Dynamic nuclear polarization with a water-soluble rigid biradical

A new biradical polarizing agent, bTbtk-py, for dynamic nuclear polarization (DNP) experiments in aqueous media is reported. The synthesis is discussed in light of the requirements of the optimum, theoretical, biradical system. To date, the DNP NMR signal enhancement resulting from bTbtk-py is the largest of any biradical in the ideal glycerol/water solvent matrix, ε = 230. EPR and X-ray crystallography are used to characterize the molecule and suggest approaches for further optimizing the biradical distance and relative orientation.     

Deuterated TEKPol Biradicals and the Spin-Diffusion Barrier in MAS DNP

The sensitivity of NMR spectroscopy is considerably enhanced by dynamic nuclear polarization (DNP). In DNP polarization is transferred from unpaired electrons of a polarizing agent to nearby proton spins. In solids, this transfer is followed by the transport of hyperpolarization to the bulk via ¹H-¹H spin diffusion. The efficiency of these steps is critical to obtain high sensitivity gains, but the pathways for polarization transfer in the region near the unpaired electron spins are unclear. Here we report a series of seven deuterated and one fluorinated TEKPol biradicals to probe the effect of deprotonation on MAS DNP at 9.4 T. The experimental results are interpreted with numerical simulations, and our findings support that strong hyperfine couplings to nearby protons determine high transfer rates across the spin diffusion barrier to achieve short build-up times and high enhancements. Specifically, ¹H DNP build-up times increase substantially with TEKPol isotopologues that have fewer hydrogen atoms in the phenyl rings, suggesting that these protons play a crucial role transferring the polarization to the bulk. Based on this new understanding, we have designed a new biradical, NaphPol, which yields significantly increased NMR sensitivity, making it the best performing DNP polarizing agent in organic solvents to date.     

Impact of Gd3+ on DNP of [1-13C]pyruvate doped with trityl OX063, BDPA, or 4-oxo-TEMPO

Hyperpolarized [1-(13)C]pyruvate has become an important diagnostic tracer of normal and aberrant cellular metabolism for in vitro and in vivo NMR spectroscopy (MRS) and imaging (MRI). In pursuit of achieving high NMR signal enhancements in dynamic nuclear polarization (DNP) experiments, we have performed an extensive investigation of the influence of Gd(3+) doping, a parameter previously reported to improve hyperpolarized NMR signals, on the DNP of this compound. [1-(13)C]Pyruvate samples were doped with varying amounts of Gd(3+) and fixed optimal concentrations of free radical polarizing agents commonly used in fast dissolution DNP: trityl OX063 (15 mM), 4-oxo-TEMPO (40 mM), and BDPA (40 mM). In general, we have observed three regions of interest, namely, (i) a monotonic increase in DNP-enhanced nuclear polarization P(dnp) upon increasing the Gd(3+) concentration until a certain threshold concentration c(1) (1-2 mM) is reached, (ii) a region of roughly constant maximum P(dnp) from c(1) until a concentration threshold c(2) (4-5 mM), and (iii) a monotonic decrease in P(dnp) at Gd(3+) concentration c > c(2). Of the three free radical polarizing agents used, trityl OX063 gave the best response to Gd(3+) doping, with a 300% increase in the solid-state nuclear polarization, whereas addition of the optimum Gd(3+) concentration on BDPA and 4-oxo-TEMPO-doped samples only yielded a relatively modest 5-20% increase in the base DNP-enhanced polarization. The increase in P(dnp) due to Gd(3+) doping is ascribed to the decrease in the electronic spin-lattice relaxation T(1e) of the free radical electrons, which plays a role in achieving lower spin temperature T(s) of the nuclear Zeeman system. These results are discussed qualitatively in terms of the spin temperature model of DNP.     

