Accessing distributions of exchange and dipolar couplings in stiff molecular rulers with Cu(II) centres.

Determining distributed exchange couplings is important for understanding the properties of synthetic magnetic molecules. Such distributions can be determined from pulsed dipolar spectroscopy (PDS) data, but this is challenging due to the similar influence of both exchange and dipolar couplings on such data. In this work we introduce two models that aim to identify these two contributions to the spin-spin couplings from frequency-domain PDS data of shape-persistent molecules having either two Cu(ii) ions, or a Cu(ii) ion and a nitroxide radical as the paramagnetic moieties. The first model assumes correlated Lorentzian or Gaussian exchange and dipole-dipole coupling distributions whose parameters are the model's unknowns. The second model relies on prior knowledge of the distance distribution and by performing Tikhonov regularization along the exchange coupling dimension yields the latter distribution model-free. Both models were able to differentiate between the absence and the presence of exchange interaction, to determine the coupling regime (ferro- or antiferromagnetic) and to estimate the distribution shape. In contrast, calculations within the exchange resilient model of the neural network analysis implemented in DeerAnalysis2018 were not able for our data to identify exchange couplings and return correct distance distributions. However, the generic model was able to identify and separate the strongly curved intermolecular background in the relaxation-induced dipolar modulation enhancement (RIDME) experiments. Our analysis revealed that in such systems exchange coupling may be present up to at least 3.3 nm in π-conjugated systems involving Cu(ii)-PyMTA, while it is negligible for distances r ≥ 4.5 nm between Cu(ii) ions and r ≥ 3.8 nm between a Cu(ii) ion and an unpaired electron of a nitroxide radical. Disruption of the π-conjugation between the ligand of the Cu(ii) complex and the nitroxide leads to negligible exchange coupling at distances r ≥ 2.6 nm in the corresponding [Cu(ii)-TAHA]-nitroxide ruler. Overall, for cases with known distance distributions, the presented analysis techniques allow to determine distributions of exchange couplings from PDS data.

Magnetic excitation and readout of methyl group tunnel coherence.

Methyl groups are ubiquitous in synthetic materials and biomolecules. At sufficiently low temperature, they behave as quantum rotors and populate only the rotational ground state. In a symmetric potential, the three localized substates are degenerate and become mixed by the tunnel overlap to delocalized states separated by the tunnel splitting ν t . Although ν t can be inferred by several techniques, coherent superposition of the tunnel-split states and direct measurement of ν t have proven elusive. Here, we show that a nearby electron spin provides a handle on the tunnel transition, allowing for its excitation and readout. Unlike existing dynamical nuclear polarization techniques, our experiment transfers polarization from the electron spin to methyl proton spins with an efficiency that is independent of the magnetic field and does not rely on an unusually large tunnel splitting. Our results also demonstrate control of quantum states despite the lack of an associated transition dipole moment.

High binding yet accelerated guest rotation within a cucurbit[7]uril complex. Toward paramagnetic gyroscopes and rolling nanomachines.

The (15-oxo-3,7,11-triazadispiro[5.1.5.3]hexadec-7-yl)oxidanyl, a bis-spiropiperidinium nitroxide derived from TEMPONE, can be included in cucurbit[7]uril to form a strong (K(a)∼ 2 × 10(5) M(-1)) CB[7]@bPTO complex. EPR and MS spectra, DFT calculations, and unparalleled increased resistance (a factor of ∼10(3)) toward ascorbic acid reduction show evidence of deep inclusion of bPTO inside CB[7]. The unusual shape of the CB[7]@bPTO EPR spectrum can be explained by an anisotropic Brownian rotational diffusion, the global tumbling of the complex being slower than rotation of bPTO around its "long molecular axis" inside CB[7]. The CB[7] (stator) with the encapsulated bPTO (rotator) behaves as a supramolecular paramagnetic rotor with increased rotational speed of the rotator that has great potential for advanced nanoscale machines requiring wheels such as cucurbiturils with virtually no friction between the wheel and the axle for optimum wheel rotation (i.e. nanopulleys and nanocars).

Relaxation and modulation interference effects in two-pulse electron spin echo envelope modulation (ESEEM).

