Dipolar Electron Paramagnetic Resonance Research Articles

Large dynamics of a phase separating arginine-glycine-rich domain revealed via nuclear and electron spins

Liquid-liquid phase separation is the key process underlying formation of membrane-less compartments in cells. A highly dynamic cellular body with rapid component exchange is Cajal body (CB), which supports the extensive compositional dynamics of the RNA splicing machinery, spliceosome. Here, we select an arginine-glycine (RG)-rich segment of coilin, the major component of CB, establish its RNA-induced phase separation, and through combined use of nuclear magnetic resonance (NMR) and electron paramagnetic resonance (EPR) probes, interrogate its dynamics within the crowded interior of formed droplets. Taking advantage of glycine-based singlet-states, we show that glycines retain a large level of sub-nanoseconds dynamics inside the coilin droplets. Furthermore, the continuous-wave (CW) and electron-electron dipolar (PELDOR) and electron-nucleus hyperfine coupling EPR data (HYSCORE) support the RNA-induced formation of dynamic coilin droplets with high coilin peptide concentrations. The combined NMR and EPR data reveal the high dynamics of the RG-rich coilin within droplets and suggest its potential role in the large dynamics of CBs.

Measuring conformational equilibria in allosteric proteins with time-resolved tmFRET

Proteins are the workhorses of biology, orchestrating a myriad of cellular functions through intricate conformational changes. Protein allostery, the phenomenon where binding of ligands or environmental changes induce conformational rearrangements in the protein, is fundamental to these processes. We have previously shown that transition metal Förster resonance energy transfer (tmFRET) can be used to interrogate the conformational rearrangements associated with protein allostery and have recently introduced novel FRET acceptors utilizing metal-bipyridyl derivatives to measure long (>20 Å) intramolecular distances in proteins. Here, we combine our tmFRET system with fluorescence lifetime measurements to measure the distances, conformational heterogeneity, and energetics of maltose-binding protein, a model allosteric protein. Time-resolved tmFRET captures near-instantaneous snapshots of distance distributions, offering insights into protein dynamics. We show that time-resolved tmFRET can accurately determine distance distributions and conformational heterogeneity of proteins. Our results demonstrate the sensitivity of time-resolved tmFRET in detecting subtle conformational or energetic changes in protein conformations, which are crucial for understanding allostery. In addition, we extend the use of metal-bipyridyl compounds, showing that Cu(phen)2+ can serve as a spin label for pulse dipolar electron paramagnetic resonance (EPR) spectroscopy, a method that also reveals distance distributions and conformational heterogeneity. The EPR studies both establish Cu(phen)2+ as a useful spin label for pulse dipolar EPR and validate our time-resolved tmFRET measurements. Our approach offers a versatile tool for deciphering conformational landscapes and understanding the regulatory mechanisms governing biological processes.

Pulse Dipolar Electron Paramagnetic Resonance Spectroscopy Distance Measurements at Low Nanomolar Concentrations: The CuII-Trityl Case.

Recent sensitivity enhancements in pulse dipolar electron paramagnetic resonance spectroscopy (PDS) have afforded distance measurements at submicromolar spin concentrations. This development opens the path for new science as more biomolecular systems can be investigated at their respective physiological concentrations. Here, we demonstrate that the combination of orthogonal spin-labeling using CuII ions and trityl yields a >3-fold increase in sensitivity compared to that of the established CuII-nitroxide labeling strategy. Application of the recently developed variable-time relaxation-induced dipolar modulation enhancement (RIDME) method yields a further ∼2.5-fold increase compared to the commonly used constant-time RIDME. This overall increase in sensitivity of almost an order of magnitude makes distance measurements in the range of 3 nm with protein concentrations as low as 10 nM feasible, >2 times lower than the previously reported concentration. We expect that experiments at single-digit nanomolar concentrations are imminent, which have the potential to transform biological PDS applications.

Confidence limits in pulse dipolar EPR spectroscopy: estimates for individual measurements.

