Time domain simulation of Gd3+–Gd3+ distance measurements by EPR

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.

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 S = 1 / 2 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.

The effect of spin-lattice relaxation on DEER background decay

The common approach to background removal in double electron-electron resonance (DEER) measurements on frozen solutions with a three-dimensional homogeneous distribution of doubly labeled biomolecules is to fit the background to an exponential decay function. Excluded volume effects or distribution in a dimension lower than three, such as proteins in a membrane, can lead to a stretched exponential decay. In this work, we show that in cases of spin labels with short spin-lattice relaxation time, up to an order of magnitude longer than the DEER trace length, relevant for metal-based spin labels, spin flips that take place during the DEER evolution time affect the background decay shape. This was demonstrated using a series of temperature-dependent DEER measurements on frozen solutions of a nitroxide radical, a Gd(III) complex, Cu(II) ions, and a bis-Gd(III) model complex. As expected, the background decay was exponential for the nitroxide, whereas deviations were noted for Gd(III) and Cu(II). Based on the theoretical approach of Keller et al. (Phys. Chem. Chem. Phys. 21 (2019) 8228-8245), which addresses the effect of spin-lattice relaxation-induced spin flips during the evolution time, we show that the background decay can be fitted to an exponent including a linear and quadratic term in t, which is the position of the pump pulse. Analysis of the data in terms of the probability of spontaneous spin flips induced by spin-lattice relaxation showed that this approach worked well for the high temperature range studied for Gd(III) and Cu(II). At the low temperature range, the spin flips that occured during the DEER evolution time for Gd(III) exceeded the measured spin-lattice relaxation rate and include contributions from spin flips due to another mechanisms, most likely nuclear spin diffusion.

Increasing the Modulation Depth of GdIII-Based Pulsed Dipolar EPR Spectroscopy (PDS) with Porphyrin-GdIII Laser-Induced Magnetic Dipole Spectroscopy

Distance determination with pulsed EPR has become an important technique for the structural investigation of biomacromolecules, with double electron-electron resonance spectroscopy (DEER) as the most important method. GdIII-based spin labels are one of the most frequently used spin labels for DEER owing to their stability against reduction, high magnetic moment, and absence of orientation selection. A disadvantage of GdIII-GdIII DEER is the low modulation depth due to the broad EPR spectrum of GdIII. Here, we introduce laser-induced magnetic dipole spectroscopy (LaserIMD) with a spin pair consisting of GdIII(PymiMTA) and a photoexcited porphyrin as an alternative technique. We show that the excited state of the porphyrin is not disturbed by the presence of the GdIII complex and that herewith modulation depths of almost 40% are possible. This is significantly higher than the value of 7.2% that was achieved with GdIII-GdIII DEER.

The effect of spin polarization on double electron-electron resonance (DEER) spectroscopy

Double electron-electron resonance (DEER) spectroscopy measures the distribution of distances between two electron spins in the nanometer range, often on doubly spin-labeled proteins, via the modulation of a refocused spin echo by the dipolar interaction between the spins. DEER is commonly conducted under conditions where the polarization of the spins is small. Here, we examine the DEER signal under conditions of high spin polarization, thermally obtainable at low temperatures and high magnetic fields, and show that the signal acquires a polarization-dependent out-of-phase component both for the intramolecular and intermolecular contributions. For the latter, this corresponds to a phase shift of the spin echo that is linear in the pump pulse position. We derive a compact analytical form of this phase shift and show experimental measurements using monoradical and biradical nitroxides at several fields and temperatures. The effect highlights a novel aspect of the fundamental spin physics underlying DEER spectroscopy.

Neural networks in pulsed dipolar spectroscopy: A practical guide

This is a methodological guide to the use of deep neural networks in the processing of pulsed dipolar spectroscopy (PDS) data encountered in structural biology, organic photovoltaics, photosynthesis research, and other domains featuring long-lived radical pairs and paramagnetic metal ions. PDS uses distance dependence of magnetic dipolar interactions; measuring a single well-defined distance is straightforward, but extracting distance distributions is a hard and mathematically ill-posed problem requiring careful regularisation and background fitting. Neural networks do this exceptionally well, but their "robust black box" reputation hides the complexity of their design and training - particularly when the training dataset is effectively infinite. The objective of this paper is to give insight into training against simulated databases, to discuss network architecture choices, to describe options for handling DEER (double electron-electron resonance) and RIDME (relaxation-induced dipolar modulation enhancement) experiments, and to provide a practical data processing flowchart.

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.

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.