Two-pulse electron spin echo envelope modulation (ESEEM) line widths are influenced by transverse electron spin relaxation, which is in turn induced by local field fluctuations. Simultaneous analysis of the decays of the unmodulated and modulated parts of the ESEEM signal provides deeper insight into the relaxation of a spin system consisting of an electron spin 1/2 coupled to N(I) nuclei with spin 1/2. Standard two-pulse ESEEM formulas either do not account for relaxation or assume uniform relaxation for all lines. In general, the relaxation rates on allowed and forbidden transitions may not be the same. Experimental results obtained on a single crystal of Cu(II)-doped L-histidine suggest that such a difference exists. Theoretical considerations show that in such a case the product rule for two-pulse ESEEM does not extend to expressions including relaxation. Product rules in general do not properly account for relaxation in three-pulse ESEEM and HYSCORE experiments. Decay of the apparently non-oscillatory part of the two-pulse echo may be strongly affected by modulation interference. Such interference of difference frequencies of matrix nuclei may cause a rather flat initial feature, which was previously attributed solely to non-exponential phase relaxation of electron spin transitions due to spin diffusion of the matrix nuclei. In addition, the sometimes observed drastic initial decay of the time domain signal is related to modulation interference of multiple-quantum coherences that arise from a strong cross-suppression effect.

Characterization of Protein Conformational Changes with Sparse Spin-Label Distance Constraints.

The combination of site-directed spin labeling with pulse EPR distance measurements can provide a moderate number of distance constraints on the nanometer length scale for proteins in different states. By adapting an existing algorithm (Zheng, W.; Brooks, B. R. Biophys. J. 2006, 90, 4327) to the problem, we address the question to what extent conformational change can be characterized when the protein structure is known for one of the states, whereas only a sparse set of distance constraints between spin labels is available for the other state. We find that the type and general direction of the conformational change can be recognized, while the amplitude may be uncertain.

Design of a permanent magnet with a mechanical sweep suitable for variable-temperature continuous-wave and pulsed EPR spectroscopy.

A magnetic system is introduced which consists of three nested rings of permanent magnets of a Halbach dipolar layout and is capable for EPR spectroscopy. Two of the rings can be rotated independently to adjust the magnetic flux in the center and even allow for mechanical field sweeps. The presented prototype achieves a magnetic flux range of 0.0282-0.3013T with a minimal sweep of 0.15mT and homogeneity of about 10(-3). First applications with CW and pulsed Mims ENDOR as well as ESEEM experiments on a sample of a glycine single crystal doped with 1% copper nitrate demonstrate that flux range, sweep accuracy and homogeneity of this prototype is sufficient for EPR experiments on most solid samples. Together with a recently improved design magnets can be build which could serve as compact and easily transportable replacement of standard electromagnets with negligible consumption of power or coolants.

Pulsed EPR determination of water accessibility to spin-labeled amino acid residues in LHCIIb.

Membrane proteins reside in a structured environment in which some of their residues are accessible to water, some are in contact with alkyl chains of lipid molecules, and some are buried in the protein. Water accessibility of residues may change during folding or function-related structural dynamics. Several techniques based on the combination of pulsed electron paramagnetic resonance (EPR) with site-directed spin labeling can be used to quantify such water accessibility. Accessibility parameters for different residues in major plant light-harvesting complex IIb are determined by electron spin echo envelope modulation spectroscopy in the presence of deuterated water, deuterium contrast in transversal relaxation rates, analysis of longitudinal relaxation rates, and line shape analysis of electron-spin-echo-detected EPR spectra as well as by the conventional techniques of measuring the maximum hyperfine splitting and progressive saturation in continuous-wave EPR. Systematic comparison of these parameters allows for a more detailed characterization of the environment of the spin-labeled residues. These techniques are applicable independently of protein size and require approximately 10-20 nmol of singly spin-labeled protein per sample. For a residue close to the N-terminus, in a domain unresolved in the existing x-ray structures of light-harvesting complex IIb, all methods indicate high water accessibility.

Relaxation-based distance measurements between a nitroxide and a lanthanide spin label.

