Theoretical Analysis of Phospholipid Vesicles and Red Blood Cell Shapes and the Effect of External Electric Field

Abstract

Phospholipid vesicles and biological cells display a variety of different shapes and the question can be asked what determines the equilibrium shape of a cell and its shape changes. As the inner solutions of red blood cells (RBC) and phospholipid vesicles (PV) do not involve any structure, the shapes of these objects depend solely on the physical and chemical state of their membranes. It is commonly believed that for a given membrane the shapes that are formed correspond to the minimum value of the membrane elastic energy. This energy can, in general, be decomposed into the sum of the stretching, shear and bending energy terms¹. It is also a general property of membranes that relatively much more energy is needed to stretch them than to cause shear deformation or bending. Consequently, the shape established by a flaccid cell or vesicle corresponds to the minimum value of the sum of the shear and bending energy terms, where its membrane area is practically constant. In particular, phospholipid membranes are two-dimensional liquids and as such do not exhibit shear elasticity. Thus their shape is determined only by the membrane bending energy. The RBC membrane is structurally more complex than the PV membrane, involving, for example, a cytoplasmic protein network and can therefore exhibit shear elasticity². However, which of the above two elastic deformations is the main determinant of the RBC shape still cannot be definitely established. At least some of the shapes observed in PV and RBC systems are alike³ which indicates a possible dominant role of the membrane bending energy. It is therefore of interest to investigate the RBC shape behavior under the assumption of a minimum value of membrane bending energy as a possible limiting case of a more general situation.