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Decoherence arises from a fluctuating spin environment, captured by its noise spectrum S ( ω ). Dynamical decoupling (DD) with n π pulses extends the dephasing time if the associated filter function attenuates S ( ω ). Inversely, DD noise spectroscopy (DDNS) reconstructs S ( ω ) from DD data by approximating the filters pass band by a δ -function. This restricts application to qubit-like spin systems with inherently long dephasing times and/or many applicable pulses. We introduce regularized DDNS to lift this limitation and thereby infer S ( ω ) from DD traces of paramagnetic centers in glassy o -terphenyl and water-glycerol matrices recorded with n ≤ 5. For nitroxide radicals at low temperatures, we utilize deuteration to identify distinct matrix- and spin center-induced spectral features. The former extends up to a matrix-specific cut-off frequency and characterizes nuclear spin diffusion. We demonstrate that rotational tunneling of intramolecular methyl groups drives the latter process, whereas at elevated temperatures S ( ω ) reflects the classical methyl group reorientation. Ultimately, S ( ω ) visualizes and quantifies variations in the electron spins couplings and thus reports on the underlying spin dynamics as a powerful decoherence descriptor.

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

We have characterized the temperature dependent transverse relaxation for 100 μM protonated and deuterated nitroxides in both protonated and deuterated o-terphenyl (OTP and dOTP) in distinct temperature regimes between 10 K and room temperature (RT). The choice of sample compositions allowed for a clear separation into slow and fast relaxation contributions based on a sum of two stretched exponential (SSE) parameterization between 10 and 60 K, and likewise at RT. The slow contribution is purely matrix dependent, while the fast process is determined by an interplay between a molecule and a matrix. Our systematic study of dynamical decoupling (DD) as a function of temperature (at 40, 80 K and RT), spin concentration, deuteration of nitroxide and/or OTP matrix and DD scheme for 1 to 5 refocusing pulses reveals that DD significantly prolongs phase memory times with respect to Hahn echo relaxation at 40 K, which we discuss in an SSE framework. At 80 K and RT, where (intra)molecular motions dominate relaxation, DD does not preserve electron spin coherence independent of the sample composition. Instead, we report a matrix nuclei dependent performance of the applied DD scheme at 40 K with Uhrig outperforming Carr-Purcell DD in OTP, and vice versa for a dOTP matrix.

A 5-pulse version of the Double Electron Electron Resonance (DEER) experiment with Carr-Purcell delays and an additional pump pulse has been shown to significantly extend the experimentally accessible distance range in cases where nuclear spin diffusion dominates electron spin phase memory loss [Borbat et al., J. Phys. Chem. Lett., 2013, 4, 170]. We show that the sequence also prolongs coherence decay for spin labels in or near lipid bilayers, where this decay is mono-exponential. Compared to 4-pulse DEER, 5-pulse DEER suffers from additional artefacts that stem from pulse imperfection and excitation band overlap. Only some of these artefacts can be suppressed by phase cycling and the remaining ones have hindered widespread utilization of the method. Here, we report previously unknown additional artefact contributions stemming from overlap between the excitation bands of the microwave pulses that introduce additional dipolar evolution pathways. Experimental conditions are analyzed in detail that suppress these as well as the already known artefacts. Such suppression results in data that contain at most the partial excitation artefact, which can be deliberately shifted in time by a change in pulse timing without affecting the wanted contribution.

Double electron electron resonance (DEER) enables determination of distance distributions in the nanometre range. A recently introduced 5-pulse version of this experiment prolongs the electron spin coherence lifetime and thus provides improved sensitivity or an extended distance range, but suffers from artefacts due to partial excitation and excitation band overlap. In particular, the partial excitation artefact is hard to eliminate experimentally at frequencies where DEER is most sensitive or on spectrometers that provide only monochromatic pulses. Here, a data post-processing method is introduced that removes the partial excitation artefact without relying on previous knowledge of its amplitude and without sensitivity loss. The method is based on acquisition of two traces with shifted positions of the artefact and computation of the artefact shape from the difference of the two traces. Artefact removal was successfully tested both on simulated and experimental data. It was found to be stable for a variety of distance distributions and down to low signal-to-noise ratios in the presence of moderate background decay. The artefact correction method also performs well in the regime of rather strong partial excitation artefacts that is usually encountered with rectangular monochromatic pump pulses on widely available commercial spectrometers.

