Liquid crystals Membrane

The strain tensor must conform to the symmetry of the liquid crystal phase, and as a result, for nonpolar, nonchiral uniaxial phases there are ten nonzero components of kij, of which four are independent ( i i, 22> A 33 and 24)- These material constants are known as torsional elastic constants for splay (k, 1), twist ( 22) bend ( 33) and saddle-splay ( 24) terms in 24 do not contribute to the free energy for configurations in which the director is constant within a plane, or parallel to a plane. The simplest torsional strains considered for liquid crystals are one dimensional, and so neglect of 24 is reasonable, but for more complex director configurations and at surfaces, k24 can contribute to the free energy [7]. In particular 24 is important for curved interfaces of liquid crystals, and so must be included in the description of lyotropic and membrane liquid crystals [8]. Evaluation of Eq. (16) making the stated assumptions, leads to [9] ... 

When discussing bulk energies, this term is usually omitted. For curved surfaces of liquid crystals, e.g., in the description of lyotropic and membrane liquid crystals, however, this term becomes important." The surface term, K24, is usually important in case of saddle-splay (potato chips type) deformations and is called saddle-splay constant. 

Hydrated bilayers containing one or more lipid components are commonly employed as models for biological membranes. These model systems exhibit a multiplicity of structural phases that are not observed in biological membranes. In the state that is analogous to fluid biological membranes, the liquid crystal or La bilayer phase present above the main bilayer phase transition temperature, Ta, the lipid hydrocarbon chains are conforma-tionally disordered and fluid ( melted ), and the lipids diffuse in the plane of the bilayer. At temperatures well below Ta, hydrated bilayers exist in the gel, or Lp, state in which the mostly all-trans chains are collectively tilted and pack in a regular two-dimensional... 

Caffrey, M. Structural, Mesomorphic and Time-Resolved Studies of Biological Liquid Crystals and Lipid Membranes Using Synchrotron X-Radiation. 151, 75-109 (1989). 

Fig. 27 a and b. Schematic representation of the molecular structure of a side chain polymeric liquid crystals b polymer model membranes studied by 2H NMR... 

The three classes of liquid crystals differ in the arrangement of their molecules. In the nematic phase, the molecules lie together, all in the same direction but staggered, like cars on a busy multilane highway (Fig. 5.49). In the smectic phase, the molecules line up like soldiers on parade and form layers (Fig. 5.50). Cell membranes are composed mainly of smectic liquid crystals. In the cholesteric phase, the molecules form ordered layers, but neighboring layers have molecules at different angles and so the liquid crystal has a helical arrangement of molecules (Fig. 5.51). 

Papahadjopoulos, D., and Watkins, J. C. (1967). Phospholipid model membranes. II. Permeability properties of hydrated liquid crystals, Biochim. Biophys. Acta. 135. 639-652. 

The thickness of the membrane phase can be either macroscopic ( thick )—membranes with a thickness greater than micrometres—or microscopic ( thin ), i.e. with thicknesses comparable to molecular dimensions (biological membranes and their models, bilayer lipid films). Thick membranes are crystalline, glassy or liquid, while thin membranes possess the properties of liquid crystals (fluid) or gels (crystalline). 

Phospholipids, which are one of the main structural components of the membrane, are present primarily as bilayers, as shown by molecular spectroscopy, electron microscopy and membrane transport studies (see Section 6.4.4). Phospholipid mobility in the membrane is limited. Rotational and vibrational motion is very rapid (the amplitude of the vibration of the alkyl chains increases with increasing distance from the polar head). Lateral diffusion is also fast (in the direction parallel to the membrane surface). In contrast, transport of the phospholipid from one side of the membrane to the other (flip-flop) is very slow. These properties are typical for the liquid-crystal type of membranes, characterized chiefly by ordering along a single coordinate. When decreasing the temperature (passing the transition or Kraft point, characteristic for various phospholipids), the liquid-crystalline bilayer is converted into the crystalline (gel) structure, where movement in the plane is impossible. 

Guizard, C., Bac, A., Barboiu, M. and Hovnanaian, N. (2000) Organic-inorganic hybrid materials with specific solute and gas transport properties for membrane and sensors applications. Molecular Crystals and Liquid Crystals, 354, 91-106. 

Cholesterol s presence in liposome membranes has the effect of decreasing or even abolishing (at high cholesterol concentrations) the phase transition from the gel state to the fluid or liquid crystal state that occurs with increasing temperature. It also can modulate the permeability and fluidity of the associated membrane—increasing both parameters at temperatures below the phase transition point and decreasing both above the phase transition temperature. Most liposomal recipes include cholesterol as an integral component in membrane construction. 

GLYCOLIPID LIQUID CRYSTALS AS NOVEL MATRICES FOR MEMBRANE PROTEIN MANIPULATIONS. 

