Rotational-resonance distance measurements in multi-spin systems

It is demonstrated that internuclear distances can be evaluated from rotational-resonance (RR) experiments in uniformly (13)C-labelled compounds. The errors in the obtained distances are less than 10% without the need to know any parameters of the spin system except the isotropic chemical shifts of all spins. We describe the multi-spin system with a simple fictitious spin-1/2 model. The influence of the couplings to the passive spins (J and dipolar coupling) is described by an empirical constant offset from the rotational-resonance condition. Using simulated data for a three-spin system, we show that the two-spin model describes the rotational-resonance transfer curves well as long as none of the passive spins is close to a rotational-resonance condition with one of the active spins. The usability of the two-spin model is demonstrated experimentally using a sample of acetylcholine perchlorate with labelling schemes of various levels of complexity. Doubly-, triply-, and fully labelled compounds lead to strongly varying RR polarization-transfer curves but the evaluated distances using the two-spin model are identical within the expected error limits and coincide with the distance from the X-ray structure. Rotational-resonance distance measurements in fully labelled compounds allow, in particular, the measurement of weak couplings in the presence of strong couplings.     

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.     

Operationally invariant measure of the distance between quantum states by complementary measurements

We propose an operational measure of distance of two quantum states, which conversely tells us their closeness. This is defined as a sum of differences in partial knowledge over a complete set of mutually complementary measurements for the two states. It is shown that the measure is operationally invariant and it is equivalent to the Hilbert-Schmidt distance. The operational measure of distance provides a remarkable interpretation of the information distance between quantum states.     

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.     

Recoil distance lifetime measurements in82Kr

The lifetimes τ=124±12, 6 _?2 ⁺⁴ and 380±100 ps of theE _x (I ^π )=3.46(8⁺), 2.92(6⁺) and 3.04(6^?) MeV states, respectively, populated by the reaction⁷⁶Ge(¹²C,α2n) were measured with the recoil distance method. In addition upper lifetime limits were obtained for nine states. The measured lifetimes and energies indicate a band crossing at aboutI ^π =8⁺, probably arising from the alignment of twog _9/2 neutrons. For the 3.04 MeV 6^? state as a second member of a band built on the 2.65 MeV 4^? state the measured lifetime points to a two-quasiparticle configuration. The positive-parity states have been discussed in the frame of the interacting boson approximation, nuclear field theory and the cranked shell model.     

Isotope shift measurements on the neutron-deficient thallium isotopes

Isotope shifts of the neutron-deficient thallium isotopes were measured on-line at the UNISOR mass separator. Spectroscopy was carried out using collinear fast beam laser spectroscopy in neutral thallium. The changes of the mean square charge radii were derived from the measurements. The changes in charge radii of the I=7 isotopes, including the newly measured¹⁸⁸Tl, are compared to the results in mercury and lead.     

The accuracy of distance measurements in solid-state NMR.

The accuracy with which distances can be measured using dipolar recoupling experiments in solid-state NMR is investigated. The relative precision of experiments in a three spin system versus an isolated spin pair is found to depend very strongly on the nature of the coupling Hamiltonian. The accuracy of distances measured in even the simplified three spin system is seen to be very poor for existing homonuclear recoupling Hamiltonians. This suggests that it would be difficult to exploit broadband homonuclear recoupling to measure geometrical information reliably in complex spin systems. These conclusions apply equally to both single-crystal studies and powder samples. In contrast, the presence of additional spins has marginal impact on the accuracy when the coupling Hamiltonians commute with each other, as in the case of heteronuclear recoupling. The possibility of creating such a Hamiltonian for homonuclear recoupling using a suitable rotor-synchronized pulse sequence is discussed.     

Statistics of dynamic speckles in application to distance measurements

We present an analysis of statistical properties of dynamic speckles to estimate the limiting accuracy of measurements achievable in a distance sensor using spatially filtered dynamic speckles. The main reason for inaccurate measurements using dynamic speckles is their stochastic nature. It is shown that the average lifetime of dynamic speckles is the key factor defining the measurement accuracy. Main conclusions of the theoretical analysis were confirmed in an experiment carried out with a fast moving rough surface. Special attention is paid to a recently proposed range sensor using dynamic speckles generated by a fast-deflecting laser beam. It is shown that this sensor possesses the best combination of accuracy and response time.     

