PITANSEMA-MAS, a solid-state NMR method to measure heteronuclear dipolar couplings under MAS

A 2D NMR method is presented for the measurement of the dipole-dipole interaction between a proton and a low-frequency nuclear spin species in the solid state under the magic angle spinning. It employs the time averaged nutation concept to dramatically reduce the required radio frequency (rf) power on the low γ nuclear channel and spin exchange at the magic angle is used to suppress (1)H-(1)H dipolar interactions and chemical shifts. The flexibility in choosing the spinning speed, rf power and the scaling factor of the pulse sequence are of considerable importance for the structural studies of biological solids. The performance of the pulse sequence has been numerically and experimentally demonstrated on several solids.     

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

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

Measuring chirality in NMR in the presence of a static electric field

The scalar Hamiltonian of nuclear spins in the presence of a static electric field supports chirality. However, the eigenvalues of the Hamiltonian are not chiral; hence, chirality is not manifested in the usual NMR experiment. In this work, we show that the magnetization response to certain radio frequency pulse sequences exhibits chirality as well as handedness.     

Compensating Pulse Imperfections in Solid‐State NMR Spectroscopy: A Key to Better Reproducibility and Performance

The power and versatility of NMR spectroscopy is strongly related to the ability to manipulate NMR interactions by the application of radio‐frequency (rf) pulse sequences. Unfortunately, the rf fields seen by the spins differ from the ones programmed by the experimentalist. Pulse transients, i.e., deviations of the amplitude and phase of the rf fields from the desired values, can have a severe impact on the performance of pulse sequences and can lead to inconsistent results. Here, we demonstrate how transient‐compensated pulses can greatly improve the efficiency and reproducibility of NMR experiments. The implementation is based on a measurement of the characteristics of the resonance circuit and does not rely on an experimental optimization of the NMR signal. We show how the pulse sequence has to be modified to use it with transient‐compensated pulses. The efficiency and reproducibility of the transient‐compensated sequence is greatly superior to the original POST‐C7 sequence.     

Diffusion damping during adiabatic z-rotation pulses for NMR spectroscopy in inhomogeneous magnetic fields

High-resolution nuclear magnetic resonance spectra from samples located in inhomogeneous static and radio frequency magnetic fields can be obtained by applying a train of z-rotation radio frequency pulses to repeatedly refocus the inhomogeneous broadening during signal detection. z-rotation pulses based on an adiabatic double passage are effective over wide bandwidths using a limited amount of radio frequency power at the expense of being time consuming and, consequently, sensitive to motion of the spin bearing molecules. The signal damping resulting from molecular self-diffusion during the pulse was studied experimentally and using Brownian dynamics simulations. The results show that the analytical expression for diffusion damping during a double spin echo is a reasonable approximation for the signal decay during an adiabatic z-rotation pulse. Methods to alleviate the effects of diffusion are discussed.     

PITANSEMA, a low-power PISEMA solid-state NMR experiment

A low radio frequency power polarization inversion spin exchange at the magic angle (PISEMA) pulse sequence is described for the measurement of heteronuclear dipolar couplings from solids. The method employs a time averaged nutation concept to significantly reduce the rf power required to spin-lock low gamma nuclear spins in PISEMA experiments. The efficacy of the 2D method is demonstrated on a single crystal of n-acetyl-L-(15)N-valyl-L-(15)N-leucine dipeptide to measure (1)H-(15)N dipolar couplings and a liquid crystal sample to measure (1)H-(13)C dipolar couplings.     

Effective Hamiltonians by optimal control: solid-state NMR double-quantum planar and isotropic dipolar recoupling

We report the use of optimal control algorithms for tailoring the effective Hamiltonians in nuclear magnetic resonance (NMR) spectroscopy through sophisticated radio-frequency (rf) pulse irradiation. Specifically, we address dipolar recoupling in solid-state NMR of powder samples for which case pulse sequences offering evolution under planar double-quantum and isotropic mixing dipolar coupling Hamiltonians are designed. The pulse sequences are constructed numerically to cope with a range of experimental conditions such as inhomogeneous rf fields, spread of chemical shifts, the intrinsic orientation dependencies of powder samples, and sample spinning. While the vast majority of previous dipolar recoupling sequences are operating through planar double-or zero-quantum effective Hamiltonians, we present here not only improved variants of such experiments but also for the first time homonuclear isotropic mixing sequences which transfers all I(x), I(y), and I(z) polarizations from one spin to the same operators on another spin simultaneously and with equal efficiency. This property may be exploited to increase the signal-to-noise ratio of two-dimensional experiments by a factor of square root 2 compared to conventional solid-state methods otherwise showing the same efficiency. The sequences are tested numerically and experimentally for a powder of (13)C(alpha),(13)C(beta)-L-alanine and demonstrate substantial sensitivity gains over previous dipolar recoupling experiments.     

