Application of the Steady-State Variable Nutation Angle Method for Faster Determinations of Long T 1s-An Approach Useful for the Design of Hyperpolarized MR Molecular Probes.

In the dissolution-dynamic nuclear polarization technique, molecular probes with long T 1s are preferred. 13C nuclei of small molecules with no directly bonded protons or sp(3 13)C nuclei with proton positions substituted by deuterons may fulfill this requirement. The T 1 determination of such new molecular probes is crucial for the success of the hyperpolarized observation. Although the inversion-recovery approach remained by and large the standard for T 1 measurements, we show here that the steady-state variable nutation angle approach is faster and may be better suited for the determination of relatively long T 1s in thermal equilibrium. Specifically, the T 1 of a new molecular probe, [uniformly labeled (UL)-13C6, UL-2H8]2-deoxy-d-glucose, is determined here and compared to that of [UL-13C6, UL-2H7]d-glucose.

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.

Correlating nuclear frequencies by two-dimensional ELDOR-detected NMR spectroscopy.

ELDOR (Electron Double Resonance)-detected NMR (EDNMR) is a pulse EPR experiment that is used to measure the transition frequencies of nuclear spins coupled to electron spins. These frequencies are further used to determine hyperfine and quadrupolar couplings, which are signatures of the electronic and spatial structures of paramagnetic centers. In recent years, EDNMR has been shown to be particularly useful at high fields/high frequencies, such as W-band (∼95 GHz, ∼3.5 T), for low γ quadrupolar nuclei. Although at high fields the nuclear Larmor frequencies are usually well resolved, the limited resolution of EDNMR still remains a major concern. In this work we introduce a two dimensional, triple resonance, correlation experiment based on the EDNMR pulse sequence, which we term 2D-EDNMR. This experiment allows circumventing the resolution limitation by spreading the signals in two dimensions and the observed correlations help in the assignment of the signals. First we demonstrate the utility of the 2D-EDNMR experiment on a nitroxide spin label, where we observe correlations between (14)N nuclear frequencies. Negative cross-peaks appear between lines belonging to different MS electron spin manifolds. We resolved two independent correlation patterns for nuclear frequencies arising from the EPR transitions corresponding to the (14)N mI=0 and mI=-1 nuclear spin states, which severely overlap in the one dimensional EDNMR spectrum. The observed correlations could be accounted for by considering changes in the populations of energy levels that S=1/2, I=1 spin systems undergo during the pulse sequence. In addition to these negative cross-peaks, positive cross-peaks appear as well. We present a theoretical model based on the Liouville equation and use it to calculate the time evolution of populations of the various energy levels during the 2D-EDNMR experiment and generated simulated 2D-EDMR spectra. These calculations show that the positive cross-peaks appear due to off resonance effects and/or nuclear relaxation effects. These results suggest that the 2D-EDNMR experiment can be also useful for relaxation pathway studies. Finally we present preliminary results demonstrating that 2D-EDNMR can resolve overlapping (33)S and (14)N signals of type 1 Cu(II) center in (33)S enriched Azurin.

Theoretical aspects of dynamic nuclear polarization in the solid state--spin temperature and thermal mixing.

Dynamic nuclear polarization is a method which allows for a dramatic increase of the NMR signals due to polarization transfer between electrons and their neighboring nuclei, via microwave irradiation. These experiments have become popular in recent years due to the ability to create hyper-polarized chemically and biologically relevant molecules, in frozen glass forming mixtures containing free radicals. Three mechanisms have been proposed for the polarization transfer between electrons and their surrounding nuclei in such non-conducting samples: the solid effect and cross effect mechanisms, which are based on quantum mechanics and relaxation on small spin systems, and thermal mixing, which originates from the thermodynamic macroscopic notion of spin temperature. We have recently introduced a spin model, which is based on the density matrix formalism and includes relaxation, and applied it to study the solid effect and cross effect mechanisms on small spin systems. In this publication we use the same model to describe the thermal mixing mechanism, and the creation of spin temperature. This is obtained without relying on the spin temperature formalism. Simulations of small model systems are used on systems with homogeneously and inhomogeneously broadened EPR lines. For the case of a homogeneously broadened line we show that the nuclear enhancement results from the thermal mixing and solid effect mechanisms, and that spin temperatures are created in the system. In the inhomogeneous case the enhancements are attributed to the solid effect and cross effect mechanisms, but not thermal mixing.

Fast passage dynamic nuclear polarization on rotating solids.

