SC模型小约化体积膜泡的形状方程的研究

目前还没有相关文献报道在自发曲率模型下探究小约化体积形状方程以及边界条件.本文应用标准的变分法,在自发曲率模型下推导了旋转轴对称情况下的小约化体积膜泡的形状方程以及讨论了相应的边界条件.我们相信数值求解该模型下的形状方程和边界条件依然会得到与实验上观察一致的膜泡.     

高亏格膜泡形状的研究

目的:磷脂双性分子在水或者油溶液中会形成各种不同的膜泡形状,在实验上已经观察到大量的扑拓亏格为0的球形扑拓膜泡和扑拓亏格等于1的环形膜泡,本文是在理论上研究在自发曲率模型下,亏格g等于4的高亏格膜泡形成的稳定形状.方法:本文是通过在Surface Evolver软件中建立亏格g等于4(膜泡的拓扑结构用拓扑的亏格g表示)的具D5h对称性的初始形状,对这个初始形状进行细分并演化一定的步数后,我们得到一个剖分面较为光滑的模型.我们去调整它的自发曲率和约化体积寻找能量最低的稳定状态.结果:这种D5h对称性的膜泡很难保持它的对称形状,而会演化到几支非对称的稳定形状.结论:我们得到了亏格为4的近D5h对称性及盘形稳定形状.这种亏格为4的稳定形状提供了新的膜泡相变分支,我们期待实验上能对这些稳定形状进行验证,从而为曲率模型的正确性提供有力支持.     

球形拓扑下对budding和multi-budding生物膜泡形状的研究

流体相磷脂双分子层在水溶液中能自组织的形成球形拓扑的膜泡,膜泡的平衡形状是由其弯曲弹性能决定的.Budding是流体相磷脂双分子膜泡的一个显著的形状.从自发曲率(SC)模型的弯曲能量和双层(BC)模型的弯曲能量在参数替换情况下,我们看到自发曲率(SC)和双层(BC)模型具有相同的形状方程.本文从双层(BC)模型的相图出发,在双层(BC)模型下,通过建立一些与目标形状相近似的初始形状,在面积A,体积V和平均曲率的积分M的约束条件和使用约化量的情况下,经Surface Evolver软件的逐次细分并长时间演化,得到了一些budding和multi-budding型的生物膜泡形状.     

数值解法研究生物膜泡形状

目的:研究生物膜泡的可能形状.方法通过数值解法中的打靶法,运用Mathematica软件进行编程.结果:获得与Udo Seifert计算基本相符的图,得到了相应的生物膜泡形状,包括双凹圆盘,长椭球和扁椭球等,且获得了新的形状.结论:本法提供了一种相对精确的寻找膜泡的方法.     

生物膜细管形成过程的研究*

我们都知道磷脂双亲分子在水或者油溶液中会形成各种不同的形状。现在我们探讨的是一种细的管状生物膜泡。它通常是指在磷脂双亲分子形成膜泡后,我们对它在显微镜下进行的一系列使用光镊施加拉力操作而形成的细的管状结构。实验显示,膜泡形成的管状结构在生物学中是普遍存在的。本文主要研究怎样应用数值计算的方法进行模拟细的管状膜泡,从而得到一些长短,粗细不同的管状生物膜泡。我们从极小曲面悬链面的角度出发,研究管状膜泡的形成结构特点。最后我们认为管状膜泡的形成不同形状是与对膜泡施加拉力、细管的半径、以及管子的长度等因素有着密切的联系。     

高亏格膜泡形状

溶液中流体相磷脂膜泡的平衡形状是由其弯曲弹性能决定的。我们用Surface Evolver软件找到了一个具体的模拟稳定膜泡形状的方法,对亏格为2的膜泡进行了研究。我们提供了具体的计算结果。     

开口膜泡形状的研究

本文报道了最近在开口膜泡研究方面的一些理论和实验进展,给出了开口膜泡的形状方程和边界条件及稳定开口膜泡的形状及其相图,并对该领域的研究存在的问题与研究趋势进行了分析.     

