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.     

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 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.     

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.     

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.     

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.     

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.     

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.     

Membrane shape remodeling by protein crowding

The steric repulsion between proteins on biological membranes is one of the most generic mechanisms that cause membrane shape changes. We present a minimal model in which a spontaneous curvature is induced by asymmetric protein crowding. Our results show that the interplay between the induced spontaneous curvature and the membrane tension determines the energy-minimizing shapes, which describes the wide range of experimentally observed membrane shapes, i.e., flat membranes, spherical vesicles, elongated tubular protrusions, and pearling structures. Moreover, the model gives precise predictions on how membrane shape changes by protein crowding can be tuned by controlling the protein size, the density of proteins, and the size of the crowded domain.     

Diffusion on Membrane Domes,Tubes, and Pearling Structures

Diffusion is a fundamental mechanism for protein distribution in cell membranes. These membranes often exhibit complex shapes, which range from shallow domes to elongated tubular or pearl-like structures. Shape complexity of the membrane influences the diffusive spreading of proteins and molecules. Despite the importance membrane geometry plays in these diffusive processes, it is challenging to establish the dependence between diffusion and membrane morphology. We solve the diffusion equation numerically on various static curved shapes representative for experimentally observed membrane shapes. Our results show that membrane necks become diffusion barriers. We determine the diffusive half-time, i.e., the time that is required to reduce the amount of protein in the budded region by one half, and find a quadratic relation between the diffusive half-time and the averaged mean curvature of the membrane shape, which we rationalize by a scaling law. Our findings thus help estimate the characteristic diffusive timescale based on the simple measure of membrane mean curvature.     

The Vesicle Trafficking Protein Sar1 Lowers Lipid Membrane Rigidity

The sculpting of membranes into dynamic, curved shapes is central to intracellular cargo trafficking. Though the generation of membrane curvature during trafficking necessarily involves both lipids and membrane-associated proteins, current mechanistic views focus primarily on the formation of rigid cages and curved scaffolds by protein assemblies. Here we report on a different mechanism for the control of membrane deformation, unrelated to the imposition of predefined curvature, involving modulation of membrane material properties: Sar1, a GTPase that regulates vesicle trafficking from the endoplasmic reticulum, lowers the rigidity of the lipid bilayer membrane to which it binds. In vitro assays in which optically trapped microspheres create controlled membrane deformations revealed a monotonic decline in bending modulus as a function of Sar1 concentration, down to nearly zero rigidity, indicating a dramatic lowering of the energetic cost of curvature generation. This is the first demonstration that a vesicle trafficking protein lowers the rigidity of its target membrane, leading to a new conceptual framework for vesicle biogenesis.     

Sar1p N-terminal helix initiates membrane curvature and completes the fission of a COPII vesicle

Secretory proteins traffic from the ER to the Golgi via COPII-coated transport vesicles. The five core COPII proteins (Sar1p, Sec23/24p, and Sec13/31p) act in concert to capture cargo proteins and sculpt the ER membrane into vesicles of defined geometry. The molecular details of how the coat proteins deform the lipid bilayer into vesicles are not known. Here we show that the small GTPase Sar1p directly initiates membrane curvature during vesicle biogenesis. Upon GTP binding by Sar1p, membrane insertion of the N-terminal amphipathic alpha helix deforms synthetic liposomes into narrow tubules. Replacement of bulky hydrophobic residues in the alpha helix with alanine yields Sar1p mutants that are unable to generate highly curved membranes and are defective in vesicle formation from native ER membranes despite normal recruitment of coat and cargo proteins. Thus, the initiation of vesicle budding by Sar1p couples the generation of membrane curvature with coat-protein assembly and cargo capture.     

