Solid-state NMR heteronuclear coherence transfer using phase and amplitude modulated rf irradiation at the Hartmann–Hahn sideband conditions

Simplified Preservation of Equivalent Pathways Spectroscopy

Inspired by the recently proposed transverse mixing optimal control pulses (TROP) approach for improving signal in multidimensional magic-angle spinning (MAS) NMR experiments, we present simplified preservation of equivalent pathways spectroscopy (SPEPS). It transfers both transverse components of magnetization that occur during indirect evolutions, theoretically enabling a √2 improvement in sensitivity for each such dimension. We compare SPEPS transfer with TROP and cross-polarization (CP) using membrane protein and fibril samples at MAS of 55 and 100 kHz. In three-dimensional (3D) (H)CANH spectra, SPEPS outperformed TROP and CP by factors of on average 1.16 and 1.69, respectively, for the membrane protein, but only a marginal improvement of 1.09 was observed for the fibril. These differences are discussed, making note of the longer transfer time used for CP, 14 ms, as compared with 2.9 and 3.6 ms for SPEPS and TROP, respectively. Using SPEPS for two transfers in the 3D (H)CANCO experiment resulted in an even larger benefit in signal intensity, with an average improvement of 1.82 as compared with CP. This results in multifold time savings, in particular considering the weaker peaks that are observed to benefit the most from SPEPS.

Windowed cross polarization at 55 kHz magic-angle spinning

Cross polarization (CP) transfers via Hartmann-Hahn matching conditions are one of the cornerstones of solid-state magic-angle spinning NMR experiments. Here we investigate a windowed sequence for cross polarization (wCP) at 55 kHz magic-angle spinning, placing one window (and one pulse) per rotor period on one or both rf channels. The wCP sequence is known to have additional matching conditions. We observe a striking similarity between wCP and CP transfer conditions when considering the flip angle of the pulse rather than the rf-field strength applied during the pulse. Using fictitious spin-1/2 formalism and average Hamiltonian theory, we derive an analytical approximation that matches these observed transfer conditions. We recorded data at spectrometers with different external magnetic fields up to 1200 MHz, for strong and weak heteronuclear dipolar couplings. These transfers, and even the selectivity of CP were again found to relate to flip angle (average nutation).

A robust heteronuclear dipolar recoupling method comparable to TEDOR for proteins in magic-angle spinning solid-state NMR

In this letter, we propose a robust heteronuclear dipolar recoupling method for proteins in magic-angle spinning (MAS) solid-state NMR. This method is as simple, robust and efficient as the well-known TEDOR in the aspect of magnetization transfer between ¹⁵N and ¹³C. Deriving from our recent band-selective dual back-to-back pulses (DBP) (Zhang et al., 2016), this method uses new phase-cycling schemes to realize broadband DBP (Bro-DBP). For broadband ¹⁵N-¹³C magnetization transfer (simultaneous ¹⁵N→¹³C' and ¹⁵N→¹³Cα), Bro-DBP has almost the same ¹⁵N→¹³Cα efficiency while offers 30-40% enhancement on ¹⁵N→¹³C' transfer, compared to TEDOR. Besides, Bro-DBP can also be used as a carbonyl (¹³C')-selected method, whose ¹⁵N→¹³C' efficiency is up to 1.7 times that of TEDOR and is also higher than that of band-selective DBP. The performance of Bro-DBP is demonstrated on the N-formyl-[U-¹³C,¹⁵N]-Met-Leu-Phe-OH (fMLF) peptide and the U-¹³C, ¹⁵N labeled β1 immunoglobulin binding domain of protein G (GB1) microcrystalline protein. Since Bro-DBP is as robust, simple and efficient as TEDOR, we believe it is very useful for protein studies in MAS solid-state NMR.

Asymmetric simultaneous phase-inversion cross-polarization in solid-state MAS NMR: relaxing selective polarization transfer condition between two dilute spins

Double cross polarization (DCP) has been widely used for heteronuclear polarization transfer between (13)C and (15)N in solid-state magic-angle spinning (MAS) NMR. However, DCP is such sensitive to experimental settings that small variations or deviations in RF fields would deteriorate its efficiency. Here, we report on asymmetric simultaneous phase-inversion cross polarization (referred as aSPICP) for selective polarization transfer between low-γ (13)C and (15)N spins. We have demonstrated through simulations and experiments using biological solids that the asymmetric duration in the simultaneous phase-inversion cross polarization scheme leads to efficient polarization transfer between (13)C and (15)N even with large chemical shift anisotropies in the presence of B1 field variations or mismatch of the Hartmann-Hahn conditions. This could be very useful in the aspect of long-duration experiments for membrane protein studies at high fields.

Adiabatic Rotor-Echo-Short-Pulse-Irradiation mediated cross-polarization

We present a new dipolar recoupling method for efficient and robust heteronuclear polarization transfer in solid-state NMR under magic-angle-spinning (MAS) conditions. The method combines the recent (RESPIRATION)CP method with a modulation of the amplitude of the rotor-synchronized pulses at one of the involved rf channels through the recoupling condition. In this manner, it is possible to achieve high transfer efficiencies while maintaining robustness towards rf-field inhomogeneities and resonance offsets. The performance of the so-called adiabatic-(RESPIRATION)CP experiment is demonstrated numerically and experimentally using uniformly (13)C,(15)N-labeled samples of alanine and ubiquitin. In particular for cases with relatively high rf inhomogeneity, the scheme offers advantages over the commonly used dipolar recoupling pulse sequences.

