Dipolar Recoupling

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

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

Effects of radial radio-frequency field inhomogeneity on MAS solid-state NMR experiments

Radio-frequency field inhomogeneity is one of the most common imperfections in NMR experiments. They can lead to imperfect flip angles of applied radio-frequency (rf) pulses or to a mismatch of resonance conditions, resulting in artefacts or degraded performance of experiments. In solid-state NMR under magic angle spinning (MAS), the radial component becomes time-dependent because the rf irradiation amplitude and phase is modulated with integer multiples of the spinning frequency. We analyse the influence of such time-dependent MAS-modulated rf fields on the performance of some commonly used building blocks of solid-state NMR experiments. This analysis is based on analytical Floquet calculations and numerical simulations, taking into account the time dependence of the rf field. We find that, compared to the static part of the rf field inhomogeneity, such time-dependent modulations play a very minor role in the performance degradation of the investigated typical solid-state NMR experiments.

Heteronuclear and homonuclear radio-frequency-driven recoupling

The radio-frequency-driven recoupling (RFDR) pulse sequence is used in magic-angle spinning (MAS) NMR to recouple homonuclear dipolar interactions. Here we show simultaneous recoupling of both the heteronuclear and homonuclear dipolar interactions by applying RFDR pulses on two channels. We demonstrate the method, called HETeronuclear RFDR (HET-RFDR), on microcrystalline SH3 samples at 10 and 55.555 kHz MAS. Numerical simulations of both HET-RFDR and standard RFDR sequences allow for better understanding of the influence of offsets and paths of magnetization transfers for both HET-RFDR and RFDR experiments, as well as the crucial role of XY phase cycling.

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

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

Optimizing symmetry-based recoupling sequences in solid-state NMR by pulse-transient compensation and asynchronous implementation

Pulse imperfections like pulse transients and radio-frequency field maladjustment or inhomogeneity are the main sources of performance degradation and limited reproducibility in solid-state nuclear magnetic resonance experiments. We quantitatively analyze the influence of such imperfections on the performance of symmetry-based pulse sequences and describe how they can be compensated. Based on a triple-mode Floquet analysis, we develop a theoretical description of symmetry-based dipolar recoupling sequences, in particular, R26₄¹¹, calculating first- and second-order effective Hamiltonians using real pulse shapes. We discuss the various origins of effective fields, namely, pulse transients, deviation from the ideal flip angle, and fictitious fields, and develop strategies to counteract them for the restoration of full transfer efficiency. We compare experimental applications of transient-compensated pulses and an asynchronous implementation of the sequence to a supercycle, SR26, which is known to be efficient in compensating higher-order error terms. We are able to show the superiority of R26 compared to the supercycle, SR26, given the ability to reduce experimental error on the pulse sequence by pulse-transient compensation and a complete theoretical understanding of the sequence.

Handling the influence of chemical shift in amplitude-modulated heteronuclear dipolar recoupling solid-state NMR

We present a theoretical analysis of the influence of chemical shifts on amplitude-modulated heteronuclear dipolar recoupling experiments in solid-state NMR spectroscopy. The method is demonstrated using the Rotor Echo Short Pulse IRrAdiaTION mediated Cross-Polarization ((RESPIRATION)CP) experiment as an example. By going into the pulse sequence rf interaction frame and employing a quintuple-mode operator-based Floquet approach, we describe how chemical shift offset and anisotropic chemical shift affect the efficiency of heteronuclear polarization transfer. In this description, it becomes transparent that the main attribute leading to non-ideal performance is a fictitious field along the rf field axis, which is generated from second-order cross terms arising mainly between chemical shift tensors and themselves. This insight is useful for the development of improved recoupling experiments. We discuss the validity of this approach and present quaternion calculations to determine the effective resonance conditions in a combined rf field and chemical shift offset interaction frame transformation. Based on this, we derive a broad-banded version of the (RESPIRATION)CP experiment. The new sequence is experimentally verified using SNNFGAILSS amyloid fibrils where simultaneous (15)N → (13)CO and (15)N → (13)Cα coherence transfer is demonstrated on high-field NMR instrumentation, requiring great offset stability.

