Perspectives of shaped pulses for EPR spectroscopy

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.

Microwave Fluorescence Detection of Spin Echoes

Counting the microwave photons emitted by an ensemble of electron spins when they relax radiatively has recently been proposed as a sensitive method for electron paramagnetic resonance spectroscopy, enabled by the development of operational single microwave photon detectors at millikelvin temperature. Here, we report the detection of spin echoes in the spin fluorescence signal. The echo manifests itself as a coherent modulation of the number of photons spontaneously emitted after a π/2_{X}-τ-π_{Y}-τ-π/2_{Φ} sequence, dependent on the relative phase Φ. We demonstrate experimentally this detection method using an ensemble of Er^{3+} ion spins in a scheelite crystal of CaWO_{4}. We use fluorescence-detected echoes to measure the erbium spin coherence time, as well as the echo envelope modulation due to the coupling to the ^{183}W nuclear spins surrounding each ion. We finally compare the signal-to-noise ratio of inductively detected and fluorescence-detected echoes, and show that it is larger with the fluorescence method.

Towards high performance dielectric microwave resonators for X-band EPR spectroscopy

Microwave (MW) resonators in Electron Paramagnetic Resonance (EPR) spectroscopy concentrate the MW magnetic field (B1) at the sample and separate the MW electric field from the sample. There are numerous experimental methods in EPR spectroscopy which all impose different requirements on MW resonators (e.g. high or low quality factor, MW conversion, and B1-field homogeneity). Although commercial spectrometers offer standardized MW resonators for a broad application range, newly emerging and highly-specialized research fields push these spectrometers to or beyond their sensitivity limits. Optimizing the MW resonator offers one direct approach to improve the sensitivity. Here we present three low-cost optimization approaches for a commercially available X-band (9-10 GHz) MW resonator for three experimental purposes (continuous-wave (CW), transient and pulse EPR). We obtain enhanced MW conversion factors for all three optimized resonators and higher quality factors for two optimized resonators. The latter is important for CW and transient EPR. Furthermore, we fabricated a resonator which features an extended area of homogeneous B1-field and, hence, improved pulse EPR performance. Our results demonstrate that small changes to a commercial MW resonator can enhance its performance in general or for specific applications.

How to Cross an Energy Barrier at Zero Kelvin without Tunneling Effect

This Letter deals with the broad class of magnetic systems having a single or collective spin S with an energy barrier, such as rare-earth elements and their compounds, single molecule magnets with uniaxial anisotropy, and more generally any other anisotropic quantum system made of single or multiple objects with discrete energy levels. Till now, the reversal of the magnetization of such systems at zero kelvin required making use of quantum tunneling with a significant transverse field or transverse anisotropy term, at resonance. Here, we show that another very simple method exists. It simply consists in the application of a particular sequence of electromagnetic radiations in the ranges of optical or microwave frequencies, depending on the characteristics of the system (spin and anisotropy values for magnetic systems). This produces oscillations of the Rabi type that pass above the barrier, thus extending these oscillations between the two energy wells with mixtures of all the 2S+1 states. In addition to its basic character, this approach opens up new directions of research in quantum information with possible breakthroughs in the current use of multiple quantum bits.

Implementation and applications of shaped pulses in EPR

In this review, we describe the application of shaped pulses for EPR spectroscopy. Pulses generated by fast arbitrary waveform generators are mostly used in the field of EPR spectroscopy for broadband (200 MHz-1 GHz) excitation of paramagnetic species. The implementation and optimization of such broadband pulses in existing EPR spectrometers, often designed and optimized for short rectangular microwave pulses, is demanding. Therefore, a major part of this review will describe in detail the implementation, testing and optimization of shaped pulses in existing EPR spectrometers. Additionally, we review applications using such pulses for broadband inversion of longitudinal magnetization as well as for the creation and manipulation of transverse magnetization in the field of dipolar and hyperfine EPR spectroscopy. They demonstrate the great potential of shaped pulses to improve the performance of pulsed EPR experiments. We give a brief theoretical description of shaped pulses and their limitations, especially for adiabatic pulses, most often used in EPR. We believe that this review can on the one hand be of practical use to EPR groups starting to work with such pulses, and on the other hand give readers an overview of the state of the art of shaped pulse applications in EPR spectroscopy.