Understanding cross-polarization (CP) NMR experiments through dipolar truncation

A theoretical model based on the phenomenon of dipolar truncation is proposed to explain the nuances of polarization transfer from abundant to less-abundant nuclei in cross-polarization (CP) NMR experiments. Specifically, the transfer of polarization from protons to carbons (in solids) in strongly coupled systems is described in terms of effective Hamiltonians based on dipolar truncation. Through suitable model spin systems, the important role of dipolar truncation in the propagation of spin polarization in CP experiments is outlined. We believe that the analytic theory presented herein provides a convenient framework for modeling polarization transfer in strongly coupled systems.

Dual-band selective double cross polarization for heteronuclear polarization transfer between dilute spins in solid-state MAS NMR

A sinusoidal modulation scheme is described for selective heteronuclear polarization transfer between two dilute spins in double cross polarization magic-angle-spinning nuclear magnetic resonance spectroscopy. During the second N→C cross polarization, the (13)C RF amplitude is modulated sinusoidally while the (15)N RF amplitude is tangent. This modulation induces an effective spin-lock field in two selective frequency bands in either side of the (13)C RF carrier frequency, allowing for simultaneous polarization transfers from (15)N to (13)C in those two selective frequency bands. It is shown by experiments and simulations that this sinusoidal modulation allows one to selectively polarize from (15)N to its covalently bonded (13)Cα and (13)C' carbons in neighboring peptide planes simultaneously, which is useful for establishing the backbone connectivity between two sequential residues in protein structural elucidation. The selectivity and efficiency were experimentally demonstrated on a uniformly (13)C,(15)N-labeled β1 immunoglobulin binding domain of protein G (GB1).

Efficient and Robust Heteronuclear Cross-Polarization for High-Speed-Spinning Biological Solid-State NMR Spectroscopy

We present a new and highly efficient approach for heteronuclear coherence transfer in solid-state NMR spectroscopy under high-speed spinning conditions. The so-called (RESPIRATION)CP experiment exploits phase-alternated recoupling on only one of the two rf channels intertwined in a synchronized train of short rf pulses on both channels. The method provides significantly higher efficiencies than state-of-the art techniques including ramped and adiabatic cross-polarization experiments with long durations of intense rf irradiation. At the same time, it is easier to setup experimentally and significantly more robust toward imperfections such as rf inhomogeneity, misadjustments, and sample-induced variations in the rf tuning. The method is described analytically, numerically, and experimentally for biological solids. We demonstrate sensitivity gains of factors of 1.3 and 1.8 for typical (1)H→(15)N and (15)N→(13)C transfers and a combined gain of a factor of 2-4 for a typical NCA experiment for biological solid-state NMR.

A comparison of NCO and NCA transfer methods for biological solid-state NMR spectroscopy

Three different techniques (adiabatic passage Hartman-Hahn cross-polarization, optimal control designed pulses, and EXPORT) are compared for transferring (15)N magnetization to (13)C in solid-state NMR experiments under magic-angle-spinning conditions. We demonstrate that, in comparison to adiabatic passage Hartman-Hahn cross-polarization, optimal control transfer pulses achieve similar or better transfer efficiencies for uniformly-(13)C,(15)N labeled samples and are generally superior for samples with non-uniform labeling schemes (such as 1,3- and 2-(13)C glycerol labeling). In addition, the optimal control pulses typically use substantially lower average RF field strengths and are more robust with respect to experimental variation and RF inhomogeneity. Consequently, they are better suited for demanding samples.

Optimal control in NMR spectroscopy: numerical implementation in SIMPSON

We present the implementation of optimal control into the open source simulation package SIMPSON for development and optimization of nuclear magnetic resonance experiments for a wide range of applications, including liquid- and solid-state NMR, magnetic resonance imaging, quantum computation, and combinations between NMR and other spectroscopies. Optimal control enables efficient optimization of NMR experiments in terms of amplitudes, phases, offsets etc. for hundreds-to-thousands of pulses to fully exploit the experimentally available high degree of freedom in pulse sequences to combat variations/limitations in experimental or spin system parameters or design experiments with specific properties typically not covered as easily by standard design procedures. This facilitates straightforward optimization of experiments under consideration of rf and static field inhomogeneities, limitations in available or desired rf field strengths (e.g., for reduction of sample heating), spread in resonance offsets or coupling parameters, variations in spin systems etc. to meet the actual experimental conditions as close as possible. The paper provides a brief account on the relevant theory and in particular the computational interface relevant for optimization of state-to-state transfer (on the density operator level) and the effective Hamiltonian on the level of propagators along with several representative examples within liquid- and solid-state NMR spectroscopy.

