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.     

Membrane bending energy and shape determination of phospholipid vesicles and red blood cells

A procedure is developed to calculate red blood cell and phospholipid vesicle shapes within the bilayer couple model of the membrane. The membrane is assumed to consist of two laterally incompressible leaflets which are in close contact but unconnected. Shapes are determined by minimizing the membrane bending energy at a given volume of a cell (V), given average membrane area (A) and given difference of the areas of two leaflets (A). Different classes of shapes exist in parts of the v/a phase diagram, where v and a are the volume and the leaflet area difference relative to the sphere with area A. The limiting shapes are composed of sections of spheres with only two values allowed for their radii. Two low energy axisymmetrical classes, which include discocyte and stomatocyte shapes are studied and their phase diagrams are analyzed. For v=0.6, the discocyte is the lowest energy shape, which transforms by decreasing a continuously into a stomatocyte. The spontaneous membrane curvature (C ₀) and compressibility of membrane leaflest can be incorporated into the model.A model, where A is free and C ₀ determines the shapes at given V and A, is also studied. In this case, by decreasing C ₀, a discocyte transforms discontinuously into an almost closed stomatocyte.     

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.     

Elastic energy of the discocyte–stomatocyte transformation

The aim of this study is to calculate the membrane elastic energy for the different shapes observed in the discocyte–stomatocyte sequence. This analysis can provide a better quantitative understanding of the hypothesis put forward over the last decades to explain how red blood cells produce and maintain their typical shape. For this purpose, we use geometrical models based on parametric equations. The energy model considered for the elastic properties of RBC membrane includes the local and nonlocal resistance effects of the bilayer to bending. In particular, the results confirm the discocyte as the lowest energy value configuration among the sets of different red blood cell deformations considered in the sequence.     

Shape transformation and burst of giant POPC unilamellar liposomes modulated by non-ionic detergent C12E8

We studied spontaneous shape transformations and burst of 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphatidylcholine (POPC) vesicles with exogeneously added non-ionic detergent octaethylene-glycol dodecylether C(12)E(8). The addition of C(12)E(8) increased the speed of the vesicle shape transformation, so that we were able to study for the first time the complete sequence of POPC vesicle shapes starting from initial spherical vesicle with long thin tubular protrusion to final shape with invagination(s). The average mean curvature of the vesicle membrane continuously decreases during this process. The shape of the invaginations is usually spherical, however also non-spherical shapes of invaginations were observed. C(12)E(8) increases amplitudes of the fluctuations of the vesicle membrane. At higher concentrations in the membrane, C(12)E(8) induces the membrane leakage and burst of the vesicles.     

La(3+) and Gd(3+) induce shape change of giant unilamellar vesicles of phosphatidylcholine

Lanthanides such as La(3+) and Gd(3+) are well known to have large effects on the function of membrane proteins such as mechanosensitive ionic channels and voltage-gated sodium channels, and also on the structure of phospholipid membranes. In this report, we have investigated effects of La(3+) and Gd(3+) on the shape of giant unilamellar vesicle (GUV) of dioleoylphosphatidylcholine (DOPC-GUV) and GUV of DOPC/cholesterol by the phase-contrast microscopy. The addition of 10-100 microM La(3+) (or Gd(3+)) through a 10-microm diameter micropipette near the DOPC-GUV (or DOPC/cholesterol-GUV) triggered several kinds of shape changes. We have found that a very low concentration (10 microM) of La(3+) (or Gd(3+)) induced a shape change of GUV such as the discocyte via stomatocyte to inside budded shape transformation, the two-spheres connected by a neck to prolate transformation, and the pearl on a string to cylinder (or tube) transformation. To understand the effect of these lanthanides on the shape of the GUV, we have also investigated phase transitions of 30 microM dipalmitoylphosphatidylcholine-multilamellar vesicle (DPPC-MLV) by the ultra-sensitive differential scanning calorimetry (DSC). The chain-melting phase transition temperature and the L(beta') to P(beta') phase transition temperature of DPPC-MLV increased with an increase in La(3+) concentration. This result indicates that the lateral compression pressure of the membrane increases with an increase in La(3+) concentration. Thereby, the interaction of La(3+) (or Gd(3+)) on the external monolayer membrane of the GUV induces a decrease in its area (A(ex)), whereas the area of the internal monolayer membrane (A(in)) keeps constant. Therefore, the shape changes of the GUV induced by these lanthanides can be explained reasonably by the decrease in the area difference between two monolayers (DeltaA=A(ex)-A(in)).     