The buckling of spherical liposomes

In the classical "first approximation" theory of thin-shell structures, the constitutive relations for a generic shell element--i.e. the elastic relations between the bending moments and membrane stresses and the corresponding changes in curvature and strain, respectively-are written as if an element of the shell is flat, although in reality it is curved. In this theory it is believed that discrepancies on account of the use of "flat" constitutive relations will be negligible provided the ratio shell-radius/thickness is of sufficiently large order. In the study of drawing of narrow, cylindrical "tethers" from liposomes it has been known for many years that it is necessary to use instead a constitutive law which explicitly describes a curved element in order to make sense of the mechanics; and indeed such tethers are generally of "thick-walled" proportions. In this paper we show that the proper constitutive relations for a curved element must also be used in the study, by means of shell equations, of the buckling of initially spherical thin-walled giant liposomes under exterior pressure: these involve the inclusion of what we call the "Mkappa" terms, which are not present in the standard "first-approximation" theory. We obtain analytical expressions for both the bifurcation buckling pressure and the slope of the post-buckling path, in terms of the dimensions and elastic constants of the lipid bi-layer, and also the initial state of bending moment in the vesicle. We explain physically how the initial bending moment can affect the bifurcation pressure, whereas it cannot in "first-approximation" theory. We use these results to map the conditions under which the vesicle buckles into an oblate, as distinct from a prolate ("rugby-ball") shape. Some of our results were obtained long ago by the use of energy methods; but our aim here has been to identify precisely what is lacking in "first-approximation" theory in relation to liposomes, and so to put the "shell equations" approach onto a firm footing in mechanics.     

Red blood cell shapes as explained on the basis of curvature elasticity.

Assuming that the shape of red blood cells is controlled by the curvature elasticity of the surrounding membrane, we fit theoretical shapes to the contours Evans and co-workers determined by interference microscopy. Very good agreement is obtained for disc shapes. The fit is not so good for less common shapes, which may result from Evans' parametric representation and from the interference of shear elasticity.     

Coupling field theory with continuum mechanics: a simulation of domain formation in giant unilamellar vesicles

Domain formation is modeled on the surface of giant unilamellar vesicles using a Landau field theory model for phase coexistence coupled to elastic deformation mechanics (e.g., membrane curvature). Smooth particle applied mechanics, a form of smoothed particle continuum mechanics, is used to solve either the time-dependent Landau-Ginzburg or Cahn-Hilliard free-energy models for the composition dynamics. At the same time, the underlying elastic membrane is modeled using smooth particle applied mechanics, resulting in a unified computational scheme capable of treating the response of the composition fields to arbitrary deformations of the vesicle and vice versa. The results indicate that curvature coupling, along with the field theory model for composition free energy, gives domain formations that are correlated with surface defects on the vesicle. In the case that external deformations are included, the domain structures are seen to respond to such deformations. The present simulation capability provides a significant step forward toward the simulation of realistic cellular membrane processes.     

Echinocyte shapes: bending, stretching, and shear determine spicule shape and spacing

We study the shapes of human red blood cells using continuum mechanics. In particular, we model the crenated, echinocytic shapes and show how they may arise from a competition between the bending energy of the plasma membrane and the stretching/shear elastic energies of the membrane skeleton. In contrast to earlier work, we calculate spicule shapes exactly by solving the equations of continuum mechanics subject to appropriate boundary conditions. A simple scaling analysis of this competition reveals an elastic length Lambda(el), which sets the length scale for the spicules and is, thus, related to the number of spicules experimentally observed on the fully developed echinocyte.     

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.     

Structural characteristics of BAR domain superfamily to sculpt the membrane

Membrane dynamics is an essential process for cell locomotion, cytokinesis, vesicular transport and organelle morphogenesis. Formation of tubes or buds from a nearly flat membrane is a widely spread feature of the membrane shape changes. The BAR (Bin/Amphiphysin/Rvs-homology) domain dimers exhibit long extended curved shapes and appear to be outstandingly suitable modules for this purpose. So far, crystal structures of 18 independent BAR domains including inverse-BAR domains and FCH-BAR domains have been reported. These atomic models show a vast variation of dimer shapes on a common and simple basic framework. Comparison of the structural variations with respect to differences in membrane sculpting properties provide useful clues about the mechanisms for modifying the framework into a particular dimer that generates and/or senses a distinct curvature set of the membrane.