Spinning-frequency-dependent narrowband RF-driven dipolar recoupling

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.

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.

Spectral editing of alanine, serine, and threonine in uniformly labeled proteins based on frequency-selective homonuclear recoupling in solid-state NMR

Spectral editing is crucial to simplify the crowded solid-state NMR spectra of proteins. New techniques are introduced to edit ¹³C-¹³C correlations of uniformly labeled proteins under moderate magic-angle spinning (MAS), based on our recent frequency-selective homonuclear recoupling sequences [Zhang et al., J. Phys. Chem. Lett. 2020, 11, 8077-8083]. The signals of alanine, serine, or threonine residues are selected out by selective ¹³Cα-¹³Cβ double-quantum filtering (DQF). The ¹³Cα-¹³Cβ correlations of alanine residues are selectively established with efficiency up to ~ 1.8 times that by dipolar-assisted rotational resonance (DARR). The techniques are shown in 2D/3D NCCX experiments and applied to the uniformly ¹³C, ¹⁵N labeled Aquaporin Z (AqpZ) membrane protein, demonstrating their potential to simplify spectral analyses in biological solid-state NMR.

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

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

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.

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.

Radio frequency-driven recoupling at high magic-angle spinning frequencies: homonuclear recoupling sans heteronuclear decoupling

We describe solid-state NMR homonuclear recoupling experiments at high magic-angle spinning (MAS) frequencies using the radio frequency-driven recoupling (RFDR) scheme. The effect of heteronuclear decoupling interference during RFDR recoupling at high spinning frequencies is investigated experimentally and via numerical simulations, resulting in the identification of optimal decoupling conditions. The effects of MAS frequency, RF field amplitude, bandwidth, and chemical shift offsets are examined. Most significantly, it is shown that broadband homonuclear correlation spectra can be efficiently obtained using RFDR without decoupling during the mixing period in fully protonated samples, thus considerably reducing the rf power requirements for acquisition of (13)C-(13)C correlation spectra. The utility of RFDR sans decoupling is demonstrated with broadband correlation spectra of a peptide and a model protein at high MAS frequencies and high magnetic field.

(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.

Frequency-selective homonuclear dipolar recoupling in solid state NMR

We introduce a new approach to frequency-selective homonuclear dipolar recoupling in solid state nuclear magnetic resonance (NMR) with magic-angle spinning (MAS). This approach, to which we give the acronym SEASHORE, employs alternating periods of double-quantum recoupling and chemical shift evolution to produce phase modulations of the recoupled dipole-dipole interactions that average out undesired couplings, leaving only dipole-dipole couplings between nuclear spins with a selected pair of NMR frequencies. In principle, SEASHORE is applicable to systems with arbitrary coupling strengths and arbitrary sets of NMR frequencies. Arbitrary MAS frequencies are also possible, subject only to restrictions imposed by the pulse sequence chosen for double-quantum recoupling. We demonstrate the efficacy of SEASHORE in experimental (13)C NMR measurements of frequency-selective polarization transfer in uniformly (15)N, (13)C-labeled L-valine powder and frequency-selective intermolecular polarization transfer in amyloid fibrils formed by a synthetic decapeptide containing uniformly (15)N, (13)C-labeled residues.

Band-selective carbonyl to aliphatic side chain 13C-13C distance measurements in U-13C,15N-labeled solid peptides by magic angle spinning NMR

We describe three-dimensional magic angle spinning NMR experiments that enable simultaneous band-selective measurement of the multiple distance constraints between carbonyl and side chain carbons in uniformly 13C,15N-labeled peptides. The approaches are designed to circumvent the dipolar truncation and to allow experimental separation of the multiple quantum (MQ) relaxation and dipolar effects. The pulse sequences employ the double quantum (DQ) rotational resonance in the tilted frame (R2TR) to perform selective polarization transfers that reintroduce the 13C'-13Cgamma,delta dipolar interactions. The scheme avoids recoupling of the strongly coupled C'-Calpha and C'-Cbeta spin pairs, therefore minimizing dipolar truncation effects. The experiment is performed in a constant time fashion as a function of the radio frequency irradiation intensity and measures the line shape of the DQ transition. The width and the intensity of this line shape are analyzed in terms of the DQ relaxation and dipolar coupling. The attenuation of the multispin effects in the presence of 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 contributions of B1-inhomogeneity, CSA orientation effects, and the effects of inhomogeneous line broadening are also estimated. The experiments are demonstrated in model U-13C,15N-labeled peptides, N-acetyl-L-Val-L-Leu and N-formyl-L-Met-L-Leu-L-Phe, where 10 and 6 distances, ranging between 3 and 6 A, were measured, respectively.

Multiple-spin analysis of chemical-shift-selective (13C, 13C) transfer in uniformly labeled biomolecules

Chemical-shift-selective (13C, 13C) polarization transfer is analyzed in uniformly labeled biomolecules. It is shown that the spin system dynamics remain sensitive to the distance of interest and can be well reproduced within a quantum-mechanical multiple-spin analysis. These results lead to a general approach on how to describe chemical-shift-selective transfer in uniformly labeled systems. As demonstrated in the case of ubiquitin, this methodology can be used to detect long-range distance constraints in uniformly labeled proteins.

