Residual dipolar couplings and some specific models for motional averaging

The measurement of residual dipolar couplings (RDCs) from partially oriented molecules is now widely used to provide restraints for NMR structure determination. Bond vibrations, random angular fluctuations around bond vectors and conformational exchange all influence the magnitude of the experimental RDCs. The effect that angular fluctuations have upon the magnitude of RDCs is quantitatively compared using three new models (elliptic, uni-dimensional, and equally populated two site jump) and three established models (static, isotropic motion in a cone and free diffusion about a fixed symmetry axis: Woessner's model) for motional averaging in the limit that the amplitude of motion beta < or = (max)15-20 degrees. The influence of the different motional models on the value of R(obs) determined from the distribution of RDCs is explored. The consequences of the different types of angular motion for the accurate determination of bond vector orientation, with respect to the alignment tensor, A, is investigated. The extent to which motion influences the magnitude of RDCs is compared to some non-dynamic factors affecting RDC size.     

Molecular-orientation analysis based on alignment-induced TROSY chemical shift changes

We present a new NMR technique for determining the alignment tensor of a weakly aligned protein using only alignment-induced ¹⁵N transverse relaxation optimized spectroscopy (TROSY) chemical shift changes. Alignment-induced TROSY chemical shift changes reflect the combined contributions from two different anisotropic spin interactions including the residual dipolar couplings (RDCs) and the residual chemical shift anisotropy effects (RCSAs). We show here that these two residual anisotropic spin interactions’ values, encoded in the TROSY chemical shift changes, can be used to determine a weakly aligned protein’s alignment tensor. To prove the significance of this method, we show that our TROSY-based analysis gives the consistent alignment angles with those determined using RDCs for ¹⁵N-labeled ubiquitin (8.6 kDa) in an aligned medium, within an uncertainty range estimated by considering experimental and structural noises, being 5° at most. Because our approach requires a pre-determined ¹⁵N CSA tensor value, we also estimated the uncertainties associated with the resultant alignment tensor values caused by variation in ¹⁵N CSA tensors. In spite of the significant variations in literature-reported ¹⁵N CSA tensors, they gave consistent orientation angles within an uncertainty range. These results ensure that our TROSY-based approach is a useful alternative to the RDC-based method to determine the alignment angles especially for large proteins in a weakly aligned state.     

Assessment of protein alignment using 1H-1H residual dipolar coupling measurements

A quick and accurate method is described for assessing protein alignment from residual dipolar coupling (RDC) measurements. In contrast to observing D(2)O resonance splitting, which reflects the orientational order of the alignment medium, the degree of alignment of a protein of interest can be estimated directly from (1)H-(1)H RDCs. In this study, RDCs between aromatic protons in unlabeled Cp-rubredoxin were measured from proton homonuclear J-resolved experiments with high sensitivity, and the alignment was assessed without the need of extensive resonance assignment. Since labeled proteins are not needed, this method provides an efficient way for screening alignment media. In situations where the protein structure is known, as in the case of Cp-rubredoxin, a full set of order tensor parameters can be determined, allowing further studies, such as those of ligand alignment relative to a target protein.     

Separating structure and dynamics in CSA/DD cross-correlated relaxation: a case study on trehalose and ubiquitin

We present two new sensitivity enhanced gradient NMR experiments for measuring interference effects between chemical shift anisotropy (CSA) and dipolar coupling interactions in a scalar coupled two-spin system in both the laboratory and rotating frames. We apply these methods for quantitative measurement of longitudinal and transverse cross-correlation rates involving interference of (13)C CSA and (13)C-(1)H dipolar coupling in a disaccharide, alpha,alpha-D-trehalose, at natural abundance of (13)C as well as interference of amide (15)N CSA and (15)N-(1)H dipolar coupling in uniformly (15)N-labeled ubiquitin. We demonstrate that the standard heteronuclear T(1), T(2), and steady-state NOE autocorrelation experiments augmented by cross-correlation measurements provide sufficient experimental data to quantitatively separate the structural and dynamic contributions to these relaxation rates when the simplifying assumptions of isotropic overall tumbling and an axially symmetric chemical shift tensor are valid.     

Improvement and analysis of computational methods for prediction of residual dipolar couplings

We describe a new, computationally efficient method for computing the molecular alignment tensor based on the molecular shape. The increase in speed is achieved by re-expressing the problem as one of numerical integration, rather than a simple uniform sampling (as in the PALES method), and by using a convex hull rather than a detailed representation of the surface of a molecule. This method is applicable to bicelles, PEG/hexanol, and other alignment media that can be modeled by steric restrictions introduced by a planar barrier. This method is used to further explore and compare various representations of protein shape by an equivalent ellipsoid. We also examine the accuracy of the alignment tensor and residual dipolar couplings (RDC) prediction using various ab initio methods. We separately quantify the inaccuracy in RDC prediction caused by the inaccuracy in the orientation and in the magnitude of the alignment tensor, concluding that orientation accuracy is much more important in accurate prediction of RDCs.     

