Computer-intensive simulation of solid-state NMR experiments using SIMPSON

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.

Application of the limited-memory quasi-Newton algorithm for multi-dimensional, large flip-angle RF pulses at 7T

OBJECTIVE

Ultrahigh field MRI provides great opportunities for medical diagnostics and research. However, ultrahigh field MRI also brings challenges, such as larger magnetic susceptibility induced field changes. Parallel-transmit radio-frequency pulses can ameliorate these complications while performing advanced tasks in routine applications. To address one class of such pulses, we propose an optimal-control algorithm as a tool for designing advanced multi-dimensional, large flip-angle, radio-frequency pulses. We contrast initial conditions, constraints, and field correction abilities against increasing pulse trajectory acceleration factors.

MATERIALS AND METHODS

On an 8-channel 7T system, we demonstrate the quasi-Newton algorithm with pulse designs for reduced field-of-view imaging with an oil phantom and in vivo with scans of the human brain stem. We used echo-planar imaging with 2D spatial-selective pulses. Pulses are computed sufficiently rapid for routine applications.

RESULTS

Our dataset was quantitatively analyzed with the conventional mean-square-error metric and the structural-similarity index from image processing. Analysis of both full and reduced field-of-view scans benefit from utilizing both complementary measures.

CONCLUSION

We obtained excellent outer-volume suppression with our proposed method, thus enabling reduced field-of-view imaging using pulse trajectory acceleration factors up to 4.

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.

Relative merits of rCW(A) and XiX heteronuclear spin decoupling in solid-state magic-angle-spinning NMR spectroscopy: A bimodal Floquet analysis

We present a bimodal Floquet analysis of the recently introduced refocused continuous wave (rCW) solid-state NMR heteronuclear dipolar decoupling method and compare it with the similar looking X-inverse X (XiX) scheme. The description is formulated in the rf interaction frame and is valid for both finite and ideal π pulse rCW irradiation that forms the refocusing element in the rCW scheme. The effective heteronuclear dipolar coupling Hamiltonian up to first order is described. The analysis delineates the difference between the two sequences to different orders of their Hamiltonians for both diagonal and off-diagonal parts. All the resonance conditions observed in experiments and simulations have been characterised and their influence on residual line broadening is highlighted. The theoretical comparison substantiates the numerical simulations and experimental results to a large extent.

Highly efficient19F heteronuclear decoupling in solid-state NMR spectroscopy using supercycled refocused-CW irradiation

We present heteronuclear¹⁹F refocused CW (rCW) decoupling pulse sequences for solid-state magic-angle-spinning NMR applications.

35Cl dynamic nuclear polarization solid-state NMR of active pharmaceutical ingredients

In this work, we show how to obtain efficient dynamic nuclear polarization (DNP) enhanced ³⁵Cl solid-state NMR (SSNMR) spectra at 9.4 T and demonstrate how they can be used to characterize the molecular-level structure of hydrochloride salts of active pharmaceutical ingredients (APIs) in both bulk and low wt% API dosage forms.

Rapid acquisition of wideline MAS solid-state NMR spectra with fast MAS, proton detection, and dipolar HMQC pulse sequences

Fast MAS and proton detection are applied to rapidly acquire wideline solid-state NMR spectra of spin-1/2 and half-integer quadrupolar nuclei.

1020MHz single-channel proton fast magic angle spinning solid-state NMR spectroscopy

This study reports a first successful demonstration of a single channel proton 3D and 2D high-throughput ultrafast magic angle spinning (MAS) solid-state NMR techniques in an ultra-high magnetic field (1020MHz) NMR spectrometer comprised of HTS/LTS magnet. High spectral resolution is well demonstrated.

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.

