Zero field splitting fluctuations induced phase relaxation of Gd3+ in frozen solutions at cryogenic temperatures

Optimisation of dynamic nuclear polarisation using "off-the-shelf" Gd(III)-based polarising agents

Complexes of paramagnetic metal ions, in particular Gd3+, have been demonstrated as efficient polarising agents for magic-angle spinning (MAS) dynamic nuclear polarisation (DNP). We recently demonstrated that commercially available and inexpensive Gd(NO3)3 is suitable for use as an "off-the-shelf" MAS DNP polarising agent, providing promising sensitivity enhancements to 1H, 13C, and 15N NMR signals. Here we expand upon this approach by investigating the impact of the Gd(NO3)3 concentration and by exploring a larger range of readily available Gd3+ sources. We found that a Gd(NO3)3 concentration of 20 mM in the case of 1H and 13C, and 40 mM in the case of 15N, offers optimum signal enhancements and is rationalised as a trade-off between DNP enhancements, polarisation build-up times, and electron paramagnetic resonance (EPR) spin-spin relaxation times. We determined that a range of different gadolinium compounds (GdCl3, Gd2(SO4)3, GdBr3, and Gd(OAc)3) are also suitable for use as polarising agents and yield 1H, 13C, and 15N signal enhancements of variable values. Gd(OAc)3 yields lower signal enhancements, which is proposed to be the result of greater local asymmetry at the Gd3+ centre leading to EPR line broadening, and the methyl group in the acetate ion acting as a relaxation sink and limiting the nuclear polarisation available.

Extending the Range of Distances Accessible by 19F Electron-Nuclear Double Resonance in Proteins Using High-Spin Gd(III) Labels

Fluorine electron-nuclear double resonance (19F ENDOR) has recently emerged as a valuable tool in structural biology for distance determination between F atoms and a paramagnetic center, either intrinsic or conjugated to a biomolecule via spin labeling. Such measurements allow access to distances too short to be measured by double electron-electron resonance (DEER). To further extend the accessible distance range, we exploit the high-spin properties of Gd(III) and focus on transitions other than the central transition (|-1/2⟩ ↔ |+1/2⟩), that become more populated at high magnetic fields and low temperatures. This increases the spectral resolution up to ca. 7 times, thus raising the long-distance limit of 19F ENDOR almost 2-fold. We first demonstrate this on a model fluorine-containing Gd(III) complex with a well-resolved 19F spectrum in conventional central transition measurements and show quantitative agreement between the experimental spectra and theoretical predictions. We then validate our approach on two proteins labeled with 19F and Gd(III), in which the Gd-F distance is too long to produce a well-resolved 19F ENDOR doublet when measured at the central transition. By focusing on the |-5/2⟩ ↔ |-3/2⟩ and |-7/2⟩ ↔ |-5/2⟩ EPR transitions, a resolution enhancement of 4.5- and 7-fold was obtained, respectively. We also present data analysis strategies to handle contributions of different electron spin manifolds to the ENDOR spectrum. Our new extended 19F ENDOR approach may be applicable to Gd-F distances as large as 20 Å, widening the current ENDOR distance window.

Gadolinium Spin Decoherence Mechanisms at High Magnetic Fields

Favorable relaxation processes, high-field spectral properties, and biological compatibility have made spin-7/2 Gd3+-based spin labels an increasingly popular choice for protein structure studies using high-field electron paramagnetic resonance. However, high-field relaxation and decoherence in ensembles of half-integer high-spin systems, such as Gd3+, remain poorly understood. We report spin-lattice (T1) and phase memory (TM) relaxation times at 8.6 T (240 GHz), and we present the first comprehensive model of high-field, high-spin decoherence accounting for both the electron spin concentration and temperature. The model includes four principal mechanisms driving decoherence: energy-conserving electron spin flip-flops, direct "T1" spin-lattice relaxation-driven electron spin flip processes, indirect T1-driven flips of nearby electron spins, and nuclear spin flip-flops. Mechanistic insight into decoherence can inform the design of experiments making use of Gd3+ as spin probes or relaxivity agents and can be used to measure local average interspin distances as long as 17 nm.

