Membranes and Elastic Surfaces

Abstract

An essential component of a cell is a biological membrane or bio-membrane; it forms and modulates an interface of the cell and cell’s various internal compartments called organelles, acting as a selectively permeable barrier between them. Bio-membranes consist mostly of phospholipid (lipid ) bilayers and the associated proteins. The bilayer is about 5 nm thick, being self-assembled from lipid molecules each with a hydrophilic head and hydrophobic tails . The lipids in a fluid membrane can move laterally within the bilayer, organizing themselves to adopt the phase or the shape at equilibrium, corresponding to free energy minimum. There are two kinds of membrane proteins that perform a variety of cellular functions: integral proteins (such as ion channel), all or part of which span the bilayer, and peripheral proteins, which lie outside the core of the bilayer (see Fig. 12.1). In this chapter we study the thermo-mechanical aspects of the membrane, with a particular focus on its mesoscopic fluctuations and conformations at equilibrium, and shape transitions . Although they are in reality very complex and heterogeneous, in this introduction, we will consider the protein-free homogeneous membranes or membrane fragments that are amenable to statistical physics analysis.