Pulsed triple electron resonance (TRIER) for dipolar correlation spectroscopy

Exploring tunneling ESEEM beyond methyl groups in nitroxides at low temperatures

Tunneling of methyl rotors coupled to an electron spin causes magnetic field independent electron spin echo envelope modulation (ESEEM) at low temperatures. For nitroxides containing alkyl substituents, we observe this effect as a contribution at the beginning of the Hahn echo decay signal occurring on a faster time scale than the matrix-induced decoherence. The tunneling ESEEM contribution includes information on the local environment of the methyl rotors, which manifests as a distribution of rotation barriers P(V3) when measuring the paramagnetic species in a glassy matrix. Here, we investigate the differences in tunneling behaviour of geminal methyl and ethyl group rotors in nitroxides while exploring different levels of theory in our previously introduced methyl quantum rotor (MQR) model. Moreover, we extend the MQR model to analyze the tunneling ESEEM originating from two different rotor types coupled to the same electron spin. We find that ethyl groups in nitroxides give rise to stronger tunneling ESEEM contributions than methyl groups because the difference between hyperfine couplings of their methyl protons better matches the tunneling frequency. The methyl rotors of both ethyl and propyl groups exhibit distributions at lower rotation barriers compared to geminal methyl groups. This is in good agreement with density functional theory (DFT) calculations of their rotation barriers and showcases that conformational flexibility impacts the hindrance of rotation. Using Monte-Carlo based fitting in combination with an identifiability analysis of the MQR model parameter space, we extract rotation barrier distributions for the individual rotor types in mixed-rotor nitroxides as well as identify which rotors dominate the observed tunneling contribution in the Hahn echo decay signal.

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.

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.

Strategies to identify and suppress crosstalk signals in double electron-electron resonance (DEER) experiments with gadoliniumIII and nitroxide spin-labeled compounds

Double electron-electron resonance (DEER) spectroscopy applied to orthogonally spin-labeled biomolecular complexes simplifies the assignment of intra- and intermolecular distances, thereby increasing the information content per sample. In fact, various spin labels can be addressed independently in DEER experiments due to spectroscopically nonoverlapping central transitions, distinct relaxation times, and/or transition moments; hence, they are referred to as spectroscopically orthogonal. Molecular complexes which are, for example, orthogonally spin-labeled with nitroxide (NO) and gadolinium (Gd) labels give access to three distinct DEER channels that are optimized to selectively probe NO-NO, NO-Gd, and Gd-Gd distances. Nevertheless, it has been previously recognized that crosstalk signals between individual DEER channels can occur, for example, when a Gd-Gd distance appears in a DEER channel optimized to detect NO-Gd distances. This is caused by residual spectral overlap between NO and Gd spins which, therefore, cannot be considered as perfectly orthogonal. Here, we present a systematic study on how to identify and suppress crosstalk signals that can appear in DEER experiments using mixtures of NO-NO, NO-Gd, and Gd-Gd molecular rulers characterized by distinct, nonoverlapping distance distributions. This study will help to correctly assign the distance peaks in homo- and heterocomplexes of biomolecules carrying not perfectly orthogonal spin labels.

DeerLab: a comprehensive software package for analyzing dipolar electron paramagnetic resonance spectroscopy data

Dipolar EPR spectroscopy (DEER and other techniques) enables the structural characterization of macromolecular and biological systems by measurement of distance distributions between unpaired electrons on a nanometer scale. The inference of these distributions from the measured signals is challenging due to the ill-posed nature of the inverse problem. Existing analysis tools are scattered over several applications with specialized graphical user interfaces. This renders comparison, reproducibility, and method development difficult. To remedy this situation, we present DeerLab, an open-source software package for analyzing dipolar EPR data that is modular and implements a wide range of methods. We show that DeerLab can perform one-step analysis based on separable non-linear least squares, fit dipolar multi-pathway models to multi-pulse DEER data, run global analysis with non-parametric distributions, and use a bootstrapping approach to fully quantify the uncertainty in the analysis.