The distribution of inter-label distances obtained by electron paramagnetic resonance (EPR) pulse dipolar spectroscopies (PDS), such as DEER aka PELDOR, gives a valuable characterization of structure on the nanometer scale. The impact of random experimental noise on such experiments is examined for three independent methods for analysing PDS data: the model-free method with Tikhonov regularization, model-free with Mellin-transformation, and a model-based method. All three methods show negative bias for the mean distance and positive bias for the distribution width. Both biases grow with increasing noise levels. The estimated confidence bands and the uncertainties obtained from a single experimental measurement by the standard bootstrapping or χ2-surface scanning approaches are inconsistent and can exclude the true distance distribution. Yet, both approaches can provide quite valuable support for hypothesis testing in PDS studies.

PDSFit: PDS data analysis in the presence of orientation selectivity, g-anisotropy, and exchange coupling.

Pulsed dipolar electron paramagnetic resonance spectroscopy (PDS), encompassing techniques such as pulsed electron-electron double resonance (PELDOR or DEER) and relaxation-induced dipolar modulation enhancement (RIDME), is a valuable method in structural biology and materials science for obtaining nanometer-scale distance distributions between electron spin centers. An important aspect of PDS is the extraction of distance distributions from the measured time traces. Most software used for this PDS data analysis relies on simplifying assumptions, such as assuming isotropic g-factors of ~2 and neglecting orientation selectivity and exchange coupling. Here, the program PDSFit is introduced, which enables the analysis of PELDOR and RIDME time traces with or without orientation selectivity. It can be applied to spin systems consisting of up to two spin centers with anisotropic g-factors and to spin systems with exchange coupling. It employs a model-based fitting of the time traces using parametrized distance and angular distributions, and parametrized PDS background functions. The fitting procedure is followed by an error analysis for the optimized parameters of the distributions and backgrounds. Using five different experimental data sets published previously, the performance of PDSFit is tested and found to provide reliable solutions.

Structural Dynamics of Protein Interactions Using Site-Directed Spin Labeling of Cysteines to Measure Distances and Rotational Dynamics with EPR Spectroscopy.

Here we review applications of site-directed spin labeling (SDSL) with engineered cysteines in proteins, to study the structural dynamics of muscle and non-muscle proteins, using and developing the electron paramagnetic resonance (EPR) spectroscopic techniques of dipolar EPR, double electron electron resonance (DEER), saturation transfer EPR (STEPR), and orientation measured by EPR. The SDSL technology pioneered by Wayne Hubbell and collaborators has greatly expanded the use of EPR, including the measurement of distances between spin labels covalently attached to proteins and peptides. The Thomas lab and collaborators have applied these techniques to elucidate dynamic interactions in the myosin-actin complex, myosin-binding protein C, calmodulin, ryanodine receptor, phospholamban, utrophin, dystrophin, β-III-spectrin, and Aurora kinase. The ability to design and engineer cysteines in proteins for site-directed covalent labeling has enabled the use of these powerful EPR techniques to measure distances, while showing that they are complementary with optical spectroscopy measurements.

Spectroscopically Orthogonal Labelling to Disentangle Site-Specific Nitroxide Label Distributions

Biomolecular applications of pulse dipolar electron paramagnetic resonance spectroscopy (PDS) are becoming increasingly valuable in structural biology. Site-directed spin labelling of proteins is routinely performed using nitroxides, with paramagnetic metal ions and other organic radicals gaining popularity as alternative spin centres. Spectroscopically orthogonal spin labelling using different types of labels potentially increases the information content available from a single sample. When analysing experimental distance distributions between two nitroxide spin labels, the site-specific rotamer information has been projected into the distance and is not readily available, and the contributions of individual labelling sites to the width of the distance distribution are not obvious from the PDS data. Here, we exploit the exquisite precision of labelling double-histidine (dHis) motifs with CuII chelate complexes. The contribution of this label to the distance distribution widths in model protein GB1 has been shown to be negligible. By combining a dHis CuII labelling site with cysteine-specific nitroxide labelling, we gather insights on the label rotamers at two distinct sites, comparing their contributions to distance distributions based on different in silico modelling approaches and structural models. From this study, it seems advisable to consider discrepancies between different in silico modelling approaches when selecting labelling sites for PDS studies.