Design Principles for the Development of Gd(III) Polarizing Agents for Magic Angle Spinning Dynamic Nuclear Polarization

Nuclear magnetic resonance suffers from an intrinsically low sensitivity, which can be overcome by dynamic nuclear polarization (DNP). Gd(III) complexes are attractive exogenous polarizing agents for magic angle spinning (MAS) DNP due to their high chemical stability in contrast to nitroxide-based radicals. However, even the state-of-the-art Gd(III) complexes have so far provided relatively low DNP signal enhancements of ca. 36 in comparison to standard DNP biradicals, which show enhancements of over 200. Here, we report a series of new Gd(III) complexes for DNP and show that the observed DNP enhancements of the new and existing Gd(III) complexes are inversely proportional to the square of the zero-field splitting (ZFS) parameter D, which is in turn determined by the ligand-type and the local coordination environment. The experimental DNP enhancements at 9.4 T and the ZFS parameters measured with pulsed electron paramagnetic resonance (EPR) spectroscopy agree with the above model, paving the way for the development of more efficient Gd(III) polarizing agents.

The decay of the refocused Hahn echo in double electron-electron resonance (DEER) experiments

Double electron-electron resonance (DEER) is a pulse electron paramagnetic resonance (EPR) technique that measures distances between paramagnetic centres. It utilizes a four-pulse sequence based on the refocused Hahn spin echo. The echo decays with increasing pulse sequence length 2 ( τ 1 + τ 2 ) , where τ 1 and τ 2 are the two time delays. In DEER, the value of τ 2 is determined by the longest inter-spin distance that needs to be resolved, and τ 1 is adjusted to maximize the echo amplitude and, thus, sensitivity. We show experimentally that, for typical spin centres (nitroxyl, trityl, and Gd(III)) diluted in frozen protonated solvents, the largest refocused echo amplitude for a given τ 2 is obtained neither at very short τ 1 (which minimizes the pulse sequence length) nor at τ 1 = τ 2 (which maximizes dynamic decoupling for a given total sequence length) but rather at τ 1 values smaller than τ 2 . Large-scale spin dynamics simulations based on the coupled cluster expansion (CCE), including the electron spin and several hundred neighbouring protons, reproduce the experimentally observed behaviour almost quantitatively. They show that electron spin dephasing is driven by solvent protons via the flip-flop coupling among themselves and their hyperfine couplings to the electron spin.

Characteristics of Gd(III) spin labels for the study of protein conformations

Gd(III) complexes are currently established as spin labels for structural studies of biomolecules using pulse dipolar electron paramagnetic resonance (PD-EPR) techniques. This has been achieved by the availability of medium- and high-field spectrometers, understanding the spin physics underlying the spectroscopic properties of high spin Gd(III) (S=7/2) pairs and their dipolar interaction, the design of well-defined model compounds and optimization of measurement techniques. In addition, a variety of Gd(III) chelates and labeling schemes have allowed a broad scope of applications. In this review, we provide a brief background of the spectroscopic properties of Gd(III) pertinent for effective PD-EPR measurements and focus on the various labels available to date. We report on their use in PD-EPR applications and highlight their pros and cons for particular applications. We also devote a section to recent in-cell structural studies of proteins using Gd(III), which is an exciting new direction for Gd(III) spin labeling.

Dynamical decoupling in water-glycerol glasses: a comparison of nitroxides, trityl radicals and gadolinium complexes

Our previous study on nitroxides in o-terphenyl (OTP) revealed two separable decoherence processes at low temperatures, best captured by the sum of two stretched exponentials (SSE) model. Dynamical decoupling (DD) extends both associated dephasing times linearly for 1 to 5 refocusing pulses [Soetbeer et al., Phys. Chem. Chem. Phys., 2018, 20, 1615]. Here we demonstrate an analogous DD behavior of water-soluble nitroxides in water-glycerol glass by using nitroxide and/or solvent deuteration for component assignment. Compared to the conventional Hahn experiment, we show that Carr-Purcell and Uhrig DD schemes are superior in resolving and identifying active dephasing mechanisms. Thereby, we observe a partial coherence loss to intramolecular nitroxide and trityl nuclei that can be alleviated, while the zero field splitting-induced losses for gadolinium labels cannot be refocused and contribute even at the central transition of this spin-7/2 system. Independent of the studied spin system, Uhrig DD leads to a characteristic convex dephasing envelope in both protonated water-glycerol and OTP glass, thus outperforming the Carr-Purcell scheme.

