Research Of Complex Vesicles In Spherical Topology

Amphiphilic molecules can aggregate spontaneously into lipid vesicles in aqueous(or oil ) environment. Great progress has been made in the study of man-made vesicles in the last twenty years. A deep research has been given to the axisymmetric vesicles with spherical topology. The phase diagram of several branches of shapes found in experiments before has been presented.As for nonaxisymmetric shapes, the research is still limited. Starfish vesicle which is a kind of important vesicles observed experimentally was researched by direct minimizing before, but only a few singular shapes were obtained without stability analysis. The relationship between these shapes and the other different branches, such as the oblate and the prolate shapes, is still unclear, and no research has been done about the transitions between them.Ou-Yang's group has found some interesting shapes which are related to red blood cells through giving dramatic changes to the area and the enclosed volume of a spherical vesicle by Surface Evolver. Without considering the effect of the protein skeleton, those shapes usually are unstable in the spontaneous-curvature (SC) model.This paper focuses on the research of the shapes with spherical topology, especially, the starfish shapes in the SC model. Realizing that the solution to the Helfrich variational problem has discrete (countable) branches and the shape with higher symmetry usually has lower energy, we choose several initial configurations with different symmetries to evolve. Through adjusting some parameters appropriately, the starfish vesicles with D_nh and C_nv symmetries can be obtained easily. Study of the stability of these shapes and the transitions between them are the main target of the paper.By investigating the shape transitions carefully, we find several interesting bifurcations. Furthermore, we also find several new stable shapes which haven't been discovered experimentally. Without constraints, we numerically show a few multifold symmetric new budding vesicles. All of our shapes have been subject to stability analysis. Our main results are as follows:(1) Through scouting the eigen modes and eigenvalues of Hessian matrix of several...