Chapter 11. Generic interactions of flexible membranes

R. Lipowsky
Institut für Festkörperforschung, Forschungszentrum Jülich, D-2425 Jülich, Germany
and Max-Planck-Institut für Kolloid- und Grenzflächenforschung,
Kantstr. 55, D-14513 Teltow-Seehof, Germany

1. Introduction

The interaction of biomembranes and lipid bilayers is characterized by the interplay of energy and entropy [1]. The forces between the molecules lead to direct interactions which are already present for immobilized or rigid membranes. The membranes considered here are, however, not rigid but rather flexible and, thus, undergo thermally excited shape fluctuations which lead to fluctuation-induced interactions [2]. The competition between direct and fluctuation-induced interactions represents an interesting renormalization problem since it involves many length scales [3]. Indeed, the spectrum of shape fluctuations contains a wide range of length scales from about 1 nm for displacements of single molecules to about 10 mm for the flicker modes of vesicles and cells.

The renormalization arising from these shape fluctuations acts to increase the repulsive part of the direct interaction. In fact, sufficiently strong fluctuations overcome the attractive part of the direct interaction and lead to unbinding or adhesion transitions between bound and unbound states of the membranes [3-5]. Similar transitions occur for interfaces and polymers where they represent wetting and adsorption transitions, respectively [6].

This chapter is organized as follows. The basic properties of the model membranes considered here are briefly described in the remainder of this introductory section. Section 2 contains a short review of the experimental methods which have been used to study the adhesion and the cohesion of membranes. The direct interaction between two rigid membranes is discussed from a theoretical point of view in section 3. The effects of thermally excited fluctuations are first treated in a heuristic way in section 4. The systematic theory starts in section 5 where the renormalization of the interaction by bending undulations is described for the case of two membranes. Stacks and bunches of many membranes are considered in section 6. The renormalization of hydration forces by protrusion modes is studied in section 7.

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