The Opening Film Bubble Shape Of The Study

The lipid-bilayer membrane in aqueous solutions is regarded as an appropriate model for biomembrane.People have observed stable shapes with talin and some detergents,a variety of physical techniques,such as electroporation and osmotic shock optical tweezers have been developed to open transient holes in membrane.The study of opening-up vesicles have gathered many scholars attentions.People have found some certain qualitative relations between talin concentration and line tension.However,only axisymmertric shapes are analyzed,nonaxisymmetric shapes will be a future work.It has been made great progress in the study of opening-up vesicles recently.The paper of Zhou Jianjun analyzed the axisymmertric shapes,he introduced the line tension contribution to the total Helfrich curvature energy,the axisymmertrial shape equation and the corresponding boundary conditions are obtained in the case of vesicle with one hole.Furthemore,R.Capovilla etl.first studied the axisymmertrial shape equation and the corresponding boundary conditions of opening-up membrane vesicle,However,Their mathematical method is very difficult to understand.Z.C.Tu and Z.C.Ou-yang introduced exterior differentials to deal with variational problems on open surfaces and obtained concisely the shape equation and boundary conditions of open lipid bilayers.Y.Suezaki used SC model and ADE model to study small da of axisymmetric vesicle detailedly based on the shooting method.The merit of shooting method is that it calculates quickly,but it can't deal with nonaxisyrnmetric vesicle shape,and it can't analyze stability.What's more,they can't calculate some shapes of da＞1,they just have guessed that the stable opening-up membrane vesicle shapes would evolve very little hole.In the minizing model,opening-up membrane vesicle shape is the result of competing between curvature energy and line tension energy.Membrane vesicle line tension energy usually is very large, so membrane vesicle shapes form closed membrane vesicle shapes.When adding talin in aqueous solutions,line tension coefficient will reduce obviously.When line tension coefficient reduces to zero,the membrane vesicle will form a disk,because curving surface energy and line tension energy are all zero in the case.Membrane vesicle shapes usually change between the two limited shapes. After considering restriction of da,it maybe appear some new shapes.People have never used the minizing method to study opening-up vesicle,we will attempt to use this method to study opening-up vesicle shapes.We find that because boundry can change freely,it is very difficult to obtain stable shapes.To get over this difficult,we may let boundry line tension keep fixed,so we can change a way to study,and fix the boundry of membrane vesicle,and let area change freely,the two methods are equivalent in the mathematics.In this way,we get similar shapes which have been observed in the experiment,these shapes match with the results of numerical calculation.Furthermore,we studied some axisymmertrial and non axisymmertrial membrane vesicle stable shapes with big da.We hope to test these shapes.We get some main results:(1) When da changes from 0 to 1,membrane vesicle shape evolves from disk to cup and it evolves a little opening-up sphere finally.Y.Suezaki has studied this case,although they can't study stability of membrane vesicle shapes.The shapes we get accord with their results,it make clear that our method is feasible.Futhermore,we find these shapes are all stable in the BC model,but in the SC model,they are not stable.And in the interzone of parameters,the same c₀ will get two shapes.(2) When da＞1,we have got opening-up vesicle shapes that three spheres are joined,though they are not stable in the SC model,they are stable in the BC model.(3) When da is very super,we get four spheres joined with one hole and some other interesting shapes,these shapes are stable in the BC model.The first study in our work is that we have used Surface Evolver which is a powerful software to simulate two -dimensional surface is used to do the simulation about the shape of closed and opening-up vesicles basing on some shape equations and the corresponding boundary conditions which have been obtained.We fix the edge of opening-up vesicle to evolve some new shapes.The second study in our work is that we analyze the stability of shapes we obtained and compare the shape obtained with obtained by some others.We find the talin molecules collected along the verge the orifice only.