"Store-bought is fine": Sensitivity considerations using shaped pulses for DEER measurements on Cu(II) labels

The narrow excitation bandwidth of monochromic pulses is a sensitivity limitation for pulsed dipolar spectroscopy on Cu(II)-based measurements. In response, frequency-swept pulses with large excitation bandwidths have been adopted to probe a greater range of the EPR spectrum. However, much of the work utilizing frequency-swept pulses in Cu(II) distance measurements has been carried out on home-built spectrometers and equipment. Herein, we carry out systematic Cu(II) based distance measurements to demonstrate the capability of chirp pulses on commercial instrumentation. More importantly we delineate sensitivity considerations under acquisition schemes that are necessary for robust distance measurements using Cu(II) labels for proteins. We show that a 200 MHz sweeping bandwidth chirp pulse can improve the sensitivity of long-range distance measurements by factors of three to four. The sensitivity of short-range distances only increases slightly due to special considerations for the chirp pulse duration relative to the period length of the modulated dipolar signal. Enhancements in sensitivity also dramatically reduce measurement collection times enabling rapid collection of orientationally averaged Cu(II) distance measurements in under two hours.

Efficient sampling of molecular orientations for Cu(II)-based DEER on protein labels

Combining rigid Cu(II) labels and pulsed-EPR techniques enables distance constraint measurements that are incisive probes of protein structure and dynamics. However, the labels can lead to a dipolar signal that is biased by the relative orientation of the two spins, which is typically unknown a priori in a bilabeled protein. This effect, dubbed orientational selectivity, becomes a bottleneck in measuring distances. This phenomenon also applies to other pulsed-EPR techniques that probe electron-nucleus interactions. In this work, we dissect orientational selectivity by generating an in silico sample of Cu(II)-labeled proteins to evaluate pulse excitation in the context of double electron-electron resonance (DEER) at Q-band frequencies. This approach enables the observation of the contribution of each protein orientation to the dipolar signal, which provides direct insights into optimizing acquisition schemes to mitigate orientational effects. Furthermore, we incorporate the excitation profile of realistic pulses to identify the excited spins. With this method, we show that rectangular pulses, despite their imperfect inversion capability, can sample similar spin orientations as other sophisticated pulses with the same bandwidth. Additionally, we reveal that the efficiency of exciting spin-pairs in DEER depends on the frequency offset of two pulses used in the experiment and the relative orientation of the two spins. Therefore, we systematically examine the frequency offset of the two pulses used in this double resonance experiment to determine the optimal frequency offset for optimal distance measurements. This procedure leads to a protocol where two measurements are sufficient to acquire orientational-independent DEER at Q-band. Notably, this procedure is feasible with any commercial pulsed-EPR spectrometer. Furthermore, we experimentally validate the computational results using DEER experiments on two different proteins. Finally, we show that increasing the amplitude of the rectangular pulse can increase the efficiency of DEER experiments by almost threefold. Overall, this work provides an attractive new approach for analyzing pulsed-EPR spectroscopy to obtain microscopic nuances that cannot be easily discerned from analytical or numerical calculations.

Intermolecular contributions, filtration effects and signal composition of SIFTER (single-frequency technique for refocusing)

To characterize structure and molecular order in the nanometre range, distances between electron spins and their distributions can be measured via dipolar spin-spin interactions by different pulsed electron paramagnetic resonance experiments. Here, for the single-frequency technique for refocusing dipolar couplings (SIFTER), the buildup of dipolar modulation signal and intermolecular contributions is analysed for a uniform random distribution of monoradicals and biradicals in frozen glassy solvent by using the product operator formalism for electron spin S = 1 / 2 . A dipolar oscillation artefact appearing at both ends of the SIFTER time trace is predicted, which originates from the weak coherence transfer between biradicals. The relative intensity of this artefact is predicted to be temperature independent but to increase with the spin concentration in the sample. Different compositions of the intermolecular background are predicted in the case of biradicals and in the case of monoradicals. Our theoretical account suggests that the appropriate procedure of extracting the intramolecular dipolar contribution (form factor) requires fitting and subtracting the unmodulated part, followed by division by an intermolecular background function that is different in shape. This scheme differs from the previously used heuristic background division approach. We compare our theoretical derivations to experimental SIFTER traces for nitroxide and trityl monoradicals and biradicals. Our analysis demonstrates a good qualitative match with the proposed theoretical description. The resulting perspectives for a quantitative analysis of SIFTER data are discussed.