High-sensitivity Gd3+-Gd3+ EPR distance measurements that eliminate artefacts seen at short distances

Gadolinium complexes are attracting increasing attention as spin labels for EPR dipolar distance measurements in biomolecules and particularly for in-cell measurements. It has been shown that flip-flop transitions within the central transition of the high-spin Gd3 + ion can introduce artefacts in dipolar distance measurements, particularly when measuring distances less than 3 nm. Previous work has shown some reduction of these artefacts through increasing the frequency separation between the two frequencies required for the double electron-electron resonance (DEER) experiment. Here we use a high-power (1 kW), wideband, non-resonant system operating at 94 GHz to evaluate DEER measurement protocols using two stiff Gd(III) rulers, consisting of two b i s -Gd3 + -PyMTA complexes, with separations of 2.1 nm and 6.0 nm, respectively. We show that by avoiding the - 1 2 → 1 2  central transition completely, and placing both the pump and the observer pulses on either side of the central transition, we can now observe apparently artefact-free spectra and narrow distance distributions, even for a Gd-Gd distance of 2.1 nm. Importantly we still maintain excellent signal-to-noise ratio and relatively high modulation depths. These results have implications for in-cell EPR measurements at naturally occurring biomolecule concentrations.

Chromium(iii)-based potential molecular quantum bits with long coherence times

Molecular quantum bits based on copper(ii) or vanadium(iv) have been shown to possess long coherence times on multiple occasions. In contrast, studies in which non-spin-½ ions are employed are relatively scarce. High-spin ions provide additional states that can be used to encode further quantum bits. Furthermore, an optical rather than a microwave readout of molecular quantum bits is highly desirable, because in principle it could allow addressing at the single quantum bit level. The chromium(iii) complex [Cr(ddpd)2]3+ (ddpd = N,N'-dimethyl-N,N'-dipyridine-2-yl-pyridine-2,6-diamine) combines both the large spin (S = 3/2) and optical activity (strong, long lived luminescence). Here we demonstrate that the compound possesses coherence times of up to 8.4(1) μs, which are much longer (at least three times) than those for other chromium(iii)-based compounds. On the other hand, it is proved to be impossible to read out or influence the quantum state by optical means, underlining that further work is needed in this direction.

Intermolecular background decay in RIDME experiments

Theoretical and experimental studies of the RIDME background reveal electron and nuclear spectral diffusion contributions.

Multi-step phase-cycling in a free-electron laser-powered pulsed electron paramagnetic resonance spectrometer

Electron paramagnetic resonance (EPR) is a powerful tool for research in chemistry, biology, physics and materials science, which can benefit significantly from moving to frequencies above 100 GHz. In pulsed EPR spectrometers driven by powerful sub-THz oscillators, such as the free electron laser (FEL)-powered EPR spectrometer at UCSB, control of the duration, power and relative phases of the pulses in a sequence must be performed at the frequency and power level of the oscillator. Here we report on the implementation of an all-quasioptical four-step phase cycling procedure carried out directly at the kW power level of the 240 GHz pulses used in the FEL-powered EPR spectrometer. Phase shifts are introduced by modifying the optical path length of a 240 GHz pulse with precision-machined dielectric plates in a procedure we call phase cycling with optomechanical phase shifters (POPS), while numerical receiver phase cycling is implemented in post-processing. The POPS scheme was successfully used to reduce experimental dead times, enabling pulsed EPR of fast-relaxing spin systems such as gadolinium complexes at temperatures above 190 K. Coherence transfer pathway selection with POPS was used to perform spin echo relaxation experiments to measure the phase memory time of P1 centers in diamond in the presence of a strong unwanted FID signal in the background. The large excitation bandwidth of FEL-EPR, together with phase cycling, enabled the quantitative measurement of instantaneous electron spectral diffusion, from which the P1 center concentration was estimated to within 10%. Finally, phase cycling enabled saturation-recovery measurements of T1 in a trityl-water solution at room temperature - the first FEL-EPR measurement of electron T1.

