Study of electron spectral diffusion process under DNP conditions by ELDOR spectroscopy focusing on the 14N solid effect.

Electron spectral diffusion (eSD) plays an important role in solid-state, static dynamic nuclear polarization (DNP) with polarizers that have inhomogeneously broadened EPR spectra, such as nitroxide radicals. It affects the electron spin polarization gradient within the EPR spectrum during microwave irradiation and thereby determines the effectiveness of the DNP process via the so-called indirect cross-effect (iCE) mechanism. The electron depolarization profile can be measured by electron-electron double resonance (ELDOR) experiments, and a theoretical framework for deriving eSD parameters from ELDOR spectra and employing them to calculate DNP profiles has been developed. The inclusion of electron depolarization arising from the 14N solid effect (SE) has not yet been taken into account in this theoretical framework and is the subject of the present work. The 14N SE depolarization was studied using W-band ELDOR of a 0.5 mM TEMPOL solution, where eSD is negligible, taking into account the hyperfine interaction of both 14N and 1H nuclei, the long microwave irradiation applied under DNP conditions, and electron and nuclear relaxation. The results of this analysis were then used in simulations of ELDOR spectra of 10 and 20 mM TEMPOL solutions, where eSD is significant using the eSD model and the SE contributions were added ad hoc employing the 1H and 14N frequencies and their combinations, as found from the analysis of the 0.5 mM sample. This approach worked well for the 20 mM solution, where a good fit for all ELDOR spectra recorded along the EPR spectrum was obtained and the inclusion of the 14N SE mechanism improved the agreement with the experimental spectra. For the 10 mM solution, simulations of the ELDOR spectra recorded along the gz position gave a lower-quality fit than for spectra recorded in the center of the EPR spectrum. This indicates that the simple approach we used to describe the 14N SE is limited when its contribution is relatively high as the anisotropy of its magnetic interactions was not considered explicitly.

Theoretical Aspects of the Cross Effect Enhancement of Nuclear Polarization under Static Dynamic Nuclear Polarization Conditions.

In this study, we perform quantum calculations of the spin dynamics of a small spin system that includes nine coupled electrons and one nucleus placed in an external magnetic field and exposed to microwave irradiation. This is an extension of a previous work in which we have demonstrated on a system of 11 coupled electron spins the dynamics of the electron polarizations composing the electron paramagnetic resonance (EPR) line during static dynamic nuclear polarization (DNP) experiments. There we have shown that the electron polarizations are determined by a spectral diffusion process, induced by the dipolar interaction and cross-relaxation. Additionally, we showed that a distinction had to be made between strong and weak dipolar-coupled systems relative to the inhomogeneity of the EPR line with only the first behaving according to the thermal mixing DNP (with two electron spin temperatures) description. The EPR spectra in the weak and strong dipolar interaction cases show different types of spectral features. In the extended spin system, we again make a distinction between weak and strong electron-electron interactions and show that the DNP spectra for the two cases are different in nature but that the DNP spectra can be derived in all cases from the EPR line shapes using the indirect cross effect.

Experimental quantification of electron spectral-diffusion under static DNP conditions.

Dynamic Nuclear Polarization (DNP) is an efficient technique for enhancing NMR signals by utilizing the large polarization of electron spins to polarize nuclei. The mechanistic details of the polarization transfer process involve the depolarization of the electrons resulting from microwave (MW) irradiation (saturation), as well as electron-electron cross-relaxation occurring during the DNP experiment. Recently, electron-electron double resonance (ELDOR) experiments have been performed under DNP conditions to map the depolarization profile along the EPR spectrum as a consequence of spectral diffusion. A phenomenological model referred to as the eSD model was developed earlier to describe the spectral diffusion process and thus reproduce the experimental results of electron depolarization. This model has recently been supported by quantum mechanical calculations on a small dipolar coupled electron spin system, experiencing dipolar interaction based cross-relaxation. In the present study, we performed a series of ELDOR measurements on a solid glassy solution of TEMPOL radicals in an effort to substantiate the eSD model and test its predictability in terms of electron depolarization profiles, in the steady-state and under non-equilibrium conditions. The crucial empirical parameter in this model is ΛeSD, which reflects the polarization exchange rate among the electron spins. Here, we explore further the physical basis of this parameter by analyzing the ELDOR spectra measured in the temperature range of 3-20 K and radical concentrations of 20-40 mM. Simulations using the eSD model were carried out to determine the dependence of ΛeSD on temperature and concentration. We found that for the samples studied, ΛeSD is temperature independent. It, however, increases with a power of ∼2.6 of the concentration of TEMPOL, which is proportional to the average electron-electron dipolar interaction strength in the sample.

