Chevron fold

Chevron fold in limestone of Miocene age, Kaikuora, South Island, New Zealand. 

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Figure 94. Thin zigzag lines run almost perpendicular to the smectic layers making a small angle / with the layer normal as shown in (a). In (b) we look at the chevron folds in the plane of the sample, in (e) perpendicular to the plane of the sample. Asymmetric chevrons (c) cannot preserve anchoring conditions at both surfaces and are therefore less frequent.

After the discovery of the chevron structures, a number of complexities in observed optical and electrooptical phenomena could be interpreted in these new terms. For a more thorough discussion in this matter, we refer to references [166-168]. Our emphasis will be on the important consequences for the physics due to the presence of chevrons, but even this requires dealing with at least some structural details. First of all, the chevron fold forces the director n to be in the interface, i.e., to be parallel to the plane of the sample in this region, regardless of how n (r) may vary through the rest of the sample and independent of the surface conditions. Although the director n is continuous at the chevron interface, the local polarization field P cannot be, as shown in Fig. 96. It makes a jump in direction at the interface, nevertheless, in such a way that... 

Figure 95. Section of a thin wall mediating the change in chevron direction. The layers in the chevron structure make the angle 5 (the chevron angle) with the normal to the glass plates. Along a chevron fold where two surfaces meet, two cone conditions have to be satisfied simultaneously for n, which can be switched between two states. At the two points of the lozenge where three surfaces meet, three conditions have to be satisfied and n is then pinned, thus cannot be switched.

Figure 103. Inside a closed loop the chevron has a unique direction (a) downwards or, (b) seen from below, towards the reader. As the lozenges connect two opposite tips in the chevron folds (b), we likewise have a uniquely determined kink direction in the wall. It is relative to this direction that we decide whether y should be counted as positive (same sense) or negative (opposite sense). Thus note that y>0 for both thin walls, even if they have geometrically opposite inclinations.

Figure 104. Zigzag wall making a closed loop. The smectic layers are assumed to be vertical in the picture. The chevron fold is always away from the zigzag inside and towards the thick wall. When the wall curves, the chevron character changes from < > for a thin wall (w< for a thick wall w>L). The wall attains its maximum thickness (relaxed state) when it runs parallel to the layers.

HS Chan, KA Dill. Protein folding m the landscape perspective Chevron plots and non-AiT-henius kinetics. Proteins 30 2-33, 1998. 

Chan, H. S., and Dill, K. A. (1998). Protein folding in the landscape perspective Chevron plots and non-Arrhenius kinetics. Proteins Struct. Fund. Genet. 30, 2-33. 

J. D. Bryngelson, J. N. Onuchic, N. D. Socci et al. Funnels, pathways, and the energy landscape of protein-folding - a synthesis. Proteins, 21 (1995), 167 D. K. Klimov and D. Thirumalai. Criterion that determines the foldability of proteins. Physical Review Letters, 76 (1996), 4070 H. S. Chan and K. A. Dill. Protein folding in the landscape perspective chevron plots and non-arrhenius kinetics. Proteins, 30 (1998), 2. 

Chan H, Dill K (1998) Protein folding in the landscape perspective chevron plots and non-arrhenius kinetics. Proteins Struct Funct Genet 30 2-33. 

A striking feature of the map is the near two-fold symmetry of two regions which appear roughly chevron-shaped in projection (dotted lines in Fig. 1). 

Figure 3 Two-state (D = F) versus three-state (D = I = F) folding, (a) Free energy surface for a two-state folder as a function of the reaction coordinate q. (b) Free energy surface for a three- state folder as a function of the reaction coordinate q. An additional minimum corresponding to an intermediate state I is present, (c) Single exponential kinetics of folding for a two-state folder, (d) Nonexponential kinetics of folding for a three-state protein, (e) Linear chevron plot for a two state folder, (f) Chevron plot with rollover for a three-state folder.

Figure 92. The shrinkage in smectic layer thickness due to the molecular tilt 0(T) in the SmC phase results in a folding instablity of the layer structure ( chevrons ). Even if the fold can he made to go everywhere in the same direction (in the figure to the right) to avoid invasive zigzag defect structures, the switching angle is now less than 2 9, which lowers brightness and contrast.

Also, the optical state (transmission, color) is very often practically the same on both sides of a zigzag wall, as in Fig. 93b. Indeed, if the director lies parallel to the surface (pretilt o =0) at the outer boundaries, the chevron looks exactly the same whether the layers fold to the right or to the left. However, if the boundary condition demands a certain pretilt a 5 0, as in Fig. 105, the two chevron structures are no longer identical. The director distribution across the cell now depends on whether the director at the boundary tilts in the same direction relative to the surface as does the cone axis, or whether the tilt is in the opposite direction. In the first case we say that the chevron has a C1 structure, in the second a C2 structure (see also Fig. 106). We may say that the Cl structure is natural in the sense that if the rubbing direction (r) is the same at both surfaces, so that the pretilt a is symmetrically inwards, the smectic layer has a natural tendency (already in the SmA phase) to fold accordingly. However, if less evident at first sight, the C2 structure is certainly possible, as demonstrated in Figs. 105 and 106. 

Nonetheless, the chevron plot shown in Fig, 9,12 exhibits a rollover, which means that the folding characteristic is not perfectly of two-state type, in which case the folding (unfolding) branches would be almost linear [217]. In this plot, the temperature dependence of the mean first passage time tmfp is presented. We define tmfp as the average number of MC steps necessary to form at least 13 native contacts in the folding simnlations,... 

In this variant of the chevron plot [217,220], the temperature T mimics the effect of the denaturant concentration that is in experimental studies the more generic external control parameter. The hypothetic intersection point of the folding and unfolding branches defines the transition state. The transition state temperature estimated from this analysis coincides very nicely with the folding temperature Tf 0.36 as identified in our earlier... 

Chevron plot of the mean-first passage times from folding ( ) and unfolding (o) events at different temperatures. The hypothetic intersection point corresponds to the transition state. From [200]. 

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