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

The rotational resonance width (R2W) experiment is a constant-time version of the rotational resonance (R2) experiment, in which the magnetization exchange is measured as a function of sample spinning frequency rather than the mixing time. The significant advantage of this experiment over conventional R2 is that both the dipolar coupling and the relaxation parameters can be independently and unambiguously extracted from the magnetization exchange profile. In this paper, we combine R2W with two-dimensional 13C-13C chemical shift correlation spectroscopy and demonstrate the utility of this technique for the site-specific measurement of multiple 13C-13C distances in uniformly labeled solids. The dipolar truncation effects, usually associated with distance measurements in uniformly labeled solids, are considerably attenuated in R2W experiments. Thus, R2W experiments are applicable to uniformly labeled biological systems. To validate this statement, multiple 13C-13C distances (in the range of 3-6 A) were determined in N-acetyl-[U-13C,15N]l-Val-l-Leu with an average precision of +/-0.5 A. Furthermore, the distance constraints extracted using a two-spin model agree well with the X-ray crystallographic data.

Band-selective recoupling of homonuclear double-quantum dipolar interaction with a generalized composite 0 degrees pulse: application to 13C aliphatic region-selective magnetization transfer in solids

Recoupling of homonuclear double quantum (DQ)-dipolar interactions is a useful technique for the structural analysis of molecules in solids. We have designed a series of elemental 0 degrees pulses for the recoupling sequences with the rf phase rotation about the z-axis, known as CN. The proposed 0 degrees pulses whose total flip angle >/=360 degrees provide spin rotation vectors in the xy-plane. Thus, the residual spin rotation can be canceled by rf phase rotation about the z-axis. An analysis by the coherent averaging theory showed that effective bandwidths of the recoupling sequences are limited not by the reduction in the dipolar scaling factor but by the increase in the residual spin rotation due to offset. A CN sequence with these elemental pulses provides an effective bandwidth of DQ-dipolar recoupling from ca. 0.5nu(R) to 4nu(R) for numerical simulations. Here, nu(R) is the sample spinning frequency. The 0 degrees pulses were applied to band-selective recoupling for the magnetization transfer in uniformly 13C-labeled molecules. Narrow-band recoupling enhances the magnetization transfer between spins within the effective range by decoupling the dipolar interactions between spins one of which is outside the range. The narrow band operation reduces rf field strength, which improves the CH decoupling. Increases in signal intensities by the use of the proposed 0 degrees pulses are experimentally shown for 13C-labeled amino acids.

Improved narrowband dipolar recoupling for homonuclear distance measurements in rotating solids

Recovery of the magnetic dipolar interaction between nuclei bearing the same gyromagnetic ratio in rotating solids can be promoted by synchronous rf irradiation. Determination of the dipolar interaction strength can serve as a tool for structural elucidation in polycrystalline powders. Spinning frequency dependent narrow-band (nb) RFDR and SEDRA experiments are utilized as simple techniques for the determination of dipolar interactions between the nuclei in coupled homonuclear spin pairs. The magnetization exchange and coherence dephasing due to a fixed number of rotor-synchronously applied pi-pulses is monitored at spinning frequencies in the vicinity of the rotational resonance (R(2)) conditions. The powder nbRFDR and nbSEDRA decay curves of spin magnetizations and coherences, respectively, as a function of the spinning frequency can be measured and analyzed using simple rate equations providing a quantitative measure of the dipolar coupling. The effects of the phenomenological relaxation parameters in these rate equations are discussed and an improved methodology is suggested for analyzing nbRFDR data for small dipolar couplings. The distance between the labeled nuclei in the 1,3-(13)C(2)-hydroxybutyric acid molecule is rederived using existing nbRFDR results and the new simulation procedure. A nbSEDRA experiment has been performed successfully on a powder sample of singly labeled 1-(13)C-L-leucine measuring the dipolar interaction between the labeled carboxyl carbon and the natural abundant beta-carbon. Both narrowband techniques are employed for the determination of the nuclear distances between the side-chain carbons of leucine and its carbonyl carbon in a tripeptide Leu-Gly-Phe that is singly (13)C-labeled at the leucine carbonyl carbon position.

Peptide torsion angle measurements: effects of nondilute spin pairs on carbon-observed, deuterium-dephased PM5-REDOR

Reintroducing dipolar coupling between spin-1/2 nuclei (e.g., (13)C, (15)N) and spin-1 (2)H, using phase-modulated deuterium dephasing pulses, provides a simple and efficient basis for obtaining peptide backbone torsion angles (phi, psi) in specific stable-isotope enriched samples. Multiple homonuclear spin-1/2 interactions due to isotopic enrichment can arise between neighboring molecules or within a multiply labeled protein after folding. The consequences of (13)C homonuclear interactions present during (13)C-observed, (2)H-dephased REDOR measurements are explored and the theoretical basis of the experimentally observed effects is investigated. Two tripeptides are taken to represent both the general case of (2)H(alpha)-alanine (in the tripeptide LAF) and the special case of (2)H(alpha)(2)-glycine (in the tripeptide LGF). The lyophilized tripeptides exhibit narrowed spectral linewidths over time due to reduced conformational dispersion. This is due to a hydration process whereby a small fraction of peptides is reorienting and the bulk peptide fraction undergoes a conformational change. The new molecular packing arrangement lacks homonuclear (13)C spin interactions, allowing determination of (phi, psi) backbone torsion angles.