Distance measurements by electron paramagnetic resonance techniques between labels attached to biomacromolecules provide structural information on systems that cannot be crystallized or are too large to be characterized by NMR methods. However, existing techniques are limited in their distance range and sensitivity. It is anticipated by theoretical considerations that these limits could be extended by measuring the enhancement of longitudinal relaxation of a nitroxide label due to a lanthanide complex label at cryogenic temperatures. The relaxivity of the dysprosium complex with the macrocyclic ligand DOTA can be determined without direct measurements of longitudinal relaxation rates of the lanthanide and without recourse to model compounds with well defined distance by analyzing the dependence of relaxation enhancement on either temperature or concentration in homogeneous glassy frozen solutions. Relaxivities determined by the two calibration techniques are in satisfying agreement with each other. Error sources for both techniques are examined. A distance of about 2.7 nm is measured in a model compound of the type nitroxide-spacer-lanthanide complex and is found in good agreement with the distance in a modeled structure. Theoretical considerations suggest that an increase of the upper distance limit requires measurements at lower fields and temperatures.

A pulsed EPR study of surfactant layer structure in composites of a synthetic layered silicate with polystyrene and polycaprolactone.

Double electron electron resonance (DEER), deuterium electron spin-echo envelope modulation (ESEEM) spectroscopy and 31P electron nuclear double resonance (ENDOR) spectroscopy were applied to site-specifically spin-labeled surfactants in the organically modified layered silicate magadiite and its composites with polystyrene (PS) and polycaprolactone (PCL). The organomagadiite consist of stacks of silicate platelets with surfactant layers between these platelets. In PS composites the stacks are dispersed in the polymer matrix as a whole, while melt processing with PCL leads to intercalation of polymer chains into the galleries between the platelets. The DEER data prove that even in the case of the non-intercalated PS composites the density of surfactant molecules changes drastically during composite formation on length scales of a few nanometers. Deuterium ESEEM data demonstrate that spin labels attached both in the middle and at the end of the alkyl chain have contact with the headgroups of neighboring surfactant molecules. By analysis of the 31P ENDOR spectra, two characteristic distances are found between the spin labels and the headgroups of phosphonium surfactants. The shorter, proximal distance can be assigned to headgroups in the same surfactant layer. By comparison with the basal spacing between consecutive silicate platelets the longer, distal distance is assigned to a layer of surfactants that is not attached to the surface of the next platelet but rather located between platelets. Altogether the data support a picture of trilayers of disordered surfactant molecules with their alkyl chains oriented nearly parallel to the surface.

Distance measurements in the borderline region of applicability of CW EPR and DEER: a model study on a homologous series of spin-labelled peptides.

Inter-spin distances between 1 nm and 4.5 nm are measured by continuous wave (CW) and pulsed electron paramagnetic resonance (EPR) methods for a series of nitroxide-spin-labelled peptides. The upper distance limit for measuring dipolar coupling by the broadening of the CW spectrum and the lower distance limit for the present optimally-adjusted double electron electron resonance (DEER) set-up are determined and found to be both around 1.6-1.9 nm. The methods for determining distances and corresponding distributions from CW spectral line broadening are reviewed and further developed. Also, the work shows that a correction factor is required for the analysis of inter-spin distances below approximately 2 nm for DEER measurements and this is calculated using the density matrix formalism.

High-resolution structure of a Na+/H+ antiporter dimer obtained by pulsed electron paramagnetic resonance distance measurements.

Transient or partial formation of complexes between biomacromolecules is a general mechanism used to control cellular functions. Several of these complexes escape structure determination by crystallographic means. We developed a new approach for determining the structure of protein dimers in the native environment (e.g., in the membrane) with high resolution in cases where the structure of the two monomers is known. The approach is based on measurements of distance distributions between spin labels in the range between 2 and 6 nanometers by a pulsed electron paramagnetic resonance technique and explicit modeling of spin label conformations. By applying this method to the membrane protein homodimer of the Na(+)/H(+) antiporter NhaA of Escherichia coli, the structure of the presumably physiological dimer was determined. It reveals two points of contact between the two monomers, with one of them confirming results of earlier cross-linking experiments.