13C → 1H transfer of light-induced hyperpolarization allows for selective detection of protons in frozen photosynthetic reaction center.

In the present study, we exploit the light-induced hyperpolarization occurring on 13C nuclei due to the solid-state photochemically induced dynamic nuclear polarization (photo-CIDNP) effect to boost the NMR signal intensity of selected protons via inverse cross-polarization. Such hyperpolarization transfer is implemented into 1H-detected two-dimensional 13C-1H correlation magic-angle-spinning (MAS) NMR experiment to study protons in frozen photosynthetic reaction centers (RCs). As a first trial, the performance of such an experiment is tested on selectively 13C labeled RCs from the purple bacteria of Rhodobacter sphaeroides. We observed response from the protons belonging to the photochemically active cofactors in their native protein environment. Such an approach is a potential heteronuclear spin-torch experiment which could be complementary to the classical heteronuclear correlation (HETCOR) experiments for mapping proton chemical shifts of photosynthetic cofactors and to understand the role of the proton pool around the electron donors in the electron transfer process occurring during photosynthesis.

Electron-Electron Cross-Relaxation and Spectral Diffusion during Dynamic Nuclear Polarization Experiments on Solids.

Recently it has been shown that experimental electron-electron double resonance (ELDOR) spectra of amorphous glasses containing free radicals with inhomogeneously broadened electron paramagnetic resonance (EPR) spectra can be analyzed using a set of coupled rate equations for the electron polarizations of frequency bins composing these spectra, named the eSD (electron spectral diffusion) model. The rate matrix defining these equations has elements depending on the microwave, the spin-lattice relaxation rates and on eSD rate constants responsible for polarization exchange. In this study, we show that in addition to the static dipolar flip-flop terms in the Hamiltonian a zero-quantum electron cross-relaxation mechanism can be responsible for the polarization exchange process in our samples. This conclusion was reached by calculating the EPR lineshapes of a system of 11 coupled electrons exposed to microwave irradiation using an eigenstate population rate equation derived from the spin density vector rate equation in Liouville space. These equations involve all terms of the Hamiltonian and in addition rate constants representing longitudinal relaxation and cross-relaxation mechanisms as well as MW irradiation. The results of these calculations are compared with the results obtained from the eSD model.

Significance of symmetry in the nuclear spin Hamiltonian for efficient heteronuclear dipolar decoupling in solid-state NMR: A Floquet description of supercycled rCW schemes.

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.

Fast and accurate MAS-DNP simulations of large spin ensembles.

A deeper understanding of parameters affecting Magic Angle Spinning Dynamic Nuclear Polarization (MAS-DNP), an emerging nuclear magnetic resonance hyperpolarization method, is crucial for the development of new polarizing agents and the successful implementation of the technique at higher magnetic fields (>10 T). Such progress is currently impeded by computational limitation which prevents the simulation of large spin ensembles (electron as well as nuclear spins) and to accurately describe the interplay between all the multiple key parameters at play. In this work, we present an alternative approach to existing cross-effect and solid-effect MAS-DNP codes that yields fast and accurate simulations. More specifically we describe the model, the associated Liouville-based formalism (Bloch-type derivation and/or Landau-Zener approximations) and the linear time algorithm that allows computing MAS-DNP mechanisms with unprecedented time savings. As a result, one can easily scan through multiple parameters and disentangle their mutual influences. In addition, the simulation code is able to handle multiple electrons and protons, which allows probing the effect of (hyper)polarizing agents concentration, as well as fully revealing the interplay between the polarizing agent structure and the hyperfine couplings, nuclear dipolar couplings, nuclear relaxation times, both in terms of depolarization effect, but also of polarization gain and buildup times.

