported UR pulses, resulting in shorter pulse durations for the same quality of broadband rotations. From a comparison of qualities of effective universal rotations, we find that the application of a single optimal refocusing pulse matches or improves the performance of two consecutive inversion pulses in INEPT-like pulse sequence elements of the same total duration.

Geometric aspects of composite pulses

Unitary operations acting on a quantum system must be robust against systematic errors in control parameters for reliable quantum computing. Composite pulse technique in nuclear magnetic resonance realizes such a robust operation by employing a sequence of possibly poor-quality pulses. In this study, we demonstrate that two kinds of composite pulses-one compensates for a pulse length error in a one-qubit system and the other compensates for a J-coupling error in a two-qubit system-have a vanishing dynamical phase and thereby can be seen as geometric quantum gates, which implement unitary gates by the holonomy associated with dynamics of cyclic vectors defined in the text.

Robust dynamical decoupling

Quantum computers, which process information encoded in quantum mechanical systems, hold the potential to solve some of the hardest computational problems. A substantial obstacle for the further development of quantum computers is the fact that the lifetime of quantum information is usually too short to allow practical computation. A promising method for increasing the lifetime, known as dynamical decoupling (DD), consists of applying a periodic series of inversion pulses to the quantum bits. In the present review, we give an overview of this technique and compare different pulse sequences proposed earlier. We show that pulse imperfections, which are always present in experimental implementations, limit the performance of DD. The loss of coherence due to the accumulation of pulse errors can even exceed the perturbation from the environment. This effect can be largely eliminated by a judicious design of pulses and sequences. The corresponding sequences are largely immune to pulse imperfections and provide an increase of the coherence time of the system by several orders of magnitude.

Slice-selective broadband refocusing pulses for the robust generation of crushed spin-echoes

A major challenge for in vivo magnetic resonance spectroscopy with point-resolved spectroscopy (PRESS) is the low signal intensity for the measurement of weakly scalar coupled spins, for example lactate. The chemical-shift displacement error between the two coupling partners of the lactate molecule leads to a signal decrease. The chemical-shift displacement error is decreased and therefore the lactate signal is increased by using refocusing pulses with a broad bandwidth. Previously, slice-selective broadband universal rotation pulses (S-BURBOP) were designed and applied as refocusing pulses in the PRESS pulse sequence (Janich MA, et al., Journal of Magnetic Resonance, 2011, 213, 126-135). However, S-BURBOP pulses leave a phase error across the slice which is superimposed on the spectra when spatially resolving the PRESS voxel. In the present novel design of slice-selective broadband refocusing pulses (S-BREBOP) this phase error is avoided. S-BREBOP pulses obtain 2.5 times the bandwidth of conventional Shinnar-Le Roux pulses and are robust against ±20% miscalibration of the B(1) amplitude. S-BREBOP pulses were validated in phantoms and in a low-grade brain tumor of a patient. Compared to conventional Shinnar-Le Roux pulses they lead to a decrease of the chemical-shift displacement error and consequently a lactate signal increase.

Improved background suppression in ¹H MAS NMR using composite pulses

A well known feature of ¹H MAS NMR spectroscopy, particularly of solids where the concentration of ¹H nuclei is low, is the presence in the spectrum of a significant broad "background" signal arising from ¹H nuclei that are outside the MAS rotor and radiofrequency coil, probably located on the surfaces of the static components of the probehead. A popular method of suppressing this unwanted signal is the "depth pulse" method, consisting of a 90° pulse followed by one or two 180° pulses that are phase cycled according to the "Exorcycle" scheme, which removes signal associated with imperfect 180° pulses. Consequently, only spins in the centre of the radiofrequency coil contribute to the ¹H MAS spectrum, while those experiencing a low B₁ field outside the coil are suppressed. Although very effective at removing background signal from the spectrum, one drawback with this approach is that significant loss of the desired signal from the sample also occurs. Here we investigate the ¹H background suppression problem and, in particular, the use of novel antisymmetric passband composite pulses to replace the simple pulses in a depth pulse experiment. We show that it is possible to improve the intensity of the ¹H signals of interest while still maintaining effective background suppression. We expect that these results will be relevant to ¹H MAS NMR studies of, for example, nominally perdeuterated biological samples or nominally anhydrous inorganic materials.