Proton chemical shift tensors determined by 3D ultrafast MAS double-quantum NMR spectroscopy

Proton NMR spectroscopy in the solid state has recently attracted much attention owing to the significant enhancement in spectral resolution afforded by the remarkable advances in ultrafast magic angle spinning (MAS) capabilities. In particular, proton chemical shift anisotropy (CSA) has become an important tool for obtaining specific insights into inter/intra-molecular hydrogen bonding. However, even at the highest currently feasible spinning frequencies (110-120 kHz), (1)H MAS NMR spectra of rigid solids still suffer from poor resolution and severe peak overlap caused by the strong (1)H-(1)H homonuclear dipolar couplings and narrow (1)H chemical shift (CS) ranges, which render it difficult to determine the CSA of specific proton sites in the standard CSA/single-quantum (SQ) chemical shift correlation experiment. Herein, we propose a three-dimensional (3D) (1)H double-quantum (DQ) chemical shift/CSA/SQ chemical shift correlation experiment to extract the CS tensors of proton sites whose signals are not well resolved along the single-quantum chemical shift dimension. As extracted from the 3D spectrum, the F1/F3 (DQ/SQ) projection provides valuable information about (1)H-(1)H proximities, which might also reveal the hydrogen-bonding connectivities. In addition, the F2/F3 (CSA/SQ) correlation spectrum, which is similar to the regular 2D CSA/SQ correlation experiment, yields chemical shift anisotropic line shapes at different isotropic chemical shifts. More importantly, since the F2/F1 (CSA/DQ) spectrum correlates the CSA with the DQ signal induced by two neighboring proton sites, the CSA spectrum sliced at a specific DQ chemical shift position contains the CSA information of two neighboring spins indicated by the DQ chemical shift. If these two spins have different CS tensors, both tensors can be extracted by numerical fitting. We believe that this robust and elegant single-channel proton-based 3D experiment provides useful atomistic-level structural and dynamical information for a variety of solid systems that possess high proton density.

Solid-state NMR methods for oriented membrane proteins

Oriented-sample solid-state NMR represents one of few experimental methods capable of characterising the membrane-bound conformation of proteins in the cell membrane. Since the technique was developed 25 years ago, the technique has been applied to study the structure of helix bundle membrane proteins and antimicrobial peptides, characterise protein-lipid interactions, and derive information on dynamics of the membrane anchoring of membrane proteins. We will review the major developments in various aspects of oriented-sample solid-state NMR, including sample-preparation methods, pulse sequences, theory required to interpret the experiments, perspectives for and guidelines to new experiments, and a number of representative applications.

Selective excitation enables assignment of proton resonances and (1)H-(1)H distance measurement in ultrafast magic angle spinning solid state NMR spectroscopy

Remarkable developments in ultrafast magic angle spinning (MAS) solid-state NMR spectroscopy enabled proton-based high-resolution multidimensional experiments on solids. To fully utilize the benefits rendered by proton-based ultrafast MAS experiments, assignment of (1)H resonances becomes absolutely necessary. Herein, we propose an approach to identify different proton peaks by using dipolar-coupled heteronuclei such as (13)C or (15)N. In this method, after the initial preparation of proton magnetization and cross-polarization to (13)C nuclei, transverse magnetization of desired (13)C nuclei is selectively prepared by using DANTE (Delays Alternating with Nutations for Tailored Excitation) sequence and then, it is transferred to bonded protons with a short-contact-time cross polarization. Our experimental results demonstrate that protons bonded to specific (13)C atoms can be identified and overlapping proton peaks can also be assigned. In contrast to the regular 2D HETCOR experiment, only a few 1D experiments are required for the complete assignment of peaks in the proton spectrum. Furthermore, the finite-pulse radio frequency driven recoupling sequence could be incorporated right after the selection of specific proton signals to monitor the intensity buildup for other proton signals. This enables the extraction of (1)H-(1)H distances between different pairs of protons. Therefore, we believe that the proposed method will greatly aid in fast assignment of peaks in proton spectra and will be useful in the development of proton-based multi-dimensional solid-state NMR experiments to study atomic-level resolution structure and dynamics of solids.