Effect of electron spectral diffusion on static dynamic nuclear polarization at 7 Tesla.

Here, we present an integrated experimental and theoretical study of 1H dynamic nuclear polarization (DNP) of a frozen aqueous glass containing free radicals at 7 T, under static conditions and at temperatures ranging between 4 and 20 K. The DNP studies were performed with a home-built 200 GHz quasi-optics microwave bridge, powered by a tunable solid-state diode source. DNP using monochromatic and continuous wave (cw) irradiation applied to the electron paramagnetic resonance (EPR) spectrum of the radicals induces the transfer of polarization from the electron spins to the surrounding nuclei of the solvent and solutes in the frozen aqueous glass. In our systematic experimental study, the DNP enhanced 1H signals are monitored as a function of microwave frequency, microwave power, radical concentration, and temperature, and are interpreted with the help of electron spin-lattice relaxation times, experimental MW irradiation parameters, and the electron spectral diffusion (eSD) model introduced previously. This comprehensive experimental DNP study with mono-nitroxide radical spin probes was accompanied with theoretical calculations. Our results consistently demonstrate that eSD effects can be significant at 7 T under static DNP conditions, and can be systematically modulated by experimental conditions.

Correction: Gd(iii)-Gd(iii) EPR distance measurements - the range of accessible distances and the impact of zero field splitting.

Correction for 'Gd(iii)-Gd(iii) EPR distance measurements - the range of accessible distances and the impact of zero field splitting' by Arina Dalaloyan et al., Phys. Chem. Chem. Phys., 2015, 17, 18464-18476.

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.

The effect of Gd on trityl-based dynamic nuclear polarisation in solids.

In dynamic nuclear polarisation (DNP) experiments performed under static conditions at 1.4 K we show that the presence of 1 mM Gd(iii)-DOTAREM increases the (13)C polarisation and decreases the (13)C polarisation buildup time of (13)C-urea dissolved in samples containing water/DMSO mixtures with trityl radical (OX063) concentrations of 10 mM or higher. To account for these observations further measurements were carried out at 6.5 K, using a combined EPR and NMR spectrometer. At this temperature, frequency swept DNP spectra of samples with 5 or 10 mM OX063 were measured, with and without 1 mM Gd-DOTA, and again a (13)C enhancement gain was observed due to the presence of Gd-DOTA. These measurements were complemented by electron-electron double resonance (ELDOR) measurements to quantitate the effect of electron spectral diffusion (eSD) on the DNP enhancements and lineshapes. Simulations of the ELDOR spectra were done using the following parameters: (i) a parameter defining the rate of the eSD process, (ii) an "effective electron-proton anisotropic hyperfine interaction parameter", and (iii) the transverse electron spin relaxation time of OX063. These parameters, together with the longitudinal electron spin relaxation time, measured by EPR, were used to calculate the frequency profile of electron polarisation. This, in turn, was used to calculate two basic solid effect (SE) and indirect cross effect (iCE) DNP spectra. A properly weighted combination of these two normalized DNP spectra provided a very good fit of the experimental DNP spectra. The best fit simulation parameters reveal that the addition of Gd(iii)-DOTA causes an increase in both the SE and the iCE contributions by similar amounts, and that the increase in the overall DNP enhancements is a result of narrowing of the ELDOR spectra (increased electron polarisation gradient across the EPR line). These changes in the electron depolarisation profile are a combined result of shortening of the longitudinal and transverse electron spin relaxation times, as well as an increase in the eSD rate and in the effective electron-proton anisotropic hyperfine interaction parameter.

Nuclear depolarization and absolute sensitivity in magic-angle spinning cross effect dynamic nuclear polarization.