Analytical solution for the inverting pulses with constant adiabaticity

The exact solution was found for inverting pulses with constant adiabaticity for spin ½. The analytical relationship between the time-varying frequency of the microwave resonant field (or RF field in the case of NMR) and its amplitude time dependence such that the adiabaticity parameter remains constant for the single isochromat throughout the pulse is found. Comparison with EPR (hyperbolic tangent)-(hyperbolic secant) pulse method was carried out. On the basis of the analytical solution the pulses with different dependences of the microwave field amplitude conserving the constant adiabaticity have been constructed. The pulses exhibit rather sharp inversion selectivity that can be used in the field of EPR, NMR and MRI.

SORDOR pulses: expansion of the Böhlen-Bodenhausen scheme for low-power broadband magnetic resonance

A novel type of efficient broadband pulse, called second-order phase dispersion by optimised rotation (SORDOR), has recently been introduced. In contrast to adiabatic excitation, SORDOR-90 pulses provide effective transverse 90∘ rotations throughout their bandwidth, with a quadratic offset dependence of the phase in the x , y plane. Together with phase-matched SORDOR-180 pulses, this enables the Böhlen-Bodenhausen broadband refocusing approach for linearly frequency-swept pulses to be extended to any type of 90∘ /180∘ pulse-delay sequence. Example pulse shapes are characterised in theory and experiment, and an example application is given with a 19 F -PROJECT experiment for measuring relaxation times with reduced distortions due to J -coupling evolution.

Light-induced pulsed dipolar EPR spectroscopy for distance and orientation analysis

Measuring distances in biology at the molecular level is of great importance for understanding the structure and function of proteins, nucleic acids and other biological molecules and their complexes. Pulsed Dipolar Spectroscopy (PDS) offers advantages with respect to other methods as it is uniquely sensitive and specific to electronic spin centers and allows measurements in near-native conditions, comprising the in-cell environment. PDS methods measure the electron spin-spin dipolar interaction, therefore they require the presence of at least two paramagnetic centers, which are often stable radicals. Recent developments have introduced transient triplet states, photo-activated by a laser pulse, as spin labels and probes, thereby establishing a new family of techniques-Light-induced PDS (LiPDS). In this chapter, an overview of these methods is provided, looking at the chromophores that can be used for LiPDS and some of the technical aspects of the experiments. A guide to the choice of technique that can yield the best results, depending on the type of system studied and the information required, is provided. Examples of previous LiPDS studies of model systems and proteins are given. Characterization data for the chromophores used in these studies is tabulated to help selection of appropriate triplet state probes in future studies.

Fullerene-based triplet spin labels: methodology aspects for pulsed dipolar EPR spectroscopy

Triplet states of photoexcited organic molecules are promising spin labels with advanced spectroscopic properties for Pulsed Dipolar Electron Paramagnetic Resonance (PD EPR) spectroscopy. Recently proposed triplet fullerene labels have shown...

Towards fully optimised and automated ESR spectroscopy

To address the problems of instrumental imperfection and time-consuming experimental setup in electron spin resonance (ESR), we present ESR-POISE, a user-friendly software package for fully automated and fast on-the-fly optimisation...

