Magic-angle Spinning Frequencies Research Articles

Dynamic Nuclear Polarization with P1 Centers in Diamond.

Substitutional nitrogen impurities within the diamond lattice, known as P1 centers, have unpaired electrons that can mediate microwave driven dynamic nuclear polarization (DNP). In this paper we explore DNP of the bulk 13C spins in micrometer-sized P1 diamond particles and demonstrate a 550-fold DNP enhancement of the bulk 13C spins at room temperature in a 9 T magnetic field or 250 GHz for g ≈ 2 electrons. We study the DNP mechanisms, exploring their dependence on sample spinning frequency and microwave irradiation frequency using both continuous wave and frequency swept microwave irradiation, and discuss the results alongside recent DNP studies in the literature. Even with a modest microwave irradiation power of 160 mW from our frequency swept solid-state microwave source, we achieve a significant 13C signal enhancement, ε = 270 at room temperature. The enhancements were found to increase with the magic angle spinning (MAS) frequency, ωr/2π, and the results provide mechanistic insights into how different electron populations contribute to the observed DNP efficiency. These findings are inherently interesting and of practical importance in view of the recently reported diamond rotors fabricated from P1 high-pressure, high-temperature (HPHT) diamond.

Probing Noncovalent Interactions by Fast Magic-Angle Spinning NMR at 100 kHz and More.

Noncovalent interactions are the basis for a large number of chemical and biological molecular-recognition processes, such as those occurring in supramolecular chemistry, catalysis, solid-state reactions in mechanochemistry, protein folding, protein-nucleic acid binding, and biomolecular phase separation processes. In this perspective article, some recent developments in probing noncovalent interactions by proton-detected solid-state Nuclear Magnetic Resonance (NMR) spectroscopy at Magic-Angle Spinning (MAS) frequencies of 100 kHz and more are reviewed. The development of MAS rotors with decreasing outer diameters, combined with the development of superconducting magnets operating at high static magnetic-field strengths up to 28.2 T (1200 MHz proton Larmor frequency) improves resolution and sensitivity in proton-detected solid-state NMR, which is the fundamental requirement for shedding light on noncovalent interactions in solids. The examples reported in this article range from protein-nucleic acid binding in large ATP-fueled motor proteins to a hydrogen-π interaction in a calixarene-lanthanide complex.

Frequency-Chirped Magic Angle Spinning Dynamic Nuclear Polarization Combined with Electron Decoupling.

Magic angle spinning (MAS) dynamic nuclear polarization (DNP) increases the signal intensity of solid-state nuclear magnetic resonance. DNP typically uses continuous wave (CW) microwave irradiation close to the resonance frequency of unpaired electron spins. In this study, we demonstrate that frequency-chirped microwaves improve DNP performance under MAS. By modulating the gyrotron anode potential, we generate a train of microwave chirps with a maximum bandwidth of 310 MHz and a maximum incident power on the spinning sample of 18 W. We characterize the efficiency of chirped DNP using the following polarizing agents: TEMTriPol-1, AsymPolPOK, AMUPol, and Finland trityl. The effects of different chirp widths and periods are analyzed at different MAS frequencies and microwave powers. Furthermore, we show that chirped DNP can be combined with electron decoupling to improve signal intensity by 59%, compared to CW DNP without electron decoupling, using Finland trityl as a polarizing agent.

Evaluating the motional timescales contributing to averaged anisotropic interactions in MAS solid-state NMR