Paramagnetic resonance of transition complexes as probes of motion during glass-to-rubber transitions in polymers

It is shown that motional averaging of the g and the A tensor of the electron paramagnetic resonance spectrum of such transition metal complexes as copper benzoyl acetonate (CuBA) and vanadyl acetonate (VAA) doped into polymers provides a sensitive probe of motion during the glass-to-rubber transition. Because of the larger and more anisotropic g and A tensors these probes are more sensitive to motional effects than the more commonly used nitroxide paramagnetic probes. The relationship between probe motion and intrinsic chain motion is examined.     

Dynamic cardiac MRI reconstruction using motion aligned locally low rank tensor (MALLRT)

Various sparse transform models have been explored for compressed sensing-based dynamic cardiac MRI reconstruction from vastly under-sampled k-space data. Recently emerged low rank tensor model using Tucker decomposition could be viewed as a special form of sparse model, where the core tensor, which is obtained using high-order singular value decomposition, is sparse in the sense that only a few elements have dominantly large magnitude. However, local details tend to be over-smoothed when the entire image is conventionally modeled as a global tensor. Moreover, low rankness is sensitive to motion as spatiotemporal correlation is corrupted by spatial misalignment between temporal frames. To overcome these limitations, this paper presents a novel motion aligned locally low rank tensor (MALLRT) model for dynamic MRI reconstruction. In MALLRT, low rank constraint is enforced on image patch-based local tensors, which correspond to overlapping blocks extracted from the reconstructed high-dimensional image after group-wise inter-frame motion registration. For solving the proposed model, this paper presents an efficient optimization algorithm by using variable splitting and alternating direction method of multipliers (ADMM). MALLRT demonstrated promising performance as validated on one cardiac perfusion MRI dataset and two cardiac cine MRI datasets using retrospective under-sampling with various acceleration factors, as well as one prospectively under-sampled cardiac perfusion MRI dataset. Compared to four state-of-the-art methods, MALLRT achieved substantially better image reconstruction quality in terms of both signal to error ratio (SER) and structural similarity index (SSIM) metrics, and visual perception in preserving spatial details and capturing temporal variations.     

Analysing the elasticity difference tensor of general relativity

The elasticity difference tensor, used in [1] to describe elasticity properties of a continuous medium filling a space-time, is here analysed. Principal directions associated with this tensor are compared with eigendirections of the material metric. Examples concerning spherically symmetric and axially symmetric space-times are then presented.     

On quadrupole and octupole gravitational radiation in the ANK formalism

Following the approach of Adamo–Newman–Kozameh (ANK) we derive the equations of motion for the center of mass and intrinsic angular moment for isolated sources of gravitational waves in axially symmetric spacetimes. The original ANK formulation is generalized so that the angular momentum coincides with the Komar integral for a rotational Killing symmetry. This is done using the Winicour–Tamburino Linkages which yields the mass dipole-angular momentum tensor for the isolated sources. The ANK formalism then provides a complex worldline in a fiducial flat space to define the notions of center of mass and spin. The equations of motion are derived and then used to analyse a very simple astrophysical process where only quadrupole and octupole contributions are included. The results are then compared with those coming from the post newtonian approximation.     

EPR and HYSCORE investigation of the electronic structure of the model complex Mn(imidazole)6: exploring Mn(II)-imidazole binding using single crystals

The electronic structure of the Mn(II)-imidazole binding was studied by EPR spectroscopy using the model complex Mn(Im)(6) diluted in a single crystal of Zn(Im)(6)Cl(2).4(H(2)O). The second rank zero-field splitting (ZFS) tensor (D tensor) of the two sites, a and b, present in the crystal was determined by measuring the orientation patterns of the echo-detected EPR spectra in three different planes at 10K (D(a)=-106, D(b)=-118, E(a)=-17, E(b)=-22x10(-4)cm(-1). Euler angles with respect to the crystal habitus: alpha(a)=13 degrees , beta(a)=76 degrees , gamma(a)=108.5 degrees , alpha(b)=14 degrees , beta(b)=73.5 degrees , gamma(b)=103.5 degrees ). The contribution of cubic ZFS terms to the spectrum allowed us to determine the orientation of the N-Mn-N directions of the complex as well (Euler angles in the D tensor reference frame alpha=100 degrees , beta=23 degrees , gamma=0 degrees , both centers having the same orientation). The hyperfine interactions with (14)N were explored by HYSCORE spectroscopy. The correlation patterns and modulation amplitudes in the 2D experiments were studied for different electron spin transitions and orientations of the crystal. Signals of three different pairs of nitrogens were found. The results were analyzed considering that the N-Mn binding directions are principal directions of the hyperfine and nuclear quadrupole tensor of (14)N. All three pairs of nitrogens were found to be almost equivalent with an isotropic contribution of A(iso) approximately 3.2MHz and an almost axial anisotropic coupling of 2T approximately 1.1MHz along the N-Mn bonding direction. The nuclear quadrupole principal values are 1.5MHz along the bonding direction, -0.6MHz in the direction perpendicular to the imidazole plane, and -0.9MHz in the direction perpendicular to both.     