Spin pair geometry revealed by high-field DEER in the presence of conformational distributions.

Orientation selection on two nitroxide-labelled shape-persistent molecules is demonstrated by high-field pulsed electron-electron double resonance experiments at a frequency of 95 GHz with a commercial spectrometer. The experiments are performed with fixed observer and pump frequencies by variation of the magnetic field, so that the variation of both the dipolar frequencies and the modulation depths can be analyzed. By applying the deadtime-free four-pulse double electron-electron resonance (DEER) sequence, the lineshapes of the dipolar spectra are obtained. In the investigated linear biradical and equilateral triradical the nitroxide labels undergo restricted dynamics, so that their relative orientations are not fixed, but are correlated to some extent. In this situation, the general dependence of the dipolar spectra on the observer field can be satisfyingly modelled by simple geometrical models that involve only one rotational degree of freedom for the biradical and two rotational degrees of freedom for the triradical. A somewhat better agreement of the dipolar lineshapes for the biradical is obtained by simulations based on a molecular dynamics trajectory. For the triradical, small but significant deviations of the lineshape are observed with both models, indicating that the technique can reveal deficiencies in modelling of the conformational ensemble of a macromolecule.

Isotope selection in distance measurements between nitroxides.

Self-assembly of spin-labeled synthetic macromolecules or biomacromolecules can lead to structures that contain more than two nitroxide radicals. Label-to-label distance distributions are then poorly resolved since established electron paramagnetic resonance techniques for distance measurements cannot select between the different pairs of nitroxides. A separation into different contributions can be achieved by partially labeling the nitroxide radicals by (15)N or by deuterium and applying pulse electron electron double resonance techniques. With (15)N labeling, strong suppression of either the (14)N or the (15)N contribution can be achieved by suitable choices of the excitation bandwidths and frequencies of the observer subsequence and pump pulse and linear combination of data sets. With deuterium labeling, interactions between only the isotope-labeled nitroxides can be selected by a two-dimensional version of the four-pulse double electron electron resonance experiment. This selection is based on the deep electron spin echo envelope modulation of deuterated nitroxides.

A site-directed spin-labeling study of surfactants in polymer-clay nanocomposites.

Polymer-clay nanocomposites exhibit much improved mechanical, physical, and chemical properties compared to the pure polymer. The interaction of polymer and organically modified silicates is mainly influenced by the surfactant layer in the system. To investigate the structure and dynamics of this surfactant layer, various electron paramagnetic spectroscopy (EPR) techniques were applied. Continuous wave EPR experiments showed a temperature-dependent heterogeneous mobility of the surfactant layer in organoclay as well as a difference in dynamics along the alkyl chain. Intercalation of polystyrene causes a significant slowdown in surfactant dynamics. Electron spin echo envelope modulation indicates a closer contact of the polymer with the mid of the surfactant tail than with the end of the tail. From the obtained data the picture of flatly lying surfactants on clay platelets with a mobility gradient along their alkyl chains can be drawn.

Separation of motional processes in a [2]catenane by combining synthetic, dual-frequency EPR and molecular modelling approaches.

Continuous-wave EPR of nitroxide spin labels at conventional (9.4 GHz) and high (94.2 GHz) frequencies is applied to characterize molecular dynamics in [2]catenanes composed of macrocycles with rigid phenyleneethynylene and flexible alkyl chain building blocks. By using a set of compounds with increasing complexity, which were all labelled at the centre of a rigid building block, it was possible to find regimes where spectral lineshapes were dominated by local motion of the spin label or those that contained information on tumbling of the building blocks. In chloroform, the macrocycles do not move as rigid objects, rather the rigid building block can reorient with some ease, with respect to the rest of the molecule. Furthermore, in that solvent the [2]catenane samples the co-conformational space on a timescale of microseconds or shorter. In a mechanical picture, chloroform can thus be considered as an effective lubricant that prevents the macrocycles from sticking together.

EPR techniques for studying radical enzymes.