Abstract. Dynamic processes in molecules can occur on a wide range of timescales, and it is important to understand which timescales of motion contribute to different parameters used in dynamics measurements. For spin relaxation, this can easily be understood from the sampling frequencies of the spectral-density function by different relaxation-rate constants. In addition to data from relaxation measurements, determining dynamically averaged anisotropic interactions in magic-angle spinning (MAS) solid-state NMR allows for better quantification of the amplitude of molecular motion. For partially averaged anisotropic interactions, the relevant timescales of motion are not so clearly defined. Whether the averaging depends on the experimental methods (e.g., pulse sequences) or conditions (e.g., MAS frequency, magnitude of anisotropic interaction, radio-frequency field amplitudes) is not fully understood. To investigate these questions, we performed numerical simulations of dynamic systems based on the stochastic Liouville equation using several experiments for recoupling the dipolar coupling, chemical-shift anisotropy or quadrupolar coupling. As described in the literature, the transition between slow motion, where parameters characterizing the anisotropic interaction are not averaged, and fast motion, where the tensors are averaged leading to a scaled anisotropic quantity, occurs over a window of motional rate constants that depends mainly on the strength of the interaction. This transition region can span 2 orders of magnitude in exchange-rate constants (typically in the microsecond range) but depends only marginally on the employed recoupling scheme or sample spinning frequency. The transition region often coincides with a fast relaxation of coherences, making precise quantitative measurements difficult. Residual couplings in off-magic-angle experiments, however, average over longer timescales of motion. While in principle one may gain information on the timescales of motion from the transition area, extracting such information is hampered by low signal-to-noise ratio in experimental spectra due to fast relaxation that occurs in the same region.

Initial Primer Synthesis of a DNA Primase Monitored by Real-Time NMR Spectroscopy.

Primases are crucial enzymes for DNA replication, as they synthesize a short primer required for initiating DNA replication. We herein present time-resolved nuclear magnetic resonance (NMR) spectroscopy in solution and in the solid state to study the initial dinucleotide formation reaction of archaeal pRN1 primase. Our findings show that the helix-bundle domain (HBD) of pRN1 primase prepares the two substrates and then hands them over to the catalytic domain to initiate the reaction. By using nucleotide triphosphate analogues, the reaction is substantially slowed down, allowing us to study the initial dinucleotide formation in real time. We show that the sedimented protein-DNA complex remains active in the solid-state NMR rotor and that time-resolved 31P-detected cross-polarization experiments allow monitoring the kinetics of dinucleotide formation. The kinetics in the sedimented protein sample are comparable to those determined by solution-state NMR. Protein conformational changes during primer synthesis are observed in time-resolved 1H-detected experiments at fast magic-angle spinning frequencies (100 kHz). A significant number of spectral changes cluster in the HBD pointing to the importance of the HBD for positioning the nucleotides and the dinucleotide.

Analyzing atomic scale structural details and nuclear spin dynamics of four macrolide antibiotics: erythromycin, clarithromycin, azithromycin, and roxithromycin.

The current investigation centers on elucidating the intricate molecular architecture and dynamic behavior of four macrolide antibiotics, specifically erythromycin, clarithromycin, azithromycin, and roxithromycin, through the application of sophisticated solid-state nuclear magnetic resonance (SSNMR) methodologies. We have measured the principal components of chemical shift anisotropy (CSA) parameters, and the site-specific spin-lattice relaxation time at carbon nuclei sites. To extract the principal components of CSA parameters, we have employed 13C 2DPASS CP-MAS SSNMR experiments at two different values of magic angle spinning (MAS) frequencies, namely 2 kHz and 600 Hz. Additionally, the spatial correlation between 13C and 1H nuclei has been investigated using 1H-13C frequency switched Lee-Goldburg heteronuclear correlation (FSLGHETCOR) experiment at a MAS frequency of 24 kHz. Our findings demonstrate that the incorporation of diverse functional groups, such as the ketone group and oxime group with the lactone ring, exerts notable influences on the structure and dynamics of the macrolide antibiotic. In particular, we have observed a significant decrease in the spin-lattice relaxation time of carbon nuclei residing on the lactone ring, desosamine, and cladinose in roxithromycin, compared to erythromycin. Overall, our findings provide detailed insight into the relationship between the structure and dynamics of macrolide antibiotics, which is eventually correlated with their biological activity. This knowledge can be utilized to develop new and more effective drugs by providing a rational basis for drug discovery and design.