Pulse EPR spectroscopy and molecular modeling reveal the origins of the local heterogeneity of dietary fibers

Optimizing human diet by including dietary fibers would be more efficient when the fibers' chain interactions with other molecules are understood in depth. Thereby, it is important to develop methods for characterizing the fiber chain to be able to monitor its structural alterations upon intermolecular interactions. Here, we demonstrate the utility of the electron paramagnetic resonance (EPR) spectroscopy, complemented by simulations in probing the atomistic details of the chain conformations for spin-labeled fibers. Barley β-glucan, a native polysaccharide with linear chain, was utilized as a test fiber system to demonstrate the technique's capabilities. Pulse dipolar EPR data show good agreement with results of the fiber chain modeling, revealing sinuous chain conformations and providing polymer shape descriptors: the gyration tensor, spin-spin distance distribution function, and information about proton density near the spin probe. Results from EPR measurements point to the fiber aggregation in aqueous solution, which agrees with the results of the dynamic light scattering. We propose that the combination of pulse EPR measurements with modeling can be a perfect experimental tool for in-depth structural investigation of dietary fibers and their interaction under such conditions, and that the presented methodology can be extended to other weakly ordered or disordered macromolecules.

The effect of the zero-field splitting in light-induced pulsed dipolar electron paramagnetic resonance (EPR) spectroscopy.

Laser-induced magnetic dipole (LaserIMD) spectroscopy and light-induced double electron-electron resonance (LiDEER) spectroscopy are important techniques in the emerging field of light-induced pulsed dipolar electron paramagnetic resonance (EPR) spectroscopy (light-induced PDS). These techniques use the photoexcitation of a chromophore to the triplet state and measure its dipolar coupling to a neighboring electron spin, which allows the determination of distance restraints. To date, LaserIMD and LiDEER have been analyzed with software tools that were developed for a pair of two spins and that neglected the zero-field splitting (ZFS) of the excited triplet. Here, we explore the limits of this assumption and show that the ZFS can have a significant effect on the shape of the dipolar trace. For a detailed understanding of the effect of the ZFS, a theoretical description for LaserIMD and LiDEER is derived, taking into account the non-secular terms of the ZFS. Simulations based on this model show that the effect of the ZFS is not that pronounced in LiDEER for experimentally relevant conditions. However, the ZFS leads to an additional decay in the dipolar trace in LaserIMD. This decay is not that pronounced in Q-band but can be quite noticeable for lower magnetic field strengths in X-band. Experimentally recorded LiDEER and LaserIMD data confirm these findings. It is shown that ignoring the ZFS in the data analysis of LaserIMD traces can lead to errors in the obtained modulation depths and background decays. In X-band, it is additionally possible that the obtained distance distribution is plagued by long distance artifacts.

Flopping-mode electron dipole spin resonance in the strong-driving regime

Achieving high-fidelity control of spin qubits with conventional electron dipole spin resonance (EDSR) requires large magnetic field gradients of about $1\phantom{\rule{0.16em}{0ex}}{\mathrm{mTnm}}^{\ensuremath{-}1}$, which also couple the qubit to charge noise, and large drive amplitudes of order 1 mV. The flopping mode is an alternative method to drive EDSR of an electron in a double quantum dot, where the large displacement between both dots increases the driving efficiency. We propose to operate the flopping mode in the strong-driving regime to use the full magnetic field difference between the two dots. In simulations, the reduced required magnetic field gradients suppress the infidelity contribution of charge noise by more than two orders of magnitude, while providing Rabi frequencies of up to $60\phantom{\rule{0.16em}{0ex}}\mathrm{M}\mathrm{Hz}$. However, the near degeneracy of the conduction band in silicon introduces a valley degree of freedom that can degrade the performance of the strong-driving mode. This necessitates a valley-dependent pulse optimization and makes operation to the strong-driving regime questionable.

