Helicoidal model

Very few structural studies have been concentrated on models of ApG adducts of cisplatin. Conformational analysis of two rotameric forms of the complex m-[Pt(NH3)2(9-MeA-A(7))(9-EtGH-A(7))]2+ has recently been described [40], One of the forms, crystallized as a PI 6 salt, can be characterized as a right-handed helicoidal model for the intrastrand ApG crosslink in double-stranded DNA. The bases in this compound assume a head-to-head orientation (Fig. 6) with the interbase dihedral angles of 81.8° and 87.5°. There are two independent complex cations in the unit cell. The left-... 

A helicoidal model has been proposed for cellulose by Viswa-nathan and Shenonda (1971). This assumption needs further investigations and is interesting since there are many twisted systems formed by cellulose or related polymers. An example of arcs given by polysaccharidic microfibrils is shown in fig. 8. 

Dauxois, T., Dynamics of breather modes in a nonlinear helicoidal model of DNA, Phys. Lett. A, 159, 390-395, 1991. 

In order to model this type of flow field geometrically, Beltrami found that it was necessary to consider a three-dimensional circular axisymmetric flow in which the velocity and vorticity field lines described a helical pattern. This helicoidal flow field was unique in that the pitch of the circular helices decreased as the radius from the central axis increased. This produces a specialized shear effect between the field lines of successively larger cylindrical tubes constituting the respective helices. In the limit of such a field, the central axis of the flow also serves as a field line (see Fig. 3). 

The physical model of the reactor is a 350 mm high cylindrical vessel, with a diameter of 200 mm and an elliptical bottom. The operation volume is V = 12 10 m. The entrance of the reactants is placed near the middle of the reactor, more exactly at 130 mm from the bottom. The reactor s exit is positioned on the top of the vessel but below the liquid level. At the vessel centre is placed a mixer with three helicoidal paddles with d/D = 0.33. It operates with a rotation speed of 150 mirnf In order to establish the reactor flow model, this is filled with pure water which continuously flushes through the reactor at a flow rate of 6.6 10 5 m /s (similar to the reactants flow rate). At time t = 0, a unitary impulse of an NaCl solution with a Cq = 3.6 kg/m is introduced into the reactor input. The time evolution of the NaCl concentration at the exit flow of the reactor is measured by the conductivity. Table 3.5 gives the data that show the evolution of this concentration at the reactor exit. 

Keratin has a crystallinity of about 30 Z. Since 1950,X-ray diffraction and electron microscopy have led to a model in which the structural elements are (13,14) the a-helix with a diameter of 10, the elementary fibril containing two to three helicoidal chains of 20 diameter, the microfibril or association of ten elementary fibrils through the amorphous regions (of 80 A diameter) and finally the fibrils or structures of several microfibrils within an amorphous matrix. 

Figure 12.18 Reprinted from Bontinck, W. and Amelinckx, S. (1957) Observation of helicoidal dislocation lines in fluorite crystals, Phil. Mag. 2, 1. With permission from Taylor and Francis, http //www.tandf.co.uk/journals Figure 12.19 Reprinted from Phillips, D.S., Plekta, B. J., Heuer, A.H., and Mitchell, T.E. (1982) An improved model of break-up of dislocation dipoles into loops application to sapphire (a-A Os), Acta Metall. 30,491. Copyright 1982, with permission Elsevier.

A similar model can be considered even when a system of polymers forms microfibrils or filaments distributed with a constant interdistance. The separation of filaments can be controlled by the balance of several forces hydration, electrical doublelayer repulsion and van der Walls attraction. This conception derives from a paper by Elliot and Rome (1969) who interpreted in that way the interdistance control between muscle cell filaments. We do not know the exact shape of the isopotential surfaces corresponding to that system of forces in the vicinity of fibrils formed by a set of chiral pol5nners, but they must show in many cases a helicoidal symmetry. The complete system can closely resemble the model suggested by Rudall (1955). 

The PB model does not take hehcosity into consideration (Figure 27.6). However, its extended version, developed by Dauxois [21,22], does. We refer to this model as Peyrard-Bishop-Dauxois (PBD) model. The helicoidal structure of the DNA chain implies that nucleotides from different strands become close enough so that they interact through water filaments. This means that a nucleotide at the site n of one strand interacts with both (n + h)th and (n — h)th nucleotides of... 

To demonstrate the feasibility of virtual model creation, it was used part of a cow femur bone once it was easily purchased from a specialist supplier. The selected part allowed about 288 tomography cuts to be taken by a helicoidally tomography scan machine from General Electric Medical Systems, model HiSpeed CT. The cut analysis interval started at the CUT 100 and finished at the CUT 140. The procedures to obtain the cloud of points were (a) removal of unwanted lines and imperfections due to the bone porosity (b) removal of the internal edge (c) edge detection techniques (d) image preparation for Cartesian coordinate s acquisition and (e) the acquisition of the Cartesian coordinates. 

Although the base sequence of DNA remains to be elucidated, Watson and Crick [90, 91] proposed a model for its tridimensional structure. Several models had been proposed prior to that enounced by Watson and Crick, but they were all discarded because they were not compatible with the established physical and chemical properties of the DNA molecule. Modern concepts of the tridimensional structure of the DNA molecule are based on four different sources of factual information (1) the base composition of the DNA molecule, (2) the physicochemical information suggesting the existence of hydrogen bonds (3) the electron microscopy data, which indicates that the molecule is a long, extended structure about 30,000 A long and 30 A wide and (4) X-ray diffraction studies of crystalline and paracrystalline DNA molecules from which the molecule is known to have a helicoidal shape. (The term spiral should not be used to describe DNA. A spiral winds around a cone and a helix winds around a cylinder.)... 

Figure 11 -2. Different cell wall textures as predicted by the geometrical model. The ribbons shown represent the tracks of CMFs, obtained from the explicit solutions to the CMF evolution equation, (a) The helicoidal texture in which the angle of orientation between subsequent lamellae changes by a constant amount, (b) A crossed polylamel-late texture with alternate lamellae with transverse and axial oriented CMFs. (c) A purely axial texture, (d) A helical texture in which the CMFs have an almost constant winding angle See Color Plate of this figure beginning on page 355)...

The geometry of the root hair changes with colchicine treatment but the helicoid does not (Emons et al. 1990). (2) and the density of neither the CMFs (Emons 1989) (3) nor the rosettes (Emons 1985) changes with the distance from the apex according to the model s assumptions. Here we take the opportunity to comment on the issues he raises. 

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