Towards optical MAS magnetic resonance using optical traps

Higher magic angle spinning (MAS) frequencies than currently available are desirable to improve spectral resolution in NMR and EPR systems. While conventional strategies employ pneumatic spinning limited by fluid dynamics, this paper demonstrates the development of an optical spinning technique in which vacuum quality dictates the maximum achievable spinning frequency. Using optical traps, we levitated a range of micron-sized samples. Under vacuum we achieved optical rotation of a single ∼10 μm diameter particle of vaterite at several mbar up to hundreds of Hz and of 20 μm diameter SiO2 particles at ≤10−2 mbar at several kHz. At ambient conditions, we optically levitated γ-irradiated alanine particles of 20–50 μm diameter. Additionally, using a single chip EPR detector operating at 11 GHz, we measured the EPR spectrum for a 30 μm γ-irradiated alanine particle in contact with the chip surface (i.e., without optical levitation) in a single scan lasting 92 s. These observations suggest that a γ-irradiated alanine particle having a diameter in the order of 30 μm is a promising candidate for our aim of demonstrating the first magnetic resonance experiment on optically levitated samples. Furthermore, we discuss strategies, limitations, and the potential of implementing MAS with optical traps for NMR and EPR.

Automation in solid state NMR

Automation in solid state NMR (ssNMR) requires appropriate hardware, from rotor loading mechanisms over highly stable rf-transmitters and probe circuitry to automatic tuning and matching capabilities including automatic magic angle adjustment for ssNMR probes. While these hardware capabilities are highly desirable and are, to various degrees, provided by manufacturers, we focus herein on automating experiment setup using radio frequency (rf) fields, which are key parameters in solid state NMR experiments. Specifically, these include spinlock fields during cross polarization (CP), or rf-fields for homo- or heteronuclear spin recoupling or decoupling. Often, these fields have specific relationships to the magic angle spinning (MAS) frequency. Relying on a well-maintained spectrometer, the experiment setup shifts from traditionally required optimization of rf-power values for each element of an experiment sequence to automatically setting all parameters correctly without any need for optimization. The proposed approach allows executing an experiment by reading its rf-amplitude requirements based on the actual MAS rotation frequency just before starting data acquisition, while all other hardware-related parameters are automatically provided through global tables and scripts. Under modest MAS frequencies, no further rf-power optimization is required while providing optimal sensitivity of better than 90% of the optimal signal to noise. Any optional parameter optimization relates only to adjusting rf-nutation frequencies to the requirements of the sample and the sample rotation frequency rather than the spectrometer hardware. Fast MAS CP experiments with MAS frequencies above 40 kHz require a semi-automated setup by optimizing Hartmann-Hahn (HH) matched rf-fields that are synchronously varied relative to the MAS-frequency. This allows for a significant reduction of setup steps by up to one order of magnitude for such experiments, avoiding the traditional grid search for optimal CPMAS conditions. The approach presented here can also be applied to decoupling or recoupling sequences, requiring rotor synchronized rf-fields, reducing the setup to a few steps addressing the spin system’s properties rather than the spectrometer hardware. Our approach permits automating all basic solid state NMR experiments for high throughput analytical tasks.

Performance of the cross-polarization experiment in conditions of radiofrequency field inhomogeneity and slow to ultrafast magic angle spinning (MAS).

In this paper, we provide an analytical description of the performance of the cross-polarization (CP) experiment, including linear ramps and adiabatic tangential sweeps, using effective Hamiltonians and simple rotations in 3Dspace. It is shown that radiofrequency field inhomogeneity induces a reduction in the transfer efficiency at increasing magic angle spinning (MAS)frequencies for both the ramp and the adiabatic CPexperiments. The effect depends on the ratio of the dipolar coupling constant and the sample rotation frequency. In particular, our simulations show that for small dipolar couplings (1 ) and ultrafast MAS (above 100 ) the transfer efficiency is below 40 % when extended contact times up to 20 are used and relaxation losses are ignored. New recoupling and magnetization transfer techniques that are designed explicitly to account for inhomogeneous radiofrequencyfields are needed.