Theoretical spin density in nitroxides

The evolution of the hyperfine tensors in the nitroxide series with increasing alkyl substitution on the NO group has been studied theoretically for radicals from H₂NO to C₅H₁₀NO. A projection technique has been applied to the UHF wave-functions in order to correct spin densities for quartet contamination. The magnitude of the isotropic and anisotropic couplings reflects the substitution effect already observed on the spin distribution maps, that is a spin transfer from oxygen to nitrogen when alkyl groups are substituted to hydrogens in H₂NO. The alternation of the signs of the couplings along the chain as well as the cos² γ law for the coupling constants of atoms (C or H) in β position are verified in the series. The orientation of the anisotropic tensors with respect to the chemical bonds depends on the position of the atoms in the molecule (radical site, α, β positions); it is not affected by further substitution, except for strongly asymmetric configurations.     

Theoretical spin density in nitroxides

The influence of alkyl substitution on the spin density distribution in nitroxide radicals is studied by performing ab initio UHF calculations on a series of radicals from H₂NO to C₅H₁₀NO. Comparison of spin populations and spin density maps in the series shows a net spin migration from oxygen to nitrogen when hydrogens are replaced by methyl groups. This result does not depend on the size of the alkyl substituents. The substitution effect explains in part the discrepancy between the theoretical spin density in H₂NO and the experimental result obtained by polarized neutron diffraction on tanol suberate biradical C₈H₁₂O₄((CH₃)₄C₅H₅NO)₂.     

A time-of-scan laser triangulation technique for distance measurements

This paper reports the development of an electro-optic device for relative distance measurement. The time-of-scan triangulation technique has been used as measurement principle and a rotating mirror employed as beam deflection system. A calibration technique is needed to calculate the geometrical parameters of the system. The device has an accuracy of 100 μm, a working distance of 20 cm and a range of 10 mm. The accuracy obtained depends on the instability of the rotation speed of the mechanical scanner that affects the measurement of the scanning time.     

Fast distance measurements by use of dynamic speckles

A technique for fast measurements of the distance to an object's surface based on spatial filtering of dynamic speckle patterns is proposed. Exploitation of two spatial filters (Ronchi rulings) enables measurements to be independent of surface speed. Experimental verification of the technique is demonstrated at speeds of the surface as high as 50 m/s. The technique may find applications in machine-vision systems for acquisition of three-dimensional images and in control systems for on-line monitoring of fast-moving parts of industrial machines.     

Isotope shift measurements in the atomic spectrum of lanthanum (LaI)

Using the reactor-produced lanthanum isotope ₅₇ ¹³⁷ La, the highly enriched rare ₅₇ ¹³⁸ La and the stable ₅₇ ¹³⁹ La, the isotope shift has been measured in five lines of the La I-spectrum with the aid of a pressure-scanned Fabry-Pérot interferometer. The isotope shift data obtained show surprisingly large specific mass effects, arising from configuration mixing of levels with a 4f electron involved. The changes in mean square charge radiusδ〈r ²〉 of these nuclei extracted from the experimental isotope shift constants C_exp are compared with the corresponding values for the isotonic barium nuclei, where similar anomalies in the isotope shifts occur.     

Pulse EPR distance measurements to study multimers and multimerisation

Pulse dipolar electron paramagnetic resonance (PD-EPR) has become a powerful tool for structural biology determining distances on the nanometre scale. Recent advances in hardware, methodology, and data analysis have widened the scope to complex biological systems. PD-EPR can be applied to systems containing lowly populated conformers or displaying large intrinsic flexibility, making them all but intractable for cryo-electron microscopy and crystallography. Membrane protein applications are of particular interest due to the intrinsic difficulties for obtaining high-resolution structures of all relevant conformations. Many drug targets involved in critical cell functions are multimeric channels or transporters. Here, common approaches for introducing spin labels for PD-EPR cause the presence of more than two electron spins per multimeric complex. This requires careful experimental design to overcome detrimental multi-spin effects and to secure sufficient distance resolution in presence of multiple distances. In addition to obtaining mere distances, PD-EPR can also provide information on multimerisation degrees allowing to study binding equilibria and to determine dissociation constants.     