Use of composite refocusing pulses to form spin echoes

The radiofrequency pulses used in NMR are subject to a number of imperfections such as those caused by inhomogeneity of the radiofrequency (B(1)) field and an offset of the transmitter frequency from precise resonance. The effect of these pulse imperfections upon a refocusing pulse in a spin-echo experiment can be severe. Many of the worst effects, those that distort the phase of the spin echo, can be removed completely by selecting the echo coherence pathway using either the "Exorcycle" phase cycle or magnetic field gradients. It is then tempting to go further and try to improve the amplitude of the spin-echo signal by replacing the simple refocusing pulse with a broadband composite 180° pulse that compensates for the relevant pulse imperfection. We show here that all composite pulses with a symmetric or asymmetric phase shift scheme will reintroduce phase distortions into the spin echo, despite the selection of the echo coherence pathway. In contrast, all antisymmetric composite pulses yield no phase distortion whatsoever, both on and off resonance, and are therefore the correct symmetry of composite refocusing pulse to use. These conclusions are verified using simulations and (31)P MAS NMR spin-echo experiments performed on a microporous aluminophosphate.

The α-helical C-terminal domain of full-length recombinant PrP converts to an in-register parallel β-sheet structure in PrP fibrils: evidence from solid state nuclear magnetic resonance

We report the results of solid state nuclear magnetic resonance (NMR) measurements on amyloid fibrils formed by the full-length prion protein PrP (residues 23−231, Syrian hamster sequence). Measurements of intermolecular 13C−13C dipole−dipole couplings in selectively carbonyl-labeled samples indicate that β-sheets in these fibrils have an in-register parallel structure, as previously observed in amyloid fibrils associated with Alzheimer’s disease and type 2 diabetes and in yeast prion fibrils. Two-dimensional 13C−13C and 15N−13C solid state NMR spectra of a uniformly 15N- and 13C-labeled sample indicate that a relatively small fraction of the full sequence, localized to the C-terminal end, forms the structurally ordered, immobilized core. Although unique site-specific assignments of the solid state NMR signals cannot be obtained from these spectra, analysis with a Monte Carlo/simulated annealing algorithm suggests that the core is comprised primarily of residues in the 173−224 range. These results are consistent with earlier electron paramagnetic resonance studies of fibrils formed by residues 90−231 of the human PrP sequence, formed under somewhat different conditions [Cobb, N. J., Sonnichsen, F. D., McHaourab, H., and Surewicz, W. K. (2007) Proc. Natl. Acad. Sci. U.S.A. 104, 18946−18951], suggesting that an in-register parallel β-sheet structure formed by the C-terminal end may be a general feature of PrP fibrils prepared in vitro.

Heteronuclear decoupling by multiple rotating frame technique

The paper describes the multiple rotating frame technique for designing modulated rf fields, that perform broadband heteronuclear decoupling in solution NMR spectroscopy. The decoupling method presented here is understood by performing a sequence of coordinate transformations, each of which demodulates a component of the rf field to a static component, that progressively averages the chemical shift and the dipolar interaction. We show that by increasing the number of modulations in the decoupling field, the ratio of dispersion in the chemical shift to the strength of the static component of the rf field is successively reduced in the progressive frames. The known decoupling methods like continuous wave decoupling, TPPM, etc., can be viewed as special cases of this method and their performance improves by adding additional modulations in the decoupling field. The technique is also expected to find use in design of broadband excitation, inversion and mixing sequences and broadband experiments in solid state NMR.

Multi-frequency improved constant amplitude pulses for broadband inversion

Optimization of constant amplitude broadband inversion pulses for maximum inversion over a range of multiple fields yields more regular pulses with better tolerance to B(1) errors than those optimized for a single field. These multi-frequency improved constant amplitude (MICA) pulses as constructed for (13)C broadband inversion give best results for HMQC and especially HSQC type experiments. Most of the advantages of MICA pulses versus other inversion pulses in these experiments can be attributed to their relatively short durations. Linearly truncated versions of these pulses do not offer any advantage over MICA pulses for these applications. MICA inversion pulses can also be used for decoupling and a (13)C decoupling example gives twice the decoupling bandwidth as the GARP1 sequence at the same power level with no appreciable increase in decoupling sidebands.