Quantitative analysis of zero-field splitting parameter distributions in Gd(iii) complexes

The magnetic properties of paramagnetic species with spin S > 1/2 are parameterized by the familiar g tensor as well as "zero-field splitting" (ZFS) terms that break the degeneracy between spin states even in the absence of a magnetic field. In this work, we determine the mean values and distributions of the ZFS parameters D and E for six Gd(iii) complexes (S = 7/2) and critically discuss the accuracy of such determination. EPR spectra of the Gd(iii) complexes were recorded in glassy frozen solutions at 10 K or below at Q-band (∼34 GHz), W-band (∼94 GHz) and G-band (240 GHz) frequencies, and simulated with two widely used models for the form of the distributions of the ZFS parameters D and E. We find that the form of the distribution of the ZFS parameter D is bimodal, consisting roughly of two Gaussians centered at D and -D with unequal amplitudes. The extracted values of D (σD) for the six complexes are, in MHz: Gd-NO3Pic, 485 ± 20 (155 ± 37); Gd-DOTA/Gd-maleimide-DOTA, -714 ± 43 (328 ± 99); iodo-(Gd-PyMTA)/MOMethynyl-(Gd-PyMTA), 1213 ± 60 (418 ± 141); Gd-TAHA, 1361 ± 69 (457 ± 178); iodo-Gd-PCTA-[12], 1861 ± 135 (467 ± 292); and Gd-PyDTTA, 1830 ± 105 (390 ± 242). The sign of D was adjusted based on the Gaussian component with larger amplitude. We relate the extracted P(D) distributions to the structure of the individual Gd(iii) complexes by fitting them to a model that superposes the contribution to the D tensor from each coordinating atom of the ligand. Using this model, we predict D, σD, and E values for several additional Gd(iii) complexes that were not measured in this work. The results of this paper may be useful as benchmarks for the verification of quantum chemical calculations of ZFS parameters, and point the way to designing Gd(iii) complexes for particular applications and estimating their magnetic properties a priori.

Improved sensitivity for W-band Gd(III)-Gd(III) and nitroxide-nitroxide DEER measurements with shaped pulses

Chirp and shaped pulses have been recently shown to be highly advantageous for improving sensitivity in DEER (double electron-electron resonance, also called PELDOR) measurements due to their large excitation bandwidth. The implementation of such pulses for pulse EPR has become feasible due to the availability of arbitrary waveform generators (AWG) with high sampling rates to support pulse shaping for pulses with tens of nanoseconds duration. Here we present a setup for obtaining chirp pulses on our home-built W-band (95GHz) spectrometer and demonstrate its performance on Gd(III)-Gd(III) and nitroxide-nitroxide DEER measurements. We carried out an extensive optimization procedure on two model systems, Gd(III)-PyMTA-spacer-Gd(III)-PyMTA (Gd-PyMTA ruler; zero-field splitting parameter (ZFS) D∼1150MHz) as well as nitroxide-spacer-nitroxide (nitroxide ruler) to evaluate the applicability of shaped pulses to Gd(III) complexes and nitroxides, which are two important classes of spin labels used in modern DEER/EPR experiments. We applied our findings to ubiquitin, doubly labeled with Gd-DOTA-monoamide (D∼550MHz) asa model for a system with a small ZFS. Our experiments were focused on the questions (i) what are the best conditions for positioning of the detection frequency, (ii) which pump pulse parameters (bandwidth, positioning in the spectrum, length) yield the best signal-to-noise ratio (SNR) improvements when compared to classical DEER, and (iii) how do the sample's spectral parameters influence the experiment. For the nitroxide ruler, we report an improvement of up to 1.9 in total SNR, while for the Gd-PyMTA ruler the improvement was 3.1-3.4 and for Gd-DOTA-monoamide labeled ubiquitin it was a factor of 1.8. Whereas for the Gd-PyMTA ruler the two setups pump on maximum and observe on maximum gave about the same improvement, for Gd-DOTA-monoamide a significant difference was found. In general the choice of the best set of parameters depends on the D parameter of the Gd(III) complex.