Pulsed pressure perturbations, an extra dimension in NMR spectroscopy of proteins

The introduction of multidimensional NMR spectroscopy was a breakthrough in biological NMR methodology because it allowed the unequivocal correlation of different spin states of the system. The introduction of large pressure perturbations in the corresponding radio frequency (RF) pulse sequences adds an extra structural dimension into these experiments. We have developed a microprocessor-controlled pressure jump unit that is able to introduce fast, strong pressure changes at any point in the pulse sequences. Repetitive pressure changes of 80 MPa in the sample tube are thus feasible in less than 30 ms. Two general forms of these experiments are proposed here, the pressure perturbation transient state spectroscopy (PPTSS) and the pressure perturbation state correlation spectroscopy (PPSCS). PPTSS can be used to measure the rate constants and the activation energies and activation volumes for the transition between different conformational states including the folded and unfolded state of proteins, for polymerization-depolymerization processes, and for ligand binding at atomic resolution. PPSCS spectroscopy correlates the NMR parameters of different pressure-induced states of the system, thus allowing the measurement of properties of a given pressure induced state such as a folding intermediate in a different state, for example, the folded state. Selected examples for PPTSS and PPSCS spectroscopy are presented in this Article.     

Towards measurement of homonuclear dipolar couplings in 1H solid-state NMR: recoupling with a rotor-synchronized decoupling scheme

We describe a magic-angle spinning NMR experiment for (1)H-(1)H homonuclear dipole-dipole coupling estimations in organic solids. The methodology involves reintroducing dipolar interactions with rotor-synchronized homonuclear decoupling pulse sequences. Frequency-selective DANTE pulses are used to isolate a specific spin pair from a natural isotopic abundance sample. The coupling of interest, between the selected spin pair, may be extracted by a non linear least-squares fit of the experimentally observed modulation of the signal intensity to an exact analytical formula. The experiment is demonstrated on natural isotopic abundance glycine and alanine powder samples.     

Spin Noise Detection of Nuclear Hyperpolarization at 1.2 K

We report proton spin noise spectra of a hyperpolarized solid sample of commonly used “DNP (dynamic nuclear polarization) juice” containing TEMPOL (4‐hydroxy‐2,2,6,6‐tetramethylpiperidine N‐oxide) and irradiated by a microwave field at a temperature of 1.2 K in a magnetic field of 6.7 T. The line shapes of the spin noise power spectra are sensitive to the variation of the microwave irradiation frequency and change from dip to bump, when the electron Larmor frequency is crossed, which is shown to be in good accordance with theory by simulations. Small but significant deviations from these predictions are observed, which can be related to spin noise and radiation damping phenomena that have been reported in thermally polarized systems. The non‐linear dependence of the spin noise integral on nuclear polarization provides a means to monitor hyperpolarization semi‐quantitatively without any perturbation of the spin system by radio frequency irradiation.     

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

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

Spherical tensor analysis of nuclear magnetic resonance signals

In a nuclear magnetic-resonance (NMR) experiment, the spin density operator may be regarded as a superposition of irreducible spherical tensor operators. Each of these spin operators evolves during the NMR experiment and may give rise to an NMR signal at a later time. The NMR signal at the end of a pulse sequence may, therefore, be regarded as a superposition of spherical components, each derived from a different spherical tensor operator. We describe an experimental method, called spherical tensor analysis (STA), which allows the complete resolution of the NMR signal into its individual spherical components. The method is demonstrated on a powder of a (13)C-labeled amino acid, exposed to a pulse sequence generating a double-quantum effective Hamiltonian. The propagation of spin order through the space of spherical tensor operators is revealed by the STA procedure, both in static and rotating solids. Possible applications of STA to the NMR of liquids, liquid crystals, and solids are discussed.     