Over the last two decades solid state Nuclear Magnetic Resonance has witnessed a breakthrough in increasing the nuclear polarization, and thus experimental sensitivity, with the advent of Magic Angle Spinning Dynamic Nuclear Polarization (MAS-DNP). To enhance the nuclear polarization of protons, exogenous nitroxide biradicals such as TOTAPOL or AMUPOL are routinely used. Their efficiency is usually assessed as the ratio between the NMR signal intensity in the presence and the absence of microwave irradiation εon/off. While TOTAPOL delivers an enhancement εon/off of about 60 on a model sample, the more recent AMUPOL is more efficient: >200 at 100 K. Such a comparison is valid as long as the signal measured in the absence of microwaves is merely the Boltzmann polarization and is not affected by the spinning of the sample. However, recent MAS-DNP studies at 25 K by Thurber and Tycko (2014) have demonstrated that the presence of nitroxide biradicals combined with sample spinning can lead to a depolarized nuclear state, below the Boltzmann polarization. In this work we demonstrate that TOTAPOL and AMUPOL both lead to observable depolarization at ≈110 K, and that the magnitude of this depolarization is radical dependent. Compared to the static sample, TOTAPOL and AMUPOL lead, respectively, to nuclear polarization losses of up to 20% and 60% at a 10 kHz MAS frequency, while Trityl OX63 does not depolarize at all. This experimental work is analyzed using a theoretical model that explains how the depolarization process works under MAS and gives new insights into the DNP mechanism and into the spin parameters, which are relevant for the efficiency of a biradical. In light of these results, the outstanding performance of AMUPOL must be revised and we propose a new method to assess the polarization gain for future radicals.

Theoretical aspects of Magic Angle Spinning - Dynamic Nuclear Polarization.

Magic Angle Spinning (MAS) combined with Dynamic Nuclear Polarization (DNP) has been proven in recent years to be a very powerful method for increasing solid-state NMR signals. Since the advent of biradicals such as TOTAPOL to increase the nuclear polarization new classes of radicals, with larger molecular weight and/or different spin properties have been developed. These have led to unprecedented signal gain, with varying results for different experimental parameters, in particular the microwave irradiation strength, the static field, and the spinning frequency. Recently it has been demonstrated that sample spinning imposes DNP enhancement processes that differ from the active DNP mechanism in static samples as upon sample spinning the DNP enhancements are the results of energy level anticrossings occurring periodically during each rotor cycle. In this work we present experimental results with regards to the MAS frequency dependence of the DNP enhancement profiles of four nitroxide-based radicals at two different sets of temperature, 110 and 160K. In fact, different magnitudes of reduction in enhancement are observed with increasing spinning frequency. Our simulation code for calculating MAS-DNP powder enhancements of small model spin systems has been improved to extend our studies of the influence of the interaction and relaxation parameters on powder enhancements. To achieve a better understanding we simulated the spin dynamics of a single three-spin system {ea-eb-n} during its steady state rotor periods and used the Landau-Zener formula to characterize the influence of the different anti-crossings on the polarizations of the system and their necessary action for reaching steady state conditions together with spin relaxation processes. Based on these model calculations we demonstrate that the maximum steady state nuclear polarization cannot become larger than the maximum polarization difference between the two electrons during the steady state rotor cycle. This study also shows the complexity of the MAS-DNP process and therefore the necessity to rely on numerical simulations for understanding parametric dependencies of the enhancements. Finally an extension of the spin system up to five spins allowed us to probe the first steps of the transfer of polarization from the nuclei coupled to the electrons to further away nuclei, demonstrating a decrease in the spin-diffusion barrier under MAS conditions.

Facing and Overcoming Sensitivity Challenges in Biomolecular NMR Spectroscopy.

