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.     

Matrix signals in electron-electron double resonance

The ΔM_{I= 0}, ELDOR spectra of nitroxide radicals in amorphous polystyrene and polypropylene matrices display absorptions at Δv = 13.5 and 27 MHz. The intensities of these signals are decreased by about 35 % in perdeuterated polystyrene. This and the frequency establishes the signals to be matrix ELDOR which results when nonbonded protons interact with the resultant of the external field and the electronic field. The 〈α_eβ′_H∥↔∥β_eα″_H〉 forbidden transition then becomes allowed. Rapid-passage results are also consistent with this model.     

Formation of the pulsed electron-electron double resonance signal in the case of a finite amplitude of microwave fields

A theoretical study of the effect of microwave (MW) fields of finite amplitude on the process of pulsed electron-electron double resonance (PELDOR) signal formation is carried out. It is shown that the behavior of the experimentally observed values can be described by four vectors of partial magnetizations whose motion is reduced to precession in effective magnetic fields. In the case of strong spin-spin interaction, the PELDOR effect can be observed when a sufficiently powerful MW field is applied at pumping frequency to affect both components of the Pake doublet. The possibility of a “two-frequency” spin echo to appear under the action of two pulses with different carrier frequencies in the system where the inhomogeneous broadening of the electron spin resonance line contour is mainly determined by the dipole-dipole interaction is demonstrated.     

Suppression of electron spin-echo envelope modulation peaks in double quantum coherence electron spin resonance

We show the use of the observer blind spots effect for the elimination of electron spin-echo envelope modulation (ESEEM) peaks in double quantum coherence (DQC) electron spin resonance (ESR). The suppression of ESEEM facilitates the routine and unambiguous extraction of distances from DQC-ESR spectra. This is also the first demonstration of this challenging methodology on commercial instrumentation.     

Pulsed electron-electron double resonance (PELDOR) distance measurements in detergent micelles

Pulsed electron-electron double resonance (PELDOR) spectroscopy is a powerful tool for measuring nanometer distances in spin-labeled systems. A common approach is doubly covalent spin-labeling of a macromolecule and measurement of the inter-spin distance, or to use singly-labeled components of a system that forms aggregates or oligomers. This situation has been described as a spin-cluster. The PELDOR signal, however, does not only contain the desired dipolar coupling between the spin-labels of the molecule or cluster under study. In samples of finite concentration the dipolar coupling between the spin-labels of the randomly distributed molecules or spin-clusters also contributes significantly. In homogeneous frozen solutions or lipid vesicle membranes this second contribution can be considered to be an exponential or stretched exponential decay, respectively. In this study, we show that this assumption is not valid in detergent micelles. Spin-labeled fatty acids that are randomly partitioned into different detergent micelles give rise to PELDOR time traces which clearly deviate from stretched exponential decays. The obtained signals can be modeled quantitatively based on the size of the micelles, their aggregation number, the spin-label concentration and the degree of spin-labeling. As a main conclusion a PELDOR signal deviating from a stretched exponential decay does not necessarily prove the observation of specific distance information on the molecule or cluster. These results are important for the interpretation of PELDOR experiments on membrane proteins or lipophilic peptides solubilized in detergent micelles or small vesicles, which often do not show pronounced dipolar oscillations in their time traces.     

Cyclotron resonance in asymmetric double quantum wells

Far-infrared magnetotransmission measurements in magnetic fields are carried out on asymmetric coupled double wells. We observe a splitting in the cyclotron resonance (CR) line for a wide range of intermediate magnetic fields and only one line at high magnetic fields. Two peaks observed in the CR spectra correspond to transitions between Landau levels in individual wells. We propose that phase transition between weak and strong coupling regimes may be responsible for the features. The characteristics of the transition are studied via an analysis of CR masses, CR splitting and line widths as a function of the magnetic field.     

The determination of pair distance distributions by pulsed ESR using Tikhonov regularization

Pulsed ESR techniques with the aid of site-directed spin labeling have proven useful in providing unique structural information about proteins. The determination of distance distributions in electron spin pairs directly from the dipolar time evolution of the pulsed ESR signals by means of the Tikhonov regularization method is reported. The difficulties connected with numerically inverting this ill-posed mathematical problem are clearly illustrated. The Tikhonov regularization with the regularization parameter determined by the L-curve criterion is then described and tested to confirm its accuracy and reliability. The method is applied to recent experimental results on doubly labeled proteins that have been studied using two pulsed ESR techniques, double quantum coherence (DQC) ESR and double electron-electron resonance (DEER). The extracted distance distributions are able to provide valuable information about the conformational constraints in various partially folded states of proteins. This study supplies a mathematically reliable method for extracting pair distributions from pulsed ESR experimental data and has extended the use of pulsed ESR to provide results of greater value for structural biology.     

