Gyroid-Like Surfaces

Cubic lipid phases have a very much more complex architecture than lamellar and hexagonal phases. Their structural characteristics have been elucidated only very recently, and it has become clear that their subtleties are the key to a variety of biological problems. We will consider those subtleties in some detail. The three fundamental cubic minimal surfaces - the P-surface, the D-surface and the gyroid (or G-surface), introduced in Chapter 1, can all be foimd in cubic lipid-water phases. The lipid bilayer is centred on the surface with the polar heads pointing outwards. Water fills the labyrinth systems on each side of the surface. These cubic phases will be termed Cp, CD and CG/ respectively. It is likely that there are other more complex IPMS morphologies in cubic phases of lipid-water mixtures, as yet uncharacterised. 

However, there is a structure consistent with both the required space group and the optical properties. The gyroid surface, which occurs frequently in lipid-water systems, provides such a possibility. If we assume that cholesterol skeletons form rod-like infinite helices, this structure represents an effective three-dimensional packing of such helices. Thus, the rods form a body-centered arrangement as shown in Fig. 5.5. In this structure, there is a helical twist between the rods, in addition to the cholesteric twist within each rod. The h)rperbolic structure is a consequence of the chirality of the esters, which induces torsion into the packing arrangement. A racemic mixture does not exhibit this phase natural cholesteric esters contain a single enantiomer only. 

The most intriguing cases of lower symmetry relatives to known mesophases are anisotropic bicon-tinuous mesophases. These are sponges whose homogeneity lies one rank below the cubic genus-three P, D and gyroid surfaces. The most likely candidates are tetragonal and rhombohedral variants. These include the rPD, tP, tD, tG and rG triply periodic minimal surfaces (18). These surface are deformations of their cubic parent structures, and can be modelled as perturbations of the known bicontinuous cubic mesophases. 

---