Studying Dynamics by Magic-Angle Spinning Solid-State NMR Spectroscopy: Principles and Applications to Biomolecules

Magic-angle spinning solid-state NMR spectroscopy is an important technique to study molecular structure, dynamics and interactions, and is rapidly gaining importance in biomolecular sciences. Here we provide an overview of experimental approaches to study molecular dynamics by MAS solid-state NMR, with an emphasis on the underlying theoretical concepts and differences of MAS solid-state NMR compared to solution-state NMR. The theoretical foundations of nuclear spin relaxation are revisited, focusing on the particularities of spin relaxation in solid samples under magic-angle spinning. We discuss the range of validity of Redfield theory, as well as the inherent multi-exponential behavior of relaxation in solids. Experimental challenges for measuring relaxation parameters in MAS solid-state NMR and a few recently proposed relaxation approaches are discussed, which provide information about time scales and amplitudes of motions ranging from picoseconds to milliseconds. We also discuss the theoretical basis and experimental measurements of anisotropic interactions (chemical-shift anisotropies, dipolar and quadrupolar couplings), which give direct information about the amplitude of motions. The potential of combining relaxation data with such measurements of dynamically-averaged anisotropic interactions is discussed. Although the focus of this review is on the theoretical foundations of dynamics studies rather than their application, we close by discussing a small number of recent dynamics studies, where the dynamic properties of proteins in crystals are compared to those in solution.

Improved transfer efficiencies in radio-frequency-driven recoupling solid-state NMR by adiabatic sweep through the dipolar recoupling condition

The homonuclear radio-frequency driven recoupling (RFDR) experiment is commonly used in solid-state NMR spectroscopy to gain insight into the structure of biological samples due to its ease of implementation, stability towards fluctuations/missetting of radio-frequency (rf) field strength, and in general low rf requirements. A theoretical operator-based Floquet description is presented to appreciate the effect of having a temporal displacement of the π-pulses in the RFDR experiment. From this description, we demonstrate improved transfer efficiency for the RFDR experiment by generating an adiabatic passage through the zero-quantum recoupling condition. We have compared the performances of RFDR and the improved sequence to mediate efficient (13)CO to (13)Cα polarization transfer for uniformly (13)C,(15)N-labeled glycine and for the fibril forming peptide SNNFGAILSS (one-letter amino acid codes) uniformly (13)C,(15)N-labeled at the FGAIL residues. Using numerically optimized sweeps, we get experimental gains of approximately 20% for glycine where numerical simulations predict an improvement of 25% relative to the standard implementation. For the fibril forming peptide, using the same sweep parameters as found for glycine, we have gains in the order of 10%-20% depending on the spectral regions of interest.

Low-power broadband homonuclear dipolar recoupling in MAS NMR by two-fold symmetry pulse schemes for magnetization transfers and double-quantum excitation

We provide an experimental, numerical, and high-order average Hamiltonian evaluation of an open-ended series of homonuclear dipolar recoupling sequences, SR [Formula: see text] with p=1,2,3,…. While operating at a very low radio-frequency (rf) power, corresponding to a nutation frequency of 1/2 of the magic-angle spinning (MAS) rate (ωnut=ωr/2), these recursively generated double-quantum (2Q) dipolar recoupling schemes offer a progressively improved compensation to resonance offsets and rf inhomogeneity for increasing pulse-sequence order p. The excellent recoupling robustness to these experimental obstacles, as well as to CSA, is demonstrated for 2Q filtering (2QF) experiments and for driving magnetization transfers in 2D NMR correlation spectroscopy, where the sequences may provide either double or zero quantum dipolar Hamiltonians during mixing. Experimental and numerical demonstrations, which mostly target conditions of "ultra-fast" MAS (≳50kHz) and high magnetic fields, are provided for recoupling of (13)C across a wide range of isotropic and anisotropic chemical shifts, as well as dipolar coupling constants, encompassing [2,3-(13)C2]alanine, [1,3-(13)C2]alanine, diammonium [1,4-(13)C2]fumarate, and [U-(13)C]tyrosine. When compared at equal power levels, a superior performance is observed for the SR [Formula: see text] sequences with p⩾3 relative to existing and well-established 2Q recoupling techniques. At ultra-fast MAS, proton decoupling is redundant during the homonuclear dipolar recoupling of dilute spins in organic solids, which renders the family of SR [Formula: see text] schemes the first efficient 2Q recoupling option for general applications, such as 2Q-1Q correlation NMR and high-order multiple-quantum excitation, under truly low-power rf conditions.