Stochastic resonance in the coherence of a quantum system

We demonstrate the noise-induced amplification of a weak periodic signal inscribed in the coherence of a two-level atom, interacting with a single mode of the quantized radiation field coupled to a dissipative environment.     

Enhanced double quantum signals in nuclear magnetic resonance

A suggestion by Yatsiv for enhancing the strength of double quantum signals in high resolution nuclear magnetic resonance by use of radio-frequency sidebands is examined and shown to be practical. The theory shows that double quantum techniques can be extended to weakly coupled systems of nuclei (including systems of nuclei of different isotopic species). The AX part (with J _AX=5·4 c/s, δ_AX/2π=99·2 c/s) of the proton magnetic resonance spectrum of maltol (3-hydroxy-2-methyl-γ-pyrone) serves to confirm experimentally the quantitative theoretical treatment for weakly coupled systems. An enhancement factor of eight was observed as can be seen in figure 2.     

Electron resonance dynamics in a double quantum well

We consider the two-level electron dynamics in a double quantum well in a periodic, anharmonic external electric field. We propose a method for solving the Schrödinger equation, which is based on the generalization of conventional resonance approximation for a system with an arbitrary number of resonances. The method is used for the case of both weak and strong fields. We obtain expressions for the quasi-energy wave functions and the electron dipole moment. It is shown that the dependence of the dipole moment on the constant component of external field is quasi-periodic, and the dipole moment changes sign at different half-periods.     

Propagation of spiking regularity and double coherence resonance in feedforward networks

We investigate the propagation of spiking regularity in noisy feedforward networks (FFNs) based on FitzHugh-Nagumo neuron model systematically. It is found that noise could modulate the transmission of firing rate and spiking regularity. Noise-induced synchronization and synfire-enhanced coherence resonance are also observed when signals propagate in noisy multilayer networks. It is interesting that double coherence resonance (DCR) with the combination of synaptic input correlation and noise intensity is finally attained after the processing layer by layer in FFNs. Furthermore, inhibitory connections also play essential roles in shaping DCR phenomena. Several properties of the neuronal network such as noise intensity, correlation of synaptic inputs, and inhibitory connections can serve as control parameters in modulating both rate coding and the order of temporal coding.     

Coherent repopulating hyperfine-structure levels by pulsed resonance fields and the quantum computer problem

A new method of polarization of atoms and nuclei by pulsed bichromatic resonance radio-frequency fields is proposed to produce an initial state of a quantum computer constructed with the use of cubits representing impurity atoms in a solid matrix having the hyperfine structure. It is shown that this method can provide strong polarization without using ultralow temperatures. The problem is considered for the interaction of three-and four-level systems with bichromatic and two-phase fields.     

Electromagnetically induced grating in double quantum dot system using spontaneously generated coherence

A model of electromagnetically induced grating (EIG) assisted by the spontaneously generated coherence (SGC) in the ladder-plus-Y double quantum dot (DQD) system is proposed. Using the density matrix theory, the amplitude and phase of the transmission function are studied. It is shown that the transmission is enhanced by the presence of SGC, and the resultant diffraction intensity can increase by controlling the phase. The SGC-assisted EIG controlled by two, three, and four coupling optical fields are studied respectively. Remarkably, we find that the system acquires a huge diffraction intensity when the wetting layer-quantum dot (WL-QD) field is high in the case of four coupling fields.     

Full counting statistics as a probe of quantum coherence in a side-coupled double quantum dot system

We study theoretically the full counting statistics of electron transport through side-coupled double quantum dot (QD) based on an efficient particle-number-resolved master equation. It is demonstrated that the high-order cumulants of transport current are more sensitive to the quantum coherence than the average current, which can be used to probe the quantum coherence of the considered double QD system. Especially, quantum coherence plays a crucial role in determining whether the super-Poissonian noise occurs in the weak inter-dot hopping coupling regime depending on the corresponding QD-lead coupling, and the corresponding values of super-Poissonian noise can be relatively enhanced when considering the spins of conduction electrons. Moreover, this super-Poissonian noise bias range depends on the singly-occupied eigenstates of the system, which thus suggests a tunable super-Poissonian noise device. The occurrence-mechanism of super-Poissonian noise can be understood in terms of the interplay of quantum coherence and effective competition between fast-and-slow transport channels.     

Proton double quantum coherence and cross-relaxation in (NH4)2SnBr6

A proton double quantum coherence signal can be observed exclusively from the T species NH4 groups (with the total spin I = 1) in ammonium compounds at low temperatures by the three-pulse sequence 90x degrees - tpr - 90x degrees - tev - 90x degrees - ta, where tpr and ta are of the magnitude of the inverse line width and tev very short. The usefulness of this pulse sequence, preceded by the additional pulse sequence 90x degrees - t1 -90(-x) degrees - t2 for creating an unbalance between the A and T species magnetizations, was demonstrated by applying it to cross-relaxation studies in (NH4)2SnBr6.     

