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Heteronuclear spin decoupling is a highly important component of solid-state NMR experiments to remove undesired coupling interactions between unlike spins for spectral resolution. Recently, experiments using a unification strategy of standard decoupling schemes were presented for high radio-frequency (RF) amplitudes and slow-intermediate magic-angle-spinning (MAS) frequencies, in the pursuit of deeper understanding of spin decoupling under phase-modulated RF irradiation [A. Equbal et al., J. Chem. Phys. 142, 184201 (2015)]. The approach, unified two-pulse heteronuclear decoupling (UTPD), incorporates the simultaneous time- and phase-modulation strategies, commonly used in solid-state NMR. Here, the UTPD based decoupling scheme is extended to the experimentally increasingly important regime of low RF amplitudes and fast MAS frequencies. The unified decoupling approach becomes increasingly effective in identifying the deleterious dipole-dipole and, in particular, J recoupling conditions which become critical for the low-amplitude RF regime. This is because J coupling is isotropic and therefore not averaged out by sample spinning unlike the anisotropic dipole-dipole coupling. Numerical simulations and analytic theory are used to understand the effects of various nuclear spin interactions on the decoupling performance of UTPD, in particular, the crucial difference between the low-phase and high-phase UTPD conditions with respect to J coupling. In the UTPD scheme, when the cycle-frequency of the pulse-sequence is comparable to the RF nutation frequency, the existence of a non-zero effective rotation in the basic two-pulse scheme becomes an essential feature for the efficient and robust averaging out of the scalar J coupling. This broad viewpoint is expected to bring different optimum low-power decoupling pulse schemes under a common footing. [ABSTRACT FROM AUTHOR]

Symmetry plays an important role in the retention or annihilation of a desired interaction Hamiltonian in NMR experiments. Here, we explore the role of symmetry in the radio-frequency interaction frame Hamiltonian of the refocused-continuous-wave (rCW) pulse scheme that leads to efficient 1H heteronuclear decoupling in solid-state NMR. It is demonstrated that anti-periodic symmetry of single-spin operators (Ix, Iy, Iz) in the interaction frame can lead to complete annihilation of the ¹H-¹H homonuclear dipolar coupling effects that induce line broadening in solid-state NMR experiments. This symmetry also plays a critical role in cancelling or minimizing the effect of ¹H chemical-shift anisotropy in the effective Hamiltonian. An analytical description based on Floquet theory is presented here along with experimental evidences to understand the decoupling efficiency of supercycled (concatenated) rCW scheme. [ABSTRACT FROM AUTHOR]

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 13CO to 13Cα polarization transfer for uniformly 13C,15N-labeled glycine and for the fibril forming peptide SNNFGAILSS (one-letter amino acid codes) uniformly 13C,15N-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. [ABSTRACT FROM AUTHOR]

The use of increasingly strong magnetic fields in magnetic resonance imaging (MRI) improves sensitivity, susceptibility contrast, and spatial or spectral resolution for functional and localized spectroscopic imaging applications. However, along with these benefits come the challenges of increasing static field (B0) and rf field (B1) inhomogeneities induced by radial field susceptibility differences and poorer dielectric properties of objects in the scanner. Increasing fields also impose the need for rf irradiation at higher frequencies which may lead to elevated patient energy absorption, eventually posing a safety risk. These reasons have motivated the use of multidimensional rf pulses and parallel rf transmission, and their combination with tailoring of rf pulses for fast and low-power rf performance. For the latter application, analytical and approximate solutions are well-established in linear regimes, however, with increasing nonlinearities and constraints on the rf pulses, numerical iterative methods become attractive. Among such procedures, optimal control methods have recently demonstrated great potential. Here, we present a Krotov-based optimal control approach which as compared to earlier approaches provides very fast, monotonic convergence even without educated initial guesses. This is essential for in vivo MRI applications. The method is compared to a second-order gradient ascent method relying on the Broyden-Fletcher-Goldfarb-Shanno (BFGS) quasi-Newton method, and a hybrid scheme Krotov-BFGS is also introduced in this study. These optimal control approaches are demonstrated by the design of a 2D spatial selective rf pulse exciting the letters 'JCP' in a water phantom. [ABSTRACT FROM AUTHOR]

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 B0 and B1 fields. Furthermore, this strategy is applied to enhance the NMR signal in an ultrafast gradient assisted single excitation two-dimensional spectroscopy experiment. [ABSTRACT FROM AUTHOR]