A unified heteronuclear decoupling strategy for magic-angle-spinning solid-state NMR spectroscopy

A unified strategy of two-pulse based heteronuclear decoupling for solid-state magic-angle spinning nuclear magnetic resonance is presented. The analysis presented here shows that different decoupling sequences like two-pulse phase-modulation (TPPM), X-inverse-X (XiX), and finite pulse refocused continuous wave (rCW(A)) are basically specific solutions of a more generalized decoupling scheme which incorporates the concept of time-modulation along with phase-modulation. A plethora of other good decoupling conditions apart from the standard, TPPM, XiX, and rCW(A) decoupling conditions are available from the unified decoupling approach. The importance of combined time- and phase-modulation in order to achieve the best decoupling conditions is delineated. The consequences of different indirect dipolar interactions arising from cross terms comprising of heteronuclear and homonuclear dipolar coupling terms and also those between heteronuclear dipolar coupling and chemical-shift anisotropy terms are presented in order to unfold the effects of anisotropic interactions under different decoupling conditions. Extensive numerical simulation results are corroborated with experiments on standard amino acids.

jsNMR: an embedded platform-independent NMR spectrum viewer

jsNMR is a lightweight NMR spectrum viewer written in JavaScript/HyperText Markup Language (HTML), which provides a cross-platform spectrum visualizer that runs on all computer architectures including mobile devices. Experimental (and simulated) datasets are easily opened in jsNMR by (i) drag and drop on a jsNMR browser window, (ii) by preparing a jsNMR file from the jsNMR web site, or (iii) by mailing the raw data to the jsNMR web portal. jsNMR embeds the original data in the HTML file, so a jsNMR file is a self-transforming dataset that may be exported to various formats, e.g. comma-separated values. The main applications of jsNMR are to provide easy access to NMR data without the need for dedicated software installed and to provide the possibility to visualize NMR spectra on web sites.

Phase cycling schemes for finite-pulse-RFDR MAS solid state NMR experiments

The finite-pulse radio frequency driven dipolar recoupling (fp-RFDR) pulse sequence is used in 2D homonuclear chemical shift correlation experiments under magic angle spinning (MAS). A recent study demonstrated the advantages of using a short phase cycle, XY4, and its super-cycle, XY4(1)4, for the fp-RFDR pulse sequence employed in 2D (1)H/(1)H single-quantum/single-quantum correlation experiments under ultrafast MAS conditions. In this study, we report a comprehensive analysis on the dipolar recoupling efficiencies of XY4, XY4(1)2, XY4(1)3, XY4(1)4, and XY8(1)4 phase cycles under different spinning speeds ranging from 10 to 100 kHz. The theoretical calculations reveal the presence of second-order terms (T(10)T(2,±2), T(1,±1)T(2,±1), etc.) in the recoupled homonuclear dipolar coupling Hamiltonian only when the basic XY4 phase cycle is utilized, making it advantageous for proton-proton magnetization transfer under ultrafast MAS conditions. It is also found that the recoupling efficiency of fp-RFDR is quite dependent on the duty factor (τ180/τR) as well as on the strength of homonuclear dipolar couplings. The rate of longitudinal magnetization transfer increases linearly with the duty factor of fp-RFDR for all the XY-based phase cycles investigated in this study. Examination of the performances of different phase cycles against chemical shift offset and RF field inhomogeneity effects revealed that XY4(1)4 is the most tolerant phase cycle, while the shortest phase cycle XY4 suppressed the RF field inhomogeneity effects most efficiently under slow spinning speeds. Our results suggest that the difference in the fp-RFDR recoupling efficiencies decreases with the increasing MAS speed, while ultrafast (>60 kHz) spinning speed is advantageous as it recouples a large amount of homonuclear dipolar couplings and therefore enable fast magnetization exchange. The effects of higher-order terms and cross terms between various interactions in the effective Hamiltonian of fp-RFDR are also analyzed using numerical simulations for various phase cycles. Results obtained via numerical simulations are in excellent agreement with ultrafast MAS experimental results from the powder samples of glycine and l-alanine.