Distance measurements by pulse electron paramagnetic resonance techniques are increasingly applied to multiple-spin systems. In the double electron-electron resonance experiment, more than two dipolar coupled spins manifest in an increased total modulation depth and in sum and difference dipolar frequency contributions that give rise to additional peaks appearing in the distance distribution, which do not correspond to the real interspin distances of the system and are hence referred to as ghost contributions. These ghost contributions may be so prominent that they might be mistaken for real distance peaks or that real distance peaks shift their position or disappear. We present a simple approximate procedure to suppress ghost distances to a great extent by manipulating the experimentally obtained form factor during data analysis by a simple power scaling with a scaling exponent ζ(N) = 1/(1-N), with N being the number of coupled spins in the system. This approach requires neither further experimental effort nor exact knowledge about labelling and inversion efficiency. This should enable routine application to biological systems. The approach is validated on simulated test cases for up to five spins and applied to synthetic model samples. The suppression of ghost distances with the presented approach works best for symmetric geometries and rigid molecules which, at the same time, are the cases where ghost contributions are most disturbing. The distance distributions obtained by power scaling are consistent with distributions that were obtained with previously obtained alternative approaches and agree, in some cases, strikingly well with the expectations for the true interspin distance distributions.

Measurement of distances with the Double Electron-Electron Resonance (DEER) experiment at X-band frequencies using a pair of nitroxides as spin labels is a popular biophysical tool for studying function-related conformational dynamics of proteins. The technique is intrinsically highly precise and can potentially access the range from 1.5 to 6-10 nm. However, DEER performance drops strongly when relaxation rates of the nitroxide spin labels are high and available material quantities are low, which is usually the case for membrane proteins reconstituted into liposomes. This leads to elevated noise levels, very long measurement times, reduced precision, and a decrease of the longest accessible distances. Here we quantify the performance improvement that can be achieved at Q-band frequencies (34.5 GHz) using a high-power spectrometer. More than an order of magnitude gain in sensitivity is obtained with a homebuilt setup equipped with a 150 W TWT amplifier by using oversized samples. The broadband excitation enabled by the high power ensures that orientation selection can be suppressed in most cases, which facilitates extraction of distance distributions. By varying pulse lengths, Q-band DEER can be switched between orientationally non-selective and selective regimes. Because of suppression of nuclear modulations from matrix protons and deuterons, analysis of the Q-band data is greatly simplified, particularly in cases of very small DEER modulation depth due to low binding affinity between proteins forming a complex or low labelling efficiency. Finally, we demonstrate that a commercial Q-band spectrometer can be readily adjusted to the high-power operation.

Studies of structure and dynamics of proteins using site-directed spin labelling rely on explicit modelling of spin label conformations. The large computational effort associated with such modelling with molecular dynamics (MD) simulations can be avoided by a rotamer library approach based on a coarse-grained representation of the conformational space of the spin label. We show here that libraries of about 200 rotamers, obtained by iterative projection of a long MD trajectory of the free spin label onto a set of canonical dihedral angles, provide a representation of the underlying trajectory adequate for EPR distance measurements. Rotamer analysis was performed on selected X-ray structures of spin labelled T4 lysozyme mutants to characterize the spin label rotamer ensemble on a single protein site. Furthermore, predictions based on the rotamer library approach are shown to be in nearly quantitative agreement with electron paramagnetic resonance (EPR) distance data on the Na(+)/H(+) antiporter NhaA and on the light-harvesting complex LHCII whose structures are known from independent cryo electron microscopy and X-ray studies, respectively. Suggestions for the selection of labelling sites in proteins are given, limitations of the approach discussed, and requirements for further development are outlined.

The biological function of protein, DNA, and RNA molecules often depends on relative movements of domains with dimensions of a few nanometers. This length scale can be accessed by distance measurements between spin labels if pulsed electron paramagnetic resonance (EPR) techniques such as electron-electron double resonance (ELDOR) and double-quantum EPR are used. The approach does not require crystalline samples and is well suited to biomacromolecules with an intrinsic flexibility as distributions of distances can be measured. Furthermore, oligomerization or complexation of biomacromolecules can also be studied, even if it is incomplete. The sensitivity of the technique and the reliability of the measured distance distribution depend on careful optimization of the experimental conditions and procedures for data analysis. Interpretation of spin-to-spin distance distributions in terms of the structure of the biomacromolecules furthermore requires a model for the conformational distribution of the spin labels.