Physical principles of cellular membrane shapes

Eukaryotic cells have a flexible plasma membrane that allows them to change their shapes to fulfill various biological functions. To modify their shapes, cells can utilize specialized proteins that bind to the membrane and have an intrinsic shape that deforms it. In addition, the cells can exert forces on the membrane using their cytoskeleton, for example, by directing polymerization of actin biopolymers against the membrane at targeted locations. This chapter provides an introduction to the physical principles behind these two generic mechanisms of membrane deformations in living cells.