A new solid-state NMR method, the double-oscillating field technique (DUO), that under magic-angle-spinning conditions produces an effective Hamiltonian proportional to the native high-field homonuclear dipole-dipole coupling operator is presented. The method exploits one part of the radio frequency (rf) field to recouple the dipolar coupling interaction with a relatively high scaling factor and to eliminate offset effects over a reasonable bandwidth while in the recoupling frame, the other part gives rise to a sufficiently large longitudinal component of the residual rf field that averages nonsecular terms and in addition ensures stability toward rf inhomogeneity and rf miscalibration. The capability of the DUO experiment to mediate transfer of polarization is described theoretically and compared numerically and experimentally with finite pulse rf driven recoupling and experimentally with dipolar-assisted rotational resonance. Two-dimensional recoupling experiments were performed on antiparallel amyloid fibrils of the decapeptide SNNFGAILSS with the FGAIL fragment uniformly labeled with 13C and 15N. [ABSTRACT FROM AUTHOR]

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 Ix, Iy, and Iz 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 √2 compared to conventional solid-state methods otherwise showing the same efficiency. The sequences are tested numerically and experimentally for a powder of 13Cα, 13Cβ-L-alanine and demonstrate substantial sensitivity gains over previous dipolar recoupling experiments. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Abstract: Refocused continuous wave (rCW) decoupling is presented as an efficient and robust means to obtain well-resolved magic-angle-spinning solid-state NMR spectra of low-γ spins, such as 13C dipolar coupled to fluorine. The rCW decoupling sequences, recently introduced for 1H decoupling, are very robust towards large isotropic and anisotropic shift ranges as often encountered for 19F spins. In rCW decoupling, the so-called refocusing pulses inserted into the CW irradiation eliminate critical residual second- and third-order dipolar coupling and dipolar-coupling against chemical shielding anisotropy cross-terms in the effective Hamiltonian through time-reversal (i.e. refocusing). As important additional assets, the rCW decoupling sequences are robust towards variations in rf amplitudes, operational at low to high spinning speeds, and easy to set-up for optimal performance experimentally. These aspects are demonstrated analytically/numerically and experimentally in comparison to state-of-the-art decoupling sequences such as TPPM, SPINAL-64, and frequency-swept variants of these. [Copyright &y& Elsevier]

Abstract: Three different techniques (adiabatic passage Hartman-Hahn cross-polarization, optimal control designed pulses, and EXPORT) are compared for transferring 15N magnetization to 13C 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-13C,15N labeled samples and are generally superior for samples with non-uniform labeling schemes (such as 1,3- and 2-13C 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. [Copyright &y& Elsevier]

Abstract: A computer program for fast and accurate numerical simulation of solid-state NMR experiments is described. The program is designed to emulate a NMR spectrometer by letting the user specify high-level NMR concepts such as spin systems, nuclear spin interactions, RF irradiation, free precession, phase cycling, coherence-order filtering, and implicit/explicit acquisition. These elements are implemented using the Tel scripting language to ensure a minimum of programming overhead and direct interpretation without the need for compilation, while maintaining the flexibility of a full-featured programming language. Basicly, there are no intrinsic limitations to the number of spins, types of interactions, sample conditions (static or spinning, powders, uniaxially oriented molecules, single crystals, or solutions), and the complexity or number of spectral dimensions for the pulse sequence. The applicability ranges from simple ID experiments to advanced multiple-pulse and multiple-dimensional experiments, series of simulations, parameter scans, complex data manipulation/visualization, and iterative fitting of simulated to experimental spectra. A major effort has been devoted to optimizing the computation speed using state-of-the-art algorithms for the time-consuming parts of the calculations implemented in the core of the program using the C programming language. Modification and maintenance of the program are facilitated by releasing the program as open source software (General Public License) currently at http://nmr.imsb.au.dk. The general features of the program are demonstrated by numerical simulations of various aspects for REDOR, rotational resonance, DRAMA, DRAWS, HORROR, C7, TEDOR, POST-C7, CW decoupling, TPPM, F-SLG, SLF, SEMA-CP, PISEMA, RFDR, QCPMG-MAS, and MQ-MAS experiments. [Copyright &y& Elsevier]