Uptake of Cell-Penetrating Peptide RL2 by Human Lung Cancer Cells: Monitoring by Electron Paramagnetic Resonance and Confocal Laser Scanning Microscopy

RL2 is a recombinant analogue of a human κ-casein fragment, capable of penetrating cells and inducing apoptosis of cancer cells with no toxicity to normal cells. The exact mechanism of RL2 penetration into cells remains unknown. In this study, we investigated the mechanism of RL2 penetration into human lung cancer A549 cells by a combination of electron paramagnetic resonance (EPR) spectroscopy and confocal laser scanning microscopy. EPR spectra of A549 cells incubated with RL2 (sRL2) spin-labeled by a highly stable 3-carboxy-2,2,5,5-tetraethylpyrrolidine-1-oxyl radical were found to contain three components, with their contributions changing with time. The combined EPR and confocal-microscopy data allowed us to assign these three forms of sRL2 to the spin-labeled protein sticking to the membrane of the cell and endosomes, to the spin-labeled protein in the cell interior, and to spin labeled short peptides formed in the cell because of protein digestion. EPR spectroscopy enabled us to follow the kinetics of transformations between different forms of the spin-labeled protein at a minimal spin concentration (3-16 μM) in the cell. The prospects of applications of spin-labeled cell-penetrating peptides to EPR imaging, DNP, and magnetic resonance imaging are discussed, as is possible research on an intrinsically disordered protein in the cell by pulsed dipolar EPR spectroscopy.

THz-enhanced dynamic nuclear polarized liquid spectrometer

Dynamic nuclear polarization (DNP) technology can be utilized to dramatically enhance NMR signal. In this paper, we report on the development of a self-constructed 5 T DNP spectrometer for liquid samples and the ¹³C DNP enhancement achieved with this spectrometer. The DNP spectrometer is comprised of a wide-bore superconducting magnet, a home-made console, a dual resonance probe and a self-built 140 GHz microwave source for the spectrometer. Specifically, a microwave source of traveling wave tube (TWT) amplifier has been developed, which can provide a maximum power output of 4.4 W and a wide frequency tuning range of 1 GHz. The excellent performance of our built liquid-state DNP spectrometer is verified by the observation of more than 100-fold DNP enhancement of the ¹³C NMR signal for liquid ¹³CCl₄ sample. Our result shows the superiority of DNP technology in the liquid-state high-field NMR spectrometer.

Application of Optimal Control Theory to Fourier Transform Ion Cyclotron Resonance

We study the application of Optimal Control Theory to Ion Cyclotron Resonance. We test the validity and the efficiency of this approach for the robust excitation of an ensemble of ions with a wide range of cyclotron frequencies. Optimal analytical solutions are derived in the case without any pulse constraint. A gradient-based numerical optimization algorithm is proposed to take into account limitation in the control intensity. The efficiency of optimal pulses is investigated as a function of control time, maximum amplitude and range of excited frequencies. A comparison with adiabatic and SWIFT pulses is done. On the basis of recent results in Nuclear Magnetic Resonance, this study highlights the potential usefulness of optimal control in Ion Cyclotron Resonance.

Going the dHis-tance: Site-Directed Cu2+ Labeling of Proteins and Nucleic Acids

In this Account, we showcase site-directed Cu²⁺ labeling in proteins and DNA, which has opened new avenues for the measurement of the structure and dynamics of biomolecules using electron paramagnetic resonance (EPR) spectroscopy. In proteins, the spin label is assembled in situ from natural amino acid residues and a metal complex and requires no post-expression synthetic modification or purification procedures. The labeling scheme exploits a double histidine (dHis) motif, which utilizes endogenous or site-specifically mutated histidine residues to coordinate a Cu²⁺ complex. Pulsed EPR measurements on such Cu²⁺-labeled proteins potentially yield distance distributions that are up to 5 times narrower than the common protein spin label-the approach, thus, overcomes the inherent limitation of the current technology, which relies on a spin label with a highly flexible side chain. This labeling scheme provides a straightforward method that elucidates biophysical information that is costly, complicated, or simply inaccessible by traditional EPR labels. Examples include the direct measurement of protein backbone dynamics at β-sheet sites, which are largely inaccessible through traditional spin labels, and rigid Cu²⁺-Cu²⁺ distance measurements that enable higher precision in the analysis of protein conformations, conformational changes, interactions with other biomolecules, and the relative orientations of two labeled protein subunits. Likewise, a Cu²⁺ label has been developed for use in DNA, which is small, is nucleotide independent, and is positioned within the DNA helix. The placement of the Cu²⁺ label directly reports on the biologically relevant backbone distance. Additionally, for both of these labeling techniques, we have developed models for interpretation of the EPR distance information, primarily utilizing molecular dynamics (MD) simulations. Initial results using force fields developed for both protein and DNA labels have agreed with experimental results, which has been a major bottleneck for traditional spin labels. Looking ahead, we anticipate new combinations of MD and EPR to further our understanding of protein and DNA conformational changes, as well as working synergistically to investigate protein-DNA interactions.

