Research Vesicles Opening Phase Diagram Under SC Models

The Hotani research group of Nagoya University first observed stable opening-up membrane vesicles in experiment. It was found that the phospholipids bubble can be opened when talin or some other chemical material is added to the liposome solution, and under certain condition this process is reversible. On the theoretical exploration, T. Umeda et al numerically calculated the equilibrium shape of cuplike vesicles and tubelike vesicles with the relaxation method, which comply with the experimental results.Whether there exist other types of opening-up membrane vesicles is an interesting problem both on experimental and theoretical aspects. In this thesis, we study systematically on the solutions of the n-budding opening-up vesicles which was found by Wang Ying et al. We will focus mainly on the properties of different branches of solution, the shape transformation in the same branch under the influences of the reduced spontaneous curvature, the reduced line tension, and the Gaussian modulus. The main results are as follows:1. The shape transformation of cuplike vesicles under different c0, and γ is studied in detail. The forming mechanism of opening-up cuplike vesicles is discussed.2. Two branches of solutions of2-budding opening-up vesicles are found. It’s a remarkable characteristic of2-budding opening-up vesicles that differs with that of cuplike vesicles. As an example, the properties of these two branches of solutions are studied under c0=2.4. AB-F branch corresponds to the transformation of dumbbell shapes to opening-up dumbbell shapes. The KG branch corresponds to the transformation of the prolate shapes to opening-up dumbbell shapes. There exists a critical line tension γc. When the line tension is less than γc, the transformation from the closed vesicle to the opening-up vesicle is continuous. There also exists a discontinuous transformation near CD in ABF branch solution.3. It is found that the relationship between c0and γc is linear.4. With decreasing spontaneous curvature (co=2.3),it is found that the AB-F branch is split into two branches, AB and CDEF. The branches of CDEF and KG are connected, i.e., C and K correspond to the same shape. Under this c0, we cannot get the limiting shape A with decreasing γ.This is remarkably different from the cuplike shape. The calculation of3-budding opening-up vesicles under c0=3.0displays the same result.5. With further decreasing spontaneous curvature(c0=2.0), F and G become nearly closed shapes. The transformation processes along the two branches are both continuous.6. The influences of Gaussian curvature elastic modulus kg on the shapes are studied in three cases. For tiny holes on the membrane, the influence of kg on the shape is similar to the case of the cuplike vesicles. For shapes with large holes of2-budding vesicles (shapes on AB and shapes near K on KG branch), closed shape can be obtained by adjusting kg continuously. The holes on the opening-up dumbbell shapes will shrink with decreasing kg, and the holes on the opening-up prolate shapes will shrink with increasing kg. It is also found that the solution may jump from one branch to another branch by adjusting kg.