Orientation Selective 2D-SIFTER Experiments at X-Band Frequencies

Frequency-correlated 2D SIFTER with broadband pulses at X-band frequencies can be used to determine the inter-spin distance and relative orientation of nitroxide moieties in macromolecules when the flexibility of the spin-labels is restricted. At X-band frequencies the EPR spectrum of nitroxides is governed by the strongly anisotropic nitrogen hyperfine coupling. For rigid spin-labels, where the orientation of the inter-connecting vector R correlates to the relative orientations of the nitroxide labels, the dipolar oscillation frequency varies over the EPR spectral line shape. Broadband shaped pulses allow excitation of the complete nitroxide EPR spectra. In this case, Fourier transform of the echo signal gives both fast and direct access to the orientation dependent dipole coupling. This allows determination of not only the inter-spin distance R, but also their mutual orientation. Here, we show the application of the frequency-correlated 2D SIFTER experiment with broadband pulses to a bis-nitroxide model compound and to a double stranded DNA sample. In both molecules, there is restricted internal mobility of the two spin-labels. The experimental results are compared to orientation selective pulsed electron double resonance (PELDOR) experiments and simulations based on a simple geometrical model or MD simulations describing the conformational flexibility of the molecules. Fourier transformation of the SIFTER echo signal yields orientation selective dipolar time traces over the complete EPR-spectral range. This leads to an improved frequency resolution and either to a reduced experimental measurement time or a larger span of frequency offsets measured compared to orientation selective PELDOR experiments. The experimental potential and limitations of the 2D SIFTER method for samples containing rigid spin-labels will be discussed.     

Geometric model-based fitting algorithm for orientation-selective PELDOR data

Pulsed electron–electron double resonance (PELDOR or DEER) spectroscopy is frequently used to determine distances between spin centres in biomacromolecular systems. Experiments where mutual orientations of the spin pair are selectively excited provide the so-called orientation-selective PELDOR data. This data is characterised by the orientation dependence of the modulation depth parameter and of the dipolar frequencies. This dependence has to be taken into account in the data analysis in order to extract distance distributions accurately from the experimental time traces. In this work, a fitting algorithm for such data analysis is discussed. The approach is tested on PELDOR data-sets from the literature and is compared with the previous results.     

Three-Pulse ELDOR Theory Revisited

The current theory of three-pulse electron double resonance (PELDOR) has been generalized to the case, when paramagnetic particles (spin labels) in pairs or groups have the electron paramagnetic resonance (EPR) spectra, which overlap essentially or coincide. The PELDOR signal modulation induced by the dipole–dipole interaction between paramagnetic spin ½ particles in pairs embedded in disordered systems has been analyzed comprehensively. It has been shown that the PELDOR signal contains additional terms in contrast to the situation considered in the current theory, when the EPR spectra of the spin labels in the pairs do not overlap. In disordered systems, the pairs of spin labels have the characteristic dipolar interaction frequency. According to the current theory for pairs of spin labels, the PELDOR signal reveals the modulation with this characteristic frequency. The additional terms, which are obtained in this work, do not change the modulation frequency of the PELDOR signal for pairs of spin labels. However, these additional terms should be taken into account when analyzing the amplitude of the PELDOR signal and the amplitude of the modulation of the PELDOR signal. The consistent approach to treating the PELDOR data for the groups containing three or more spin labels has been outlined on the basis of the results for pairs of spin labels. It has been also analyzed how the spin flips and molecular motion or molecular isomerization can affect the manifestation of the interaction between the spin labels in PELDOR experiments. PELDOR experiments for the stable biradicals (biradicals I containing 1-oxyl-2,2,5,5-tetramethylpyrroline-3-yl spin labels and biradicals II containing 3-imidazoline spin labels) have been performed. The results have been interpreted within the theory developed in this work.     