Chirped ordered pulses for ultra-broadband ESR spectroscopy

Recently, applications of swept-frequency pulses proved to be a useful approach to circumvent the problem of limited excitation bandwidth in pulsed ESR posed by conventional pulses. Here, we present a chirped excitation sequence, CHirped ORdered pulses for Ultra-broadband Spectroscopy (CHORUS), for ultra-broadband ESR spectroscopy. It will be demonstrated that the application of this sequence can address the problems of excitation non-uniformity and sensitivity to instrumental instabilities to a greater extent compared to the current state of the art. This sequence is highly promising for finding applications beyond single excitation in many ESR experiments. Theoretical and experimental results for the proposed method are presented along with calibration strategies for experimental implementation.

Multiquantum Counting of Trityl Radicals

We demonstrate a series of multitrityl radical compounds where accurate spin-counting by pulsed electron paramagnetic resonance (EPR) can be achieved at X-band (9 GHz) frequencies, even for molecules with very short and flexible linkers. Multiquantum filter experiments, well-known from NMR, were used to count the number of coupled electron spins in these compounds. The six pulse double quantum filter sequence used in EPR for distance determinations in biradicals was used. Precise phase settings to separate higher quantum coherences were achieved by an arbitrary waveform generator. The trityl radicals have narrow spectral width so that homogeneous excitation of all spins by the pulses is possible. The transversal relaxation times of higher quantum coherences of trityl radicals are sufficiently long to allow their detection. Our results on model compounds show the potential of this approach to determine oligomeric states in protein complexes in their native environment using functionalized trityl spin labels.

Optimising broadband pulses for DEER depends on concentration and distance range of interest

EPR distance determination in the nanometre region has become an important tool for studying the structure and interaction of macromolecules. Arbitrary waveform generators (AWGs), which have recently become commercially available for EPR spectrometers, have the potential to increase the sensitivity of the most common technique, double electron-electron resonance (DEER, also called PELDOR), as they allow the generation of broadband pulses. There are several families of broadband pulses, which are different in general pulse shape and the parameters that define them. Here, we compare the most common broadband pulses. When broadband pulses lead to a larger modulation depth, they also increase the background decay of the DEER trace. Depending on the dipolar evolution time, this can significantly increase the noise level towards the end of the form factor and limit the potential increase in the modulation-to-noise ratio (MNR). We found asymmetric hyperbolic secant (HS{ 1 , 6 } ) pulses to perform best for short DEER traces, leading to a MNR improvement of up to 86 % compared to rectangular pulses. For longer traces we found symmetric hyperbolic secant (HS{ 1 , 1 } ) pulses to perform best; however, the increase compared to rectangular pulses goes down to 43 %.

Conformational tuning of a DNA-bound transcription factor

Transcription factors are involved in many cellular processes that take place remote from their cognate DNA sequences. The efficiencies of these activities are thus in principle counteracted by high binding affinities of the factors to their cognate DNAs. Models such as facilitated diffusion or dissociation address this apparent contradiction. We show that the MYC associated transcription factor X (MAX) undergoes nanoscale conformational fluctuations in the DNA-bound state, which is consistent with facilitated dissociation from or diffusion along DNA strands by transiently reducing binding energies. An integrative approach involving EPR, NMR, crystallographic and molecular dynamics analyses demonstrates that the N-terminal domain of MAX constantly opens and closes around a bound DNA ligand thereby dynamically tuning the binding epitope and the mode of interaction.

