The Sc Model, New Openings In Vesicle Shape The Inquiry

Lipid molecule is a parent molecule, which consists of a hydrophilic polar head and one or two of the non-polar hydrophobic tail (hydrocarbon chain) , composed of lipid molecules in aqueous solution tend to form outside the head, hydrocarbon chains inside the bilayer, the lipid bilayer will be formed at an appropriate concentration of the foam closure. Experimentally observed shape of the closed-rich membrane vesicles, we have this film as a bubble under certain conditions an equilibrium state.Canham first put forward membrane curvature elastic model, and later Helfrich made spontaneous curvature (SC) model. Taking into account the double-membrane structure, it also raised the double-coupled (BC) model and the area difference elasticity (ADE) model. The main points of these models is that the structure of membrane vesicles is not determined by their surface tension, but its curved surface. Based on three curvature models, the shape of the bubble membrane closure has been a great deal of calculation.People in the past believed that only the closure of the membrane vesicles is stable, but recent studies have found a number of organic reagents such as Protein Talin (a protein) can open the lipid membrane of the holes which can be stable. In 1998, such as Japan's A.Saitoh first used a certain concentration of the elements Talin to open the closed membrane vesicles, and the size of the opening varies with the concentration of Talin, a process that under certain conditions is reversible.In theory, R. Capovilla from Mexico's first gave the opening film of the bubble equilibrium equations and boundary conditions in a certain line tension. Mr Tu zhan -chun and Ou-Yang used differentiation to deal with outside surface of the variational problem, derived the same result. Membrane vesicles of openings, the Euler- Lagrange equation is the same to the closed membrane vesicles, but the border would like to add two independent boundary conditions, so the numerical method should make the corresponding changes.Due to the shape of the bubble membrane equations is higher-order nonlinear partial differential equations, people are only aware of the limited special solution. In order to compare with experimental results we must use the numerical calculation. Vesicle shape on the numerical calculation, points to two situations:(1) the shape of rotational symmetry, the equation can be translated into the numerical solution of ordinary differential equations.(2) non-rotational symmetry of shape, because there is no solution of partial differential equations of the general numerical method, commonly used method of direct minimization. At present, the most commonly used is calculated under the Evolver.Membrane vesicles of openings, there is no direct minimization of the results. Rotational symmetry of the vesicle, T. Umeda and others in the SC model and the ADE model has made numerical calculation of the cup and the shape of the balance tube. compared to the wealth of closed membrane vesicles, the current to explore the shape of the opening-up vesicles is still very limited.In this paper, under the SC model we study the closed and openings membrane vesicles and their evolution. Numerical solution is designed to solue a closed-membrane vesicles and vesicle openings approach, combined with Mathematica software, for axisymmetric bubble shape of the membrane we get the main results are as follows:(1)With a small number of known analytical comparison of the results, such as spherical, we have discussed in depth the issue of calculation errors;(2)Through continuous improvement methodology, we find the solution method of closed membrane vesicles, defined as two-dimensional method, the closure membrane vesicles has been enriched, oblate,prolate,sanye, pear-shaped, stomach, etc;(3) theory derived the corresponding spontaneous curvature c₀ = 2n^1/2 from the shape of n-budding closed vesicles . On this basis of n-budding vesicle openings may exist in the department of c₀ < 2n^1/2 .Theory derived the relationship of the opening three border membrane vesicles and received only two are independent;(4) Use the two-dimensional method for calculating the shape of the openings and validate its scale invariance;(5) Finding the method of three-dimensional method vesicle for the openings. On the method used in ours,we give the cup-shaped openings on the vesicle shape and energy calculation, which is the same to T. Umeda and Y. Suezaki's results;(6) When use the three-dimensional method in c₀ = 2.3, the 2-budding in the opening of the new shape is obtained and given the shape of the bubble membrane as well as the energy and the relationship between line tension coefficient;(7)When use the three-dimensional method in c₀ = 3 and c₀ =3.5 we have the shape of 3-budding openings.