Nonselective excitation of pulsed ELDOR using multi-frequency microwaves

The use of a polychromatic microwave pulse to expand the pumping bandwidth in pulsed electron-electron double resonance (PELDOR) was investigated. The pumping pulse was applied in resonance with the broad (～100 mT) electron paramagnetic resonance (EPR) signal of the manganese cluster of photosystem II in the S2 state. The observation pulses were in resonance with the narrow EPR signal of the tyrosine radical, YD·. It was found that in the case of the polychromatic pumping pulse containing five harmonics with the microwave frequencies between 8.5 and 10.5 GHz the PELDOR effect corresponding to the dipole interaction between the Mn cluster and YD· was about 2.9 times larger than that achieved with a monochromatic pulse. In addition to the dipolar modulation, the nuclear modulation effects were observed. The effects could be suppressed by averaging the PELDOR trace over the time interval between the observation microwave pulses. The polychromatic excitation technique described will be useful for improving the PELDOR sensitivity in the measurements of long distances in biological samples, where the pair consists of a radical with a narrow EPR spectrum and slow phase relaxation, and a metal center that has a broad EPR spectrum and a short phase relaxation time.     

Fractons in proteins: can they lead to anomalously decaying time autocorrelations?

Motivated by recent studies on the fractal nature of folded proteins, we analyze the time-dependent autocorrelation function < x (-->)(t).x(-->)(0) >of the distance between two points on a thermally vibrating fractal. Using fractons, the vibrational excitations of a fractal, we show that for both strongly underdamped and overdamped vibrations this correlation function decays anomalously, displaying a crossover from a nearly stretched exponential decay at short times to a slow algebraic decay at long times. Relationship to single molecule experiments is discussed.     

Random walks in a closed space

We present simulations for random walks on a giant cluster in a randomly occupied hypercube. A new algorithm does away with the need for large memory requirements. The data can be fitted to high precision using stretched exponentials; confirming earlier conclusions, the results underline the strong resemblance between the decay behaviour in this mathematical model and that observed numerically or experimentally in glassy systems.     

High-frequency 180 GHz PELDOR

For aromatic organic radicals, pulsed electron-electron double resonance (PELDOR) experiments at high magnetic fields offer the possibility to achieve orientation-selective pumping and detection that could allow one not only to determine the distance between paramagnetic species but also their relative orientation with respect to the interconnecting dipolar axis. We present a PELDOR two-frequency setup that was introduced into our homebuilt 180 GHz pulsed electron paramagnetic resonance (EPR) spectrometer and we discuss its technical and experimental features. The capability of 180 GHz PELDOR has been tested using the three-pulse ELDOR sequence on the protein RNR-R2 (ribonucleotide reductase) fromEscherichia coli, which contains two tyrosyl radicals at a distance of 3.3 nm. At 180 GHz, orientation selectivity is observed and the modulation frequency was found in good agreement with theoretical predictions, which take into account the relative orientation of the radicals from X-ray data.     

Homonuclear Dipolar Coupling and CPMG Spin-Echoes in NQR

The nuclear quadrupole resonance signals from both a single crystal and a powder sample of spin-1 nuclei under a Carr?CPurcell?CMeiboom?CGill are modeled numerically. While the single crystal clearly shows the effects of dipolar coupling for on-resonant pulses, the powder does not. However, for certain off-resonant conditions, the powder sample exhibits the same response as the single crystal. Experimentally, this corresponds to the observation of a rapid decay at these conditions. Using a powder sample of NaNO₂, the functional form of the echo train, when the dipolar coupling is not refocused, is clearly different than the decay for an on-resonance sequence, and can be used to characterize the dipolar coupling.     

Triplet-state spin labels for highly sensitive pulsed dipolar spectroscopy

ABSTRACT

Pulsed dipolar spectroscopic methods allow nanometer distance measurements between pairs of spin labels. We have proposed a new spin labelling approach, based on the population of a chromophore triplet under light excitation, testing it on a peptide-based spectroscopic ruler and a photosynthetic protein. We have applied a modified Pulsed Electron DOuble Resonance (PELDOR) sequence where the photogeneration of the triplet spin precedes the conventional 4-pulse PELDOR sequence. In this experiment, the triplet-state serves as detection spin while the stable nitroxide is the pump spin. Alternatively, a new method, Laser-Induced Magnetic Dipole spectroscopy (LaserIMD), has been proposed: the nitroxide signal is detected while a time varying laser pulse acts as a pump to generate the triplet state [C. Hintze, D. Bücker, S. Domingo Köhler, G. Jeschke and M. Drescher, J. Phys. Chem. Lett. 7 (12), 2204 (2016)]. For the first time, in this work, we compare the two dipolar techniques performing X-band experiments in the same experimental conditions and deriving analytical expressions for the echo modulation by the density matrix formalism.     

