The seventh Datta Lecture. Membrane bending energy concept of vesicle- and cell-shapes and shape-transitions.

The main objective of this lecture is to discuss the role of lipid-bilayer elasticity (1) for the self-organization of lipid/protein-bilayers (2) for the stabilization of domain structures and shapes of cell membranes and (3) for the control of shape transitions (e.g. bud- and pit-formation) and shape instabilities (vesicle fission). It is demonstrated that many complex shape transitions of cell membranes can be mimicked by single lipid bilayer vesicles by simply varying the area-to-volume ratio or by chemically induced bending moments suggesting that these processes are governed by the universal minimum bending energy concept of closed shells composed of stratified membranes. The essential role of the coupling between curvature and phase separation in mixed membranes for the formation and stabilization of local pits and buds or the fission of budded vesicles is demonstrated. Finally, we discuss the consequences of the pronounced thermally excited bending undulations of the hyperelastic membranes for the membrane tension, the material exchange at membrane surfaces and the control of the adhesion of vesicles (or cells) on solid substrates.