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.     

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

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。     

与生物膜泡形状相关的奇特数字

本文基于Helfrich自发曲率弹性模型讨论生物膜泡的形状,给出生物膜泡形状相关的一些奇特数字:如磷脂分子形成的环面,其两个生成圆的半径比恰好为2~(1/2);红细胞的自发曲率与等表面积球的半径的乘积约等于黄金分割率的相反数1.618.     

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.     

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.     

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。     

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.     

小约化体积膜泡形状的研究

目的:研究ADE模型下小约化体积膜泡的形状。方法:应用数值计算方法中的打靶法,运用Mathematica 7.0软件进行编程。结果:在ADE模型下,计算得到了一系列小约化体积的膜泡的形状,解决了已往小约化体积区域内不存在稳定膜泡的问题。结论:研究表明,在ADE模型下通过适当的边界条件把黏附双层区域的接触势能考虑进去,数值计算结果与实验上的非常相似。     

H~+诱导心磷脂的六角形Ⅱ相和H~+的跨膜转运

本文报告H~ 能诱导心磷脂由双层排列转变为六角形Ⅱ相.含心磷脂的多层脂囊泡的~(31)P中核磁共振谱显示高场峰低场肩的双层排列特点,当pH降到2时,~(31)P核磁共振谱表现为低场峰高场肩的六角形Ⅱ相特点,表明H~ 对心磷脂多形性转变的诱导作用.用oxonol-V作为探剂.H~ 可使结合在人工脂膜上的oxonl-V的吸收峰红移和光吸收增加,表明心磷脂的六角形Ⅱ相在人工脂膜上具有H~ 的载体特性,易化H~ 的跨膜转运.     

Mechanics of curved plasma membrane vesicles: resting shapes, membrane curvature, and in-plane shear elasticity

Highly curved cell membrane structures, such as plasmalemmal vesicles (caveolae) and clathrin-coated pits, facilitate many cell functions, including the clustering of membrane receptors and transport of specific extracellular macromolecules by endothelial cells. These structures are subject to large mechanical deformations when the plasma membrane is stretched and subject to a change of its curvature. To enhance our understanding of plasmalemmal vesicles we need to improve the understanding of the mechanics in regions of high membrane curvatures. We examine here, theoretically, the shapes of plasmalemmal vesicles assuming that they consist of three membrane domains: an inner domain with high curvature, an outer domain with moderate curvature, and an outermost flat domain, all in the unstressed state. We assume the membrane properties are the same in these domains with membrane bending elasticity as well as in-plane shear elasticity. Special emphasis is placed on the effects of membrane curvature and in-plane shear elasticity on the mechanics of vesicle during unfolding by application of membrane tension. The vesicle shapes were computed by minimization of bending and in-plane shear strain energy. Mechanically stable vesicles were identified with characteristic membrane necks. Upon stretch of the membrane, the vesicle necks disappeared relatively abruptly leading to membrane shapes that consist of curved indentations. While the resting shape of vesicles is predominantly affected by the membrane spontaneous curvatures, the membrane shear elasticity (for a range of values recorded in the red cell membrane) makes a significant contribution as the vesicle is subject to stretch and unfolding. The membrane tension required to unfold the vesicle is sensitive with respect to its shape, especially as the vesicle becomes fully unfolded and approaches a relative flat shape.     

Chained vesicles in vascular endothelial cells.

There is extensive ultrastructural evidence in endothelium for the presence of chained vesicles or clusters of attached vesicles, and they are considered to be involved in specific transport mechanisms, such as the formation of trans-endothelial channels. However, few details are known about their mechanical characteristics. In this study, the formation mechanism and mechanical aspects of vascular endothelial chained vesicles are investigated theoretically, based on membrane bending strain energy analysis. The shape of the axisymmetric vesicles was computed on the assumption that the cytoplasmic side of the vesicle has a molecular layer or cytoskeleton attached to the lipid bilayer, which induces a spontaneous curvature in the resting state. The bending strain energy is the only elasticity involved, while the shear elasticity is assumed to be negligible. The surface area of the membrane is assumed to be constant due to constant lipid bilayer thickness. Mechanically stable shapes of chained vesicles are revealed, in addition to a cylindrical tube shape. Unfolding of vesicles into a more flattened shape is associated with increase in bending energy without a significant increase in membrane tension. These results provide insights into the formation mechanism and mechanics of the chained vesicle.     

Exploring the binding dynamics of BAR proteins

We used a continuum model based on the Helfrich free energy to investigate the binding dynamics of a lipid bilayer to a BAR domain surface of a crescent-like shape of positive (e.g. I-BAR shape) or negative (e.g. F-BAR shape) intrinsic curvature. According to structural data, it has been suggested that negatively charged membrane lipids are bound to positively charged amino acids at the binding interface of BAR proteins, contributing a negative binding energy to the system free energy. In addition, the cone-like shape of negatively charged lipids on the inner side of a cell membrane might contribute a positive intrinsic curvature, facilitating the initial bending towards the crescent-like shape of the BAR domain. In the present study, we hypothesize that in the limit of a rigid BAR domain shape, the negative binding energy and the coupling between the intrinsic curvature of negatively charged lipids and the membrane curvature drive the bending of the membrane. To estimate the binding energy, the electric potential at the charged surface of a BAR domain was calculated using the Langevin-Bikerman equation. Results of numerical simulations reveal that the binding energy is important for the initial instability (i.e. bending of a membrane), while the coupling between the intrinsic shapes of lipids and membrane curvature could be crucial for the curvature-dependent aggregation of negatively charged lipids near the surface of the BAR domain. In the discussion, we suggest novel experiments using patch clamp techniques to analyze the binding dynamics of BAR proteins, as well as the possible role of BAR proteins in the fusion pore stability of exovesicles.     

