Ribbons, helical/twisted

Figure 5.46 Schematic representation of helical and twisted ribbons as discussed in Ref. 165. Top Platelet or flat ribbon. Helical ribbons (helix A), precursors of tubules, feature inner and outer faces. Twisted ribbons (helix B), formed by some gemini surfactant tartrate complexes, have equally curved faces and C2 symmetry axis. Bottom Consequences of cylindrical and saddlelike curvatures in multilayered structures. In stack of cylindrical sheets, contact area from one layer to next varies. This is not the case for saddlelike curvature, which is thus favored when the layers are coordinated. Reprinted with permission from Ref. 165. Copyright 1999 by Macmillan Magazines.

From the sum total of the evidence it appears that the globular proteins have a structure similar to the form of the k-m-e-f group of the fibrous proteins, that is, a helical twist with 3-6 residues per turn or 18 residues per 5 turns. However, this does not explain the compactness of the globular proteins. It appears that the polypeptide ribbons are bunched into compact globules and held by lateral linkages between the chains. 

Figure 5.3 Electron micrographs of diastereomers of A-octyl-D-aldonamide (a) helical rods from D-Glu-8 (1, bar = 50 nm), (b) rolled-up sheets from D-Man-8 (2, bar = 300 nm), and (c) twisted ribbons from D-Gal-8 (3, bar = 300 nm). Reprinted with permission from Ref. 31. Copyright 1990 by the American Chemical Society.

Addition of 5% ganglioside Gmi into the L-Glu-Bis-3 resulted in the appearance of vesicles along with twisted ribbons, while addition of nonchiral 10,12-docosadiynedioic acid caused the formation of platelets.97 These results affirm the importance of packing geometry, along with head group chirality, for the formation of helical structures. 

Figure 5.24 Model of hierarchical self-assembly of chiral rodlike monomers.109 (a) Local arrangements (c-f) and corresponding global equilibrium conformations (c -f) for hierarchical selfassembling structures formed in solutions of chiral molecules (a), which have complementary donor and acceptor groups, shown by arrows, via which they interact and align to form tapes (c). Black and the white surfaces of rod (a) are reflected in sides of helical tape (c), which is chosen to curl toward black side (c ). (b) Phase diagram of solution of twisted ribbons that form fibrils. Scaled variables relative helix pitch of isolated ribbons h hh /a. relative side-by-side attraction energy between fibrils eaur/e. Reprinted with permission from Ref. 109. Copyright 2001 by the National Academy of Sciences, U.S.A.

Furthermore, Oda et al. pointed out that there are two topologically distinct types of chiral bilayers, as shown in Figure 5.46.165 Helical ribbons (helix A) have cylindrical curvature with an inner face and an outer face and are the precursors of tubules. These are, for example, the same structures that are observed in the diacetylenic lipid systems discussed in Section 4.1. By contrast, twisted ribbons (helix B) have Gaussian saddlelike curvature, with two equally curved faces and a C2 symmetry axis. They are similar to the aldonamide and peptide ribbons discussed in Sections 2 and 3, respectively. The twisted ribbons in the tartrate-gemini surfactant system were found to be stable in water for alkyl chains with 14-16 carbons. Only micelles form... 

The Helfrich-Prost model was extended in a pair of papers by Ou-Yang and Liu.181182 These authors draw an explicit analogy between tilted chiral lipid bilayers and cholesteric liquid crystals. The main significance of this analogy is that the two-dimensional membrane elastic constants of Eq. (5) can be interpreted in terms of the three-dimensional Frank constants of a liquid crystal. In particular, the kHp term that favors membrane twist in Eq. (5) corresponds to the term in the Frank free energy that favors a helical pitch in a cholesteric liquid crystal. Consistent with this analogy, the authors point out that the typical radius of lipid tubules and helical ribbons is similar to the typical pitch of cholesteric liquid crystals. In addition, they use the three-dimensional liquid crystal approach to derive the structure of helical ribbons in mathematical detail. Their results are consistent with the three conclusions from the Helfrich-Prost model outlined above. 

Figure 5.51 Scenario for kinetic evolution of flat membranes into tubules.68,132 (a) When membrane is cooled into tilted phase, it develops stripes in tilt direction and then breaks up along domain walls to form ribbons, (b) Each ribbon twists in solution to form helix, (c) Helical ribbon may remain stable or may grow wider to form tubule. Reprinted with permission from Ref. 139. Copyright 2001 by the American Chemical Society.

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