UWB DEER and RIDME distance measurements in Cu(II)-Cu(II) spin pairs

Distance determination by Electron Paramagnetic Resonance (EPR) based on measurements of the dipolar coupling are technically challenging for electron spin systems with broad spectra due to comparatively narrow microwave pulse excitation bandwidths. With Na₄[{Cu^II(PyMTA)}-(stiff spacer)-{Cu^II(PyMTA)}] as a model compound, we compared DEER and RIDME measurements and investigated the use of frequency-swept pulses. We found very large improvements in sensitivity when substituting the monochromatic pump pulse by a frequency-swept one in DEER experiments with monochromatic observer pulses. This effect was especially strong in X band, where nearly the whole spectrum can be included in the experiment. The RIDME experiment is characterised by a trade-off in signal intensity and modulation depth. Optimal parameters are further influenced by varying steepness of the background decay. A simple 2-point optimization experiment was found to serve as good estimate to identify the mixing time of highest sensitivity. Using frequency-swept pulses in the observer sequences resulted in lower SNR in both the RIDME and the DEER experiment. Orientation selectivity was found to vary in both experiments with the detection position as well as with the settings of the pump pulse in DEER. In RIDME, orientation selection by relaxation anisotropy of the inverted spin appeared to be negligible as form factors remain relatively constant with varying mixing time. This reduces the overall observed orientation selection to the one given by the detection position. Field-averaged data from RIDME and DEER with a shaped pump pulse resulted in the same dipolar spectrum. We found that both methods have their advantages and disadvantages for given instrumental limitations and sample properties. Thus the choice of method depends on the situation at hand and we discuss which parameters should be considered for optimization.

Shaping EPR: Phase and amplitude modulated microwave pulses

The advent of fast arbitrary waveform generators in the sub-nanosecond time regime recently enabled new experimental developments in the field of pulsed EPR. In this article, the new possibilities of such fast phase/amplitude modulated microwave pulses are shortly described with respect to applications in pulsed dipolar spectroscopy. Some of the specific challenges of an accurate creation of such pulses in the field of EPR are outlined. Finally, a short outlook of potential applications is given and some specific experimental conditions are discussed, where shaped pulses might have an especially important impact in the future.

Quo vadis EPR?

Complexity of paramagnetic catalysts and materials increases, and the same applies to systems targeted by integrative structural biology. Hence, EPR spectroscopists must find ways to enhance information content of their data. I argue that a third major wave of method development in EPR spectroscopy, which is triggered by recent advances in digital electronics and computing, can achieve this. Transfer of NMR methods to EPR will go on, but part of the new EPR methodology will depend on completely new concepts.

Shaped pulses for transient compensation in quantum-limited electron spin resonance spectroscopy

In high sensitivity inductive electron spin resonance spectroscopy, superconducting microwave resonators with large quality factors are employed. While they enhance the sensitivity, they also distort considerably the shape of the applied rectangular microwave control pulses, which limits the degree of control over the spin ensemble. Here, we employ shaped microwave pulses compensating the signal distortion to drive the spins faster than the resonator bandwidth. This translates into a shorter echo, with enhanced signal-to-noise ratio. The shaped pulses are also useful to minimize the dead-time of our spectrometer, which allows to reduce the wait time between successive drive pulses.

Thermo-mechanical analysis of a probe for electron paramagnetic resonance spectroscopy operating at cryogenic temperatures

In this article, we present the thermo-mechanical analysis of an electron paramagnetic resonance (EPR) probe operating at cryogenic temperatures using finite element analysis. Thermo-mechanical analysis plays a key role in the mechanical design evaluation process as EPR probes are often subjected to large stresses under such extreme conditions. For simplification, we assume thermal conduction to be the dominant mode of heat transfer over convection and radiation. The simulation model consists of a cryostat-probe assembly with appropriate thermal and structural boundary conditions. The predicted temperature distributions from the steady-state thermal analysis is then used for the stress analysis of the EPR probe. The stress analysis indicated that stresses in the EPR probe are below the ultimate strengths of each component, and thus safe for running EPR experiments. Furthermore, the simulation results were confirmed experimentally, and we found that the predicted heat losses for the EPR probe assembly and the sample holder are in excellent agreement with the experimental measurements.