Nuclear spin diffusion under fast magic-angle spinning in solid-state NMR.

Solid-state nuclear spin diffusion is the coherent and reversible process through which spin order is transferred via dipolar couplings. With the recent increases in magic-angle spinning (MAS) frequencies and magnetic fields becoming routinely applied in solid-state nuclear magnetic resonance, understanding how the increased 1H resolution obtained affects spin diffusion is necessary for interpretation of several common experiments. To investigate the coherent contributions to spin diffusion with fast MAS, we have developed a low-order correlation in Liouville space model based on the work of Dumez et al. (J. Chem. Phys. 33, 224501, 2010). Specifically, we introduce a new method for basis set selection, which accounts for the resonance-offset dependence at fast MAS. Furthermore, we consider the necessity of including chemical shift, both isotropic and anisotropic, in the modeling of spin diffusion. Using this model, we explore how different experimental factors change the nature of spin diffusion. Then, we show case studies to exemplify the issues that arise in using spin diffusion techniques at fast spinning. We show that the efficiency of polarization transfer via spin diffusion occurring within a deuterated and 100% back-exchanged protein sample at 60kHz MAS is almost entirely dependent on resonance offset. We additionally identify temperature-dependent magnetization transfer in beta-aspartyl L-alanine, which could be explained by the influence of an incoherent relaxation-based nuclear Overhauser effect.

Simultaneous recoupling of chemical shift tensors of two nuclei by R-symmetry sequences

Chemical shift tensors (CSTs) are sensitive probes of structure and dynamics. R-symmetry pulse sequences (RNCSA) can efficiently recouple CSTs of varying magnitudes in magic angle spinning (MAS) NMR experiments, for a broad range of conditions and MAS frequencies. Herein, we introduce dual-channel R-symmetry pulse sequences for simultaneously recording CSTs of two different nuclei in a single experiment (DORNE-CSA). We demonstrate the performance of DORNE-CSA sequences for simultaneous measurement of 13C and 15N CSTs, on a U-13C,15N-labeled microcrystalline l-histidine. We show that the DORNE-CSA method is robust, provides accurate CST parameters, and takes only half of the measurement time compared to a pair of RNCSA experiments otherwise required for recording the CSTs of individual nuclei. DORNE-CSA approach is broadly applicable to a wide range of biological and inorganic systems.

Nitroxide-based triradical dopants for efficient low-temperature dynamic nuclear polarization in aqueous solutions over a broad pH range

Dynamic nuclear polarization (DNP) can provide substantial sensitivity enhancements in solid state nuclear magnetic resonance (ssNMR) measurements on frozen solutions, thereby enabling experiments that would otherwise be impractical. Previous work has shown that nitroxide-based triradical compounds are particularly effective as dopants in DNP-enhanced measurements at moderate magic-angle spinning frequencies and moderate magnetic field strengths, generally leading to a more rapid build-up of nuclear spin polarizations under microwave irradiation than the more common biradical dopants at the same electron spin concentrations. Here we report the synthesis and DNP performance at 25 K and 9.41 T for two new triradical compounds, sulfoacetyl-DOTOPA and PEG12-DOTOPA. Under our experimental conditions, these compounds exhibit ssNMR signal enhancements and DNP build-up times that are nearly identical to those of previously described triradical dopants. Moreover, these compounds have high solubility in aqueous buffers and water/glycerol mixtures at both acidic and basic pH values, making them useful in a wide variety of experiments on biomolecular systems.

1H Detected Relayed Dynamic Nuclear Polarization.