Mechanical behavior of closed lamellar membranes as a possible common mechanism for the establishment of developmental shapes.

The mechanical behavior of a closed membrane composed of two layers in contact is described as it is obtained by finding the minimum of the membrane bending energy at constant membrane area, constant difference between the areas of the two layers, and constant enclosed volume. It is shown that the membrane bending energy is a discontinuous function of the volume (v) and difference between the layer areas (delta a) defined relative to the volume and area difference of a sphere with the same membrane area, respectively. However, for different classes of shapes it is possible to obtain regions in the v/delta a diagram within which the shapes change continuously with v and delta a. These regions are shown for the egg, dumbbell and cup shape classes, respectively. The results of the shape analysis are used in the discussion of cell polarity, cytokinesis and gastrulation. Cell polarity is related to the decrease in symmetry during the transition from the radially symmetrical spherical shape to the asymmetrical shapes of the egg class. It is proposed that symmetrical cytokinesis occurs within the dumbbell class and that asymmetrical cytokinesis occurs within the egg class. Gastrulation is described as shape transformations within the class of cup shapes.     

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.     

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.     

The effect of corticosteroids on microvillous vesicles from the small intestine of adult rats: an automated, morphometric analysis

The hypothesis that the corticosterone-induced enhancement of D-glucose uptake by brush-border membrane vesicles from the small intestine of adult rats is caused by an alteration in vesicle volume was tested by means of structural morphometric computerized analysis. By using a Ca2+ precipitation method, microvillous membrane vesicles were prepared from different groups of adult rats: normal controls; animals sacrificed 8 days after adrenalectomy; sham-operated pair-fed controls; animals treated with corticosterone (1 or 10 mg x 100 g b.wt.-1 daily i.p. for 8 days); corticosterone vehicle-treated controls. The vesicles were processed by conventional electron microscopy techniques. Morphometric computerized analysis was carried out on electron micrographs at a 20,000 x magnification, after selecting by an interactive method the vesicles showing certain morphologic features. The morphometric parameters determined for the vesicles from each experimental group were diameter, shape factor (minimal to maximal diameter ratio), surface area and volume. The following main findings were obtained: the vesicles were consistently spherical, with the glycocalyx on the outer side; sham-operation and pair-feeding with adrenalectomized rats, as well as corticosterone-vehicle injection, significantly reduced vesicular volume as compared to normal controls; adrenalectomy significantly decreased vesicular volume as compared to pair-feeding; excess of corticosteroids caused opposite changes (i.e. a significant increase of vesicle volumes as compared to vehicle injection), which were apparently dose-dependent. A comparison with D-glucose vesicular transport data previously obtained under the same experimental conditions revealed the existence of a positive relationship between vesicular volume and D-glucose half-filling time (t 1/2). A positive relationship between vesicular volume and D-glucose vesicular space was found for all experimental conditions except vehicle injection. As a whole, the morphometric results were consistent with functional findings, supporting our previous hypothesis that the corticosterone-induced increase in D-glucose transport by small intestinal microvillous vesicles is due, at least in part, to enlargement of the vesicle.     

Slow Sedimentation and Deformability of Charged Lipid Vesicles

The study of vesicles in suspension is important to understand the complicated dynamics exhibited by cells in in vivo and in vitro. We developed a computer simulation based on the boundary-integral method to model the three dimensional gravity-driven sedimentation of charged vesicles towards a flat surface. The membrane mechanical behavior was modeled using the Helfrich Hamiltonian and near incompressibility of the membrane was enforced via a model which accounts for the thermal fluctuations of the membrane. The simulations were verified and compared to experimental data obtained using suspended vesicles labelled with a fluorescent probe, which allows visualization using fluorescence microscopy and confers the membrane with a negative surface charge. The electrostatic interaction between the vesicle and the surface was modeled using the linear Derjaguin approximation for a low ionic concentration solution. The sedimentation rate as a function of the distance of the vesicle to the surface was determined both experimentally and from the computer simulations. The gap between the vesicle and the surface, as well as the shape of the vesicle at equilibrium were also studied. It was determined that inclusion of the electrostatic interaction is fundamental to accurately predict the sedimentation rate as the vesicle approaches the surface and the size of the gap at equilibrium, we also observed that the presence of charge in the membrane increases its rigidity.     