Gd(III) complexes as paramagnetic tags: Evaluation of the spin delocalization over the nuclei of the ligand

Complexes of the Gd(III) ion are currently being established as spin labels for distance determination in biomolecules by pulse dipolar spectroscopy. Because Gd(III) is an f ion, one expects electron spin density to be localized on the Gd(III) ion - an important feature for the mentioned application. Most of the complex ligands have nitrogens as Gd(III) coordinating atoms. Therefore, measurement of the (14)N hyperfine coupling gives access to information on the localization of the electron spin on the Gd(III) ion. We carried out W-band, 1D and 2D (14)N and (1)H ENDOR measurements on the Gd(III) complexes Gd-DOTA, Gd-538, Gd-595, and Gd-PyMTA that serve as spin labels for Gd-Gd distance measurements. The obtained (14)N spectra are particularly well resolved, revealing both the hyperfine and nuclear quadrupole splittings, which were assigned using 2D Mims ENDOR experiments. Additionally, the spectral contributions of the two different types of nitrogen atoms of Gd-PyMTA, the aliphatic N atom and the pyridine N atom, were distinguishable. The (14)N hyperfine interaction was found to have a very small isotropic hyperfine component of -0.25 to -0.37MHz. Furthermore, the anisotropic hyperfine interactions with the (14)N nuclei and with the non-exchangeable protons of the ligands are well described by the point-dipole approximation using distances derived from the crystal structures. We therefore conclude that the spin density is fully localized on the Gd(III) ion and that the spin density distribution over the nuclei of the ligands is rightfully ignored when analyzing distance measurements.

RIDME distance measurements using Gd(iii) tags with a narrow central transition

Methods based on pulse electron paramagnetic resonance allow measurement of the electron–electron dipolar coupling between two high-spin labels.

Overcoming artificial broadening in Gd3+–Gd3+ distance distributions arising from dipolar pseudo-secular terms in DEER experiments

Double electron–electron resonance (DEER) is used to probe structure of Gd³⁺-tagged biomolecules by determining Gd³⁺–Gd³⁺ distances.

Gd(III) complexes for electron-electron dipolar spectroscopy: Effects of deuteration, pH and zero field splitting

Spectral parameters of Gd(III) complexes are intimately linked to the performance of the Gd(III)-nitroxide or Gd(III)-Gd(III) double electron-electron resonance (DEER or PELDOR) techniques, as well as to that of relaxation induced dipolar modulation enhancement (RIDME) spectroscopy with Gd(III) ions. These techniques are of interest for applications in structural biology, since they can selectively detect site-to-site distances in biomolecules or biomolecular complexes in the nanometer range. Here we report relaxation properties, echo detected EPR spectra, as well as the magnitude of the echo reduction effect in Gd(III)-nitroxide DEER for a series of Gadolinium(III) complexes with chelating agents derived from tetraazacyclododecane. We observed that solvent deuteration does not only lengthen the relaxation times of Gd(III) centers but also weakens the DEER echo reduction effect. Both of these phenomena lead to an improved signal-to-noise ratios or, alternatively, longer accessible distance range in pulse EPR measurements. The presented data enrich the knowledge on paramagnetic Gd(III) chelate complexes in frozen solutions, and can help optimize the experimental conditions for most types of the pulse measurements of the electron-electron dipolar interactions.

Gd(iii)–Gd(iii) EPR distance measurements – the range of accessible distances and the impact of zero field splitting

Gd rulers were designed in the 2–8 nm range for in-depth evaluation of Gd(iii) complexes as spin labels for EPR distance measurements.