Magic Angle Spinning (MAS) Dynamic Nuclear Polarization (DNP) has proven to be a very powerful way to improve the signal to noise ratio of NMR experiments on solids. The experiments have in general been interpreted considering the Solid-Effect (SE) and Cross-Effect (CE) DNP mechanisms while ignoring the influence of sample spinning. In this paper, we show experimental data of MAS-DNP enhancements of (1)H and (13)C in proline and SH3 protein in glass forming water/glycerol solvent containing TOTAPOL. We also introduce a theoretical model that aims at explaining how the nuclear polarization is built in MAS-DNP experiments. By using Liouville space based simulations to include relaxation on two simple spin models, {electron-nucleus} and {electron-electron-nucleus}, we explain how the basic MAS-SE-DNP and MAS-CE-DNP processes work. The importance of fast energy passages and short level anti-crossing is emphasized and the differences between static DNP and MAS-DNP is explained. During a single rotor cycle the enhancement in the {electron-electron-nucleus} system arises from MAS-CE-DNP involving at least three kinds of two-level fast passages: an electron-electron dipolar anti-crossing, a single quantum electron MW encounter and an anti-crossing at the CE condition inducing nuclear polarization in- or decrements. Numerical, powder-averaged, simulations were performed in order to check the influence of the experimental parameters on the enhancement efficiencies. In particular we show that the spinning frequency dependence of the theoretical MAS-CE-DNP enhancement compares favorably with the experimental (1)H and (13)C MAS-DNP enhancements of proline and SH3.

Dynamic Nuclear Polarization in the solid state: a transition between the cross effect and the solid effect.

Proton Dynamic Nuclear Polarization (DNP) experiments were conducted on a 3.4 T homebuilt hybrid pulsed-EPR-NMR spectrometer, on static samples containing 10 mM or 40 mM TEMPOL in frozen glassy solutions of DMSO/water. During DNP experiments proton-NMR signals are enhanced with the help of microwave (MW) irradiation on or close to the Electron Paramagnetic Resonance (EPR) spectrum of the free radicals in the sample, transferring polarization from the free electrons to the nuclei. In the solid state a distinction is made between three DNP enhancement mechanisms: the Solid Effect (SE), the Cross Effect (CE) and Thermal Mixing (TM). In an effort to determine the dominant DNP mechanisms responsible for the enhancement of the nuclear signals, electron and nuclear spin-lattice relaxation rates, enhancement buildup times and microwave (MW) swept DNP spectra were measured as a function of temperature and MW irradiation strength. We observed lineshape variations of the DNP spectra that indicated changes in the relative contributions of SE-DNP and CE-DNP with temperature and MW power. Using a theoretical model describing the SE-DNP and CE-DNP the DNP spectra could be analyzed without involving the TM-DNP mechanism and the relative SE-DNP and CE-DNP contributions to the nuclear enhancement could be determined. From this analysis it follows that lowering the temperature beyond 20 K increases the SE-DNP and decreases the CE-DNP contributions. Possible explanations for this behavior are suggested.

Theoretical aspects of Dynamic Nuclear Polarization in the solid state - the cross effect.

In recent years Dynamic Nuclear Polarization (DNP) signal enhancement techniques have become an important and integral part of modern NMR and MRI spectroscopy. The DNP mechanisms transferring polarization from unpaired electrons to the nuclei in the sample is accomplished by microwave (MW) irradiation. For solid samples a distinction is made between three main enhancement processes: Solid Effect (SE), Cross Effect (CE) and Thermal Mixing (TM) DNP. In a recent study we revisited the solid state SE-DNP mechanism at high magnetic fields, using a spin density operator description involving spin relaxation, for the case of an isolated electron spin interacting with neighboring nuclei. In this publication we extend this study by considering the hyper-polarization of nuclei in systems containing two interacting electrons. In these spin systems both processes SE-DNP and CE-DNP are simultaneously active. As previously, a quantum description taking into account spin relaxation is used to calculate the dynamics of spin systems consisting of interacting electron pairs coupled to (core) nuclei. Numerical simulations are used to demonstrate the dependence of the SE- and CE-DNP enhancements on the MW irradiation power and frequency, on electron, nuclear and cross relaxation mechanisms and on the spin interactions. The influence of the presence of many nuclei on the hyper-polarization of an individual core nucleus is examined, showing the similarities between the two DNP processes. These studies also indicate the advantages of the CE- over the SE-DNP processes, both driving the polarization of the bulk nuclei, via the nuclear dipole-dipole interactions.

A Dynamic Nuclear Polarization spectrometer at 95 GHz/144 MHz with EPR and NMR excitation and detection capabilities.

A spectrometer specifically designed for systematic studies of the spin dynamics underlying Dynamic Nuclear Polarization (DNP) in solids at low temperatures is described. The spectrometer functions as a fully operational NMR spectrometer (144 MHz) and pulse EPR spectrometer (95 GHz) with a microwave (MW) power of up to 300 mW at the sample position, generating a MW B(1) field as high as 800 KHz. The combined NMR/EPR probe comprises of an open-structure horn-reflector configuration that functions as a low Q EPR cavity and an RF coil that can accommodate a 30-50 µl sample tube. The performance of the spectrometer is demonstrated through some basic pulsed EPR experiments, such as echo-detected EPR, saturation recovery and nutation measurements, that enable quantification of the actual intensity of MW irradiation at the position of the sample. In addition, DNP enhanced NMR signals of samples containing TEMPO and trityl are followed as a function of the MW frequency. Buildup curves of the nuclear polarization are recorded as a function of the microwave irradiation time period at different temperatures and for different MW powers.

