Category Archives: Theory

Dynamic nuclear polarization via the cross effect and thermal mixing: B. Energy transport #DNPNMR

Wenckebach, W.Th. “Dynamic Nuclear Polarization via the Cross Effect and Thermal Mixing: B. Energy Transport.” Journal of Magnetic Resonance 299 (February 2019): 151–67.

The fundamental process of dynamic nuclear polarization (DNP) via the cross effect (CE) and thermal mixing (TM) is a triple spin flip, in which two interacting electron spins and a nuclear spin interacting with one of these electron spins flip together. In the previous article (Wenckebach, 2018) these triple spin flips were treated by first determining the eigenstates of the two interacting electron spins exactly and next investigating transitions involving these exact eigenstates and the nuclear spin states. It was found that two previously developed approaches—the scrambled states approach and the fluctuating field approach—are just two distinct limiting cases of this more general approach. It was also shown that triple spin flips constitute a single process causing two flows of energy: a flow originating in the electron Zeeman energy and a flow originating in the mutual interactions between the electron spins. In order to render their definitions more precise, the former flow was denoted as the CE and the latter as TM.

Dynamic nuclear polarization via the cross effect and thermal mixing: A. The role of triple spin flips #DNPNMR

Wenckebach, W.Th. “Dynamic Nuclear Polarization via the Cross Effect and Thermal Mixing: A. The Role of Triple Spin Flips.” Journal of Magnetic Resonance 299 (February 2019): 124–34. 


In dynamic nuclear polarization (DNP) via the cross effect (CE) and thermal mixing (TM) a microwave field first reduces the polarization of some electron spins, so the electron spin system deviates from thermal equilibrium with the lattice. Next, the mutual interactions combine with their interaction with the nuclear spins to transform this deviation into nuclear spin polarization.

De novo prediction of cross-effect efficiency for magic angle spinning dynamic nuclear polarization #DNPNMR

Mentink-Vigier, Frédéric, Anne-Laure Barra, Johan van Tol, Sabine Hediger, Daniel Lee, and Gaël De Paëpe. “De Novo Prediction of Cross-Effect Efficiency for Magic Angle Spinning Dynamic Nuclear Polarization.” Physical Chemistry Chemical Physics 21, no. 4 (2019): 2166–76.

Magic angle spinning dynamic nuclear polarization (MAS-DNP) has become a key approach to boost the intrinsic low sensitivity of NMR in solids. This method relies on the use of both stable radicals as polarizing agents (PAs) and suitable high frequency microwave irradiation to hyperpolarize nuclei of interest. Relating PA chemical structure to DNP efficiency has been, and is still, a long-standing problem. The complexity of the polarization transfer mechanism has so far limited the impact of analytical derivation. However, recent numerical approaches have profoundly improved the basic understanding of the phenomenon and have now evolved to a point where they can be used to help design new PAs. In this work, the potential of advanced MAS-DNP simulations combined with DFT calculations and high-field EPR to qualitatively and quantitatively predict hyperpolarization efficiency of particular PAs is analyzed. This approach is demonstrated on AMUPol and TEKPol, two widely-used bis-nitroxide PAs. The results notably highlight how the PA structure and EPR characteristics affect the detailed shape of the DNP field profile. We also show that refined simulations of this profile using the orientation dependency of the electron spin–lattice relaxation times can be used to estimate the microwave B1 field experienced by the sample. Finally, we show how modelling the nuclear spin–lattice relaxation times of close and bulk nuclei while accounting for PA concentration allows for a prediction of DNP enhancement factors and hyperpolarization build-up times.

Overhauser Dynamic Nuclear Polarization for the Study of Hydration Dynamics, Explained #DNPNMR #ODNP

Franck, John M., and Songi Han. “Overhauser Dynamic Nuclear Polarization for the Study of Hydration Dynamics, Explained.” In Methods in Enzymology, 615:131–75. Elsevier, 2019.

We outline the physical properties of hydration water that are captured by Overhauser Dynamic Nuclear Polarization (ODNP) relaxometry and explore the insights that ODNP yields about the water and the surface that this water is coupled to. As ODNP relies on the pairwise cross-relaxation between the electron spin of a spin probe and a proton nuclear spin of water, it captures the dynamics of single-particle diffusion of an ensemble of water molecules moving near the spin probe. ODNP principally utilizes the same physics as other nuclear magnetic resonance (NMR) relaxometry (i.e., relaxation measurement) techniques. However, in ODNP, electron paramagnetic resonance (EPR) excites the electron spins probes and their high net polarization acts as a signal amplifier. Furthermore, it renders ODNP parameters highly sensitive to water moving at rates commensurate with the EPR frequency of the spin probe (typically 10 GHz). Also, ODNP selectively enhances the NMR signal contributions of water moving within close proximity to the spin label. As a result, ODNP can capture ps–ns movements of hydration waters with high sensitivity and locality, even in samples with protein concentrations as dilute as 10 μM. 