Abstract: Aimed at performing dipolar recoupling as part of biological solid-state NMR experiments without using excessively strong rf irradiation, we present a series of low-power supercycled symmetry-based and exponentially modulated pulse sequences facilitating efficient recoupling over specified chemical shift ranges even at high-speed spinning conditions. The experiments are designed through simple phase modulation of known ‘lower-quality’ symmetry-based pulse sequences or highly rf-demanding exponentially modulated recoupling experiments. The methods are described analytically and numerically and demonstrated experimentally by one- and two-dimensional correlation spectra of 2,3-13C2-L-alanine and the fibrillating-core decapeptide SNNFGAILSS of human Islet Amyloid Poly-Peptide (hIAPP, or amylin) uniformly 13C,15N-labeled at the FGAIL residues. [Copyright &y& Elsevier]

The successful application of solid-state NMR spectroscopy for structural study of biological macromolecules requires high spectral resolution. In presence of abundant H 1 spins, the resolution of the prevailing C 13 or N 15 chemical shift encoding experiments critically depends on the availability of efficient and robust heteronuclear decoupling methods in addition to the use of high-field instrumentation and fast sample spinning. Robustness of the decoupling method towards alterations in amplitude/offset of radio frequency fields due to varying sample states is important to ensure recording of spectra with high resolution over long sampling periods for insensitive samples. Here, we present a phase-alternated refocused continuous-wave decoupling method offering better resolution, easier setup, and higher robustness than previous methods. Improved decoupling is in part ascribed to more efficient cancellation of the residual heteronuclear, H 1 – C 13 , dipolar coupling interactions which are induced by homonuclear, H 1 – H 1 , dipolar coupling interactions. [ABSTRACT FROM AUTHOR]

There is an increasing need for development of advanced radio-frequency (RF) pulse techniques in modern magnetic resonance imaging (MRI) systems driven by recent advancements in ultra-high magnetic field systems, new parallel transmit/receive coil designs, and accessible powerful computational facilities. 2D spatially selective RF pulses are an example of advanced pulses that have many applications of clinical relevance, e.g., reduced field of view imaging, and MR spectroscopy. The 2D spatially selective RF pulses are mostly generated and optimised with numerical methods that can handle vast controls and multiple constraints. With this study we aim at demonstrating that numerical, optimal control (OC) algorithms are efficient for the design of 2D spatially selective MRI experiments, when robustness towards e.g. field inhomogeneity is in focus. We have chosen three popular OC algorithms; two which are gradient-based, concurrent methods using first- and second-order derivatives, respectively; and a third that belongs to the sequential, monotonically convergent family. We used two experimental models: a water phantom, and an in vivo human head. Taking into consideration the challenging experimental setup, our analysis suggests the use of the sequential, monotonic approach and the second-order gradient-based approach as computational speed, experimental robustness, and image quality is key. All algorithms used in this work were implemented in the MATLAB environment and are freely available to the MRI community. [ABSTRACT FROM AUTHOR]

Radio frequency (RF) spectrally selective multiband pulses or tagging pulses, are applicable in a broad range of magnetic resonance methods. We demonstrate through simulations and experiments a new phase-modulation-only RF pulse for RF tagging based on the Frank poly-phase perfect sequence. In addition, we introduce an extended version with a WURST modulation (Frank-WURST). The new pulses exhibit interesting and flexible spin tagging properties and are easily implemented in existing MR sequences, where they can substitute slice-selective pulses with no additional alterations. [ABSTRACT FROM AUTHOR]

Rapid developments in solid-state NMR methodologyhave boosted this technique into a highly versatile tool for structural biology. The invention of increasingly advanced rf pulse sequences that take advantage of better hardware and sample preparation have played an important part in these advances. In the development of these new pulse sequences, researchers have taken advantage of analytical tools, such as average Hamiltonian theory or lately numerical methods based on optimal control theory. [ABSTRACT FROM AUTHOR]

Abstract: It is demonstrated that a simple analogy between single-spin composite radiofrequency (rf) pulses and solid-state NMR dipolar recoupling may be exploited to reduce the operator space dimensionality in design of recoupling experiments by optimal control based algorithms. The use of single-spin calculations speeds up numerical optimizations by an order of magnitude and allows for fast development of high-sensitivity experiments with good compensation for experimental artifacts such as off-resonance effects and rf inhomogeneity. By optimization in terms of error-compensating composite rf pulses, the corresponding recoupling experiments intrinsically benefit from reduced powder-angle dependencies and thereby offer higher transfer efficiencies than commonly used γ-encoded recoupling experiments. We demonstrate 50% gain in sensitivity for a 2D NCO experiment on 13C,15N-labeled ubiquitin using composite recoupling experiments with 9–30 pulse elements. [Copyright &y& Elsevier]