PELDOR at S- and X-band frequencies and the separation of exchange coupling from dipolar coupling

A pulsed electron double resonance (PELDOR) setup working at S-band frequencies is introduced and its performance compared with an X-band setup. Furthermore, to verify experimentally that it is possible to disentangle the dipolar coupling nu(Dip) from the exchange coupling J by PELDOR we synthesized and investigated four bisnitroxide radicals. They exhibit in pairs the same distances r(AB) between the nitroxide moieties but only one of each pair possesses a non-zero J. The experimental values for r(AB) match the ones from molecular modeling very well for the molecules without exchange coupling. For one bisnitroxide it was possible to separate nu(Dip) from J and to ascertain the magnitude and sign of J to +11 MHz (antiferromagnetic spin-spin coupling).     

Random walk in a random multiplicative environment

We investigate the dynamics of a random walk in a random multiplicative medium. This results in a random, but correlated, multiplicative process for the spatial distribution of random walkers. We show how the details of these correlations determine the asymptotic properties of the walk, i.e., the central limit theorem does not apply to these multiplicative processes. We also study a periodic source-trap medium in which a unit cell contains one source, followed byL–1 traps. We calculate the asymptotic behavior of the number of particles, and determine the conditions for which there is growth or decay in this average number. Finally, we discuss the asymptotic behavior of a random walk in the presence of randomly distributed, partially-absoprbing traps. For this case, a temporal regime of purely exponential decay of the density can occur, before the asymptotic stretched exponential decay, exp(–at ^1/3), sets in.     

Nonequilibrium critical dynamics at surfaces: cluster dissolution and nonalgebraic correlations

We study nonequilibrium dynamical properties at a free surface after the system is quenched from the high-temperature phase into the critical point. We show that if the spatial surface correlations decay sufficiently rapidly the surface magnetization and/or the surface manifold autocorrelations have a qualitatively different universal short time behavior than the same quantities in the bulk. At a free surface cluster dissolution may take place instead of domain growth, yielding stationary dynamical correlations that decay in a stretched exponential form. This phenomenon takes place in the three-dimensional Ising model and should be observable in real ferromagnets.     

Proton residual dipolar couplings by NMR magnetization exchange in cross-linked elastomers: determination and imaging.

Proton nuclear magnetic resonance (NMR) magnetization exchange is used to investigate residual dipolar couplings in a series of cross-linked poly(styrene-cobutadiene) elastomers. A new model for the dipolar unit is used for the evaluation of the signal decay in magnetization exchange experiments. It takes into account an extended residual dipolar coupling network along the polymer chain. It is shown that in the regime of short mixing times, information about the residual dipolar coupling between methine and methylene protons can be obtained which is not affected by other inter- and intramolecular dipolar couplings. The dynamic order parameter of methine-methylene protons is measured and correlated with cross-link density. This study certifies the quality of a filter for magnetization from residual dipolar couplings which exploit magnetization exchange. The filter can be used to generate contrast in NMR images of heterogeneous elastomers. The first proton NMR parameter image of a dynamic order parameter is presented for a phantom made from poly(styrene-cobutadiene) samples with different cross-link densities.     

Pulsed electron double resonance (PELDOR) and its applications in free-radicals research

The papers related to the theoretical background and experimental investigations by pulsed electron double resonance (PELDOR) are reviewed. The main aim of this pulsed ESR application is to study the dipole-dipole spin interaction. In PELDOR the ESR spectrum is excited by two ESE pulses at frequencyω _a and additional pumping pulse atω _b. Decay functionV(T) of the ESE signal, when the time intervalT between the first ESE pulse and pumping pulse is varied, contains the information on dipole-dipole couplings in the spin system. The kinetics ofV(T) decay strongly depends upon distance, mutual orientation inside interacting spin pairs and space distribution of radicals throughout the sample. The distances between spins which were measured or estimated using PELDOR in the papers reviewed are in the range of 15 ÷ 130 Å. This pulsed ESR technique turns now to be a powerful supplement to conventional ESE in studying the free radicals space distribution..     