Spin dynamics during chirped pulses: applications to homonuclear decoupling and broadband excitation

Swept-frequency pulses have found applications in a wide range of areas including spectroscopic techniques where efficient control of spins is required. For many of these applications, a good understanding of the evolution of spin systems during these pulses plays a vital role, not only in describing the mechanism of techniques, but also in enabling new methodologies. In magnetic resonance spectroscopy, broadband inversion, refocusing, and excitation using these pulses are among the most used applications in NMR, ESR, MRI, and in vivo MRS. In the present survey, a general expression for chirped pulses will be introduced, and some numerical approaches to calculate the spin dynamics during chirped pulses via solutions of the well-known Liouville-von Neumann equation and the lesser-explored Wei-Norman Lie algebra along with comprehensive examples are presented. In both cases, spin state trajectories are calculated using the solution of differential equations. Additionally, applications of the proposed methods to study the spin dynamics during the PSYCHE pulse element for broadband homonuclear decoupling and the CHORUS sequence for broadband excitation will be presented.

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 %.

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.

Pulse EPR in biological systems - Beyond the expert's courtyard

Application of EPR to biological systems includes many techniques and applications. In this short perspective, which dares to look into the future, I focus on pulse EPR, which is my field of expertise. Generally, pulse EPR techniques can be divided into two main groups: (1) hyperfine spectroscopy, which explores electron-nuclear interactions, and (2) pulse-dipolar (PD) EPR spectroscopy, which is based on electron-electron spin interactions. Here I focus on PD-EPR because it has a better chance of becoming a widely applied, easy-to-use table-top method to study the structural and dynamic aspects of bio-molecules. I will briefly introduce this technique, its current state of the art, the challenges it is facing, and finally I will describe futuristic scenarios of low-cost PD-EPR approaches that can cross the diffusion barrier from the core of experts to the bulk of the scientific community.

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.

General regularization framework for DEER spectroscopy

Tikhonov regularization is the standard processing technique for the inversion of double electron-electron resonance (DEER) data to distance distributions without assuming a parametrized model. In other fields it has been surpassed by modern regularization methods. We analyze such alternative regularization methods based on the Tikhonov, total variation (TV) and Huber penalties with and without the use of Bregman iterations. For this, we provide a general mathematical framework and its open-source software implementation. We extend an earlier approach by Edwards and Stoll for the selection of an optimal regularization parameter to all of these penalties and use their big test data set of noisy DEER traces with known ground truth for assessment. The results indicate that regularization methods based on Bregman iterations provide an improvement upon Tikhonov regularization in recognizing features and recovering distribution width at moderate signal-to-noise ratio, provided that noise variance is known. Bregman-iterative methods are robust with respect to the method used in the choice of regularization parameter.

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.

Treating Biomacromolecular Conformational Variability

The function of a biomacromolecule is related not only to its structure but also to the different conformations that its structural elements can sample. It is therefore important to determine the extent of the structural fluctuations and to identify the states that are actually populated as a result of the rearrangement. However, this accomplishment is undermined by an intrinsic limitation: the amount of experimental data is by and large inferior to the number of the states that a biomacromolecule can actually sample. This means that additional, a priori information must be applied in order to derive the most from the available experimental data but not to run into overinterpretation. In this chapter we will give a summary of the experimental observables that can be used towards the reconstruction of structural ensembles, how the data can be profitably combined and to what extent the data are affected by error; finally we will give an overview of the computational methods that have been developed to model structural ensembles, highlighting their difference and similarities, advantages and disadvantages.

Deep neural network processing of DEER data

The established model-free methods for the processing of two-electron dipolar spectroscopy data [DEER (double electron-electron resonance), PELDOR (pulsed electron double resonance), DQ-EPR (double-quantum electron paramagnetic resonance), RIDME (relaxation-induced dipolar modulation enhancement), etc.] use regularized fitting. In this communication, we describe an attempt to process DEER data using artificial neural networks trained on large databases of simulated data. Accuracy and reliability of neural network outputs from real experimental data were found to be unexpectedly high. The networks are also able to reject exchange interactions and to return a measure of uncertainty in the resulting distance distributions. This paper describes the design of the training databases, discusses the training process, and rationalizes the observed performance. Neural networks produced in this work are incorporated as options into Spinach and DeerAnalysis packages.