波形生物膜泡的数值法研究

磷脂双亲分子在水溶液中会形成各种各样形状的膜泡,实验显示,存在有一维的周期性柱面膜泡.扩展的Delaunay曲面是由Ou-Yang等首次给出的Helfrich变分问题的解析特解,与Delaunay曲面不同的是它所代表的曲面为非常数平均曲率曲面,其中之一为波形周期曲面.本文用数值计算的方法探讨了波形曲面形状,并与已知的解析解进行了比较.与球形拓扑不同的是,做数值计算时所采用的欧拉-拉格朗日方程中参数不取为零,加入周期性边界条件数值求解该方程,得到了与扩展的Delaunay曲面一致的波形曲面.目前我们还没有得到扩展的Delaunay曲面之外的周期波形形状.扩展的Delaunay曲面是否给出了非常数平均曲率的波形曲面的通解,仍然是需要进一步探讨的问题.然后根据形状方程和轴对称的微分方程绘出了自发曲率取不同数值时的二维波形图,并且得出结论:随着自发曲率的增加,参数的值逐渐减小,与解析法得到的结果一致.     

磷酸化TrkA受体在与其核转位相关的运输膜泡内的定位

大量的跨膜受体能靶向并定位于细胞核内, 但细胞表面的受体是如何转运到细胞核内尚不清楚. 报道了磷酸化的TrkA在人脑胶质瘤细胞株U251中的定位. 利用免疫细胞化学和免疫荧光技术, 发现磷酸化的TrkA主要定位于一系列的运输泡和细胞核内, 这些膜泡包括: 细胞膜侧的环状泡、核周的大核心泡和小核心泡; 同时还观察到大核心泡出芽成小核心泡, 以及小核心泡与核膜相互作用. 基于上述结果认为这些膜泡可能与跨膜受体TrkA转位到核的通路相关.     

pH对紫膜表面电位的影响

用荧光标记物1,8-AMS与紫膜结合,测量了能化态和非能化态下紫膜表面电位随介质pH的变化.在pH5.5以下,紫膜表面电位随pH的降低而下降,但囊泡中的紫膜表面电位变化幅度较大;在pH5.5以上,处于非能化态的紫膜(无论是紫膜碎片还是处于囊泡中)的表面电位都没有明显变化,处于能化态时,紫膜碎片的表面电位在pH9.2出现一个峰.     

Osmotically induced shape changes of large unilamellar vesicles measured by dynamic light scattering

Static and dynamic light scattering measurements have been used to characterize the size, size distribution, and shape of extruded vesicles under isotonic conditions. Dynamic light scattering was then used to characterize osmotically induced shape changes by monitoring changes in the hydrodynamic radius (R(h)) of large unilamellar vesicles (LUVs). These changes are compared to those predicted for several shapes that appear in trajectories through the phase diagram of the area difference elasticity (ADE) model (. Phys. Rev. E. 52:6623-6634). Measurements were performed on dioleoylphosphatidylcholine (DOPC) vesicles using two membrane-impermeant osmolytes (NaCl and sucrose) and a membrane-permeant osmolyte (urea). For all conditions, we were able to produce low-polydispersity, nearly spherical vesicles, which are essential for resolving well-defined volume changes and consequent shape changes. Hyper-osmotic dilutions of DOPC vesicles in urea produced no change in R(h), whereas similar dilutions in NaCl or sucrose caused reductions in vesicle volume resulting in observable changes to R(h). Under conditions similar to those of this study, the ADE model predicts an evolution from spherical to prolate then oblate shapes on increasing volume reduction of LUVs. However, we found that DOPC vesicles became oblate at all applied volume reductions.     