To date, the utility of the ODNP technique has been demonstrated for two major applications: the characterization of the spatial variation in the properties of the hydration layer of proteins or other surfaces displaying topological diversity, and the identification of structural properties emerging from highly disordered proteins and protein domains. The former has been shown to correlate well with the properties of hydration water predicted by MD simulations and has been shown capable of evaluating the hydrophilicity or hydrophobicity of a surface. The latter has been demonstrated for studies of an interhelical loop of proteorhodopsin, the partial structure of α-synuclein embedded at the lipid membrane surface, incipient structures adopted by tau proteins en route to fibrils, and the structure and hydration profile of a transmembrane peptide. 

This chapter focuses on offering a mechanistic understanding of the ODNP measurement and the molecular dynamics encoded in the ODNP parameters. In particular, it clarifies how the electron–nuclear dipolar coupling encodes information about the molecular dynamics in the nuclear spin self-relaxation and, more importantly, the electron–nuclear spin cross-relaxation rates. The clarification of the molecular dynamics underlying ODNP should assist in establishing a connection to theory and computer simulation that will offer far richer interpretations of ODNP results in future studies.

Experimental quantification of electron spectral-diffusion under static DNP conditions #DNPNMR

Kundu, Krishnendu, Marie Ramirez Cohen, Akiva Feintuch, Daniella Goldfarb, and Shimon Vega. “Experimental Quantification of Electron Spectral-Diffusion under Static DNP Conditions.” Physical Chemistry Chemical Physics 21, no. 1 (2019): 478–89.

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 LeSD, 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 LeSD on temperature and concentration. We found that for the samples studied, LeSD is temperature independent. It, however, increases with a power of B2.6 of the concentration of TEMPOL, which is proportional to the average electron–electron dipolar interaction strength in the sample.

Maximizing nuclear hyperpolarization in pulse cooling under MAS #DNPNMR

Björgvinsdóttir, Snædís, Brennan J. Walder, Nicolas Matthey, and Lyndon Emsley. “Maximizing Nuclear Hyperpolarization in Pulse Cooling under MAS.” Journal of Magnetic Resonance 300 (March 1, 2019): 142–48.

It has recently been shown how dynamic nuclear polarization can be used to hyperpolarize the bulk of proton-free solids. This is achieved by generating the polarization in a wetting phase, transferring it to nuclei near the surface and relaying it towards the bulk through homonuclear spin diffusion between weakly magnetic nuclei. Pulse cooling is a strategy to achieve this that uses a multiple contact cross-polarization sequence for bulk hyperpolarization. Here, we show how to maximize sensitivity using the pulse cooling method by experimentally optimizing pulse parameters and delays on a sample of powdered SnO2. To maximize sensitivity we introduce an approach where the magic angle spinning rate is modulated during the experiment: the CP contacts are carried out at a slow spin rate to benefit from faster spin diffusion, and the spin rate is then accelerated before detection to improve line narrowing. This method can improve the sensitivity of pulse cooling for 119Sn spectra of SnO2 by an additional factor of 3.5.

Absolute 1H polarization measurement with a spin-correlated component of magnetization by hyperpolarized MAS-DNP solid-state NMR #DNPNMR

To my knowledge, this is one of the few methods that allows to measure the absolute polarization of a spin ensemble. Often the on/off signal ratio is used to characterize the efficiency of the DNP – a method that does not take depolarization effects into account. The method is related to the SPY-MR method to measure absolute spin polarization in dissolution DNP experiments.

Sugishita, Tomoaki, Yoh Matsuki, and Toshimichi Fujiwara. “Absolute 1H Polarization Measurement with a Spin-Correlated Component of Magnetization by Hyperpolarized MAS-DNP Solid-State NMR.” Solid State Nuclear Magnetic Resonance 99 (July 2019): 20–26.

Sensitivity of magic-angle spinning (MAS) NMR spectroscopy has been dramatically improved by the advent of high-field dynamic nuclear polarization (DNP) technique and its rapid advances over the past decades. In this course, discussions on ways to improve the DNP enhancement factor or the overall sensitivity gain have been numerous, and led to a number of methodological and instrumental breakthroughs. Beyond the sensitivity gain, however, discussions on accurate quantification of the 1H polarization amplitude achievable in a sample with DNP have been relatively rare. Here, we propose a new method for quantifying the local 1H hyperpolarization amplitude, which is applicable to un-oriented/powdered solid samples under MAS NMR conditions. The method is based on the ability to observe the high-order spin-correlated term (2IzSz) intrinsic to a hyperpolarized I-S two-spin state, separately from the lowest-order Zeeman term (Sz) in quasi-equilibrium magnetization. The quantification procedure does not require evaluation of signal amplitudes for a “microwave-off” condition and for an un-doped reference sample, and thus enables quick and accurate quantification unaffected by the effects of the paramagnetic quenching and the MAS-induced depolarization. The method is also shown to elucidate spatial polarization distribution through the 2IzSz term prepared domain selectively. As a potential application, we also demonstrate 2D DQ-SQ spectroscopy utilizing the 2IzSz term that is generated in a spatially selective manner without using I-S dipolar or J coupling. These salient features may be evolved into a way for characterizing mesoscopic molecular assemblies of medical/biological importance.