EPR studies on radical enzymes are reviewed under the aspects of the information that they can provide and of the techniques that are used. An overview of organic radicals derived from amino acids, modified amino acids, and cofactors is given and g tensor data are compiled. The information accessible from a spectroscopic point of view is contrasted with the information required to understand enzyme structure and function, and some precautions are discussed that must be taken to derive the latter kind of information from the former. Structural dynamics is identified as an aspect that has rarely been addressed in the past although it is highly relevant for enzyme function. It is proposed that techniques introduced recently on other classes of proteins could help to close this gap.

Sensitivity enhancement in pulse EPR distance measurements.

Established pulse EPR approaches to the measurement of small dipole-dipole couplings between electron spins rely on constant-time echo experiments to separate relaxational contributions from dipolar time evolution. This requires a compromise between sensitivity and resolution to be made prior to the measurement, so that optimum data are only obtained if the magnitude of the dipole-dipole coupling is known beforehand to a good approximation. Moreover, the whole dipolar evolution function is measured with relatively low sensitivity. These problems are overcome by a variable-time experiment that achieves suppression of the relaxation contribution by reference deconvolution. Theoretical and experimental results show that this approach leads to significant sensitivity improvements for typical systems and experimental conditions. Further sensitivity improvements or, equivalently, an extension of the accessible distance range can be obtained by matrix deuteration or digital long-pass filtering of the time-domain data. Advantages and limitations of the new variable-time experiment are discussed by comparing it to the established analogous constant-time experiment for measurements of end-to-end distances of 5 and 7.5 nm on rod-like shape-persistent biradicals and for the measurement of a broadly distributed transmembrane distance in a doubly spin-labeled mutant of plant light harvesting complex II.

2D TRIPLE in orientationally disordered samples--a means to resolve and determine relative orientation of hyperfine tensors.

The two-dimensional (2D) TRIPLE experiment provides correlations between electron-nuclear double resonance (ENDOR) frequencies that belong to the same electron-spin manifold, M(S), and therefore allows to assign ENDOR lines to their specific paramagnetic centers and M(S) manifolds. This, in turn, also provides the relative signs of the hyperfine couplings. So far this experiment has been applied only to single crystals, where the cross-peaks in the 2D spectrum are well resolved with regular shapes. Here we introduce the application of the 2D TRIPLE experiment to orientationally disordered systems, where it can resolve overlapping powder patterns. Moreover, analysis of the shape of the cross-peaks shows that it is highly dependent on the relative orientation of the hyperfine tensors of the two nuclei contributing to this particular peak. This is done initially through a series of simulations and then demonstrated experimentally at a high field (W-band, 95 GHz). The first example concerned the (1)H hyperfine tensors of the stable radical alpha,gamma-bisdiphenylene-beta-phenylallyl (BDPA) immobilized in a polystyrene matrix. Then, the experiment was applied to a more complex system, a frozen solution of Cu(II)-bis(2,2':6',2'' terpyridine) complex. There, the 2D TRIPLE experiment was combined with the variable mixing time (VMT) ENDOR experiment, which determined the absolute sign of the hyperfine couplings involved, and orientation selective ENDOR experiments. Analysis of the three experiments gave the hyperfine tensors of a few coupled protons.

Magic-angle sample spinning electron paramagnetic resonance--instrumentation, performance, and limitations.

An electron paramagnetic resonance (EPR) setup for line narrowing experiments with fast sample spinning at variable angles between the rotation axis and the static magnetic field is described and applied in the magic-angle sample spinning (MAS) EPR experiment at X-band frequencies (9.5 GHz). Sample spinning speeds up to 17 kHz at temperatures down to 200 K can be achieved with rotors of 4-mm outer and 2.5-mm inner diameter without severe losses in microwave amplitude compared to standard pulse EPR probeheads. A phase cycle is introduced that provides pure absorption MAS EPR spectra and allows one to distinguish between positive and negative frequency offsets (pseudo-quadrature detection). Possible broadening mechanisms in MAS EPR spectra are discussed. It is demonstrated both by theory and by experiment that the MAS EPR experiment requires excitation bandwidths that are comparable to the total spectral width, since otherwise destructive interference between contributions of spins with similar resonance offsets suppresses the signal. Experimental observations on the E(1) center in gamma-irradiated silica glass and on the SO(-)(3) radical in gamma-irradiated sulfamic acid are reported.