Residual methyl protonation in perdeuterated proteins for multi-dimensional correlation experiments in MAS solid-state NMR spectroscopy

NMR studies involving perdeuterated proteins focus in general on exchangeable amide protons. However, non-exchangeable sites contain as well a small amount of protons as the employed precursors for protein biosynthesis are not completely proton depleted. The degree of methyl group protonation is in the order of 9% for CD2H using >97% deuterium enriched glucose. We show in this manuscript that this small amount of residual protonation is sufficient to perform 2D and 3D MAS solid-state NMR experiments. In particular, we suggest a HCCH-TOBSY type experiment which we successfully employ to assign the methyl resonances in aliphatic side chains in a perdeuterated sample of the SH3 domain of chicken alpha-spectrin.

Broadband homonuclear TOCSY with amplitude and phase-modulated RF mixing schemes

We have explored the design of broadband scalar coupling mediated (13)C-(13)C and cross-relaxation suppressed (1)H-(1)H TOCSY sequences employing phase/amplitude modulated inversion pulses. Considering a variety of supercycles, pulsewidths and a RF field strength of 10 kHz, the Fourier coefficients defining the amplitude and phase modulation profiles of the 180 degrees pulses were optimised numerically so as to obtain efficient magnetisation transfer within the desired range of resonance offsets. The coherence transfer characteristics of the mixing schemes were assessed via numerical simulations and experimental measurements and were compared with commonly used sequences based on rectangular RF pulses. The efficacies of the clean (1)H-(1)H TOCSY sequences were also examined via numerical simulations for application to weakly oriented systems and sequences with efficient, broadband and clean dipolar transfer characteristics were identified. In general, the amplitude and phase modulated TOCSY sequences presented here have moderately better performance characteristics than the sequences currently employed in biomolecular NMR spectroscopy.

Extending the scope of singlet-state spectroscopy

Different decoupling sequences are tested-using various shaped radio-frequency (RF) pulses-to achieve the longest possible lifetimes of singlet-state populations over the widest possible bandwidths, that is, ranges of offsets and relative chemical shifts of the nuclei involved in the singlet states. The use of sinc or refocusing broadband universal rotation pulses (RE-BURP) for decoupling during the intervals where singlet-state populations are preserved allows one to extend the useful bandwidth with respect to prior state-of-the-art methods based on composite-pulse WALTZ decoupling. The improved sinc decoupling sequences afford a more reliable and sensitive measure of the lifetimes of singlet states in pairs of spins that have widely different chemical shifts, such as the two aromatic protons H(5) and H(6) in uracil. Similar advantages are expected for nucleotides in RNA and DNA. Alternative approaches, in particular frequency-modulated decoupling sequences, also appear to be effective in preserving singlet-state populations, even though the profiles of the apparent relaxation rate constants as a function of the offset are somewhat perturbed. The best decoupling sequences prove their utility in sustaining longer lifetimes of singlet states than previously achieved for the side-chain tyrosine protons in bovine pancreatic trypsin inhibitor (BPTI) at 600 MHz (14.1 T), where the differences of chemical shifts between coupled protons are a challenge.

13C-detection in RNA bases: revealing structure-chemical shift relationships

The chemical shifts of the unprotonated carbons in the proton-deficient nucleobases of RNA are rarely reported, despite the valuable information that they contain about base-pairing and base-stacking. We have developed 13C-detected 2D-experiments to identify the unprotonated 13C in the RNA bases and have assigned all the base nuclei of uniformly 13C,15N-labeled HIV-2 TAR-RNA. The 13C chemical shift distributions revealed perturbations correlated with the base-pairing and base-stacking properties of all four base-types. From this work, we conclude that the information contained in the chemical shift perturbations within the base rings can provide valuable restraint information for solving RNA structures, especially in conformational averaged regions, where NOE-based information is not available.

Adiabatic 1H decoupling scheme for very accurate intensity measurements in 13C NMR

Adiabatic proton decoupling has been optimized in order to obtain accurate quantitative measurements of intensities on 13C NMR spectra. For each offset, the minimum adiabaticity factor (Km) reached during the pulse was computed. This K(m) profile was used to optimize the peak value and the swept frequency range of the adiabatic pulses. With a cosinus amplitude modulation, offset-independent-adiabaticity, and the M4P5-M4P9-M4P5'-M4P9' phase cycle, an accuracy of 2 per thousand for the 13C NMR measurements was reached. An approach using bi-labeled 13C acetic acid and ethanol at 99% allowed a fine experimental determination of the uniformity of the decoupling profile. The comparison with WALTZ-16 highlights the improvements in the uniformity of the proton decoupling.

