On the Shape Problems of Vesicles of Lipid Bilayers

Yoshihisa Enomoto¹ and Toshio Sekimura²

¹Department of Physics, Nagoya Institute of Technology, Gokiso, Nagoya 466, Japan
²College of Engineering, Chubu University, Kasugai, Aichi 487, Japan

(Received May 17, 1996; Accepted August 19, 1996)

Keywords: Lipid Bilayer, Liposome, Shape Problem, Elastic Bending Energy

Abstract. We review recent theoretical understandings of the shape problems of lipid bilayer vesicles. Three simple models are proposed to discuss the shape problems, where lipid bilayer liposomes are regarded as mathematical two-dimensional closed surfaces. These models are based on the elastic bending energy functional, which represents a stored energy associated with curved surfaces and is described in terms of the surface curvature. Such bending energy functional is also revealed to be derived from the different point of view by using an analogy between vesicles and surfactant interfaces of microemulsion. Equilibrium shapes of vesicles are determined by solving the shape equations under proper conditions, which are obtained from the variational principal for the bending energy functional associated with the infinitesimal surface deformations. Based on numerical calculations of the shape equation for the bilayer-couple model, we briefly discuss the shape diagram for axisymmetric vesicle shape. Finally, an importance of hydrodynamical effects on shape fluctuations is pointed out.