Recently, it has been shown that methods based on the dynamics of 1H nuclear hyperpolarization in magic angle spinning (MAS) NMR experiments can be used to determine mesoscale structures in complex materials. However, these methods suffer from low sensitivity, especially since they have so far only been feasible with indirect detection of 1H polarization through dilute heteronuclei such as 13C or 29Si. Here we combine relayed-DNP (R-DNP) with fast MAS using 0.7 mm diameter rotors at 21.2 T. Fast MAS enables direct 1H detection to follow hyperpolarization dynamics, leading to an acceleration in experiment times by a factor 16. Furthermore, we show that by varying the MAS rate, and consequently modulating the 1H spin diffusion rate, we can record a series of independent R-DNP curves that can be analyzed jointly to provide an accurate determination of domain sizes. This is confirmed here with measurements on microcrystalline l-histidine·HCl·H2O at MAS frequencies up to 60 kHz, where we determine a Weibull distribution of particle sizes centered on a radius of 440 ± 20 nm with an order parameter of k = 2.2.

Solid‐state heteronuclear multiple‐quantum spectroscopy under a magic‐angle spinning frequency of 150kHz

AbstractWe hereby demonstrate that1H detected15N‐1H heteronuclear multiple‐quantum spectroscopy can be carried out at a magic angle spinning frequency of 150 kHz. While the15N‐1H multiple‐quantum coherences can be directly excited from the dipolar order created by the method of adiabatic demagnetization in the rotating frame, it is technically more advantageous to acquire the chemical shift evolution of the heteronuclear multiple‐quantum coherence by two separate chemical shift evolution periods for1H and15N. We also show that the heteronuclear multiple‐quantum correlation spectrum can be obtained by shearing the corresponding heteronuclear single‐quantum correlation spectrum.

Hybrid quantum-classical simulations of magic angle spinning dynamic nuclear polarization in very large spin systems.

Solid-state nuclear magnetic resonance can be enhanced using unpaired electron spins with a method known as dynamic nuclear polarization (DNP). Fundamentally, DNP involves ensembles of thousands of spins, a scale that is difficult to match computationally. This scale prevents us from gaining a complete understanding of the spin dynamics and applying simulations to design sample formulations. We recently developed an ab initio model capable of calculating DNP enhancements in systems of up to ∼1000 nuclei; however, this scale is insufficient to accurately simulate the dependence of DNP enhancements on radical concentration or magic angle spinning (MAS) frequency. We build on this work by using ab initio simulations to train a hybrid model that makes use of a rate matrix to treat nuclear spin diffusion. We show that this model can reproduce the MAS rate and concentration dependence of DNP enhancements and build-up time constants. We then apply it to predict the DNP enhancements in core-shell metal-organic-framework nanoparticles and reveal new insights into the composition of the particles' shells.

Highly Efficient Polarizing Agents for MAS‐DNP of Proton‐Dense Molecular Solids

AbstractEfficiently hyperpolarizing proton‐dense molecular solids through dynamic nuclear polarization (DNP) solid‐state NMR is still an unmet challenge. Polarizing agents (PAs) developed so far do not perform well on proton‐rich systems, such as organic microcrystals and biomolecular assemblies. Herein we introduce a new PA, cAsymPol‐POK, and report outstanding hyperpolarization efficiency on 12.76 kDa U‐13C,15N‐labeled LecA protein and pharmaceutical drugs at high magnetic fields (up to 18.8 T) and fast magic angle spinning (MAS) frequencies (up to 40 kHz). The performance of cAsymPol‐POK is rationalized by MAS‐DNP simulations combined with electron paramagnetic resonance (EPR), density functional theory (DFT) and molecular dynamics (MD). This work shows that this new biradical is compatible with challenging biomolecular applications and unlocks the rapid acquisition of 13C–13C and 15N–13C correlations of pharmaceutical drugs at natural isotopic abundance, which are key experiments for structure determination.

Highly Efficient Polarizing Agents for MAS-DNP of Proton-Dense Molecular Solids.