NMR R1 rho rotating-frame relaxation with weak radio frequency fields

NMR spin relaxation in the rotating frame (R(1 rho)) is one of few methods available to characterize chemical exchange kinetic processes occurring on micros-ms time scales. R(1 rho) measurements for heteronuclei in biological macromolecules generally require decoupling of (1)H scalar coupling interactions and suppression of cross-relaxation processes. Korzhnev and co-workers demonstrated that applying conventional (1)H decoupling schemes while the heteronuclei are spin-locked by a radio frequency (rf) field results in imperfect decoupling [Korzhnev, Skrynnikov, Millet, Torchia, Kay. J. Am. Chem. Soc. 2002, 124, 10743-10753]. Experimental NMR pulse sequences were presented that provide accurate measurements of R(1 rho) rate constants for radio frequency field strengths > 1000 Hz. This paper presents new two-dimensional NMR experiments that allow the use of weak rf fields, between 150 and 1000 Hz, in R(1 rho) experiments. Fourier decomposition and average Hamiltonian theory are employed to analyze the spin-lock sequence and provide a guide for the development of improved experiments. The new pulse sequences are validated using ubiquitin and basic pancreatic trypsin inhibitor (BPTI). The use of weak spin-lock fields in R(1 rho) experiments allows the study of the chemical exchange process on a wider range of time scales, bridging the gap that currently exists between Carr-Purcell-Meiboom-Gill and conventional R(1 rho) experiments. The new experiments also extend the capability of the R(1 rho) technique to study exchange processes outside the fast exchange limit.     

Quadrupolar nuclear magnetic resonance spectroscopy in solids using frequency-swept echoing pulses

The acquisition of ideal powder line shapes remains a recurring challenge in solid-state wideline nuclear magnetic resonance (NMR). Certain species, particularly quadrupolar spins in sites associated with large electric field gradients, are difficult to excite uniformly and with good efficiencies. This paper discusses some of the opportunities that arise upon departing from standard spin-echo excitation approaches and switching to echo sequences that use low-power, frequency-swept radio frequency (rf) pulses instead. The reduced powers demanded by such swept rf fields allow one to excite spins in different crystallites efficiently and with orientation-independent pulse angles, while the large bandwidths of interest that are needed by the measurement can be covered, thanks to the use of broadband frequency sweeps. The fact that the spins' evolution and ensuing dephasing starts at the beginning of such rf manipulation calls for the use of spin-echo sequences; a number of alternatives capable of providing the desired line shapes both in the frequency and in the time domains are introduced and experimentally demonstrated. Sensitivity- and lineshape-wise these experiments are competitive vis-a-vis current implementations of wideline quadrupolar NMR based on hard rf pulses; additional opportunities that may derive from these ideas are also briefly discussed.     

Fourier decompositions and pulse sequence design algorithms for nuclear magnetic resonance in inhomogeneous fields

In this paper, we introduce algorithms based on Fourier synthesis for designing phase compensating rf pulse sequences for high-resolution nuclear magnetic resonance (NMR) spectroscopy in an inhomogeneous B0 field. We show that using radio frequency pulses and time varying linear gradients in three dimensions, it is possible to impart the transverse magnetization of spins phase, which is a desired function of the spatial (x,y,z) location. Such a sequence can be used to precompensate the phase that will be acquired by spins at different spatial locations due to inhomogeneous magnetic fields. With this precompensation, the chemical shift information of the spins can be reliably extracted and high resolution NMR spectrum can be obtained.     

A new phase modulated binomial‐like selective‐inversion sequence for solvent signal suppression in NMR

A new 8 ‐pulse P hase M odulated binomial‐like selective inversion pulse sequence, dubbed ‘8PM’, was developed by optimizing the nutation and phase angles of the constituent radio‐frequency pulses so that the inversion profile resembled a target profile. Suppression profiles were obtained for both the 8PM and W5 based excitation sculpting sequences with equal inter‐pulse delays. Significant distortions were observed in both profiles because of the offset effect of the radio frequency pulses. These distortions were successfully reduced by adjusting the inter‐pulse delays. With adjusted inter‐pulse delays, the 8PM and W5 based excitation sculpting sequences were tested on an aqueous lysozyme solution. The 8 PM based sequence provided higher suppression selectivity than the W5 based sequence. Two‐dimensional nuclear Overhauser effect spectroscopy experiments were also performed on the lysozyme sample with 8PM and W5 based water signal suppression. The 8PM based suppression provided a spectrum with significantly increased (~ doubled) cross‐peak intensity around the suppressed water resonance compared to the W5 based suppression. Copyright © 2016 John Wiley & Sons, Ltd.     