Two heteronuclear dipolar results at the price of one: quantifying Na/P contacts in phosphosilicate glasses and biomimetic hydroxy-apatite

The analysis of S{I} recoupling experiments applied to amorphous solids yields a heteronuclear second moment M(2)(S-I) that represents the effective through-space dipolar interaction between the detected S spins and the neighboring I-spin species. We show that both M(2)(S-I) and M(2)(I-S) values are readily accessible from a sole S{I} or I{S} experiment, which may involve either S or I detection, and is naturally selected as the most favorable option under the given experimental conditions. For the common case where I has half-integer spin, an I{S} REDOR implementation is preferred to the S{I} REAPDOR counterpart. We verify the procedure by (23)Na{(31)P} REDOR and (31)P{(23)Na} REAPDOR NMR applied to Na(2)O-CaO-SiO(2)-P(2)O(5) glasses and biomimetic hydroxyapatite, where the M(2)(P-Na) values directly determined by REAPDOR agree very well with those derived from the corresponding M(2)(Na-P) results measured by REDOR. Moreover, we show that dipolar second moments are readily extracted from the REAPDOR NMR protocol by a straightforward numerical fitting of the initial dephasing data, in direct analogy with the well-established procedure to determine M(2)(S-I) values from REDOR NMR experiments applied to amorphous materials; this avoids the problems with time-consuming numerically exact simulations whose accuracy is limited for describing the dynamics of a priori unknown multi-spin systems in disordered structures.

Mechanism of dilute-spin-exchange in solid-state NMR

In the stationary, aligned samples used in oriented sample (OS) solid-state NMR, (1)H-(1)H homonuclear dipolar couplings are not attenuated as they are in magic angle spinning solid-state NMR; consequently, they are available for participation in dipolar coupling-based spin-exchange processes. Here we describe analytically the pathways of (15)N-(15)N spin-exchange mediated by (1)H-(1)H homonuclear dipolar couplings. The mixed-order proton-relay mechanism can be differentiated from the third spin assisted recoupling mechanism by setting the (1)H to an off-resonance frequency so that it is at the "magic angle" during the spin-exchange interval in the experiment, since the "magic angle" irradiation nearly quenches the former but only slightly attenuates the latter. Experimental spectra from a single crystal of N-acetyl leucine confirm that this proton-relay mechanism plays the dominant role in (15)N-(15)N dilute-spin-exchange in OS solid-state NMR in crystalline samples. Remarkably, the "forbidden" spin-exchange condition under "magic angle" irradiation results in (15)N-(15)N cross-peaks intensities that are comparable to those observed with on-resonance irradiation in applications to proteins. The mechanism of the proton relay in dilute-spin-exchange is crucial for the design of polarization transfer experiments.

Chain dynamics of surfactants in mesoporous silica

Mesostructured porous materials possess unique surface, structural, and bulk properties that lead to important practical applications. By retaining structure-directing species in the product material, mesostructured organic-inorganic composites are obtained which are of broad interest for fundamental studies of confinement effects and surface interaction on structural and dynamic properties of organic molecules. In the present study, solid state dipolar (13)C-(1)H NMR spectroscopy is applied to quantitatively characterize the conformational dynamics of organic surfactants in the mesostructured composite CTAB-MCM41. Such an approach does not require assumptions and adjustable parameters and reflects the changes in conformational dynamics without relying on specific motional models. The conformational dynamics of the surfactant confined in solid hexagonal arrays is compared to that in hexagonal aggregates formed in a concentrated aqueous solution. The study showed that in cylindrical pores of hexagonal mesoporous silica the order parameter gradually decreases towards the end of the chain. The degree of order and the order parameter profile is similar to that observed in hexagonal liquid crystalline phases. However, the mobility of segments close to the head group is more restricted compared to that in the mesophase, as the result of interaction with the solid silica interface.

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.