Persistence of manifolds in nonequilibrium critical dynamics

We study the persistence probability P(t) that, starting from a random initial condition, the magnetization of a d'-dimensional manifold of a d-dimensional spin system at its critical point does not change sign up to time t. For d'>0 we find three distinct late-time decay forms for P(t): exponential, stretched exponential, and power law, depending on a single parameter zeta=(D-2+eta)/z, where D=d-d' and eta,z are standard critical exponents. In particular, we predict that for a line magnetization in the critical d=2 Ising model, P(t) decays as a power law while, for d=3, P(t) decays as a power of t for a plane magnetization but as a stretched exponential for a line magnetization. Numerical results are consistent with these predictions.     

A Note on Exponential Decay in the Random Field Ising Model

For the two-dimensional random field Ising model (RFIM) with bimodal (i.e., two-valued) external field, we prove exponential decay of correlations either (i) when the temperature is larger than the critical temperature of the Ising model without external field and the magnetic field strength is small or (ii) at any temperature when the magnetic field strength is sufficiently large. Unlike previous work on exponential decay, our approach is not based on cluster expansions but rather on arguably simpler methods; these combine an analysis of the Kertész line and a coupling of Ising measures (and also their random cluster representations) with different boundary conditions. We also show similar but weaker results for the RFIM with a general field distribution and in any dimension.     

Effect of Pumping Pulse Duration on Echo Signal Amplitude in Four-Pulse PELDOR

The impact of pumping pulse duration on four-pulse pulsed electron?Celectron double resonance (PELDOR) data was experimentally studied. For biradicals with known distances between two spin labels, it is shown that refocused echo amplitude decreases with increasing the pumping pulse duration and decreasing the distance between spin labels. The effect becomes substantial when the pumping pulse duration is comparable or exceeds the inverse value of the dipole?Cdipole interaction between spin labels. This effect is essential for determination of distance distribution between labels in double-labeled molecules and for determination of the number of labels in clusters of spin-labeled molecules. PELDOR signal distortion was observed when the pumping pulse position in the time scale coincided with those of the detecting pulses. An approach of signal correction to eliminate this distortion is proposed.     

Visualization of distance distribution from pulsed double electron-electron resonance data

Double electron-electron resonance (DEER), also known as pulsed electron-electron double resonance (PELDOR), is a time-domain electron paramagnetic resonance method that can measure the weak dipole-dipole interactions between unpaired electrons. DEER has been applied to discrete pairs of free radicals in biological macromolecules and to clusters containing small numbers of free radicals in polymers and irradiated materials. The goal of such work is to determine the distance or distribution of distances between radicals, which is an underdetermined problem. That is, the spectrum of dipolar interactions can be readily calculated for any distribution of free radicals, but there are many, quite different distributions of radicals that could produce the same experimental dipolar spectrum. This paper describes two methods that are useful for approximating the distance distributions for the large subset of cases in which the mutual orientations of the free radicals are uncorrelated and the width of the distribution is more than a few percent of its mean. The first method relies on a coordinate transformation and is parameter-free, while the second is based on iterative least-squares with Tikhonov regularization. Both methods are useful in DEER studies of spin-labeled biomolecules containing more than two labels.     

Dark-state mechanism for the long-time transfer of excitations in a donor–acceptor system

The excitation energy transfer between a donor–acceptor pair with fixed distance apart through energy exchanging with environment is investigated. The total system is modeled as two two-level systems (TLSs) interacting with many harmonic oscillators. The pair behaves coherently or incoherently, depending on whether the dipolar coupling is stronger or weaker than the TLS–environment coupling. The environmental linear dispersion relation gives an analytical solution to the pair?s probability involving all the retardation times. We found that the long-time trapping of energy within the pair is caused by the inhibiting dark-state radiative decay when two TLSs are at half a resonant wavelength.     

Evidence for light-induced hole polarons in LiNbO3

Transient light-induced absorption in LiNbO3 is observed in the blue-green spectral range after pulsed illumination with 532 nm. Its buildup and decay in Fe-doped LiNbO3 is satisfactorily described by a sum of two stretched exponential functions. For undoped LiNbO3, however, only one stretched exponential decay is observed. These experimental results are explained by the formation of both small Nb(Li)4+ electron polarons and O- hole polarons. The mechanism is discussed on the basis of a proposed band scheme.