In the Spring of 2013, NMR spectroscopists convened at the Weizmann Institute in Israel to brainstorm on approaches to improve the sensitivity of NMR experiments, particularly when applied in biomolecular settings. This multi-author interdisciplinary Review presents a state-of-the-art description of the primary approaches that were considered. Topics discussed included the future of ultrahigh-field NMR systems, emerging NMR detection technologies, new approaches to nuclear hyperpolarization, and progress in sample preparation. All of these are orthogonal efforts, whose gains could multiply and thereby enhance the sensitivity of solid- and liquid-state experiments. While substantial advances have been made in all these areas, numerous challenges remain in the quest of endowing NMR spectroscopy with the sensitivity that has characterized forms of spectroscopies based on electrical or optical measurements. These challenges, and the ways by which scientists and engineers are striving to solve them, are also addressed.

Gd(III)-Gd(III) EPR distance measurements--the range of accessible distances and the impact of zero field splitting.

Gd(III) complexes have emerged as spin labels for distance determination in biomolecules through double-electron-electron resonance (DEER) measurements at high fields. For data analysis, the standard approach developed for a pair of weakly coupled spins with S = 1/2 was applied, ignoring the actual properties of Gd(III) ions, i.e. S = 7/2 and ZFS (zero field splitting) ≠ 0. The present study reports on a careful investigation on the consequences of this approach, together with the range of distances accessible by DEER with Gd(III) complexes as spin labels. The experiments were performed on a series of specifically designed and synthesized Gd-rulers (Gd-PyMTA-spacer-Gd-PyMTA) covering Gd-Gd distances of 2-8 nm. These were dissolved in D2O-glycerol-d8 (0.03-0.10 mM solutions) which is the solvent used for the corresponding experiments on biomolecules. Q- and W-band DEER measurements, followed by data analysis using the standard data analysis approach, used for S = 1/2 pairs gave the distance-distribution curves, of which the absolute maxima agreed very well with the expected distances. However, in the case of the short distances of 2.1 and 2.9 nm, the distance distributions revealed additional peaks. These are a consequence of neglecting the pseudo-secular term in the dipolar Hamiltonian during the data analysis, as is outlined in a theoretical treatment. At distances of 3.4 nm and above, disregarding the pseudo-secular term leads to a broadening of a maximum of 0.4 nm of the distance-distribution curves at half height. Overall, the distances of up to 8.3 nm were determined, and the long evolution time of 16 µs at 10 K indicates that a distance of up to 9.4 nm can be accessed. A large distribution of the ZFS parameter, D, as is found for most Gd(III) complexes in a frozen solution, is crucial for the application of Gd(III) complexes as spin labels for distance determination via Gd(III)-Gd(III) DEER, especially for short distances. The larger ZFS of Gd-PyMTA, in comparison to that of Gd-DOTA, makes Gd-PyMTA a better label for short distances.

Simultaneous DNP enhancements of (1)H and (13)C nuclei: theory and experiments.

DNP on heteronuclear spin systems often results in interesting phenomena such as the polarization enhancement of one nucleus during MW irradiation at the "forbidden" transition frequencies of another nucleus or the polarization transfer between the nuclei without MW irradiation. In this work we discuss the spin dynamics in a four-spin model system of the form {ea-eb-((1)H,(13)C)}, with the Larmor frequencies ωa, ωb, ωH and ωC, by performing Liouville space simulations. This spin system exhibits the common (1)H solid effect (SE), (13)C cross effect (CE) and in addition high order CE-DNP enhancements. Here we show, in particular, the "proton shifted (13)C-CE" mechanism that results in (13)C polarization when the model system, at one of its (13)C-CE conditions, is excited by a MW field at the zero quantum or double quantum electron-proton transitions ωMW = ωa ± ωH and ωMW = ωb ± ωH. Furthermore, we introduce the "heteronuclear" CE mechanism that becomes efficient when the system is at one of its combined CE conditions |ωa - ωb| = |ωH ± ωC|. At these conditions, simulations of the four-spin system show polarization transfer processes between the nuclei, during and without MW irradiation, resembling the polarization exchange effects often discussed in the literature. To link the "microscopic" four-spin simulations to the experimental results we use DNP lineshape simulations based on "macroscopic" rate equations describing the electron and nuclear polarization dynamics in large spin systems. This approach is applied based on electron-electron double resonance (ELDOR) measurements that show strong (1)H-SE features outside the EPR frequency range. Simulated ELDOR spectra combined with the indirect (13)C-CE (iCE) mechanism, result in additional "proton shifted (13)C-CE" features that are similar to the experimental ones. These features are also observed experimentally in (13)C-DNP spectra of a sample containing 15 mM of trityl in a glass forming solution of (13)C-glycerol/H2O and are analyzed by calculating the basic (13)C-SE and (13)C-iCE shapes using simulated ELDOR spectra that were fitted to the experimental ones.

