Some aspects of membrane elasticity

Phospholipids referred in the following as lipids serve as building blocks of membranes of cells and cell organels. Stimulated by their biological relevance, the membranes consisting of lipid molecular layers are the subject of extensive experimental and theoretical studies. Recent successful applications of advanced experimental techniques revealed a broad spectrum of membranes shapes formed spontaneously by various classes of lipids in the process of their self-assembly, and made it possible to study quantitatively the elastic properties of the membranes of different congurations. Attempts to understand the physics of these systems require development of sophisticated theoretical models treating the elastic behaviour of lipid membranes characterised by high and inhomogeneous curvatures. Consideration of some of these theories is the goal of this overview. In the following, I give a short phenomenological description of structures formed by the lipid molecules and survey the main theoretical ideas involved in the analysis of these structures.