3D Density Distribution Research Articles

Alignment of 3D structures of macromolecular assemblies.

A number of macromolecular assemblies are being reconstructed in 3D from electron micrographs. The analysis yields a 3D matrix representing the protein density map. In reconstruction processes and in comparing the results of different experiments, it is often necessary to obtain all models oriented the same way in three dimensions. The problem is not trivial since there exist no 3D counterpart of correlation analysis used for 2D images. It is usually solved by time consuming trial and error algorithms. 3D density distributions can be brought to a 'canonical' orientation. The tensor of inertia of the distribution is determined and its eigenvectors are oriented along the coordinate axes. The method is fast and essentially free of reference. It is suitable for structures whose inertial axes do not completely degenerate as they do in icosahedral viruses or if symmetry is cubic. Applications are presented for asymmetric objects and for molecules possessing symmetry axes higher than twofold. The implementation simply requires the accumulation of the inertial tensor and its diagonalisation. Volume data rotation has been already illustrated in this journal by the authors.

Density functional theory of nonuniform colloidal suspensions: 3D density distributions and depletion forces

We present a density functional approach for inhomogeneous charge-stabilized colloidal suspensions which is based on the hybrid weighted-density approximation. Making use of an analytic expression recently proposed for the free energy of the homogeneous system, a free energy functional for the inhomogeneous fluid can be found that is particularly easy to evaluate numericalLY because of the explicit nature of its input functions. Due to this numerical efficiency our calculation can be extended to relatively large three dimensional systems. After performing various explicit tests of our model we consider the case of two large hard spheres immersed in the suspension and calculate from the 3D density distribution of the fluid the effective pair potential between the spheres.

Measurement of 3D Density and Velocity Distribution using HPIV. 1st Report. Evaluation of Simultaneous Recording and Filtering Extraction.

In this study, the simultaneous measurement technique for three-dimensional density and three-dimensional velocity distributions was evaluated. The Holographic Particle Image Velocimetry (HPIV) was the technique to record the three-dimensional position of the tracer particle on the hologram. When there were density distributions in the interrogation region, the plane optical wave may be modulated because of the difference of the refraction indices. Then, both of the plane wave modulated by density and the spherical wave by particle scatter were interfered with the reference beam, being recorded on the single hologram. With reconstructing the hologram, the both of the modulated plane wave and spherical wave were reconstructed. Since the plane wave and spherical wave belong to low and high spacial frequency, respectively, the plane wave was reconstructed with the low-pass filter, resulting in the information of the density distributions to be obtained. With the high pass filter, the particle three dimensional positions were determined, i.e., the same procedure with the original HPIV technique. The effectiveness of the proposed technique (Filtering Extraction: FX) was confirmed through the Helium Jet experiment. The information of the density and velocity were separately measured.

Noninvasive Tomographic and Velocimetric Monitoring of Multiphase Flows

A condensed review of recent advances accomplished in the development and the applications of noninvasive tomographic and velocimetric measurement techniques to multiphase flows and systems is presented. In recent years utilization of such noninvasive techniques has become widespread in many engineering disciplines that deal with systems involving two immiscible phases or more. Tomography provides concentration, holdup, or 2D or 3D density distribution of at least one component of the multiphase system, whereas velocimetry provides the dynamic features of the phase of interest such as the flow pattern, the velocity field, the 2D or 3D instantaneous movements, etc. The following review is divided into two parts. The first part summarizes progress and developments in flow imaging techniques using γ-ray and X-ray transmission tomography; X-ray radiography; neutron transmission tomography and radiography; positron emission tomography; X-ray diffraction tomography; nuclear magnetic resonance imaging; electrica...