Variable angle spinning (VAS) experiments for strongly oriented systems: methods development and preliminary results

Variable angle spinning (VAS) experiments provide a useful method for measuring long-range dipolar couplings and obtaining isotropic-anisotropic correlation spectra. These experiments make it possible to obtain correlations between isotropic and anisotropic spectra without altering the chemical composition of the sample. They also allow working with very strongly oriented systems that are not accessible to solution-state techniques. In this communication, we discuss recent hardware developments in our laboratory and show representative data from small molecules in strongly oriented liquid-crystalline samples.

Optimal control based NCO and NCA experiments for spectral assignment in biological solid-state NMR spectroscopy

We present novel pulse sequences for magic-angle-spinning solid-state NMR structural studies of (13)C,(15)N-isotope labeled proteins. The pulse sequences have been designed numerically using optimal control procedures and demonstrate superior performance relative to previous methods with respect to sensitivity, robustness to instrumental errors, and band-selective excitation profiles for typical biological solid-state NMR applications. Our study addresses specifically (15)N to (13)C coherence transfers being important elements in spectral assignment protocols for solid-state NMR structural characterization of uniformly (13)C,(15)N-labeled proteins. The pulse sequences are analyzed in detail and their robustness towards spin system and external experimental parameters are illustrated numerically for typical (15)N-(13)C spin systems under high-field solid-state NMR conditions. Experimentally the methods are demonstrated by 1D (15)N-->(13)C coherence transfer experiments, as well as 2D and 3D (15)N,(13)C and (15)N,(13)C,(13)C chemical shift correlation experiments on uniformly (13)C,(15)N-labeled ubiquitin.

Composite dipolar recoupling: Anisotropy compensated coherence transfer in solid-state nuclear magnetic resonance

The efficiency of dipole-dipole coupling driven coherence transfer experiments in solid-state nuclear magnetic resonance (NMR) spectroscopy of powder samples is limited by dispersion of the orientation of the internuclear vectors relative to the external magnetic field. Here we introduce general design principles and resulting pulse sequences that approach full polarization transfer efficiency for all crystallite orientations in a powder in magic-angle-spinning experiments. The methods compensate for the defocusing of coherence due to orientation dependent dipolar coupling interactions and inhomogeneous radio-frequency fields. The compensation scheme is very simple to implement as a scaffold (comb) of compensating pulses in which the pulse sequence to be improved may be inserted. The degree of compensation can be adjusted and should be balanced as a compromise between efficiency and length of the overall pulse sequence. We show by numerical and experimental data that the presented compensation protocol significantly improves the efficiency of known dipolar recoupling solid-state NMR experiments.

Sensitivity considerations in polarization transfer and filtering using dipole-dipole couplings: implications for biomineral systems

The robustness and sensitivities of different polarization-transfer methods that exploit heteronuclear dipole-dipole couplings are compared for a series of heterogeneous solid systems, including polycrystalline tetrakis(trimethylsilyl)silane (TKS), adamantane, a physical mixture of doubly (13)C,(15)N-enriched and singly (13)C-enriched polycrystalline glycine, and a powder sample of siliceous marine diatoms, Thalossiosira pseudonana. The methods were analyzed according to their respective frequency-matching spectra or resultant signal intensities. For a series of (13)C{(1)H} cross-polarization experiments, adiabatic passage Hartmann-Hahn cross-polarization (APHH-CP) was shown to have several advantages over other methods, including Hartmann-Hahn cross-polarization (HHCP), variable-amplitude cross-polarization (VACP), and ramped-amplitude cross-polarization (RACP). For X-Y systems, such as (13)C{(15)N}, high and comparable sensitivities were obtained by using APHH-CP with Lee-Goldburg decoupling or by using the transferred-echo double resonance (TEDOR) experiment. The findings were applied to multinuclear (1)H, (13)C, (15)N, and (29)Si CP MAS characterization of a powder diatom sample, a challenging inorganic-organic hybrid solid that places high demands on NMR signal sensitivity.

Probing segmental order in lipid bilayers at variable hydration levels by amplitude- and phase-modulated cross-polarization NMR

The conformational response of dimyristoylphosphatidylcholine bilayers in the liquid crystalline phase to hydration is investigated by a novel magic-angle spinning cross-polarization NMR technique.

Heteronuclear dipolar recoupling in solid-state nuclear magnetic resonance by amplitude-, phase-, and frequency-modulated Lee–Goldburg cross-polarization

This paper presents a theoretical, numerical, and experimental study of phase- and frequency-switched Lee-Goldburg cross-polarization (FSLG-CP) under magic-angle spinning conditions. It is shown that a well-defined amplitude modulation of one of the two radio-frequency (rf) fields in the FSLG-CP sequence results in highly efficient heteronuclear dipolar recoupling. The recoupled dipolar interaction is gamma-encoded and, under ideal conditions, the effective spin Hamiltonian is equivalent to that in continuous-wave Lee-Goldburg CP. In practice, however, FSLG-CP is less susceptible to rf field mismatch and inhomogeneity, and provides better suppression of (1)H spin diffusion. The performance of FSLG-CP is experimentally demonstrated on liquid-crystalline samples exhibiting motionally averaged dipolar couplings.