Phospholipid membrane bending as assessed by the shape sequence of giant oblate phospholipid vesicles

Vesicle shape transformations caused by decreasing the difference between the equilibrium areas of membrane monolayers were studied on phospholipid vesicles with small volume to membrane area ratios. Slow transformations of the vesicle shape were induced by lowering of the concentration of lipid monomers in the solution outside the vesicle. The complete sequence of shapes consisted of a string of pearls, and wormlike, starfish, discocyte and stomatocyte shapes. The transformation from discocyte to stomatocyte vesicle shapes was analyzed theoretically to see whether these observations accord with the area difference elasticity (ADE) model. The membrane shape equation and boundary conditions were derived for axisymmetrical shapes for low volume vesicles, part of whose membranes are in contact. Calculated shapes were arranged into a phase diagram. The theory predicts that the transition between discocyte and stomatocyte shapes is discontinuous for relatively high volumes and continuous for low volumes. The calculated shape sequences matched well with the observed ones. By assuming a linear decrease of the equilibrium area difference with time, the ratio between the nonlocal and local bending constants is in agreement with reported values.     

Phospholipid membrane bending as assessed by the shape sequence of giant oblate phospholipid vesicles

Vesicle shape transformations caused by decreasing the difference between the equilibrium areas of membrane monolayers were studied on phospholipid vesicles with small volume to membrane area ratios. Slow transformations of the vesicle shape were induced by lowering of the concentration of lipid monomers in the solution outside the vesicle. The complete sequence of shapes consisted of a string of pearls, and wormlike, starfish, discocyte and stomatocyte shapes. The transformation from discocyte to stomatocyte vesicle shapes was analyzed theoretically to see whether these observations accord with the area difference elasticity (ADE) model. The membrane shape equation and boundary conditions were derived for axisymmetrical shapes for low volume vesicles, part of whose membranes are in contact. Calculated shapes were arranged into a phase diagram. The theory predicts that the transition between discocyte and stomatocyte shapes is discontinuous for relatively high volumes and continuous for low volumes. The calculated shape sequences matched well with the observed ones. By assuming a linear decrease of the equilibrium area difference with time, the ratio between the nonlocal and local bending constants is in agreement with reported values.     

Amplitude Hierarchy of Vesicle Shapes

Shapes of fluid lipid vesicles are governed by the bending elasticity of their membrane as described by the Area-Difference-Elasticity (ADE) model. These shapes can be quantified using a suitable modal representation of the vesicle contour. Prolate vesicles are characterized by a hierarchy in their shape amplitudes. Experimentally, we find an ordering of the amplitudes with mode number both in large (100 nm) as well as giant (10 m) unilamellar vesicles. Mean shapes are found only within the small energetically stable region of the prolate phase. Our study demonstrates that bending energy concepts may be quantitatively used on cellular length scales ranging from the size of organelles to the plasma membrane.     

Dynamics of vesicles in a wall-bounded shear flow

We report a detailed study of the behavior (shapes, experienced forces, velocities) of giant lipid vesicles subjected to a shear flow close to a wall. Vesicle buoyancy, size, and reduced volume were separately varied. We show that vesicles are deformed by the flow and exhibit a tank-treading motion with steady orientation. Their shapes are characterized by two nondimensional parameters: the reduced volume and the ratio of the shear stress with the hydrostatic pressure. We confirm the existence of a force, able to lift away nonspherical buoyant vesicles from the substrate. We give the functional variation and the value of this lift force (up to 150 pN in our experimental conditions) as a function of the relevant physical parameters: vesicle-substrate distance, wall shear rate, viscosity of the solution, vesicle size, and reduced volume. Circulating deformable cells disclosing a nonspherical shape also experience this force of viscous origin, which contributes to take them away from the endothelium and should be taken into account in studies on cell adhesion in flow chambers, where cells membrane and the adhesive substrate are in relative motion. Finally, the kinematics of vesicles along the flow direction can be described in a first approximation with a model of rigid spheres.     