Influence of proton coupling on symmetry-based homonuclear (19)F dipolar recoupling experiments

We study the efficiency of two symmetry based homonuclear (19)F double-quantum recoupling sequences for moderate (R142(6)) and ultra-fast (R144(5)) MAS under the influence of strong (1)H-(1)H and (1)H-(19)F dipolar interactions and (1)H continuous wave decoupling. Simulations based on various spin systems derived from the organic solid 1,3,5-tris(2-fluoro-2-methylpropionylamino)benzene (F-BTA), used as a model system, reveal that the strong-decoupling limit is not accessible even for moderate spinning speeds. Additionally, for the no-decoupling limit improved DQ efficiencies are predicted for both moderate and ultra-fast MAS. Strong perturbations of build-up curves can be avoided by additional stabilisation through supercycling. Additional (1)H cw decoupling during (19)F recoupling rapidly reduces the maximum DQ efficiency when deviating from the no-decoupling limit. These effects were confirmed by experimental data on F-BTA. For moderate spinning the influence of (1)H-(1)H and (1)H-(19)F couplings is markedly stronger compared to ultra-fast MAS. For the latter case those influences reduce to a constant scaling if only short excitation times up to the first minimum are taken into account. Based on this analysis the experimental build-up curves of 1,3,5-tris(2-fluoro-2-methylpropionylamino)benzene can be refined with homonuclear (19)F spin systems which allow to probe even subtle structural differences for the fluorine atoms of F-BTA.

A cross-polarization based rotating-frame separated-local-field NMR experiment under ultrafast MAS conditions

Rotating-frame separated-local-field solid-state NMR experiments measure highly resolved heteronuclear dipolar couplings which, in turn, provide valuable interatomic distances for structural and dynamic studies of molecules in the solid-state. Though many different rotating-frame SLF sequences have been put forth, recent advances in ultrafast MAS technology have considerably simplified pulse sequence requirements due to the suppression of proton-proton dipolar interactions. In this study we revisit a simple two-dimensional (1)H-(13)C dipolar coupling/chemical shift correlation experiment using (13)C detected cross-polarization with a variable contact time (CPVC) and systematically study the conditions for its optimal performance at 60 kHz MAS. In addition, we demonstrate the feasibility of a proton-detected version of the CPVC experiment. The theoretical analysis of the CPVC pulse sequence under different Hartmann-Hahn matching conditions confirms that it performs optimally under the ZQ (w1H-w1C=±wr) condition for polarization transfer. The limits of the cross polarization process are explored and precisely defined as a function of offset and Hartmann-Hahn mismatch via spin dynamics simulation and experiments on a powder sample of uniformly (13)C-labeled L-isoleucine. Our results show that the performance of the CPVC sequence and subsequent determination of (1)H-(13)C dipolar couplings are insensitive to (1)H/(13)C frequency offset frequency when high RF fields are used on both RF channels. Conversely, the CPVC sequence is quite sensitive to the Hartmann-Hahn mismatch, particularly for systems with weak heteronuclear dipolar couplings. We demonstrate the use of the CPVC based SLF experiment as a tool to identify different carbon groups, and hope to motivate the exploration of more sophisticated (1)H detected avenues for ultrafast MAS.

PRESTO polarization transfer to quadrupolar nuclei: implications for dynamic nuclear polarization

We show both experimentally and numerically that in experiments involving transfer of magnetization from ¹H to the quadrupolar nuclei under MAS, the PRESTO technique consistently outperforms the traditionally used CP method, affording more quantitative intensities, improved lineshapes, better sensitivity, and easier optimization.

Coherent and stochastic averaging in solid-state NMR

A new approach for calculating solid-state NMR lineshapes of uniaxially rotating membrane proteins under the magic-angle spinning conditions is presented. The use of stochastic Liouville equation (SLE) allows one to account for both coherent sample rotation and stochastic motional averaging of the spherical dipolar powder patterns by uniaxial diffusion of the spin-bearing molecules. The method is illustrated via simulations of the dipolar powder patterns of rigid samples under the MAS conditions, as well as the recent method of rotational alignment in the presence of both MAS and rotational diffusion under the conditions of dipolar recoupling. It has been found that it is computationally more advantageous to employ direct integration over a spherical grid rather than to use a full angular basis set for the SLE solution. Accuracy estimates for the bond angles measured from the recoupled amide ¹H-¹⁵N dipolar powder patterns have been obtained at various rotational diffusion coefficients. It has been shown that the rotational alignment method is applicable to membrane proteins approximated as cylinders with radii of approximately 20Å, for which uniaxial rotational diffusion within the bilayer is sufficiently fast and exceeds the rate 2×10⁵s^-1.