Feedback control optimisation of ESR experiments

Numerically optimised microwave pulses are used to increase excitation efficiency and modulation depth in electron spin resonance experiments performed on a spectrometer equipped with an arbitrary waveform generator. The optimisation procedure is sample-specific and reminiscent of the magnet shimming process used in the early days of nuclear magnetic resonance - an objective function (for example, echo integral in a spin echo experiment) is defined and optimised numerically as a function of the pulse waveform vector using noise-resilient gradient-free methods. We found that the resulting shaped microwave pulses achieve higher excitation bandwidth and better echo modulation depth than the pulse shapes used as the initial guess. Although the method is theoretically less sophisticated than simulation based quantum optimal control techniques, it has the advantage of being free of the linear response approximation; rapid electron spin relaxation also means that the optimisation takes only a few seconds. This makes the procedure fast, convenient, and easy to use. An important application of this method is at the final stage of the implementation of theoretically designed pulse shapes: compensation of pulse distortions introduced by the instrument. The performance is illustrated using spin echo and out-of-phase electron spin echo envelope modulation experiments. Interface code between Bruker SpinJet arbitrary waveform generator and Matlab is included in versions 2.2 and later of the Spinach library.

Light-induced dipolar spectroscopy - A quantitative comparison between LiDEER and LaserIMD

Nanometric distance measurements with EPR spectroscopy yield crucial information on the structure and interactions of macromolecules in complex systems. The range of suitable spin labels for such measurements was recently expanded with a new class of light-inducible labels: the triplet state of porphyrins. Importantly, accurate distance measurements between a triplet label and a nitroxide have been reported with two distinct light-induced spectroscopy techniques, (light-induced) triplet-nitroxide DEER (LiDEER) and laser-induced magnetic dipole spectroscopy (LaserIMD). In this work, we set out to quantitatively compare the two techniques under equivalent conditions at Q band. Since we find that LiDEER using a rectangular pump pulse does not reach the high modulation depth that can be achieved with LaserIMD, we further explore the possibility of improving the LiDEER experiment with chirp inversion pulses. LiDEER employing a broadband pump pulse results in a drastic improvement of the modulation depth. The relative performance of chirp LiDEER and Laser-IMD in terms of modulation-to-noise ratio is found to depend on the dipolar evolution time: While LaserIMD yields higher modulation-to-noise ratios than LiDEER at short dipolar evolution times (τ=2μs), the high phase memory time of the triplet spins causes the situation to revert at τ=6μs.

Improved signal fidelity in 4-pulse DEER with Gaussian pulses

The introduction of arbitrary waveform generator (AWG) technology and the availability of high power microwave amplifiers mark a "new era" in pulse EPR due to significant sensitivity improvements and the possibility to perform novel types of experiments. We present an optimized 4-pulse DEER setup that uses Gaussian observer pulses (GaussDEER) in connection with a Gaussian/shaped pump pulse. Gaussian pulses allow to experimentally remove the "2+1" pulse train ESE signal which is intrinsically present in any DEER experiment performed with rectangular pulses. Further signal improvements are obtained with shaped pump pulses, which can significantly increase the modulation depth of the DEER experiment due to their tailored excitation bandwidth. Although sequences like CP (Carr-Purcell) DEER offer advantages such as a prolongation of the dipolar evolution time, they suffer from post-processing of the time-domain data to remove artifacts. Therefore, it is worth having a 4-pulse DEER experiment free of residual "2+1" signal since this is still the main dipolar spectroscopic technique used in structural biology. In this work we focus on nitroxides, which are the spin probes primarily used in site-directed spin labeling studies of biomolecules, however, the advantages introduced by Gaussian pulses can be extended to any spin type.