Efficient Dynamic Nuclear Polarization at 800 MHz/527 GHz with Trityl‐Nitroxide Biradicals

Cross‐effect (CE) dynamic nuclear polarization (DNP) is a rapidly developing technique that enhances the signal intensities in magic‐angle spinning (MAS) NMR spectra. We report CE DNP experiments at 211, 600, and 800 MHz using a new series of biradical polarizing agents referred to as TEMTriPols, in which a nitroxide (TEMPO) and a trityl radical are chemically tethered. The TEMTriPol molecule with the optimal performance yields a record ¹H NMR signal enhancement of 65 at 800 MHz at a concentration of 10 mM in a glycerol/water solvent matrix. The CE DNP enhancement for the TEMTriPol biradicals does not decrease as the magnetic field is increased in the manner usually observed for bis‐nitroxides. Instead, the relatively strong exchange interaction between the trityl and nitroxide moieties determines the magnetic field at which the optimum enhancement is observed.     

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.     

A Method for Dynamic Nuclear Polarization Enhancement of Membrane Proteins

Dynamic nuclear polarization (DNP) magic‐angle spinning (MAS) solid‐state NMR (ssNMR) spectroscopy has the potential to enhance NMR signals by orders of magnitude and to enable NMR characterization of proteins which are inherently dilute, such as membrane proteins. In this work spin‐labeled lipid molecules (SL‐lipids), when used as polarizing agents, lead to large and relatively homogeneous DNP enhancements throughout the lipid bilayer and to an embedded lung surfactant mimetic peptide, KL₄. Specifically, DNP MAS ssNMR experiments at 600 MHz/395 GHz on KL₄ reconstituted in liposomes containing SL‐lipids reveal DNP enhancement values over two times larger for KL₄ compared to liposome suspensions containing the biradical TOTAPOL. These findings suggest an alternative sample preparation strategy for DNP MAS ssNMR studies of lipid membranes and integral membrane proteins.     

Bis‐Gadolinium Complexes for Solid Effect and Cross Effect Dynamic Nuclear Polarization

High‐spin complexes act as polarizing agents (PAs) for dynamic nuclear polarization (DNP) in solid‐state NMR spectroscopy and feature promising aspects towards biomolecular DNP. We present a study on bis(Gd‐chelate)s which enable cross effect (CE) DNP owing to spatial confinement of two dipolar‐coupled electron spins. Their well‐defined Gd⋅⋅⋅Gd distances in the range of 1.2–3.4 nm allowed us to elucidate the Gd⋅⋅⋅Gd distance dependence of the DNP mechanism and NMR signal enhancement. We found that Gd⋅⋅⋅Gd distances above 2.1 nm result in solid effect DNP while distances between 1.2 and 2.1 nm enable CE for ¹H, ¹³C, and ¹⁵N nuclear spins. We compare 263 GHz electron paramagnetic resonance (EPR) spectra with the obtained DNP field profiles and discuss possible CE matching conditions within the high‐spin system and the influence of dipolar broadening of the EPR signal. Our findings foster the understanding of the CE mechanism and the design of high‐spin PAs for specific applications of DNP.     

Spin‐Labeled Heparins as Polarizing Agents for Dynamic Nuclear Polarization

A potentially biocompatible class of spin‐labeled macromolecules, spin‐labeled (SL) heparins, and their use as nuclear magnetic resonance (NMR) signal enhancers are introduced. The signal enhancement is achieved through Overhauser‐type dynamic nuclear polarization (DNP). All presented SL‐heparins show high ¹H DNP enhancement factors up to E=?110, which validates that effectively more than one hyperfine line can be saturated even for spin‐labeled polarizing agents. The parameters for the Overhauser‐type DNP are determined and discussed. A striking result is that for spin‐labeled heparins, the off‐resonant electron paramagnetic resonance (EPR) hyperfine lines contribute a non‐negligible part to the total saturation, even in the absence of Heisenberg spin exchange (HSE) and electron spin‐nuclear spin relaxation (T_1ne). As a result, we conclude that one can optimize the use of, for example, biomacromolecules for DNP, for which only small sample amounts are available, by using heterogeneously distributed radicals attached to the molecule.     