Lyotropic lamellar (La) liquid crystals (LC), in a form of vesicle or planar membrane, are important for membrane research to elucidate both functional and structural aspects of membrane proteins. Membrane proteins so far investigated are receptors, substrate carriers, energy-transducting proteins, channels, and ion-motivated ATPases [1-11], The L liquid crystals have also been proved useful in the two-dimensional crystallization of membrane proteins[12, 13], in the fabrication of protein micro-arrays[14], and biomolecular devices[15]. Usefulness of an inverted cubic LC in the three-dimensional crystallization of membrane proteins has also been recognized[16]. 

The mixing of nematogenic compounds with chiral solutes has been shown to lead to cholesteric phases without any chemical interactions.147 Milhaud and Michels describe the interactions of multilamellar vesicles formed from dilauryl-phosphotidylcholine (DLPC) with chiral polyene antibiotics amphotericin B (amB) and nystatin (Ny).148 Even at low concentrations of antibiotic (molar ratio of DLPC to antibiotic >130) twisted ribbons are seen to form just as the CD signals start to strengthen. The results support the concept that chiral solutes can induce chiral order in these lyotropic liquid crystalline systems and are consistent with the observations for thermotropic liquid crystal systems. Clearly the lipid membrane can be chirally influenced by the addition of appropriate solutes. 

The earliest approach to explain tubule formation was developed by de Gen-nes.168 He pointed out that, in a bilayer membrane of chiral molecules in the Lp/ phase, symmetry allows the material to have a net electric dipole moment in the bilayer plane, like a chiral smectic-C liquid crystal.169 In other words, the material is ferroelectric, with a spontaneous electrostatic polarization P per unit area in the bilayer plane, perpendicular to the axis of molecular tilt. (Note that this argument depends on the chirality of the molecules, but it does not depend on the chiral elastic properties of the membrane. For that reason, we discuss it in this section, rather than with the chiral elastic models in the following sections.)... 

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. 

The second issue concerns the anisotropy of the membrane. The models presented in this section all assume that the membrane has the symmetry of a chiral smectic-C liquid crystal, so that the only anisotropy in the membrane plane comes from the direction of the molecular tilt. With this assumption, the membrane has a twofold rotational symmetry about an axis in the membrane plane, perpendicular to the tilt direction. It is possible that a membrane... 

It is also possible that a membrane might have an even lower symmetry than a chiral smectic-C liquid crystal in particular, it might lose the twofold rotational symmetry. This would occur if the molecular tilt defines one orientation in the membrane plane and the direction of one-dimensional chains defines another orientation. In that case, the free energy would take a form similar to Eq. (5) but with additional elastic constants favoring curvature. The argument for tubule formation presented above would still apply, but it would become more mathematically complex because of the extra elastic constants. As an approximation, we can suppose that there is one principal direction of elastic anisotropy, with some slight perturbations about the ideal twofold symmetry. In that approximation, we can use the results presented above, with 4) representing the orientation of the principal elastic anisotropy. 

To discuss the models in this section, we should mention two issues. First, the models assume the membrane is sufficiently soft that the tilt direction can vary with an energy cost that scales as (Vc(j)2. This is appropriate if the membrane is in a fluid phase like a smectic-C liquid crystal, with order in the tilt direction but not in the positions of the molecules. It is also appropriate if the membrane is in a tilted hexatic phase, with order in the orientations of the intermolecular bonds as well as the tilt. However, this assumption is not appropriate if the membrane is in a crystalline phase, because the tilt direction would be locked to the crystalline axes, and varying it would cost more energy than (V(f>)2. 

So far we have considered the formation of tubules in systems of fixed molecular chirality. It is also possible that tubules might form out of membranes that undergo a chiral symmetry-breaking transition, in which they spontaneously break reflection symmetry and select a handedness, even if they are composed of achiral molecules. This symmetry breaking has been seen in bent-core liquid crystals which spontaneously form a liquid conglomerate composed of macroscopic chiral domains of either handedness.194 This topic is extensively discussed in Walba s chapter elsewhere in this volume. Some indications of this effect have also been seen in experiments on self-assembled aggregates.195,196... 

Organic compounds which show reversible color change by a photochemical reaction are potentially applicable to optical switching and/or memory materials. Azobenzenes and its derivatives are one of the most suitable candidates of photochemical switching molecular devices because of their well characterized photochromic behavior attributed to trans-cis photoisomerization reaction. Many works on photochromism of azobenzenes in monolayers LB films, and bilayer membranes, have been reported. Photochemical isomerization reaction of the azobenzene chromophore is well known to trigger phase transitions of liquid crystals [29-31]. Recently we have found the isothermal phase transition from the state VI to the state I of the cast film of CgAzoCioN+ Br induced by photoirradiation [32]. 

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