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.     

Membrane Bending Energy and Fusion Pore Kinetics in Ca-Triggered Exocytosis

A fusion pore composed of lipid is an obligatory kinetic intermediate of membrane fusion, and its formation requires energy to bend membranes into highly curved shapes. The energetics of such deformations in viral fusion is well established, but the role of membrane bending in Ca²⁺-triggered exocytosis remains largely untested. Amperometry recording showed that during exocytosis in chromaffin and PC12 cells, fusion pores formed by smaller vesicles dilated more rapidly than fusion pores formed by larger vesicles. The logarithm of 1/(fusion pore lifetime) varied linearly with vesicle curvature. The vesicle size dependence of fusion pore lifetime quantitatively accounted for the nonexponential fusion pore lifetime distribution. Experimentally manipulating vesicle size failed to alter the size dependence of fusion pore lifetime. Manipulations of membrane spontaneous curvature altered this dependence, and applying the curvature perturbants to the opposite side of the membrane reversed their effects. These effects of curvature perturbants were opposite to those seen in viral fusion. These results indicate that during Ca²⁺-triggered exocytosis membrane bending opposes fusion pore dilation rather than fusion pore formation. Ca²⁺-triggered exocytosis begins with a proteinaceous fusion pore with less stressed membrane, and becomes lipidic as it dilates, bending membrane into a highly curved shape.     

Frequency-dependent electrodeformation of giant phospholipid vesicles in AC electric field

A model of vesicle electrodeformation is described which obtains a parametrized vesicle shape by minimizing the sum of the membrane bending energy and the energy due to the electric field. Both the vesicle membrane and the aqueous media inside and outside the vesicle are treated as leaky dielectrics, and the vesicle itself is modeled as a nearly spherical shape enclosed within a thin membrane. It is demonstrated (a) that the model achieves a good quantitative agreement with the experimentally determined prolate-to-oblate transition frequencies in the kilohertz range and (b) that the model can explain a phase diagram of shapes of giant phospholipid vesicles with respect to two parameters: the frequency of the applied alternating current electric field and the ratio of the electrical conductivities of the aqueous media inside and outside the vesicle, explored in a recent paper (S. Aranda et al., Biophys J 95:L19–L21, 2008). A possible use of the frequency-dependent shape transitions of phospholipid vesicles in conductometry of microliter samples is discussed.     

Modeling morphological instabilities in lipid membranes with anchored amphiphilic polymers

Anchoring molecules, like amphiphilic polymers, are able to dynamically regulate membrane morphology. Such molecules insert their hydrophobic groups into the bilayer, generating a local membrane curvature. In order to minimize the elastic energy penalty, a dynamic shape instability may occur, as in the case of the curvature-driven pearling instability or the polymer-induced tubulation of lipid vesicles. We review recent works on modeling of such instabilities by means of a mesoscopic dynamic model of the phase-field kind, which take into account the bending energy of lipid bilayers.     

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.     

Massive Formation of Intracellular Membrane Vesicles in Escherichia coli by a Monotopic Membrane-bound Lipid Glycosyltransferase

The morphology and curvature of biological bilayers are determined by the packing shapes and interactions of their participant molecules. Bacteria, except photosynthetic groups, usually lack intracellular membrane organelles. Strong overexpression in Escherichia coli of a foreign monotopic glycosyltransferase (named monoglycosyldiacylglycerol synthase), synthesizing a nonbilayer-prone glucolipid, induced massive formation of membrane vesicles in the cytoplasm. Vesicle assemblies were visualized in cytoplasmic zones by fluorescence microscopy. These have a very low buoyant density, substantially different from inner membranes, with a lipid content of ≥60% (w/w). Cryo-transmission electron microscopy revealed cells to be filled with membrane vesicles of various sizes and shapes, which when released were mostly spherical (diameter ≈100 nm). The protein repertoire was similar in vesicle and inner membranes and dominated by the glycosyltransferase. Membrane polar lipid composition was similar too, including the foreign glucolipid. A related glycosyltransferase and an inactive monoglycosyldiacylglycerol synthase mutant also yielded membrane vesicles, but without glucolipid synthesis, strongly indicating that vesiculation is induced by the protein itself. The high capacity for membrane vesicle formation seems inherent in the glycosyltransferase structure, and it depends on the following: (i) lateral expansion of the inner monolayer by interface binding of many molecules; (ii) membrane expansion through stimulation of phospholipid synthesis, by electrostatic binding and sequestration of anionic lipids; (iii) bilayer bending by the packing shape of excess nonbilayer-prone phospholipid or glucolipid; and (iv) potentially also the shape or penetration profile of the glycosyltransferase binding surface. These features seem to apply to several other proteins able to achieve an analogous membrane expansion.