Shapes of Vesicles and Cells under Forces Exerted on the Enclosing Membrane

Abstract

Shapes of vesicles and cells are governed and in simpler cases also determined by the mechanical properties of closed lamellar membranes1. Lamellarity of biological membranes is manifested by the bilayer structure of phospholipid membranes and by the membrane skeletons and glycocalices positioned in parallel to the bilayer. When the layers forming a closed membrane are in contact but can slide in the lateral direction one past the other, the essential deformational modes are the area expansivity of the membrane neutral surface, the local membrane bending and the non-local membrane bending. Shapes of freely suspended vesicles or cells without internal structures can be predicted by assuming that they correspond to the minimum of the respective membrane elastic energy. When either external or internal, mainly skeleton-derived forces are exerted on their membranes, the shapes of vesicles and cells correspond to the minimum of the free energy of the system which in addition to the membrane elastic energy involves the potential energies of the forces. In this communication we shall first describe the contributions to the elastic energy of a closed bilayer and show the consequent shapes of freely suspended vesicles. Then two examples of how forces exerted on the vesicle membrane affect the vesicle shape will be presented. First we shall deal with the axial pulling force, and then by forces due to the external electric field.