A slowly relaxing rigid biradical for efficient dynamic nuclear polarization surface-enhanced NMR spectroscopy: expeditious characterization of functional group manipulation in hybrid materials

A new nitroxide-based biradical having a long electron spin-lattice relaxation time (T(1e)) has been developed as an exogenous polarization source for DNP solid-state NMR experiments. The performance of this new biradical is demonstrated on hybrid silica-based mesostructured materials impregnated with 1,1,2,2-tetrachloroethane radical containing solutions, as well as in frozen bulk solutions, yielding DNP enhancement factors (ε) of over 100 at a magnetic field of 9.4 T and sample temperatures of ~100 K. The effects of radical concentration on the DNP enhancement factors and on the overall sensitivity enhancements (Σ(?)) are reported. The relatively high DNP efficiency of the biradical is attributed to an increased T(1e), which enables more effective saturation of the electron resonance. This new biradical is shown to outperform the polarizing agents used so far in DNP surface-enhanced NMR spectroscopy of materials, yielding a 113-fold increase in overall sensitivity for silicon-29 CPMAS spectra as compared to conventional NMR experiments at room temperature. This results in a reduction in experimental times by a factor >12,700, making the acquisition of (13)C and (15)N one- and two-dimensional NMR spectra at natural isotopic abundance rapid (hours). It has been used here to monitor a series of chemical reactions carried out on the surface functionalities of a hybrid organic-silica material.     

(2)H-decoupling-accelerated (1)H spin diffusion in dynamic nuclear polarization with photoexcited triplet electrons

In dynamic nuclear polarization (DNP) experiments applied to organic solids for creating nonequilibrium, high (1)H spin polarization, an efficient buildup of (1)H polarization is attained by partially deuterating the material of interest with an appropriate (1)H concentration. In such a dilute (1)H spin system, it is shown that the (1)H spin diffusion rate and thereby the buildup efficiency of (1)H polarization can further be enhanced by continually applying radiofrequency irradiation for deuterium decoupling during the DNP process. As experimentally confirmed in this work, the electron spin polarization of the photoexcited triplet state is mainly transferred only to those (1)H spins, which are in the vicinity of the electron spins, and (1)H spin diffusion transports the localized (1)H polarization over the whole sample volume. The (1)H spin diffusion coefficients are estimated from DNP repetition interval dependence of the initial buildup rate of (1)H polarization, and the result indicates that the spin diffusion coefficient is enhanced by a factor of 2 compared to that without (2)H decoupling.     

Highly bioresistant,hydrophilic and rigidly linked trityl-nitroxide biradicals for cellular high-field dynamic nuclear polarization

Cellular dynamic nuclear polarization (DNP) has been an effective means of overcoming the intrinsic sensitivity limitations of solid-state nuclear magnetic resonance (ssNMR) spectroscopy, thus enabling atomic-level biomolecular characterization in native environments. Achieving DNP signal enhancement relies on doping biological preparations with biradical polarizing agents (PAs). Unfortunately, PA performance within cells is often limited by their sensitivity to the reductive nature of the cellular lumen. Herein, we report the synthesis and characterization of a highly bioresistant and hydrophilic PA (StaPol-1) comprising the trityl radical OX063 ligated to a gem-diethyl pyrroline nitroxide via a rigid piperazine linker. EPR experiments in the presence of reducing agents such as ascorbate and in HeLa cell lysates demonstrate the reduction resistance of StaPol-1. High DNP enhancements seen in small molecules, proteins and cell lysates at 18.8 T confirm that StaPol-1 is an excellent PA for DNP ssNMR investigations of biomolecular systems at high magnetic fields in reductive environments.

The new polarizing agent combines extraordinarily high bioresistance with excellent DNP performance at high magnetic fields and provides uniform DNP enhancement of 183 at 18.8 T for [¹³C, ¹⁵N]-ubiquitin in HeLa cell lysates.     

Rigid orthogonal bis-TEMPO biradicals with improved solubility for dynamic nuclear polarization

The synthesis and characterization of oxidized bis-thioketal-trispiro dinitroxide biradicals that orient the nitroxides in a rigid, approximately orthogonal geometry are reported. The biradicals show better performance as polarizing agents in dynamic nuclear polarization (DNP) NMR experiments as compared to biradicals lacking the constrained geometry. In addition, the biradicals display improved solubility in aqueous media due to the presence of polar sulfoxides. The results suggest that the orientation of the radicals is not dramatically affected by the oxidation state of the sulfur atoms in the biradical, and we conclude that a biradical polarizing agent containing a mixture of oxidation states can be used for improved solubility without a loss in performance.     