Temperature-Dependent Nuclear Spin Relaxation Due to Paramagnetic Dopants Below 30 K: Relevance to DNP-Enhanced Magnetic Resonance Imaging #DNPNMR

Chen, Hsueh-Ying, and Robert Tycko. “Temperature-Dependent Nuclear Spin Relaxation Due to Paramagnetic Dopants Below 30 K: Relevance to DNP-Enhanced Magnetic Resonance Imaging.” The Journal of Physical Chemistry B 122, no. 49 (December 13, 2018): 11731–42.

Dynamic nuclear polarization (DNP) can increase nuclear magnetic resonance (NMR) signal strengths by factors of 100 or more at low temperatures. In magnetic resonance imaging (MRI), signal enhancements from DNP potentially lead to enhancements in image resolution. However, the paramagnetic dopants required for DNP also reduce nuclear spin relaxation times, producing signal losses that may cancel the signal enhancements from DNP. Here we investigate the dependence of 1H NMR relaxation times, including T1ρ and T2, under conditions of Lee–Goldburg 1H–1H decoupling and pulsed spin locking, on temperature and dopant concentration in frozen solutions that contain the trinitroxide compound DOTOPA. We find that relaxation times become longer at temperatures below 10 K, where DOTOPA electron spins become strongly polarized at equilibrium in a 9.39 T magnetic field. We show that the dependences of relaxation times on temperature and DOTOPA concentration can be reproduced qualitatively (although not quantitatively) by detailed simulations of magnetic field fluctuations due to flip-flop transitions in a system of dipole-coupled electron spin magnetic moments. These results have implications for ongoing attempts to reach submicron resolution in inductively detected MRI at very low temperatures.

Tuning nuclear depolarization under MAS by electron T1e #DNPNMR

Lund, Alicia, Asif Equbal, and Songi Han. “Tuning Nuclear Depolarization under MAS by Electron T1e.” Physical Chemistry Chemical Physics, 2018, 19.

Cross-Effect (CE) Dynamic Nuclear Polarization (DNP) mechanism under Magic Angle Spinning (MAS) induces depletion or “depolarization” of the NMR signal, in the absence of microwave irradiation. In this study, the role of T1e on nuclear depolarization under MAS was tested experimentally by systematically varying the local and global electron spin concentration using mono-, bi- and tri-radicals. These spin systems show different depolarization effects that systematically tracked with their different T1e rates, consistent with theoretical predictions. In order to test whether the effect of T1e is directly or indirectly convoluted with other spin parameters, the tri-radical system was doped with different concentrations of GdCl3, only tuning the T1e rates, while keeping other parameters unchanged. Gratifyingly, the changes in the depolarization factor tracked the changes in the T1e rates. The experimental results are corroborated by quantum mechanics based numerical simulations which recapitulated the critical role of T1e. Simulations showed that the relative orientation of the two g-tensors and e-e dipolar interaction tensors of the CE fulfilling spin pair also plays a major role in determining the extent of depolarization, besides the enhancement. This is expected as orientations influence the efficiency of the various level anti-crossings or the “rotor events” under MAS. However, experimental evaluation of the empirical spectral diffusion parameter at static condition showed that the local vs. global e-e dipolar interaction network is not a significant variable in the commonly used nitroxide radical system studied here, leaving T1e rates as the major modulator of depolarization.

Continuous wave electron paramagnetic resonance of nitroxide biradicals in fluid solution #DNPNMR

Biradicals are very important polarizing agents used in DNP-enhanced NMR spectroscopy. Specifically in solid-state experiments they often out-perform monoradicals. Understanding the influence of all the different interactions present in a biradical is still ongoing research and only by using liquid and solid state EPR spectroscopy is it possible to characterize, understand and finally optimize polarizing agents for DNP.

Eaton, Sandra S., Lukas B. Woodcock, and Gareth R. Eaton. “Continuous Wave Electron Paramagnetic Resonance of Nitroxide Biradicals in Fluid Solution.” Concepts in Magnetic Resonance Part A, May 25, 2018, e21426.

Nitroxide biradicals have been prepared with electron-electron spin-spin exchange interaction, J, ranging from weak to very strong. EPR spectra of these biradicals in fluid solution depend on the ratio of J to the nitrogen hyperfine coupling, AN, and the rates of interconversion between conformations with different values of J. For relatively rigid biradicals EPR spectra can be simulated as the superposition of AB splitting patterns arising from different combinations of nitrogen nuclear spin states. For more flexible biradicals spectra can be simulated with a Liouville representation of the dynamics that interconvert conformations with different values of J on the EPR timescale. Analysis of spectra, factors that impact J, and examples of applications to chemical and biophysical problems are discussed.

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