Optimisation of electron spin qubits in electrically driven multi-donor quantum dots

Multi-donor quantum dots have been at the forefront of recent progress in Si-based quantum computation. Among them, 2P: 1P spin qubits have a built-in dipole moment, making them ideal for electron dipole spin resonance (EDSR) using the donor hyperfine interaction, and thus all-electrical spin operation. We report fast EDSR, with Tπ ~ 10 − 50 ns and a Rabi ratio (T1/Tπ) ~ 106. The fastest EDSR time Tπ occurs when the 2P: 1P axis is ∥ [111], while the best Rabi ratio occurs when it is ∥ [100]. Sensitivity to random telegraph noise due to nearby charge defects depends strongly on the location of the nearby defects. The qubit is robust against 1/f noise provided it is operated away from the charge anti-crossing. Entanglement via exchange is several orders of magnitude faster than dipole-dipole coupling. These findings pave the way towards fast, low-power, coherent and scalable donor dot-based quantum computing.

Pulse Dipolar Electron Paramagnetic Resonance Spectroscopy Reveals Buffer-Modulated Cooperativity of Metal-Templated Protein Dimerization.

Self-assembly of protein monomers directed by metal ion coordination constitutes a promising strategy for designing supramolecular architectures complicated by the noncovalent interaction between monomers. Herein, two pulse dipolar electron paramagnetic resonance spectroscopy (PDS) techniques, pulse electron–electron double resonance and relaxation-induced dipolar modulation enhancement, were simultaneously employed to study the CuII-templated dimerization behavior of a model protein (Streptococcus sp. group G, protein G B1 domain) in both phosphate and Tris-HCl buffers. A cooperative binding model could simultaneously fit all data and demonstrate that the cooperativity of protein dimerization across α-helical double-histidine motifs in the presence of CuII is strongly modulated by the buffer, representing a platform for highly tunable buffer-switchable templated dimerization. Hence, PDS enriches the family of techniques for monitoring binding processes, supporting the development of novel strategies for bioengineering structures and stable architectures assembled by an initial metal-templated dimerization.

DEER Data Analysis Software: A Comparative Guide.

Pulsed dipolar electron paramagnetic resonance (PDEPR) spectroscopy experiments measure the dipolar coupling, and therefore nanometer-scale distances and distance distributions, between paramagnetic centers. Of the family of PDEPR experiments, the most commonly used pulsed sequence is four-pulse double electron resonance (DEER, also known as PELDOR). There are several ways to analyze DEER data to extract distance distributions, and this may appear overwhelming at first. This work compares and reviews six of the packages, and a brief getting started guide for each is provided.

A Low-Spin CoII/Nitroxide Complex for Distance Measurements at Q-Band Frequencies

Pulse dipolar electron paramagnetic resonance spectroscopy (PDS) is continuously furthering the understanding of chemical and biological assemblies through distance measurements in the nanometer range. New paramagnets and pulse sequences can provide structural insights not accessible through other techniques. In the pursuit of alternative spin centers for PDS, we synthesized a low-spin CoII complex bearing a nitroxide (NO) moiety, where both the CoII and NO have an electron spin S of 1/2. We measured CoII-NO distances with the well-established double electron–electron resonance (DEER aka PELDOR) experiment, as well as with the five- and six-pulse relaxation-induced dipolar modulation enhancement (RIDME) spectroscopies at Q-band frequencies (34 GHz). We first identified challenges related to the stability of the complex in solution via DEER and X-ray crystallography and showed that even in cases where complex disproportionation is unavoidable, CoII-NO PDS measurements are feasible and give good signal-to-noise (SNR) ratios. Specifically, DEER and five-pulse RIDME exhibited an SNR of ~100, and while the six-pulse RIDME exhibited compromised SNR, it helped us minimize unwanted signals from the RIDME traces. Last, we demonstrated RIDME at a 10 μM sample concentration. Our results demonstrate paramagnetic CoII to be a feasible spin center in medium magnetic fields with opportunities for PDS studies involving CoII ions.

