The Conformation of Flexible Membranes
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THE CONFORMATION
OF FLEXIBLE
MEMBRANES
REINHARD LIPOWSKY and JOANNA COOK-R6DER Institut ffir Festk6rperforschung, Forschungszentrum Jiilich Postfach 1913, D-5170 Jiilich, Germany ABSTRACT. Membranes such as lipid bilayers are highly flexible surfaces which determine the architecture of biological systems and provide a basic structural element for the mesophases of complex fluids.' Two aspects of their conformational behavior will be considered. First, the morphology of vesicles and membranes is briefly reviewed. Then, recent theoretical work on adhesion (or cohesion) phenomena which involve whole bunches of membranes will be discussed. 1. Morphology of vesicles and membranes 1.1
Shape of free vesicles
In aqueous solution, lipid bilayers typically form closed surfaces or vesicles. Several preparation methods are available by which one can obtain large unilamellar vesicles with a linear size of the order of 10 pm which can be studied by light microscopy. Such observations have shown that lipid vesicles exhibit a large variety of different shapes, see Fig. 1. In particular, they can exhibit the nonspherical, biconcave shape which is typical for red blood cells.
10 R
Cgm
Figure 1: Shape transformations of a lipid vesicle induced by temperature changes. 2 -4 The shapes are axisymmetric with respect to the broken line. The shape of vesicles is primarily determined by bending elasticity and curvature. 5 In thermal equilibrium, the vesicle should then attain a shape which corresponds to a minimum of its bending energies. 4" The experimentally observed shapes and shape transformations as shown in Fig. 1 can be explained by such minimal shapes if one assumes that the two monolayers of the bilayer exhibit a small asymmetry.2-4 Mat. Res. Soc. Symp. Proc. Vol. 248. @1992 Materials Research Society
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All shapes shown in Fig. I have the topology of a sphere. Recently, it has been theo7 can have the topology of a torus. ', retically predicted that minimal shapes of fluid vesicles 9 experimentally. Such tori have now been observed 1.2 Shape fluctuations of membranes When viewed under the microscope, the membranes of vesicles exhibit thermally-excited shape fluctuations. Quite generally, low-dimensional objects such as interfaces, membranes or polymers undergo such fluctuations in order to increase their configurational entropy. A membrane is usually more flexible than an interface but less flexible than a polymer. The character of its shape fluctuations depends on the internal state of the membrane. The lipid-protein bilayer of biomembranes is typically fluid, i.e., the molecules can diffuse rapidly within the membrane. In addition, biomembranes often contain 2-dimensional networks. Two examples are the cell wall of bacterial cells which contains a peptidoclycan network and the cytoskeleton in some eucaryotic cells such as the spectrin network of red blood cells. These networks provide examples for polymerized or solid-like membranes. On length scales which are large compared to the meshsize of the network, a polymerize
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