Recoil distance half-life measurements of the excited states in 145Sm

A recoil distance method was used to measure half-lives of the excited states of ₁₄₅Sm. The reaction used was ₁₃₉La(₁₀B, 4n)₁₄₅Sm. A plunger system was used. Half-lives were determined for two excited states for the first time. The yrast 27/2₊ state was found to have a half-life of 1.1 ± 0.2 ns corresponding to the retardation of 3.1 × 10₋₄ comparing with the single particle estimate of M1. The excitation energy of this state was well reproduced by the shell model calculation having a mixed configuration of [π{h^11/2(g^7/2)₋₂ (d^5/2)₋₁}¹⁰⁻, νf^7/2] + [π{h^11/2(g^7/2)₋₁}⁹⁻,νh^9/2]. Another retarded E1 transition was also found in a decay of a 21/2₊ state. Its retardation was 1.6 × 10₋₄ comparing with the single particle value. Received: 9 September 1997 / Revised version: 12 June 1998     

Improved narrowband dipolar recoupling for homonuclear distance measurements in rotating solids

Recovery of the magnetic dipolar interaction between nuclei bearing the same gyromagnetic ratio in rotating solids can be promoted by synchronous rf irradiation. Determination of the dipolar interaction strength can serve as a tool for structural elucidation in polycrystalline powders. Spinning frequency dependent narrow-band (nb) RFDR and SEDRA experiments are utilized as simple techniques for the determination of dipolar interactions between the nuclei in coupled homonuclear spin pairs. The magnetization exchange and coherence dephasing due to a fixed number of rotor-synchronously applied pi-pulses is monitored at spinning frequencies in the vicinity of the rotational resonance (R(2)) conditions. The powder nbRFDR and nbSEDRA decay curves of spin magnetizations and coherences, respectively, as a function of the spinning frequency can be measured and analyzed using simple rate equations providing a quantitative measure of the dipolar coupling. The effects of the phenomenological relaxation parameters in these rate equations are discussed and an improved methodology is suggested for analyzing nbRFDR data for small dipolar couplings. The distance between the labeled nuclei in the 1,3-(13)C(2)-hydroxybutyric acid molecule is rederived using existing nbRFDR results and the new simulation procedure. A nbSEDRA experiment has been performed successfully on a powder sample of singly labeled 1-(13)C-L-leucine measuring the dipolar interaction between the labeled carboxyl carbon and the natural abundant beta-carbon. Both narrowband techniques are employed for the determination of the nuclear distances between the side-chain carbons of leucine and its carbonyl carbon in a tripeptide Leu-Gly-Phe that is singly (13)C-labeled at the leucine carbonyl carbon position.     

Isotope shift measurements and charge radii of152–158Yb

Isotope shifts have been measured for the neutron deficient even Yb isotopes up to the neutron shell closure at N=82. The isotope shifts were measured using the 556-nm atomic resonance transition from the¹ S ₀ ground state to the³ P ₁ level. The heavier isotopes of Yb have been investigated by Buchinger et al./1/. The change in (r ²) observed for Yb isotopes with N=82–90 has considerably different behavior than for the lighter rare earths.     

Isotope shift measurements of 11, 9, 7Be+

We have performed precision atomic spectroscopy of trapped radioactive Be isotopes aiming at studies of the charge and magnetization radii of these nuclei especially for a single-neutron halo nucleus ¹¹Be . Some experimental results and the status of the analysis are discussed.     

Isotope shift measurements of muonic X-rays in134, 136, 138Barium

The isotope shifts of muonic X-rays for the three stable Ba-isotopes^{134, 136, 138}Ba have been measured with high accuracy. Especially the differences in the rms radiiΔ〈r ²〉 have been determined in a model independent way and have been used to calibrate optical isotope shift data.     

Pulsed EPR imaging of nitroxides in mice

Nitroxides, unlike trityl radicals, have shorter T₂s which until now were not detectable in vivo by a time-domain pulsed Electron Paramagnetic Resonance (EPR) spectrometer at 300 MHz since their phase memory times were shorter than the spectrometer recovery times. In the current version of the time-domain EPR spectrometer with improved spectrometer recovery times, the feasibility of detecting signals from nitroxide radicals was tested. Among the nitroxides evaluated, deuterated ¹⁵N-Tempone (¹⁵N-PDT) was found to have the longest T₂. The signal intensity profile as a function of concentration of these agents was evaluated and a biphasic behavior was observed; beyond a nitroxide concentration of 1.5 mM, signal intensity was found to decrease as a result of self-broadening. Imaging experiments were carried out with ¹⁵N-PDT in solutions equilibrated with 0%, 5%, 10%, and 21% oxygen using the single point imaging (SPI) modality in EPR. The image intensity in these tubes was found to depend on the oxygen concentration which in turn influences the T₂ of ¹⁵N-PDT. In vivo experiments were demonstrated with ¹⁵N-PDT in anesthetized mice where the distribution and metabolism of ¹⁵N-PDT could be monitored. This study, for the first time shows the capability to image a cell-permeable nitroxide in mice using pulsed EPR in the SPI modality.