Compactness regularization in the analysis of dipolar EPR spectroscopy data

Dipolar electron paramagnetic resonance (EPR) experiments, such as double electron–electron resonance (DEER), measure distributions of nanometer-scale distances between paramagnetic centers, which are valuable for structural characterization of proteins and other macromolecular systems. One challenge in the least-squares fitting analysis of dipolar EPR data is the separation of the inter-molecular contribution (background) and the intra-molecular contribution. For noisy experimental traces of insufficient length, this separation is not unique, leading to identifiability problems for the background model parameters and the long-distance region of the intra-molecular distance distribution. Here, we introduce a regularization approach that mitigates this by including an additional penalty term in the objective function that is proportional to the variance of the distance distribution and thereby penalizes non-compact distributions. We examine the reliability of this approach statistically on a large set of synthetic data and illustrate it with an experimental example. The results show that the introduction of compactness can improve identifiability.

Universal set of quantum gates for the flip-flop qubit in the presence of 1/f noise

Impurities hosted in semiconducting solid matrices represent an extensively studied platform for quantum computing applications. In this scenario, the so-called flip-flop qubit emerges as a convenient choice for scalable implementations in silicon. Flip-flop qubits are realized implanting phosphorous donor in isotopically purified silicon, and encoding the logical states in the donor nuclear spin and in its bound electron. Electrically modulating the hyperfine interaction by applying a vertical electric field causes an Electron Dipole Spin Resonance (EDSR) transition between the states with antiparallel spins {|downarrow Uparrow rangle ,|uparrow Downarrow rangle }, that are chosen as the logical states. When two qubits are considered, the dipole-dipole interaction is exploited to establish long-range coupling between them. A universal set of quantum gates for flip-flop qubits is here proposed and the effect of a realistic 1/f noise on the gate fidelity is investigated for the single qubit R_{z}(-frac{pi }{2}) and Hadamard gate and for the two-qubit sqrt{mathit{iSWAP}} gate.

New progress of silicon-based semiconductor quantum computation

<sec>Spin qubits in silicon-based semiconductor quantum dots have become one of the prominent candidates for realizing fault-tolerant quantum computing due to their long coherence time, good controllability, and compatibility with modern advanced integrated circuit manufacturing processes. In recent years, due to the remarkable advances in silicon-based materials, the structure of quantum dot and its fabrication process, and qubit manipulation technology, the great progress of high-fidelity state preparation and readout, single- and two-qubit gates of spin qubits for silicon based semiconductor quantum computation has been achieved. The control fidelities for single- and two-qubit gates all exceed 99%—fault tolerance threshold required by the surface code known for its exceptionally high tolerance to errors. In this paper, we briefly introduce the basic concepts of silicon-based semiconductor quantum dots, discuss the state-of-art technologies used to improve the fidelities of single- and two-qubit gates, and finally highlight the research directions that should be focused on.</sec><sec>This paper is organized as follows. Firstly, we introduce three major types of quantum dot (QD) devices fabricated on different silicon-based substrates, including Si/SiGe heterojunction and Si/SiO<sub>2</sub>. The spin degree of electron or nucleus hosted in QD can be encoded into spin qubits. Electron spin qubits can be thermally initialized to ground state by using an electron reservoirs, and can be read out by spin-charge conversion mechanism: energy-selective readout (Elzerman readout) with reservoirs or Pauli spin blockade (PSB) without reservoirs. Additionally, high fidelity single-shot readout has been demonstrated by using radio-frequency gate reflectometry combined with the PSB, which has unique advantages in large-scale qubit array. To coherently control the spin qubits, electron dipole resonance (ESR) or electron dipole spin resonance (EDSR) for electron and nuclear magnetic resonance (NMR) for nucleus are introduced. With the help of isotope purification greatly improving the dephasing time of qubit and fast single-qubit manipulation based on EDSR, fidelity above 99.9% can be reached. For the two-qubit gates based on exchange interaction between electron spins, the strength of interaction <inline-formula><tex-math id="M1">\begin{document}$ J $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="23-20221900_M1.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="23-20221900_M1.png"/></alternatives></inline-formula> combined with Zeeman energy difference <inline-formula><tex-math id="M2">\begin{document}$ \Delta {E}_{z} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="23-20221900_M2.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="23-20221900_M2.png"/></alternatives></inline-formula> determines the energy levels of system, which lead to the different two-qubit gates, such as controlled-Z (CZ), controlled-Rotation (CROT), and the square root of the SWAP gate (<inline-formula><tex-math id="M3">\begin{document}$ \sqrt{\rm{S}\rm{W}\rm{A}\rm{P}} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="23-20221900_M3.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="23-20221900_M3.png"/></alternatives></inline-formula>) gates. In order to improve the fidelity of two-qubit gates, a series of key technologies is used experimentally, they being isotope purification, symmetry operation, careful Hamiltonian engineering, and gate set tomography. Fidelity of two-qubit gates exceeding 99% has been demonstrated for electron spin qubits in Si/SiGe quantum dots and nuclear spin qubits in donors. These advances have pushed the silicon-based spin qubit platform to become a major stepping stone towards fault-tolerant quantum computation. Finally, we discuss the future study of spin qubits, that is, how to effectively expand the number of qubits, and many other problems to be explored and solved.</sec>

