Membrane bending energy and shape determination of phospholipid vesicles and red blood cells

A procedure is developed to calculate red blood cell and phospholipid vesicle shapes within the bilayer couple model of the membrane. The membrane is assumed to consist of two laterally incompressible leaflets which are in close contact but unconnected. Shapes are determined by minimizing the membrane bending energy at a given volume of a cell (V), given average membrane area (A) and given difference of the areas of two leaflets (delta A). Different classes of shapes exist in parts of the v/delta a phase diagram, where v and delta a are the volume and the leaflet area difference relative to the sphere with area A. The limiting shapes are composed of sections of spheres with only two values allowed for their radii. Two low energy axisymmetrical classes, which include discocyte and stomatocyte shapes are studied and their phase diagrams are analyzed. For v= 0.6, the discocyte is the lowest energy shape, which transforms by decreasing delta a continuously into a stomatocyte. The spontaneous membrane curvature (C0) and compressibility of membrane leaflets can be incorporated into the model. A model, where delta A is free and C0 determines the shapes at given V and A, is also studied. In this case, by decreasing C0, a discocyte transforms discontinuously into an almost closed stomatocyte.