Controllable optical bistability and multistability in asymmetric double quantum wells via spontaneously generated coherence

We investigate the nonlinear optical phenomena of the optical bistability and multistability via spontaneously generated coherence in an asymmetric double quantum well structure coupled by a weak probe field and a controlling field. It is shown that the threshold and hysteresis cycle of the optical bistability can be conveniently controlled only by adjusting the intensity of the SGC or the controlling field. Moreover, switching between optical bistability and multistability can be achieved. These studies may have practical significance for the preparation of optical bistable switching device.     

Simultaneous spectral editing for gamma-aminobutyric acid and taurine using double quantum coherence transfer

Conventional double quantum (DQ) editing techniques recover resonances of one metabolite at a time and are thus inefficient for monitoring metabolic changes involving several metabolites. A DQ coherence transfer double editing sequence using a dual-band DQ coherence read pulse is described here. The sequence permits simultaneous spectral editing for two metabolites with similar J coupling constants in a single scan. Simultaneous editing for taurine and gamma-aminobutyric acid (GABA) is demonstrated using solution phantoms and rat brain tissue. Selectivity of the double editing sequence for the target metabolites is as good as that achieved using conventional DQ editing which selects each metabolite individually. With experimental parameters of the double editing sequence chosen to optimize GABA editing, the sensitivity for GABA detection is the same as that with GABA editing only, while the sensitivity for taurine detection is decreased slightly compared to that with taurine editing only.     

Maximum entropy: a complement to Tikhonov regularization for determination of pair distance distributions by pulsed ESR

Tikhonov regularization (TIKR) has been demonstrated as a powerful and valuable method for the determination of distance distributions of spin-pairs in bi-labeled biomolecules directly from pulsed ESR signals. TIKR is a direct method, which requires no iteration, and, therefore, provides a rapid and unique solution. However, the distribution obtained tends to exhibit oscillatory excursions with negative portions in the presence of finite noise, especially in the peripheral regions of the distribution. The Shannon-Jaynes entropy of a probability distribution provides an intrinsic non-negativity constraint on the probability distribution and an unbiased way of obtaining information from incomplete data. We describe how the maximum entropy regularization method (MEM) may be applied to solve the ill-posed nature of the dipolar signal in pulsed ESR. We make use of it to suppress the negative excursions of the distance distribution and to increase the tolerance to noise in the dipolar signal. Model studies and experimental data are investigated, and they show that, with the initial or "seed" probability distribution that is required for MEM taken as the TIKR result, then MEM is able to provide a regularized solution, subject to the non-negativity constraint, and it is effective in dealing with noise that is problematic for TIKR. In addition we have incorporated into our MEM method the ability to extract the intermolecular dipolar component, which is embedded in the raw experimental data. We find that MEM minimization, which is implemented iteratively, is greatly accelerated using the TIKR result as the seed, and it converges more successfully. Thus we regard the MEM method as a complement to TIKR by securing a positive pair distance distribution and enhancing the accuracy of TIKR.     

Distance measurements in disodium ATP hydrates by means of 31P double quantum two-dimensional solid-state NMR spectroscopy

POST-C7 measurements provide constraints allowing distinguishing crystal lattice organization and establishing intra and/or intermolecular distances between phosphorus atoms of triphosphate chains for different hydrates of disodium ATP salts. Double-quantum efficiency in function of excitation time obtained from series of two-dimensional spectra for POST-C7 experiments was used to set up of buildup curves and semi-quantitative measure of 31P-31P length.     

Site-selective electron nuclear double resonance in the exchange-narrowed regime of the ESR in conducting solids

Electron nuclear magnetic double resonance on conduction electrons reveals the hyperfine interaction hidden by the fast electron spin exchange. We used the Overhauser shift technique to investigate the electron spin density of the conduction band of gallium oxide, beta-Ga(2)O(3). Due to the monoclinic structure, the conduction band of beta-Ga(2)O(3) is anisotropic and it is dominated by contributions from the two nonequivalent Ga sites. The large quadrupole couplings of the two gallium isotopes (69)Ga and (71)Ga (both with I = 3/2) are completely resolved in our double-resonance experiments. This resolved quadrupole interaction allows the determination of the electric field gradients at both gallium sites with high precision and high sensitivity. The resolved quadrupole splitting is the key to the site-selected determination of the hyperfine interaction. The concepts behind these double-resonance techniques are rather general and should be applicable in similar semiconductor systems.