Efficiently hyperpolarizing proton-dense molecular solids through dynamic nuclear polarization (DNP) solid-state NMR is still an unmet challenge. Polarizing agents (PAs) developed so far do not perform well on proton-rich systems, such as organic microcrystals and biomolecular assemblies. Herein we introduce a new PA, cAsymPol-POK, and report outstanding hyperpolarization efficiency on 12.76 kDa U-13 C,15 N-labeled LecA protein and pharmaceutical drugs at high magnetic fields (up to 18.8 T) and fast magic angle spinning (MAS) frequencies (up to 40 kHz). The performance of cAsymPol-POK is rationalized by MAS-DNP simulations combined with electron paramagnetic resonance (EPR), density functional theory (DFT) and molecular dynamics (MD). This work shows that this new biradical is compatible with challenging biomolecular applications and unlocks the rapid acquisition of 13 C-13 C and 15 N-13 C correlations of pharmaceutical drugs at natural isotopic abundance, which are key experiments for structure determination.

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 (∼10kHz) to ultra-fast (150kHz) 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-Nn 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 designof homonuclear recoupling sequences with arbitrary frequency bandwidths.

Maximizing efficiency of dipolar recoupling in solid-state NMR using optimal control sequences.

Dipolar recoupling is a central concept in the nuclear magnetic resonance spectroscopy of powdered solids and is used to establish correlations between different nuclei by magnetization transfer. The efficiency of conventional cross-polarization methods is low because of the inherent radio frequency (rf) field inhomogeneity present in the magic angle spinning (MAS) experiments and the large chemical shift anisotropies at high magnetic fields. Very high transfer efficiencies can be obtained using optimal control–derived experiments. These sequences had to be optimized individually for a particular MAS frequency. We show that by adjusting the length and the rf field amplitude of the shaped pulse synchronously with sample rotation, optimal control sequences can be successfully applied over a range of MAS frequencies without the need of reoptimization. This feature greatly enhances their applicability on spectrometers operating at differing external fields where the MAS frequency needs to be adjusted to avoid detrimental resonance effects.

Improved NMR transfer of magnetization from protons to half-integer spin quadrupolar nuclei at moderate and high magic-angle spinning frequencies.

Half-integer spin quadrupolar nuclei are the only magnetic isotopes for the majority of the chemical elements. Therefore, the transfer of polarization from protons to these isotopes under magic-angle spinning (MAS) can provide precious insights into the interatomic proximities in hydrogen-containing solids, including organic, hybrid, nanostructured and biological solids. This transfer has recently been combined with dynamic nuclear polarization (DNP) in order to enhance the NMR signal of half-integer quadrupolar isotopes. However, the cross-polarization transfer lacks robustness in the case of quadrupolar nuclei, and we have recently introduced as an alternative technique a -RINEPT (through-space refocused insensitive nuclei enhancement by polarization transfer) scheme combining a heteronuclear dipolar recoupling built from adiabatic pulses and a continuous-wave decoupling. This technique has been demonstrated at 9.4 T with moderate MAS frequencies, -15 kHz, in order to transfer the DNP-enhanced H polarization to quadrupolar nuclei. Nevertheless, polarization transfers from protons to quadrupolar nuclei are also required at higher MAS frequencies in order to improve the H resolution. We investigate here how this transfer can be achieved at and 60 kHz. We demonstrate that the -RINEPT sequence using adiabatic pulses still produces efficient and robust transfers but requires large radio-frequency (rf) fields, which may not be compatible with the specifications of most MAS probes. As an alternative, we introduce robust and efficient variants of the -RINEPT and PRESTO (phase-shifted recoupling effects a smooth transfer of order) sequences using symmetry-based recoupling schemes built from single and composite pulses. Their performances are compared using the average Hamiltonian theory and experiments at T on -alumina and isopropylamine-templated microporous aluminophosphate (AlPO-14), featuring low and significant H-H dipolar interactions, respectively. These experiments demonstrate that the H magnetization can be efficiently transferred to Al nuclei using -RINEPT with (27090) recoupling and using PRESTO with (180) or (27090) schemes at or 62.5 kHz, respectively. The -RINEPT and PRESTO recoupling schemes complement each other since the latter is affected by dipolar truncation, whereas the former is not. We also analyze the losses during these recoupling schemes, and we show how these magnetization transfers can be used at kHz to acquire in 72 min 2D HETCOR (heteronuclear correlation) spectra between H and quadrupolar nuclei, with a non-uniform sampling (NUS).