Overhauser DNP with 15N labelled Frémy's salt at 0.35 Tesla

The effectiveness of dynamic nuclear polarization (DNP) as a tool to enhance the sensitivity of liquid state NMR critically depends on the choice of the optimal polarizer molecule. In this study the performance of (15)N labelled Frémy's salt as a polarizing agent in Overhauser DNP is investigated in detail at X-band (0.35 T, 9.7 GHz EPR, 15 MHz (1)H NMR) and compared to that of TEMPONE-D,(15)N employed in previous studies. Both radicals provide similar maximum enhancements of the solvent water protons under similar conditions but a different saturation behaviour. The factors determining the enhancement and effective saturation were measured independently by EPR, ELDOR and NMRD and are shown to fulfil the Overhauser equation. In particular, following the theory of EPR saturation we provide analytical solutions for the dependence of the enhancement on the microwave field strength in terms of saturation transfer between two coupled hyperfine lines undergoing spin exchange. The negative charge of the radical in Frémy's salt solutions can explain the peculiar properties of this polarizing agent and indicates different suitable application areas for the two types of nitroxide radicals.     

Correlation of the EPR properties of perchlorotriphenylmethyl radicals and their efficiency as DNP polarizers

Water soluble perchlorinated trityl (PTM) radicals were found to be effective 95 GHz DNP (dynamic nuclear polarization) polarizers in ex situ (dissolution) (13)C DNP (Gabellieri et al., Angew Chem., Int. Ed. 2010, 49, 3360). The degree of the nuclear polarization obtained was reported to be dependent on the position of the chlorine substituents on the trityl skeleton. In addition, on the basis of the DNP frequency sweeps it was suggested that the (13)C NMR signal enhancement is mediated by the Cl nuclei. To understand the DNP mechanism of the PTM radicals we have explored the 95 GHz EPR characteristics of these radicals that are relevant to their performance as DNP polarizers. The EPR spectra of the radicals revealed axially symmetric g-tensors. A comparison of the spectra with the (13)C DNP frequency sweeps showed that although the solid effect mechanism is operational the DNP frequency sweeps reveal some extra width suggesting that contributions from EPR forbidden transitions involving (35,37)Cl nuclear flips are likely. This was substantiated experimentally by ELDOR (electron-electron double resonance) detected NMR measurements, which map the EPR forbidden transitions, and ELDOR experiments that follow the depolarization of the electron spin upon irradiation of the forbidden EPR transitions. DFT (density functional theory) calculations helped to assign the observed transitions and provided the relevant spin Hamiltonian parameters. These results show that the (35,37)Cl hyperfine and nuclear quadrupolar interactions cause a considerable nuclear state mixing at 95 GHz thus facilitating the polarization of the Cl nuclei upon microwave irradiation. Overlap of Cl nuclear frequencies and the (13)C Larmor frequency further facilitates the polarization of the (13)C nuclei by spin diffusion. Calculation of the (13)C DNP frequency sweep based on the Cl nuclear polarization showed that it does lead to an increase in the width of the spectra, improving the agreement with the experimental sweeps, thus supporting the existence of a new heteronuclear assisted DNP mechanism.     

TOTAPOL: a biradical polarizing agent for dynamic nuclear polarization experiments in aqueous media

In a previous publication, we described the use of biradicals, in that case two TEMPO molecules tethered by an ethylene glycol chain of variable length, as polarizing agents for microwave driven dynamic nuclear polarization (DNP) experiments. The use of biradicals in place of monomeric paramagnetic centers such as TEMPO yields enhancements that are a factor of approximately 4 larger (epsilon approximately 175 at 5 T and 90 K) and concurrently the concentration of the polarizing agent is a factor of 4 smaller (10 mM electron spins), reducing the residual electron nuclear dipole broadening. In this paper we describe the synthesis and characterization by EPR and DNP/NMR of an improved polarizing agent 1-(TEMPO-4-oxy)-3-(TEMPO-4-amino)propan-2-ol (TOTAPOL). Under the same experimental conditions and using 2.5 mm magic angle rotors, this new biradical yields larger enhancements (epsilon approximately 290) at lower concentrations (6 mM electron spins) and has the additional important property that it is compatible with experiments in aqueous media, including salt solutions commonly used in the study of proteins and nucleic acids.     