Conversion of parahydrogen induced longitudinal two-spin order to evenly distributed single spin polarisation by optimal control pulse sequences

Strongly enhanced spin polarization in the form of longitudinal spin order can be generated on target molecules by using parahydrogen in a catalyzed hydrogenation reaction. An optimal control algorithm was used to generate radiofrequency pulse sequences which convert the arising longitudinal two-spin order into single-spin Zeeman order with high efficiency and distribute it evenly between three coupled spins within the same molecule. The pulses are designed to be very robust towards variations in the B(0) and B(1) fields. Furthermore, this strategy is applied to enhance the NMR signal in an ultrafast gradient assisted single excitation two-dimensional spectroscopy experiment.     

Parahydrogen‐Induced Radio Amplification by Stimulated Emission of Radiation

Radio amplification by stimulated emission of radiation (RASER) was recently discovered in a low‐field NMR spectrometer incorporating a highly specialized radio‐frequency resonator, where a high degree of proton‐spin polarization was achieved by reversible parahydrogen exchange. RASER activity, which results from the coherent coupling between the nuclear spins and the inductive detector, can overcome the limits of frequency resolution in NMR. Here we show that this phenomenon is not limited to low magnetic fields or the use of resonators with high‐quality factors. We use a commercial bench‐top 1.4 T NMR spectrometer in conjunction with pairwise parahydrogen addition producing proton‐hyperpolarized molecules in the Earth's magnetic field (ALTADENA condition) or in a high magnetic field (PASADENA condition) to induce RASER without any radio‐frequency excitation pulses. The results demonstrate that RASER activity can be observed on virtually any NMR spectrometer and measures most of the important NMR parameters with high precision.     

Symmetry in the design of NMR multiple-pulse sequences

The symmetry principles of NMR pulse-sequence design are summarized. The discussion is guided by an analogy with tiling schemes in the decorative arts. The symmetry operations for NMR pulse sequences are discussed in terms of excitation field modifiers and temporal modifiers. The quantum operators which describe the effect of these modifiers on the excitation field spin Hamiltonian are provided. The symmetry transformations of spin propagators, and the different types of pulse-sequence elements are discussed. The common types of symmetry expansion are treated using the propagator transformations and the Euler angles for the excitation field propagators. The selection rules associated with symmetrical pulse sequences are discussed using average Hamiltonian theory.     

The effects of molecular diffusion in ultrafast two-dimensional nuclear magnetic resonance

The so-called "ultrafast" nuclear magnetic resonance (NMR) methods enable the collection of multidimensional spectra within a single scan. These experiments operate by replacing traditional t(1) time increments, with a series of combined radiofrequency-irradiation/magnetic-field-gradient manipulations that spatially encode the effects of the indirect-domain spin interactions. Barring the presence of sizable displacements, the spatial patterns thus imparted can be read out following a mixing period with the aid of oscillating acquisition gradients, leading to a train of t(2)-modulated echoes carrying in their positions and phases the indirect- and the direct-domain spin interactions. Both the initial spatial encoding as well as the subsequent spatial decoding procedures underlying ultrafast NMR were designed under the assumption that spins remain static within the sample during their execution. Most often this is not the case, and motion-related effects can be expected to affect the outcome of these experiments. The present paper focuses on analyzing the effects of diffusion in ultrafast two-dimensional (2D) NMR. Toward this end both analytical and numerical formalisms are derived, capable of dealing with the nonuniform spin manipulations, macroscopic sample sizes, and microscopic displacements involved in this kind of sequences. After experimentally validating the correctness of these formalisms these were used to analyze the effects of diffusion for a variety of cases, including ultrafast experiments on both rapidly and slowly diffusing molecules. A series of prototypical schemes were considered including discrete and continuous encoding modes, constant- and real-time manipulations, homo- and heteronuclear acquisitions, and single versus multiple quantum modalities. The effects of molecular diffusion were also compared against typical relaxation-driven losses as they happen in these various prototypical situations; from all these situations, general guidelines for choosing the optimal ultrafast 2D NMR scheme for a particular sample and condition could be deduced.