Refocused Out-Of-Phase (ROOPh) DEER: A pulse scheme for suppressing an unmodulated background in double electron-electron resonance experiments

EPR pulsed dipolar spectroscopy (PDS) is indispensable for measurements of nm-scale distances between electronic spins in biological and other systems. While several useful modifications and pulse sequences for PDS have been developed in recent years, DEER experiments utilizing pump and observer pulses at two different frequencies remain the most popular for practical applications. One of the major drawbacks of all the available DEER approaches is the presence of a significant unmodulated fraction in the detected signal that arises from an incomplete inversion of the coupled spins by the pump pulse. The latter fraction is perceived as one of the major sources of error for the reconstructed distance distributions. We describe an alternative detection scheme - a Refocused Out-Of-Phase DEER (ROOPh-DEER) - to acquire only the modulated fraction of the dipolar DEER signal. When Zeeman splitting is small compared to the temperature, the out-of-phase magnetization components cancel each other and are not observed in 4-pulse DEER experiment. In ROOPh-DEER these components are refocused by an additional pump pulse while the in-phase component containing an unmodulated background is filtered out by a pulse at the observed frequency applied right at the position of the refocused echo. Experimental implementation of the ROOPh-DEER detection scheme requires at least three additional pulses as was demonstrated on an example of a 7-pulse sequence. The application of 7-pulse ROOPh-DEER sequence to a model biradical yielded the interspin distance of 1.94 ± 0.07 nm identical to the one obtained with the conventional 4-pulse DEER, however, without the unmodulated background present as a dominant fraction in the latter signal.

Frequency-Swept Integrated and Stretched Solid Effect Dynamic Nuclear Polarization

We investigate a new time domain approach to dynamic nuclear polarization (DNP), the frequency-swept integrated solid effect (FS-ISE), utilizing a high power, broadband 94 GHz (3.35 T) pulse EPR spectrometer. The bandwidth of the spectrometer enabled measurement of the DNP Zeeman frequency/field profile that revealed two dominant polarization mechanisms, the expected ISE, and a recently observed mechanism, the stretched solid effect (S2E). At 94 GHz, despite the limitations in the microwave chirp pulse length (10 μs) and the repetition rate (2 kHz), we obtained signal enhancements up to ∼70 for the S2E and ∼50 for the ISE. The results successfully demonstrate the viability of the FS-ISE and S2E DNP at a frequency 10 times higher than previous studies. Our results also suggest that these approaches are candidates for implementation at higher magnetic fields.

Cooperative broadband spin echoes through optimal control

The Hahn echo sequence is one of the most common building blocks in magnetic resonance, consisting of an excitation pulse and a refocusing pulse. Conventional approaches to improve the performance of echo experiments focused on the optimization of individual pulses, compensating their own imperfections. Here we present an approach to concurrently design both pulses such that they also compensate each others imperfections. The fact that for such cooperative pulses the individual pulses do not need to be perfect provides additional degrees of freedom, resulting in improved overall Hahn echo performance. Single-scan cooperative pulses are compared to conventional approaches by simulations as well as experiments.

Nitroxide–nitroxide and nitroxide–metal distance measurements in transition metal complexes with two or three paramagnetic centres give access to thermodynamic and kinetic stabilities

Broadband and highly resolved EPR distance measurements reveal multimers and their kinetic stabilities.

Performance of PELDOR, RIDME, SIFTER, and DQC in measuring distances in trityl based bi- and triradicals: exchange coupling, pseudosecular coupling and multi-spin effects

The performance of pulsed EPR methods for distance measurements is evaluated on three different trityl model systems.

Pulsed triple electron resonance (TRIER) for dipolar correlation spectroscopy

A new pulse sequence is presented for correlating dipolar frequencies in molecules with more than two paramagnetic centers. This triple electron resonance experiment (TRIER) is an extension the double electron-electron resonance (DEER) experiment, which is widely used for distance determination in the nanometer range. We use linear chirp pulses with smoothed edges to create a refocused observer echo, and two hyperbolic secant pulses with distinct excitation windows to excite two other subsets of spins. These pumped spins are coupled to the observed spin through the dipole-dipole interaction. A two-dimensional dipolar modulation pattern is recorded by variation of the position of the two pump pulses. By two-dimensional Fourier transform of the echo integral, a plot is obtained that correlates dipolar frequencies within the same molecule. Such correlation patterns can be used in conjunction with DEER, with which distance distributions are usually determined for several doubly labeled molecules with different spin-labeling sites. In the presence of two conformers, DEER traces give two distances and assignment to an individual conformer is not trivial and usually requires a trial and error approach. TRIER can potentially provide the missing connection between distances as correlations between dipolar frequencies.