High-frequency dynamic nuclear polarization using mixtures of TEMPO and trityl radicals

In a previous communication [Hu et al., J. Am. Chem. Soc. 126, 10844 (2004)], an approach was demonstrated that improves the efficiency of the cross-effect polarization mechanism employed in high field dynamic nuclear polarization (DNP) experiments. Specifically, it was shown that tethering two TEMPO (2,2,6,6-tetramethylpiperidin-1-oxyl) radicals increases the electron-electron dipole coupling from approximately 1 MHz in solutions of monomeric TEMPO to approximately 25 MHz in a tethered biradical. The larger coupling resulted in an increase in the DNP enhancements by a factor of approximately 3-4, from 45-50 to approximately 165. Here, a second approach to improving the efficiency of the polarization process is described that involves approximately satisfying the matching condition |omega(2e)-omega(1e)|=omega(n), where omega(2e) and omega(1e) are two frequencies in the electron paramagnetic resonance (EPR) spectrum and omega(n) is the Larmor frequency of the nuclear spins being polarized. Specifically, in a mixture of TEMPO and trityl [tris (8-carboxy-2,2,6,6-tetramethyl(-d3)-benzo[1,2d:4,5-d']bis(1,3)dithiol-4-yl) methyl] radicals, the intensity maxima in the EPR spectra of these two species are approximately separated by the (1)H NMR frequency. In this case the frequency difference between the g(yy) value of TEMPO and the narrow pseudo-isotropic g-value of trityl is approximately 224 MHz and the (1)H Larmor frequency is 211 MHz. The optimal magnetic field for DNP using the mixtures was found to coincide with the trityl EPR resonance. At 90 K and 5 T, a mixture of 20 mM TEMPO and 20 mM trityl enhanced the (1)H polarization by a factor of approximately 160, an improvement over the enhancement of approximately 50 with 40 mM TEMPO. The reasons for the improvement are discussed and evidence is presented suggesting that DNP enhancement can be improved further by tethering TEMPO and trityl or two similar radicals.     

Matrix‐Free DNP‐Enhanced NMR Spectroscopy of Liposomes Using a Lipid‐Anchored Biradical

Magic‐angle spinning dynamic nuclear polarization (MAS‐DNP) has been proven to be a powerful technique to enhance the sensitivity of solid‐state NMR (SSNMR) in a wide range of systems. Here, we show that DNP can be used to polarize lipids using a lipid‐anchored polarizing agent. More specifically, we introduce a C16‐functionalized biradical, which allows localization of the polarizing agents in the lipid bilayer and DNP experiments to be performed in the absence of excess cryo‐protectant molecules (glycerol, dimethyl sulfoxide, etc.). This constitutes another original example of the matrix‐free DNP approach that we recently introduced.     

High-field Overhauser dynamic nuclear polarization in silicon below the metal-insulator transition