Probing the solution structure of the E. coli multidrug transporter MdfA using DEER distance measurements with nitroxide and Gd(III) spin labels

Methodological and technological advances in EPR spectroscopy have enabled novel insight into the structural and dynamic aspects of integral membrane proteins. In addition to an extensive toolkit of EPR methods, multiple spin labels have been developed and utilized, among them Gd(III)-chelates which offer high sensitivity at high magnetic fields. Here, we applied a dual labeling approach, employing nitroxide and Gd(III) spin labels, in conjunction with Q-band and W-band double electron-electron resonance (DEER) measurements to characterize the solution structure of the detergent-solubilized multidrug transporter MdfA from E. coli. Our results identify highly flexible regions of MdfA, which may play an important role in its functional dynamics. Comparison of distance distribution of spin label pairs on the periplasm with those calculated using inward- and outward-facing crystal structures of MdfA, show that in detergent micelles, the protein adopts a predominantly outward-facing conformation, although more closed than the crystal structure. The cytoplasmic pairs suggest a small preference to the outward-facing crystal structure, with a somewhat more open conformation than the crystal structure. Parallel DEER measurements with the two types of labels led to similar distance distributions, demonstrating the feasibility of using W-band spectroscopy with a Gd(III) label for investigation of the structural dynamics of membrane proteins.

Tracking Conformational Changes in Calmodulin in vitro, in Cell Extract, and in Cells by Electron Paramagnetic Resonance Distance Measurements

It is an open question whether the conformations of proteins sampled in dilute solutions are the same as in the cellular environment. Here we address this question by double electron-electron resonance (DEER) distance measurements with Gd(III) spin labels to probe the conformations of calmodulin (CaM) in vitro, in cell extract, and in human HeLa cells. Using the CaM mutants N53C/T110C and T34C/T117C labeled with maleimide-DOTA-Gd(III) in the N- and C-terminal domains, we observed broad and varied interdomain distance distributions. The in vitro distance distributions of apo-CaM and holo-CaM in the presence and absence of the IQ target peptide can be described by combinations of closed, open, and collapsed conformations. In cell extract, apo- and holo-CaM bind to target proteins in a similar way as apo- and holo-CaM bind to IQ peptide in vitro. In HeLa cells, however, in the presence or absence of elevated in-cell Ca²⁺ levels CaM unexpectedly produced more open conformations and very broad distance distributions indicative of many different interactions with in-cell components. These results show-case the importance of in-cell analyses of protein structures.

Assessing protein conformational landscapes: integration of DEER data in Maximum Occurrence analysis

The properties of the conformational landscape of a biomolecule are of capital importance to understand its function. It is widely accepted that a statistical ensemble is far more representative than a single structure, especially for proteins with disordered regions. While experimental data provide the most important handle on the conformational variability that the system is experiencing, they usually report on either time or ensemble averages. Since the available conformations largely outnumber the (independent) available experimental data, the latter can be equally well reproduced by a variety of ensembles. We have proposed the Maximum Occurrence (MaxOcc) approach to provide an upper bound of the statistical weight of each conformation. This method is expected to converge towards the true statistical weights by increasing the number of independent experimental datasets. In this paper we explore the ability of DEER (Double Electron Electron Resonance) data, which report on the distance distribution between two spin labels attached to a biomolecule, to restrain the MaxOcc values and its complementarity to previously introduced experimental techniques such as NMR and Small-Angle X-ray Scattering. We here present the case of Ca2+ bound calmodulin (CaM) as a test case and show that DEER data impose a sizeable reduction of the conformational space described by high MaxOcc conformations.

High Sensitivity In-Cell EPR Distance Measurements on Proteins using an Optimized Gd(III) Spin Label

Distance measurements by electron-electron double resonance (DEER) carried out on spin-labeled proteins delivered into cells provide new insights into the conformational states of proteins in their native environment. Such measurements depend on spin labels that exhibit high redox stability and high DEER sensitivity. Here we present a new Gd(III)-based spin label, BrPSPy-DO3A-Gd(III), which was derived from an earlier label, BrPSPy-DO3MA-Gd(III), by removing the methyl group from the methyl acetate pending arms. The small chemical modification led to a reduction in the zero-field splitting and to a significant increase in the phase memory time, which together culminated in a remarkable improvement of in-cell DEER sensitivity, while maintaining the high distance resolution. The excellent performance of BrPSPy-DO3A-Gd(III) in in-cell DEER measurements was demonstrated on doubly labeled ubiquitin and GB1 delivered into HeLa cells by electroporation.

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.

Small neutral Gd(iii) tags for distance measurements in proteins by double electron–electron resonance experiments

Small Gd(iii) tags based on DO3A deliver narrow and readily predictable distances by double electron–electron resonance (DEER) measurements.

Generic tags for Mn(ii) and Gd(iii) spin labels for distance measurements in proteins

The coordination mode of the metal ion in the spin label affects the distance distribution determined by DEER distance measurements.