三区域膜泡相分离模式之间转变的研究

Phase separation pattern transition of three-domain vesicles

基于Helfrich弹性曲率模型,结合实验参数,用直接极小化方法对三区域膜泡的两种相分离模式的稳定形状,及其之间的相变进行了计算,得出相变点为?_o*=0.49,与实验结果 ?_o*=0.5很接近.用直接极小化方法还研究了三区域膜泡发生发芽的必要条件,指出只有当约化线张力系数足够大,并且膜泡内外溶剂能自由渗透时,才可能发生发芽形变,并对渗透的可能机制进行了探讨.

Based on the Helfrich elastic curvature energy model, the stable shapes for the two patterns of three-domain phase separation are studied in detail for the experimental parameters with direct minimization method in order to explain the interesting experimental results by Yanagisawa et al.（2010 Phys. Rev. E 82 051928）. According to their experimental results, there are two transition processes. In the first process, the three-domain vesicles are formed, which are metastable. After several tens of minutes, the three-domain vesicles begin to bud, which is the second process. In the first process, the three-domain vesicles are formed with two patterns. The pattern with the liquid-ordered（Lo） phase in the middle with roughly cylindrical shape and two cap-shape liquid disordered（Ld） domains on each side of the Lo domain is termed pattern I in our paper, and the pattern with Lddomain in the middle with roughly cylindrical shape and two cap-shape Lo domains on each side is referred to as pattern II. In the same paper of M. Yanagisawa et al., an approximate calculation is made with the vesicle shapes of the two patterns approximately represented by spheroids.Their calculation shows that the transition point of the two patterns is at ф＊o≈ 0.27 in the case of ξ = 0.02（or v = 0.942）and σ = 50, in contrast with the experimental result of ф＊o≈ 0.5. Here фo is the area fraction of Lo phase, and ξ is the excess area（which is usually represented by reduced volume v in the previous literatures）, σ is the reduced line tension at the boundary of two adjacent domains. Thus the problem comes down to whether the transition point of the two patterns conforming with the experimental result can be obtained by the Helfrich elastic curvature energy theory if one performs a more precise calculation. Our calculation is performed with the direct minimization method, with the two boundaries of domains constrained in two parallel planes, this is an effective method to guarantee the smoothness of the boundary. To allow the vesicle to have a sufficient freedom to evolve, only constraints of fixed reduced volume and area fraction are imposed（The usual implementation method of constraints with the enclosed volume and the area of each phase fixed is not appropriate in this case. It does not allow the vesicle to have enough freedom to evolve, since the two boundaries are constrained in two preassigned planes）. For the experimental parameters of σ = 50 and ξ = 0.02,the transition point for the two patterns is obtained to be ф＊o= 0.49, which is quite close to the experimental result of ф＊o= 0.5. In order to understand the budding process in the second process, a detailed study is also made with the direct minimization method. It is found that the budding process can occur only for high enough σ value（σ 7.0）and permeable membrane（in other words, no constraint of reduced volume is exerted）. One possible mechanism of the permeation is the temporary passage caused by the defect in the bilayer membrane due to large reduced line tension,which needs to be further checked experimentally. The three-domain vesicles found in the experiment have rotational symmetry in the case of small ξ（or large v）. What is more, they have a reflective symmetric plane perpendicular to the rotational symmetric axis, thus only vesicles with D∞hsymmetry are considered in this paper.