Quantification of rate constants for successive enzymatic reactions with DNP hyperpolarized MR.

A kinetic model is provided to obtain reaction rate constants in successive enzymatic reactions that are monitored using NMR spectroscopy and hyperpolarized substrates. The model was applied for simulation and analysis of the successive oxidation of choline to betaine aldehyde, and further to betaine, by the enzyme choline oxidase. This enzymatic reaction was investigated under two different sets of conditions: two different choline molecular probes were used, [1,1,2,2-D4 , 1-(13) C]choline chloride and [1,1,2,2-D4 , 2-(13) C]choline chloride, in different MR systems (clinical scanner and high-resolution spectrometer), as well as in different reactors and reaction volumes (4.8 and 0.7 mL). The kinetic analysis according to the model yielded similar results in both set-ups, supporting the robustness of the model. This was achieved despite the complex and negating influences of reaction kinetics and polarization decay, and in the presence of uncontrolled mixing characteristics, which may introduce uncertainties in both effective timing and effective pulses. The ability to quantify rate constants using hyperpolarized MR in the first seconds of consecutive enzyme activity is important for further development of the utilization of dynamic nuclear polarization-MR for biological determinations.

Static (1)H dynamic nuclear polarization with the biradical TOTAPOL: a transition between the solid effect and the cross effect.

To study the solid state (1)H-DNP mechanism of the biradical TOTAPOL under static conditions the frequency swept DNP enhancement spectra of samples containing 20 mM and 5 mM TOTAPOL were measured as a function of MW irradiation time and temperature. We observed that under static DNP conditions the biradical TOTAPOL behaves similar to the monoradical TEMPOL, in contrast to MAS DNP where TOTAPOL is considerably more effective. As previously done for TEMPOL, the TOTAPOL DNP spectra were analyzed taking a superposition of a basic SE-DNP lineshape and a basic CE-DNP lineshape with different amplitudes. The analysis of the steady state DNP spectra showed that the SE was dominant in the 6-10 K range and the CE was dominant above 10 K. DNP spectra obtained as a function of MW irradiation time allowed resolving the individual SE and CE buildup times. At low temperatures the SE buildup time was faster than the CE buildup time and at all temperatures the CE buildup time was close to the nuclear spin-lattice relaxation time, T1n. Polarization calculations involving nuclear spin-diffusion for a model system of one electron and many nuclei suggested that the shortening of the T1n for increasing temperatures is the reason why the SE contribution to the overall enhancement was reduced.

A Floquet description of phase alternated sequences for efficient homonuclear recoupling in solid perdeuterated systems.

A Floquet description of a phase alternated homonuclear recoupling scheme for perdeuterated systems is presented. As a result, we demonstrate improvements in the recoupling efficiency of the DOuble Nucleus Enhanced Recoupling [DONER; J. Am. Chem. Soc. 131 (2009) 17054] technique by utilizing Phase Alternated Recoupling Irradiation Schemes [PARIS; Chem. Phys. Lett. 469 (2009) 342]. The effect of proton and deuterium radio frequency irradiation during recoupling has been systematically studied and theoretical observations have been verified experimentally using a deuterated model compound, L-Alanine, at 10 and 20 kHz magic angle spinning frequency. Experimental results are well in agreement with theoretical observations, thereby significantly increasing the recoupling efficiency of conventional DONER in perdeuterated systems.