Local helical axis

The stereoselected Cda conformation of the BPDE i(-) and Il(-) adducts to N6(a) were chosen for study in a reoriented complex with an externally bound pyrene moiety. In Figure 13, the adduct is shown in its optimum orientation in B-DNA with adenine after an anti - syn transformation for which the non-bonded contacts are poor, and with the normal anti base orientation with favorable contacts. The fit improves for the anti base as ax 30°. The orientation of the pyrene moiety is a(BPDE) =31° and the local helical axis of the DNA is oriented at y(DNA) = 15° Calculations were not performed with externally bound BPDE-DNA adducts to 06(G) and NU(C). Calculations of externally bound BPDE I(-)-N6(a) adducts with kinked DNA with ax + 30° yields an orientation a(BPDE) = 31° in good agreement with experimental results for the externally bound component (51). 

Some spirochaetes exhibit a creeping motihty. If the organism approaches a soUd surface the external viscous shear will be largest when the cell and the surface are closest. If the protoplasmic cylinder is long and irregular, it may not be fi-ee to rotate, and the roll of the exterior layers cause the cell to slide in a direction nearly parallel to the local helical axis, i.e. producing a creeping-type motility. 

Geometrical methods to induce bending of nucleic acids molecules. Leftpanefi "self bent" DNA mini-circle system. Rightpanels) duplex DNA oligonucleotide bent by the load imposed at its two ends when restraining the angle between two vector-handles (Curuksu et al. 2008). The vector-handles local helical axis) are indicated as lines and the local axis vectors as short arrows... 

Mesophase with a helicoidal supramolecular structure of blocks of molecules with a local smectic C structure. The layer normal to the blocks rotates on a cone to create a helix-like director in the smectic C. The blocks are separated by plane boundaries perpendicular to the helical axis. At the boundary, the smectic order disappears but the nematic order is maintained. In the blocks the director rotates from one boundary to the other to allow the rotation of the blocks without any discontinuity in the thermomolecular orientation. 

Figure 23-34 Structure of PSII with assignment of protein subunits and cofactors. (A) Arrangement of transmembrane a-helices and cofactors in PSII. One monomer of the dimer is shown completely, with part of the second monomer related by the local-C2 axis (filled ellipse on the dotted interface). Chlorophyll a head groups and hemes are indicated by black wire drawings. The view direction is from the luminal side, perpendicular to the membrane plane. The a-helices of Dl, D2, and Cyt b-559 are labeled. D1/D2 are highlighted by an ellipse and antennae, and CP43 and CP47 by circles. Seven unassigned a-helices are shown in gray.

If the molecules of a liquid crystal are optically active Ichiral), then the nematic phase is not formed. Instead of the director being locally constant as is the case for nematics, the director rotates in helical fashion throughout the sample, Within any plane perpendicular to the helical axis the order is nematic-like. In other words, as in a nematic there is only orienlalional order in chiral nematic liquid crystals, and no positional order. 

Molecules that contain a chiral center can form chiral liquid crystalline phases, where the orientation direction rotates in a helical fashion as one moves along the helical axis, which is perpendicular to the locally preferred direction of orientation. Both nematic and smectic phases can be chiral. In a chiral nematic phase, also known as a cholesteric, as one moves along the helical axis, the director rotates sinusoidally (see Fig. 10-31. Thus, if z is... 

The crystal structure of the lysin dimer resembles an extended S shape when viewed along its local twofold axis, which relates the helical bundles of the two monomers (Figure 13A Shaw et al., 1995). When viewed ifom the side, the dimer is essentially flat on one side and slightly convex on the other (Figure 13B). A polar view of the dimer emphasizes the asymmetric clustering of the hydrophobic patches of the two monomers (Figure 13C). The four termini of the two monomers... 

The local symmetry group of the Sc phase is a C2 group and thus the Sc phase has helical electricity. The spontaneous polarization, Ps, is perpendicular to the layer normal and molecular axis. Due to its helical structure Ps changes its direction uniformly, evolving along the helical axis so that the Sc phase does not show a measurable ferroelectricity except in the unwinding of its helical structure. The Sc phase is one of the very important liquid crystal phases that has a prospective application in fast response display. The detailed structure of the Sc phase will be shown in Chapter 6. 

Fig. 6. A view through the Rb. sphaeroides RC along the local symmetry axis showing the helical transmembrane segments from the L-, M- and H-subunits. The two parallel macrocycles of the primary donor, D /Db, are shown in black.

There are a number of possible structures for TGBC phases. The following structural features need to be considered with respect to each possibility. Firstly, the orientation of the layers can be either tilted with respect to the heli-axis or parallel, secondly, the local spontaneous polarization of the smectic layers can be either parallel or perpendicular to the heli-axis, thirdly, the smectic blocks can have a local helical structure caused by a precession in the tilt of the molecules perpendicular to the layers or alternatively the twist can be expelled to the grain boundaries, and fourthly, the rotation of the blocks about the heli-axis can be either rational (commensurate) or irrational (incommensurate). 

The local order in a cholesteric may be expected to be very weakly biaxial. The director fluctuations in a plane containing the helical axis are necessarily different from those in an orthogonal plane and result in a phase biaxiality . Further, there will be a contribution due to the molecular biaxiality as well. It turns out that the phase biaxiality plays a significant role in determining the temperature dependence of the pitch. Goossens has developed a general model taking this into account. The theory now involves four order parameters the pitch depends on all four of them and is temperature dependent. However, a comparison of the theory with experiment is possible only if the order parameters can be measured. 

Let both the helical axis and the electric field are parallel to the normal z of a cholesteric liquid crystal layer of thickness d and >0. In the case of a very weak field the elastic forces tend to preserve the original stack-like arrangement of the cholesteric quasi-layers as shown in Fig. 12.15a. On the contrary, in a very strong field, the dielectric torque causes the local directors to be parallel to the cell normal, as shown in Fig. 12.15c. At intermediate fields, due to competition of the elastic and electric forces an undulation pattern appears pictured in Fig. 12.15b. Such a structure has two wavevectors, one along the z-axis (nld) and the other along the arbitrary direction x within the xy-plane. The periodicity of the director pattern results in periodicity in the distribution of the refractive index. Hence, a diffraction grating forms. Let us find a threshold field for this instability. 

Fig. 12.15 A planar cholesteric structure in the electric field parallel to the helical axis (fi > 0). The local director oiicaitaticm is shown by solid lines field-off planar alignment (a), undulated structure in a weak field > E> E,h (b), and the homeotropic structure in the field exceeding the threshold fin helix tmwinding E > E (c)...

In Eqs. (1) through (3), n and are the extraordinary and ordinary refractive indices of the locally uniaxial system, X is the wavelength of light in vacuum and p is the pitch of the twisted structure defined as the distance measured along the helical axis for the local optic axis to twist around a full 360 . It follows from Eqs. (l)-(3) that the major and minor axes of vibration of both elliptical eigenwaves are either parallel or perpendicular to the local optic axis L. The ellipticities of the eigenwaves, e. and e, are defined by... 

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