Dipolar pathways in dipolar EPR spectroscopy.

Dipolar electron paramagnetic resonance (EPR) experiments such as double electron-electron resonance (DEER) measure distributions of nanometer-scale distances between unpaired electrons, which provide valuable information for structural characterization of proteins and other macromolecular systems. To determine these distributions from the experimental signal, it is critical to employ an accurate model of the signal. For dilute samples of doubly spin-labeled molecules, the signal is a product of an intramolecular and an intermolecular contribution. We present a general model based on dipolar pathways valid for dipolar EPR experiments with spin-1/2 labels. Our results show that the intramolecular contribution consists of a sum and the intermolecular contribution consists of a product over individual dipolar pathway contributions. We examine several commonly used dipolar EPR experiments in terms of dipolar pathways and show experimental results confirming the theoretical predictions. This multi-pathway model makes it possible to analyze a wide range of dipolar EPR experiments within a single theoretical framework.

Dipolar pathways in multi-spin and multi-dimensional dipolar EPR spectroscopy.

Dipolar electron paramagnetic resonance (EPR) experiments, such as double electron-electron resonance (DEER), measure distributions of nanometer-scale distances between unpaired electrons, which provide valuable information for structural characterization of proteins and other macromolecular systems. We present an extension to our previously published general model based on dipolar pathways valid for multi-dimensional dipolar EPR experiments with more than two spin-1/2 labels. We examine the 4-pulse DEER and TRIER experiments in terms of dipolar pathways and show experimental results confirming the theoretical predictions. This extension to the dipolar pathways model allows the analysis of previously challenging datasets and the extraction of multivariate distance distributions.

PELDOR Measurements on Nitroxide-Labeled Oligonucleotides.

In the past decades, pulsed dipolar electron paramagnetic resonance spectroscopy (PDS) has emerged as a powerful tool in biophysical chemistry to study the structure, dynamics, and function of biomolecules like oligonucleotides and proteins. Structural information is obtained from PDS methods in form of a distribution of distances between spin centers. Such spin centers can either be intrinsically present paramagnetic metal ions and organic radicals or may be attached to the biomolecule by means of site-directed spin labeling. The most common PDS experiment for probing interspin distances in the nanometer range is pulsed electron-electron double resonance (PELDOR or DEER). In the protocol presented here, we provide a step-by-step workflow on how to set up a PELDOR experiment on a commercially available pulsed EPR spectrometer, outline the data analysis, and highlight potential pitfalls. We suggest PELDOR measurements on nitroxide-labeled oligonucleotides to study the structure of either RNA-cleaving DNAzymes in complex with their RNA targets or modified DNAzymes with different functions and targets, in which deoxynucleotides are substituted by nitroxide-labeled nucleotides.