Quantitative measurement feasibility for 3D distributions of hydrodynamic quantities in the turbulent mixing zone of two gases

In doing research on the turbulent mixing (TM) of two gases different in density, it is of great interest to study experimentally the 3D density distribution pattern of chemically nonreactive gases in the TM zone. For this purpose, noncontact and, particularly, optical techniques to obtain experimental data may be attractive. This article discusses the possibility of using pulsed laser interferometry in this application. Based on this technique, the experiment should result in the mixture density distribution integrated along the light path. Requirements for high-quality interference patterns have been analyzed in application to typical experimental conditions, to show that they may be produced with specific restrictions set on the mixture constitution. Generally, the TM zone has no symmetry. Therefore, the problem of reconstructing 3D density distributions (TDD) of gases can be solved by sufficiently providing many TM zone integral projections (or aspects). It is technically difficult and expensive to achieve this large number of aspects (N> 10). Therefore, it is essential that a reconstruction method be selected to allow the solution of the problem with the least possible number of aspects. Given that the experiment data are incomplete, the reconstruction methods that are based on the concept of maximum data entropy did well. Information a priori about the solution to be sought for an isobaric gas mixture is that its each constituent has invariable density. Thus, a functional data entropy can be defined that is similar to Fermi gas in statistical physics. An algorithm has been suggested for reconstruction as a modified maximum-bounded entropy procedure (Bashurin et al. 1995). This makes reasonable good reconstruction achievable even with as few aspects as N = 4. Experiments on the study of TM of a propane jet in air using a four-aspects laser interferometer were provided and reconstruction of propane concentration distribution was conducted. The results allow determination of the TM zone spectral characteristics.

A technique for mapping three-dimensional number densities of species in laser produced plumes

The potential of a diagnostic technique to provide quantitative three-dimensional (3D) density distributions of species in a low temperature laser-produced plume is shown. An expanded, short pulse, tunable dye laser is used to probe the plume at a set time during the expansion. Simultaneous recording of two-dimensional in-line absorbance maps and orthogonal recording of laser induced fluorescence permits the 3D density mapping by scanning the dye laser frequency. Preliminary data, supported by a simple model, is presented for the case of Ba II ions in a YBCO plume heated by a KrF laser.

Correlation of 3D-computerized tomographic scans and 2D-colour image analysis of Westphalian coal by means of multivariate statistics

Core material containing Westphalian vitrinite-rich coal from the north of Belgium (Campine Basin) has been investigated by colour image analysis and computerized tomography. The relative 3D density distribution of the investigated core material was determined by non-destructive X-ray computerized tomography. Colour image analyses of polished sections of the same piece of core material provided data concerning the corresponding maceral composition and mineral content of the coal. The application of both methods to the same piece of rock allowed for a first-order cross-correlation of different rock properties by multivariate statistical analysis. Density estimates of macerals were made. The combination of both techniques is very useful in a study of fracture systems in core material and density calibration of computerized tomographic scans of rock constituents.

緩やかな３次元濃度分布の線形計画法による可視化計測

This paper is concerned with a theoretical possibility of a new visualizing measurement method based on an optimum 3D reconstruction from a few selected projections. A theory of optimum 3D reconstruction by a linear programming is discussed, utilizing a few projections for sampled 3D smooth-density-distribution model which satisfies the condition of the 3D sampling theorem. First by use of the sampling theorem, it is shown that we can set up simultaneous simple equations which corresponds to the case of the parallel beams. Then we solve the simultaneous simple equations by means of linear programming algorithm, and we can get an optimum 3D density distribution images with minimum error in the reconstruction. The results of computer simulation with the algorithm are presented.

Automatic 3D alignment of projection images of randomly oriented objects

Reconstruction of the 3D density distribution of macromolecular structures from their 2D projection images or electron micrographs requires knowledge of the relative orientations of the 2D projections. Using a technique that combines the principles of the common axis theorem and quaternion mathematics, the projection directions may be determined a posteriori from the images. This technique is applied to stimulated electron micrographs of the Klenow fragment of DNA polymerase I. These simulated images, with graded signal-to-noise ratios, are subjected to image processing procedures, such as 2D translational and rotational registration and multivariate statistical classification, that would normally be applied to electron micrographs to improve their quality. The alignment procedure is able to determine the relative 3D orientations of the projections correctly even when the images have an initial signal-to-noise ratio of 3.1 and when images within a single class of views are deliverately perturbed in orientation. A relationship is obtained between the parameters used to describe the success of the 3D alignment algorithm and the quality of the 3D reconstruction that might be expected.

