Small Reduction Size And Adhesion Situation Vesicle Shape Research

At present, hot research topics on the shapes of the phospholipid bilayer vesicles has been shifted from the closed vesicles to the opening-up vesicles, from vesicles with larger reduced volume to small reduced volume, from free membrane vesicles to adhering membrane vesicles, and the research on the dynamical processing of the formation of the membrane vesicle.In Charpter 1 and 2 we introduce the background knowledge and theoretical model of the biomembrane, which provide the necessary basic knowledge for the following discussions.In recently experiment, people have observed that there exist stable oblate and stomatocyte vesicles at small reduced volume, but the central parts of the vesicle do not self-intersect as predicted by U. Seifert et al., but adhere to each other. In Charpter 3 we first calculate the shapes of the free membrane vesicles. Our result shows that the central part will self-intersect for small reduced volume (In other words, flat oblate or stomatocyte vesicle will turn into self-intersecting shapes). Then we consider the case when the central membranes are adhered to each other. Regarding that the vesicle is consisted of two parts which are connected by proper boundary conditions, we preliminarily conduct the numerical calculation on the membrane vesicle for the small reduced volume around v= 0.3. The shapes are much similar to the experimetal and theoretical results of J. Majhenc et al.In Charpter 4 we take a further study on the n-Budding opening-up vesicle. Wang Ying first discovered the stationary shapes of the n-Budding opening-up vesicles. But the 3-budding opening-up shapes cannot transform into the 3-budding closed shape with increasing line tension, instead, it turns into a spherical shape adding a prolate. As we know, the stable shape in this parameter interval is 3-budding shape, namely, three spherical shapes connected via narrow necks (whose energy is less than a spherical shape adding a prolate shape). Therefore, there should exist another branch of solution for the opening-up shapes. This problem puzzled researchers for a long time, but no answer for another branch was found. Now, we have found the other branch solution, so we can have a complete and deeper understanding about the processing of the 2-budding and 3-budding shapes from opening-up to closing. We believe that this shape can be observed in experiment.Cell adhesion is ubiquitous in various life phenomena, and is one of the most important problems in cell(molecular) bio-mechanics field. Cell can survive only by adhering on certain substrates so as to realize various functions of life activity. Moreover, A large number of virus and nano-particles enter into the cell by adhesion. For this reason, studying the rules of equilibrium, stability, adhesion of cells exerted by outside force has important basic meaning. In Chapter 5 we preliminary studied the adhesion of vesicles in theory. First we make a review on the shape equation for the opening-up vesicles and the closed vesicles and their corresponding boundary conditions. Then we make some preliminary numerical calculations using the Mathematica software. Special attenion is paid to some pertinent references have reported two important contacting conditions:general contacting condition for adhesion vesicles and contacting condition for opening vesicles.