Shape variation of bilayer membrane daughter vesicles induced by anisotropic membrane inclusions

A theoretical model of a two-component bilayer membrane was used in order to describe the influence of anisotropic membrane inclusions on shapes of membrane daughter micro and nano vesicles. It was shown that for weakly anisotropic inclusions the stable vesicle shapes are only slightly out-of-round. In contrast, for strongly anisotropic inclusions the stable vesicle shapes may significantly differ from spheres, i.e. they have a flattened oblate shape at small numbers of inclusions in the membrane, and an elongated cigar-like prolate shape at high numbers of inclusions in the vesicle membrane.     

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.     

Cylindrical shapes of closed lipid bilayer structures correspond to an extreme area difference between the two monolayers of the bilayer

The shapes of extreme area difference between the outer and the inner layer (ΔA) of the closed lipid bilayer structures at fixed membrane area (A) and fixed volume (V) are determined by stating and analytically solving a variational problem for axisymmetric shapes. It is shown that the spheres with at most two different radii and the cylinder are the solutions of this variational problem. The cylinder ended by a hemisphere on each end is the shape combined from these solutions and is therefore, itself the shape of the extreme ΔA at fixed V and A. The related cylindrical shapes of stearoyl–oleoyl–phosphocholine vesicles are shown.     

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.     

Red blood cell shape and deformability in the context of the functional evolution of its membrane structure

It is proposed that it is possible to identify some of the problems that had to be solved in the course of evolution for the red blood cell (RBC) to achieve its present day effectiveness, by studying the behavior of systems featuring different, partial characteristics of its membrane. The appropriateness of the RBC volume to membrane area ratio for its circulation in the blood is interpreted on the basis of an analysis of the shape behavior of phospholipid vesicles. The role of the membrane skeleton is associated with preventing an RBC from transforming into a budded shape, which could form in its absence due to curvature-dependent transmembrane protein-membrane interaction. It is shown that, by causing the formation of echinocytes, the skeleton also acts protectively when, in vesicles with a bilayer membrane, the budded shapes would form due to increasing difference between the areas of their outer and inner layers.     

La and Gd induce shape change of giant unilamellar vesicles of phosphatidylcholine

Lanthanides such as La³⁺ and Gd³⁺ are well known to have large effects on the function of membrane proteins such as mechanosensitive ionic channels and voltage-gated sodium channels, and also on the structure of phospholipid membranes. In this report, we have investigated effects of La³⁺ and Gd³⁺ on the shape of giant unilamellar vesicle (GUV) of dioleoylphosphatidylcholine (DOPC-GUV) and GUV of DOPC/cholesterol by the phase-contrast microscopy. The addition of 10-100 μM La³⁺ (or Gd³⁺) through a 10-μm diameter micropipette near the DOPC-GUV (or DOPC/cholesterol-GUV) triggered several kinds of shape changes. We have found that a very low concentration (10 μM) of La³⁺ (or Gd³⁺) induced a shape change of GUV such as the discocyte via stomatocyte to inside budded shape transformation, the two-spheres connected by a neck to prolate transformation, and the pearl on a string to cylinder (or tube) transformation. To understand the effect of these lanthanides on the shape of the GUV, we have also investigated phase transitions of 30 μM dipalmitoylphosphatidylcholine-multilamellar vesicle (DPPC-MLV) by the ultra-sensitive differential scanning calorimetry (DSC). The chain-melting phase transition temperature and the L_β′ to P_β′ phase transition temperature of DPPC-MLV increased with an increase in La³⁺ concentration. This result indicates that the lateral compression pressure of the membrane increases with an increase in La³⁺ concentration. Thereby, the interaction of La³⁺ (or Gd³⁺) on the external monolayer membrane of the GUV induces a decrease in its area (A^ex), whereas the area of the internal monolayer membrane (Aⁱⁿ) keeps constant. Therefore, the shape changes of the GUV induced by these lanthanides can be explained reasonably by the decrease in the area difference between two monolayers (ΔA=A^ex−Aⁱⁿ).     

Electric pulses induce cylindrical deformations on giant vesicles in salt solutions

In this article, we report for the first time unusual shape changes of vesicles subjected to strong electric pulses in salt solutions of low concentration. The electric field is created by two parallel electrodes between which the vesicle solution is located. Surprisingly, the vesicles assume cylindrical shapes during the pulse. These deformations are short-lived (their lifetime is approximately 1 ms) and occur only in the presence of salt outside the vesicles, irrespective of their content. When the solution conductivities inside and outside are the same, vesicles with square cross section are observed. Using a fast digital camera, we were able to record these deformations and study the vesicle shape dynamics. The aims of this article are to report the new vesicle morphologies and their dynamics and to provoke theoretical work in this direction.