Single crystal silicon is an excellent system to explore dynamic nuclear polarization (DNP), as it exhibits a continuum of properties from metallic to insulating as a function of doping concentration and temperature. At low doping concentrations DNP has been observed to occur via the solid effect, while at very high-doping concentrations an Overhauser mechanism is responsible. Here we report the hyperpolarization of (29)Si in n-doped silicon crystals, with doping concentrations in the range of (1-3)?× 10(17) cm(-3). In this regime exchange interactions between donors become extremely important. The sign of the enhancement in our experiments and its frequency dependence suggest that the (29)Si spins are directly polarized by donor electrons via an Overhauser mechanism within exchange-coupled donor clusters. The exchange interaction between donors only needs to be larger than the silicon hyperfine interaction (typically much smaller than the donor hyperfine coupling) to enable this Overhauser mechanism. Nuclear polarization enhancement is observed for a range of donor clusters in which the exchange energy is comparable to the donor hyperfine interaction. The DNP dynamics are characterized by a single exponential time constant that depends on the microwave power, indicating that the Overhauser mechanism is a rate-limiting step. Since only about 2% of the silicon nuclei are located within 1 Bohr radius of the donor electron, nuclear spin diffusion is important in transferring the polarization to all the spins. However, the spin-diffusion time is much shorter than the Overhauser time due to the relatively weak silicon hyperfine coupling strength. In a 2.35 T magnetic field at 1.1 K, we observed a DNP enhancement of 244 ± 84 resulting in a silicon polarization of 10.4 ± 3.4% following 2 h of microwave irradiation.     

Solid effect dynamic nuclear polarization and polarization pathways

Using dynamic nuclear polarization (DNP)/nuclear magnetic resonance instrumentation that utilizes a microwave cavity and a balanced rf circuit, we observe a solid effect DNP enhancement of 94 at 5 T and 80 K using trityl radical as the polarizing agent. Because the buildup rate of the solid effect increases with microwave field strength, we obtain a sensitivity gain of 128. The data suggest that higher microwave field strengths would lead to further improvements in sensitivity. In addition, the observation of microwave field dependent enhancements permits us to draw conclusions about the path that polarization takes during the DNP process. By measuring the time constant for the polarization buildup and enhancement as a function of the microwave field strength, we are able to compare models of polarization transfer, and show that the major contribution to the bulk polarization arises via direct transfer from electrons, rather than transferring first to nearby nuclei and then transferring to bulk nuclei in a slow diffusion step. In addition, the model predicts that nuclei near the electron receive polarization that can relax, decrease the electron polarization, and attenuate the DNP enhancement. The magnitude of this effect depends on the number of near nuclei participating in the polarization transfer, hence the size of the diffusion barrier, their T(1), and the transfer rate. Approaches to optimizing the DNP enhancement are discussed.     

Quantum mechanical theory of dynamic nuclear polarization in solid dielectrics

Microwave driven dynamic nuclear polarization (DNP) is a process in which the large polarization present in an electron spin reservoir is transferred to nuclei, thereby enhancing NMR signal intensities. In solid dielectrics there are three mechanisms that mediate this transfer--the solid effect (SE), the cross effect (CE), and thermal mixing (TM). Historically these mechanisms have been discussed theoretically using thermodynamic parameters and average spin interactions. However, the SE and the CE can also be modeled quantum mechanically with a system consisting of a small number of spins and the results provide a foundation for the calculations involving TM. In the case of the SE, a single electron-nuclear spin pair is sufficient to explain the polarization mechanism, while the CE requires participation of two electrons and a nuclear spin, and can be used to understand the improved DNP enhancements observed using biradical polarizing agents. Calculations establish the relations among the electron paramagnetic resonance (EPR) and nuclear magnetic resonance (NMR) frequencies and the microwave irradiation frequency that must be satisfied for polarization transfer via the SE or the CE. In particular, if δ, Δ < ω(0I), where δ and Δ are the homogeneous linewidth and inhomogeneous breadth of the EPR spectrum, respectively, we verify that the SE occurs when ω(M) = ω(0S) ± ω(0I), where ω(M), ω(0S) and ω(0I) are, respectively, the microwave, and the EPR and NMR frequencies. Alternatively, when Δ > ω(0I) > δ, the CE dominates the polarization transfer. This two-electron process is optimized when ω(0S(1))-ω(0S(2)) = ω(0I) and ω(M)~ω(0S(1)) or ω(0S(2)), where ω(0S(1)) and ω(0S(2)) are the EPR Larmor frequencies of the two electrons. Using these matching conditions, we calculate the evolution of the density operator from electron Zeeman order to nuclear Zeeman order for both the SE and the CE. The results provide insights into the influence of the microwave irradiation field, the external magnetic field, and the electron-electron and electron-nuclear interactions on DNP enhancements.