Three-dimensional transmitted brightfield imaging: pragmatic data collection and preprocessing considerations

We have been developing algorithms for 3D image reconstruction of biological specimens with absorbing stains. This is important because there are many absorbing stains which are widely used in conjunction with transmitted light brightfield (TLB) microscopy, yet most of the 3D microscopic imaging research has been directed toward fluorescence microscopy. For instance, horseradish peroxidase (HRP) is used widely in the neurosciences for its many advantages as a tracer and intracellular marker. It is readily injected into individual neurons, transported long distances, and fills both the dendritic and axonal fields, while it may double as an electron microscopy stain for correlative analysis. With such advantages, it is clear that absorbing stains will continue to be widely used. Their utility will furthermore broaden with 3D visualization and quantitation.The main principles behind our methodology are the following. Standard optical serial sectioning data collection is used. The iterative, constrained image reconstruction algorithm is designed to reconstruct the 3D optical density distribution .

Three-dimensional reconstruction from dark-field electron micrographs of macromolecules at random unknown angles

Electron microscopy produces 2D images of 3D objects with resolutions generally from about 2-5 nm for stained or shadowed specimens, to as good as 0.3-0.5 nm for unstained specimens using bright field or dark field techniques. Many groups have worked on methods that attempt to recover the 3D information that is lost in the 2D representation. We have built on and extended previous techniques, and report here the development and application of a robust, unbiased quaternion-based alignment procedure to facilitate 3D reconstruction of molecules imaged at random unknown orientations. The approach is demonstrated using dark field electron micrographs of the Klenow fragment of DNA polymerase.Many procedures for 3D structure determination using electron microscopy have been reported. For fairly simple, small proteins it has been possible to derive a correct high resolution 3D structure by folding the known amino acid chain using dark field electron micrographs as geometric constraintse.g.. However, in general the reconstruction of a 3D density distribution requires knowledge of the relative orientation of different projection images of the object. To determine such orientations a variety of techniques have been employed, frequently adapted to the specimen of interest.

Semiclassical wavepacket construction of quantum resonance states from classical resonant orbits for the F + H 2 reaction

The semiclassical interpretation of reactive resonances as dynamically confined orbits is extended for the F + H 2 reaction by construction of resonant-state wavefunctions according to a time-dependent formalism for Gaussian wavepacket dynamics. The partitioning of nodal curves between entrance and exit channels for the collinear resonances agrees with adiabatic theory and nodal surfaces for the 3D probability density distribution qualitatively agree with quantal calculations.

3dDensity Distribution and the Intrinsic Temperature Dependence of the Mössbauer Isomer Shift in Iron Compounds

<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mn>3</mml:mn><mml:mi>d</mml:mi></mml:math>Density Distribution and the Intrinsic Temperature Dependence of the Mössbauer Isomer Shift in Iron Compounds

3d(t2g) density distribution in covalent transition metal complexes from Mossbauer and EPR experiments

Analysis of the Mossbauer hyperfine interaction data for the octahedral 3d(t2g5) FeIII complex in K3Co1-xFex(CN)6 results in a magnetic contact term of (HC/2S)=+255+or-5 kOe and an (r-3)m approximately 1.0 au for the 3d(t2g) wavefunction. A comparison with the corresponding theoretical free-ion values for Fe3+, -126 kOe and 5.7 au, discloses an extensive overall expansion of the 3d(t2g) wavefunction accompanied by a significant 4s participation in the bonding of the central transition metal ion. Similar results are obtained from the analysis of EPR data for the 3d(t2g5) electronic configuration in K4Fe1-xMnx(CN)6.3H2O. These results are in accord with the available EPR data for several octahedral covalent complexes of V4+, Cr5+ and Mo5+, which have the complementary electronic configurations 3d(t2g1) and 4d(t2g1). Supporting evidence is derived from the analysis of the quadrupole splitting, isomer shift and molecular vibrations in K3Fe(CN)6.