Radial projection

Horizontal Chemical analysis Magnification by radial projection X- and Y-piezo controlled motion... 

Figure 5-21 Nucleosomes. (A) Electron micrographs of individual nucleosomes reconstituted from 256-bp DNA fragments and separated proteins. From Hamiche et al.213 Courtesy of Ariel Prunell. (B) Model of a nucleosome core. The 1.75-tum (145-bp) DNA superhelix winds around the histone octomer which consists of two subunits apiece of histones H2A, H2B, H3, and H4. In addition, two elongated molecules of proteins HMG-14 or HMG-17 are indicated (see also Chapter 27). (C) Schematic radial projection of the doublehelical DNA showing areas protected from cleavage by hydroxyl radicals (see Fig. 5-50) by the bound proteins. The shaded areas are those protected by HMGs. The zigzag lines near the dyad axis indicate the most prominent regions of protection. (B) and (C) are from Alfonso et al.2U...

Figure 7-6 (A) Heterologous bonding of subunits to form a helix. (B) Radial projection of subunits arranged as in helix A. Different bonding regions of the subunit are designated a, b, c, j, k, and l.

Fig. 9. Representation of a 13/6 actin filament together with its illustration by means of a radial net. In (A) an imaginary piece of paper is wrapped round the filament and on it are marked all the positions of the actin monomers. The paper is then unwrapped as in (B) and the helical tracks in (A) become straight lines. The final result in (C) is the radial projection or radial net. The 59 A pitch length (P) and 27.5 A subunit axial translation (h) are indicated in (C).

Cartesian coordinates (x,y,z) of the ligands radially projected upon the unit sphere, or its direction cosines (a,/ ,y). From Table 3 one obtains... 

NPS, in. Maximum radial projection of imperfections that are no deeper than the bottom of the serrations, in. Maximum depth and radial projection of imperfections that are deeper than the bottom of the serrations, in. 

Imperfections must be separated by at least four times the permissible radial projection. Protrusions above the serrations are not permitted. 

The first issue is to define the innermost layer. For this, a distance from the rod is chosen which contains many counterions but virtually no coions. A distance of roughly 11.5 A from the rod axis turned out to be quite suitable. This is about a third ion diameter farther out than the distance of closest approach. To avoid difficulties with remaining coions, only the counterions within this distance are taken into account in what follows. In a second step, the coordinates of those ions are radially projected onto the surface of the cylinder of closest approach, and this surface is then rolled out to a flat plane see Figure 23 for an illustration of this procedure. Finally, the two-dimensional pair correlation function g(r) of these projected points is computed. 

FIG. 23 Illustration of the computation of surface correlations. Counterions within a certain small distance from the rod constitute the innermost condensed layer. Their coordinates are radially projected onto the surface, which after that is unrolled to a flat plane. The two-dimensional pair correlation function g(r) is then determined from the projected points. 

Fig. 3. Cryo-EM reconstruction of a complex between HRV16 and a low-glycosylation form of ICAM-1 D1D2 (Bella et al., 1998). There are 60 copies of the receptor fragment, visible as radial projections on the viral surface.

Figure 4.20b Comparisons of the exact radial projections of the hydrogen Is and 2s radial functions with those of the two linear combinations resulting from the calculations in fig4-20ab.xls. The second linear combination is a primitive approximation to the hydrogen 2s radial function to the extent that it is orthonormal to the Is function [cells canonical K 24 to SM 24].

A notable feature of the spiral structures is the lack of a heavy core as seen in spiral galaxies, such as M51, shown in Plate 5.1. A reasonable explanation of this and of the uniform alignment and chirality of the spirals is that they originate in turbulent flow firom a central point, and therefore seen oriented in the same radial projection. In hydrodynamics such structures are known as vortices or eddies. Each of the eddies generated by the turbulent expansion is the potential nucleus of a new galaxy. 

An example of the current state of the art is the HP xenon lung image in a rat shown in Fig. 19, which illustrates an impressive level of detail. The in-plane resolution of the 3D image is 0.39 x 0.39 mm, with a field of view of 5 cm. A 100 mL xenon/oxygen bolus was delivered over the course of 80 breaths, and the image was acquired using a radial projection encoding sequence. 

To obtain Monte Carlo averages in the microcanonical ensemble, one can radially project the velocities Vp onto the hypersphere of constant energy. 

In order to estimate atomic polarizabilities, it is noted that the inverse of charge density at the crests of the spherical-wave representation of atoms, in units of a je, should be such a measure. This quantity has been calculated before [6] from a spherical standing-wave model of the atom, shown schematically as a radial projection in Fig. 7. 

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