On “Gauge Renormalization” in Classical Electrodynamics

In this paper we pay attention to the inconsistency in the derivation of the symmetric electromagnetic energy–momentum tensor for a system of charged particles from its canonical form, when the homogeneous Maxwell’s equations are applied to the symmetrizing gauge transformation, while the non-homogeneous Maxwell’s equations are used to obtain the motional equation. Applying the appropriate non-homogeneous Maxwell’s equations to both operations, we obtained an additional symmetric term in the tensor, named as “compensating term”. Analyzing the structure of this “compensating term”, we suggested a method of “gauge renormalization”, which allows transforming the divergent terms of classical electrodynamics (infinite self-force, self-energy and self-momentum) to converging integrals. The motional equation obtained for a non-radiating charged particle does not contain its self-force, and the mass parameter includes the sum of mechanical and electromagnetic masses. The motional equation for a radiating particle also contains the sum of mechanical and electromagnetic masses, and does not yield any “runaway solutions”. It has been shown that the energy flux in a free electromagnetic field is guided by the Poynting vector, whereas the energy flux in a bound EM field is described by the generalized Umov’s vector, defined in the paper. The problem of electromagnetic momentum is also examined.     

Signature Inversion in Odd-odd Nuclei

Signature inversion in odd-odd nuclei is investigated by using a proton and a neutron coupling to the coherent state of the core.Two parameters are employed in the Hamiltonian to set the energy scales of rotation,neutron-proton coupling and their competition.Typical level staggering is extracted from the calculated level energies.The calculation can approximately reproduce experimental signature inversion.Signature inversion is attributed to the rotational motion and neutronproton residual interaction having reversed signature splitting rules.It is found signature inversion can appear at axially symmetric shape and high-K band.     

二维相对论运动等离子体的介电率张量

定义了相对论性运动等离子体的物理模型.利用荷流体的微扰理论，研究了该系统二维扰动现象及背景离子下的束-波互作用问题，导出了该系统的介电率张量.研究表明，相对论运动等离子体系统属复杂的色散荷流体介质并呈复杂的空间电磁不均匀性.数值模拟计算给出了相对论运动等离子体系统的介电率对波频率、电子能量以及空间坐标的响应. 关键词： 等离子体 荷流体 介质 电磁理论     

Accurate measurement of one-bond H-X heteronuclear dipolar couplings in MAS solid-state NMR

The accurate experimental determination of dipolar-coupling constants for one-bond heteronuclear dipolar couplings in solids is a key for the quantification of the amplitudes of motional processes. Averaging of the dipolar coupling reports on motions on time scales up to the inverse of the coupling constant, in our case tens of microseconds. Combining dipolar-coupling derived order parameters that characterize the amplitudes of the motion with relaxation data leads to a more precise characterization of the dynamical parameters and helps to disentangle the amplitudes and the time scales of the motional processes, which impact relaxation rates in a highly correlated way. Here. we describe and characterize an improved experimental protocol--based on REDOR--to measure these couplings in perdeuterated proteins with a reduced sensitivity to experimental missettings. Because such effects are presently the dominant source of systematic errors in experimental dipolar-coupling measurements, these compensated experiments should help to significantly improve the precision of such data. A detailed comparison with other commonly used pulse sequences (T-MREV, phase-inverted CP, R18(2)(5), and R18(1)(7)) is provided.     

The axially symmetric flow-through problem for the Navier-Stokes equations in variables “vorticity-stream function”

The axially symmetric steady-state motion of a viscous incompressible fluid in a region of the type of a spherical layer is considered. The boundary problem for the Navier-Stokes equations is formulated in terms of the stream function and vorticity. The solvability of this problem was previously established provided that the fluid flow rate through each layer boundary is sufficiently small. The main result of this study is in proving the solvability of the axially symmetric flow-through problem without limitations on the magnitude of the flow rate. The proof is based on the a priori Dirichlet estimate of the flow velocity field. The asymptotic properties of the solution near the symmetry axis are established conditionally. The proof procedure admits the generalization to the case of axially symmetric problems in multiply-connected domains.     

Integrable cases of a rigid body dynamics and integrable systems on the ellipsoids

Infinite-dimensional sets of integrable cases are found for the equations of a rigid body rotation around a fixed point in an axially symmetric potential field and also in more complicated fields in the presence of some symmetry of the rigid body inertia tensor.     

Field enhancement analysis of an apertureless near field scanning optical microscope probe with finite element method

Plasmonic field enhancement in a fully coated dielectric near field scanning optical microscope (NSOM)probe under radial polarization illumination is analyzed using an axially symmetric three-dimensional (3D)finite element method (FEM) model. The enhancement factor strongly depends on the illumination spot size, taper angle of the probe, and the metal film thickness. The tolerance of the alignment angle is investigated. Probe designs with different metal coatings and their enhancement performance are studied as well. The nanometric spot size at the tip apex and high field enhancement of the apertureless NSOM probe have important potential application in semiconductor metrology.