Shapes of discoid intracellular compartments with small relative volumes

A prominent feature of many intracellular compartments is a large membrane surface area relative to their luminal volume, i.e., the small relative volume. In this study we present a theoretical analysis of discoid membrane compartments with a small relative volume and then compare the theoretical results to quantitative morphological assessment of fusiform vesicles in urinary bladder umbrella cells. Specifically, we employ three established extensions of the standard approach to lipid membrane shape calculation and determine the shapes that could be expected according to three scenarios of membrane shaping: membrane adhesion in the central discoid part, curvature driven lateral segregation of membrane constituents, and existence of stiffer membrane regions, e.g., support by protein scaffolds. The main characteristics of each scenario are analyzed. The results indicate that even though all three scenarios can lead to similar shapes, there are values of model parameters that yield qualitatively distinctive shapes. Consequently, a distinctive shape of an intracellular compartment may reveal its membrane shaping mechanism and the membrane structure. The observed shapes of fusiform vesicles fall into two qualitatively different classes, yet they are all consistent with the theoretical results and the current understanding of their structure and function.     

Equilibrium shapes of erythrocytes in rouleau formation

A well known physiological property of erythrocytes is that they can aggregate and form a rouleau. We present a theoretical analysis of erythrocyte shapes in a long rouleau composed of cells with identical sizes. The study is based on the area difference elasticity model of lipid membranes, and takes into consideration the adhesion of curved axisymmetric membranes. The analysis predicts that the erythrocytes in the rouleau can have either a discoid or a cup-like shape. These shapes are analogous to the discoid and stomatocyte shapes of free erythrocytes. The transitions between the discoid and cup-like shapes in the rouleau are characterized. The occurrence of these transitions depends on three model parameters: the cell relative volume, the preferred difference between the areas of the membrane bilayer leaflets, and the strength of the adhesion between the membranes. The cup-like shapes are favored at small relative volumes and small preferred area differences, and the discoid shapes are favored at large values of these parameters. Increased adhesion strength enlarges the contact area between the cells, flattens the cells, and consequently promotes the discoid shapes.     

Shape transitions and shape stability of giant phospholipid vesicles in pure water induced by area-to-volume changes.

Shape transformations of vesicles of dimyristoylphosphatidylcholine (= DMPC) and palmitoyloleylphosphatidylcholine (= POPC) in ion-free water were induced by changing the area-to-volume ratio via temperature variations. Depending on the pretreatment we find several types of shape changes for DMPC (in pure water) at increasing area-to-volume ratio: (a) budding transitions leading to the formation of a chain of vesicles at further increase of the area-to-volume ratio, (b) discocyte-stomatocyte transitions, (c) reentrant dumbbell-pear-dumbbell transitions, and (d) spontaneous blebbing and/or tether formation of spherical vesicles. Beside these transitions a more exotic dumbbell-discocyte transition (e) was found which proceeded via local instabilities. Pears, discocytes, and stomatocytes are stable with respect to small temperature variations unless the excess area is close to values corresponding to limiting shapes of budded vesicles where temperature variations of less than or equal to 0.1 degree C lead to spontaneous budding to the inside or the outside. For POPC we observed only budding transitions to the inside leading either to chains of vesicles or to distributions of equally sized daughter vesicles protruding to the inside of the vesicle. Preliminary experiments concerning the effect of solutes are also reported. The first three types of shape transitions can be explained in terms of the bilayer coupling model assuming small differences in thermal expansivities of the two monolayers. This does not hold for the observed instabilities close to the limiting shapes.     

Mathematical multi-scale model of the cardiovascular system including mitral valve dynamics. Application to ischemic mitral insufficiency

The aim of this research is to propose a small intestine model for electrically propelled capsule endoscopy. The electrical stimulus can cause contraction of the small intestine and propel the capsule along the lumen. The proposed model considered the drag and friction from the small intestine using a thin walled model and Stokes' drag equation. Further, contraction force from the small intestine was modeled by using regression analysis. From the proposed model, the acceleration and velocity of various exterior shapes of capsule were calculated, and two exterior shapes of capsules were proposed based on the internal volume of the capsules. The proposed capsules were fabricated and animal experiments were conducted. One of the proposed capsules showed an average (SD) velocity in forward direction of 2.91 ± 0.99 mm/s and 2.23 ± 0.78 mm/s in the backward direction, which was 5.2 times faster than that obtained in previous research. The proposed model can predict locomotion of the capsule based on various exterior shapes of the capsule.