New DEFT sequences for the acquisition of one-dimensional carbon NMR spectra of small unlabelled molecules

The acquisition time and quality of 1D 13C{1H} spectra can be improved substantially by using a modified driven equilibrium Fourier transform (DEFT) sequence, which is specifically designed to compensate for the effects of B1 inhomogeneity, pulse miscalibration and frequency offsets. The new sequence, called uniform driven equilibrium Fourier transform (UDEFT), returns the carbon magnetization with a high accuracy along its equilibrium position after each transient is complete. Thus, the sequence allows the use of relaxation delays (RD), which are much shorter than the carbon T1 of the molecule, thereby speeding up the acquisition process of 1D 13C{1H} spectra. To achieve this level of performance, UDEFT employs a refocusing element constituted by a composite adiabatic carbon pulse surrounded by two 90 degrees carbon pulses whose phases are designed to compensate for 90 degrees pulse miscalibrations in an MLEV manner (90 degrees+x-tau(FID)-180+y(Adia)-tau-90 degrees+x-180 degrees+x(Adia)). A version of the UDEFT sequence allows recording 1D 13C{1H} spectra devoid of heteronuclear NOE by using a matched adiabatic 1H decoupling scheme where an even number of 180 degrees adiabatic pulses is applied during the UDEFT module. Spectra of a solution of 300 mM camphor that contains some carbon nuclei with very long T1 relaxation times (90 s and 78 s) were acquired with 128 scans in 10 min using a 5 s relaxation delay.

Simultaneous 1H- or 2H-, 15N- and multiple-band-selective 13C-decoupling during acquisition in 13C-detected experiments with proteins and oligonucleotides

Significant resolution improvement in 13C,13C-TOCSY spectra of uniformly deuterated and 13C, 15N-labeled protein and 13C,15N-labeled RNA samples is achieved by introduction of multiple-band-selective 13C-homodecoupling applied simultaneously with 1H- or 2H- and 15N-decoupling at all stages of multidimensional experiments including signal acquisition period. The application of single, double or triple band-selective 13C-decoupling in 2D-[13C,13C]-TOCSY experiments during acquisition strongly simplifies the homonuclear splitting pattern. The technical aspects of complex multiple-band homonuclear decoupling and hardware requirements are discussed. The use of this technique (i) facilitates the resonance assignment process as it reduces signal overlap in homonuclear 13C-spectra and (ii) possibly improves the signal-to-noise ratio through multiplet collapse. It can be applied in any 13C-detected experiment.

TEDOR with adiabatic inversion pulses: Resonance assignments of 13C/15N labelled RNAs

We have examined via numerical simulations the performance characteristics of different 15N RF pulse schemes employed in the transferred echo double resonance (TEDOR) experimental protocol for generating 13C-15N dipolar chemical shift correlation spectra of isotopically labelled biological systems at moderate MAS frequencies (omega(r) approximately 10 kHz). With an 15N field strength of approximately 30-35 kHz that is typically available in 5 mm triple resonance MAS NMR probes, it is shown that a robust TEDOR sequence with significant tolerance to experimental imperfections sa as H1 inhomogeneity and resonance offsets can be effectively implemented using adiabatic heteronuclear dipolar recoupling pulse schemes. TEDOR-based 15N-13C and 15N-13C-13C chemical shift correlation experiments were carried out for obtaining 13C and 15N resonance assignments of an RNA composed of 97 (CUG) repeats which has been implicated in the neuromuscular disease myotonic dystrophy.

Broadband relaxation-optimized polarization transfer in magnetic resonance

Many applications of magnetic resonance are limited by rapid loss of spin coherence caused by large transverse relaxation rates. In NMR of large proteins, increased relaxation losses lead to poor sensitivity of experiments and increased measurement time. In this article, we develop broadband relaxation-optimized pulse sequences that approach fundamental limits of coherence transfer efficiency in the presence of very general relaxation mechanisms that include cross-correlated relaxation. These broadband transfer schemes use techniques of chemical shift refocusing (specific trajectory adapted refocusing echoes) that are tailored to specific trajectories of coupled spin evolution. We present simulations and experimental data indicating significant enhancement in the sensitivity of multidimensional NMR experiments of large molecules through these methods.