Dynamic nuclear polarization assisted spin diffusion for the solid effect case.

The dynamic nuclear polarization (DNP) process in solids depends on the magnitudes of hyperfine interactions between unpaired electrons and their neighboring (core) nuclei, and on the dipole-dipole interactions between all nuclei in the sample. The polarization enhancement of the bulk nuclei has been typically described in terms of a hyperfine-assisted polarization of a core nucleus by microwave irradiation followed by a dipolar-assisted spin diffusion process in the core-bulk nuclear system. This work presents a theoretical approach for the study of this combined process using a density matrix formalism. In particular, solid effect DNP on a single electron coupled to a nuclear spin system is considered, taking into account the interactions between the spins as well as the main relaxation mechanisms introduced via the electron, nuclear, and cross-relaxation rates. The basic principles of the DNP-assisted spin diffusion mechanism, polarizing the bulk nuclei, are presented, and it is shown that the polarization of the core nuclei and the spin diffusion process should not be treated separately. To emphasize this observation the coherent mechanism driving the pure spin diffusion process is also discussed. In order to demonstrate the effects of the interactions and relaxation mechanisms on the enhancement of the nuclear polarization, model systems of up to ten spins are considered and polarization buildup curves are simulated. A linear chain of spins consisting of a single electron coupled to a core nucleus, which in turn is dipolar coupled to a chain of bulk nuclei, is considered. The interaction and relaxation parameters of this model system were chosen in a way to enable a critical analysis of the polarization enhancement of all nuclei, and are not far from the values of (13)C nuclei in frozen (glassy) organic solutions containing radicals, typically used in DNP at high fields. Results from the simulations are shown, demonstrating the complex dependences of the DNP-assisted spin diffusion process on variations of the relevant parameters. In particular, the effect of the spin lattice relaxation times on the polarization buildup times and the resulting end polarization are discussed, and the quenching of the polarizations by the hyperfine interaction is demonstrated.

Theoretical aspects of dynamic nuclear polarization in the solid state - the solid effect.

Dynamic nuclear polarization has gained high popularity in recent years, due to advances in the experimental aspects of this methodology for increasing the NMR and MRI signals of relevant chemical and biological compounds. The DNP mechanism relies on the microwave (MW) irradiation induced polarization transfer from unpaired electrons to the nuclei in a sample. In this publication we present nuclear polarization enhancements of model systems in the solid state at high magnetic fields. These results were obtained by numerical calculations based on the spin density operator formalism. Here we restrict ourselves to samples with low electron concentrations, where the dipolar electron-electron interactions can be ignored. Thus the DNP enhancement of the polarizations of the nuclei close to the electrons is described by the Solid Effect mechanism. Our numerical results demonstrate the dependence of the polarization enhancement on the MW irradiation power and frequency, the hyperfine and nuclear dipole-dipole spin interactions, and the relaxation parameters of the system. The largest spin system considered in this study contains one electron and eight nuclei. In particular, we discuss the influence of the nuclear concentration and relaxation on the polarization of the core nuclei, which are coupled to an electron, and are responsible for the transfer of polarization to the bulk nuclei in the sample via spin diffusion.

EPR detected polarization transfer between Gd3+ and protons at low temperature and 3.3 T: the first step of dynamic nuclear polarization.

Electron-electron double resonance pulsed electron paramagnetic resonance (EPR) at 95 GHz (3.3 T) is used to follow the dynamics of the electron spin polarization during the first stages of dynamic nuclear polarization in solids. The experiments were performed on a frozen solution of Gd(+3) (S=7/2) in water/glycerol. Focusing on the central vector -1/2 --> vector +1/2 transition we measured the polarization transfer from the Gd(3+) electron spin to the adjacent (1)H protons. The dependence of the echo detected EPR signal on the length of the microwave irradiation at the EPR "forbidden" transition corresponding to an electron and a proton spin flip is measured for different powers, showing dynamics on the microsecond to millisecond time scales. A theoretical model based on the spin density matrix formalism is suggested to account for this dynamics. The central transition of the Gd(3+) ion is considered as an effective S = 1/2 system and is coupled to (1)H (I = 1/2) nuclei. Simulations based on a single electron-single nucleus four level system are shown to deviate from the experimental results and an alternative approach taking into account the more realistic multinuclei picture is shown to agree qualitatively with the experiments.