Vesicle self-reproduction: The involvement of membrane hydraulic and solute permeabilities

Conditions for self-reproduction are sought for a growing vesicle with its growth defined by an exponential increase of vesicle membrane area and by adequate flow of the solution across the membrane. In the first step of the presumed vesicle self-reproduction process, the initially spherical vesicle must double its volume in the doubling time of the membrane area and, through the appropriate shape transformations, attain the shape of two equal spheres connected by an infinitesimally thin neck. The second step involves separation of the two spheres and relies on conditions that cause the neck to be broken. In this paper we consider the first step of this self-reproduction process for a vesicle suspended in a solution whose solute can permeate the vesicle membrane. It is shown that vesicle self-reproduction occurs only for certain combinations of the values of membrane hydraulic and solute permeabilities and the external solute concentration, these quantities being related to the mechanical properties of the membrane and the membrane area doubling time. The analysis includes also the relaxation of a perturbed system towards stationary self-reproduction behavior and the case where the final shape consists of two connected spheres of different radii.     

双凹盘形解开口膜泡形状的解析法研究

随着开口膜泡在实验上的发现,对开口泡形状的数值及解析研究逐渐成为该领域的一个热点.讨论了如何由欧阳双凹盘形闭合解构造开口泡的解析解的问题.首先将开口泡要满足的三个不独立的边界条件简化为两个独立的边界条件,给出高斯测地曲率kg=-2,边界条件2可满足,然后由边界条件1得到确定膜泡边界的几何方程.进而讨论了由欧阳双凹盘解可构造的开口泡的各种可能形状,得到了三类管型拓扑解,它们是外凸管形解、类环管形解、类悬链面管形解.     

Model system of self-reproducing vesicles

Development of self-reproducing vesicle systems is the first step for autopoietic cycles. We established a model self-reproducing vesicle system without the membrane molecule synthesis route. The model vesicle composed of cylinder- and inverse-cone-shaped lipids formed inclusion vesicles inside the mother vesicle, and the inclusion vesicles were then expelled by a temperature cycling. By changing the vesicle composition, the mother vesicles showed a budding-type self-reproduction pathway. A key concept of this system is the coupling of the main-chain transition and the shape of lipids.     

Physics of cell elasticity,shape and adhesion

We review recent theoretical work that analyzes experimental measurements of the shape, fluctuations and adhesion properties of biological cells. Particular emphasis is placed on the role of the cytoskeleton and cell elasticity and we contrast the shape and adhesion of elastic cells with fluid-filled vesicles. In red blood cells (RBC), the cytoskeleton consists of a two-dimensional network of spectrin proteins. Our analysis of the wavevector and frequency dependence of the fluctuation spectrum of RBC indicates that the spectrin network acts as a confining potential that reduces the fluctuations of the lipid bilayer membrane. However, since the cytoskeleton is only sparsely connected to the bilayer, one cannot regard the composite cytoskeleton–membrane as a polymerized object with a shear modulus. The sensitivity of RBC fluctuations and shapes to ATP concentration may reflect topological defects induced in the cytoskeleton network by ATP. The shapes of cells that adhere to a substrate are strongly determined by the cytoskeletal elasticity that can be varied experimentally by drugs that depolymerize the cytoskeleton. This leads to a tension-driven retraction of the cell body and a pearling instability of the resulting ray-like protrusions. Recent experiments have shown that adhering cells exert polarized forces on substrates. The interactions of such “force dipoles” in either bulk gels or on surfaces can be used to predict the nature of self-assembly of cell aggregates and may be important in the formation of artificial tissues. Finally, we note that cell adhesion strongly depends on the forces exerted on the adhesion sites by the tension of the cytoskeleton. The size and shape of the adhesion regions are strongly modified as the tension is varied and we present an elastic model that relates this tension to deformations that induce the recruitment of new molecules to the adhesion region. In all these examples, cell shape and adhesion differ from vesicle shape and adhesion due to the presence of the elastic cytoskeleton and to the fact that active processes (ATP, molecular motors) within the cell modify cytoskeletal elasticity and tension.     

Negative tension induced by lipid uptake

Membrane fusion is an important process in cell biology. While the molecular mechanisms of fusion are actively studied at a very local scale, the consequences of fusion at a larger scale on the shape and stability of the membrane are still not explored. In this Letter, the evolution of the membrane tension during the fusion of positive small unilamellar vesicles with a negative giant unilamellar vesicle has been experimentally investigated and compared to an existing theoretical model. The tension has been deduced using videomicroscopy from the measurement of the fluctuation spectrum and of the time correlation function of the fluctuations. We show that fusion induces a strong decrease in the effective tension of the membrane which eventually reaches negative values. Under these conditions, we show that localized instabilities appear on the vesicle. The membrane finally collapses, forming dense lipid structures.     

Direct Visualization of Vesicle Maturation and Plasma Membrane Protein Trafficking

Internalization and intracellular trafficking of membrane proteins are now recognized as essential mechanisms that contribute to a number of cellular processes. Current methods lack the ability to specifically label the plasma membrane of a live cell, follow internalization of labeled membrane molecules, and conclusively differentiate newly formed membrane-derived vesicles from pre-existing endocytic or secretory structures in the cytoplasm. Here, we detail a visualization method for surface biotinylation of plasma membrane-derived vesicles that allows us to follow their progress from membrane to cytosol at specific time points. Using the transmembrane receptor RET as a model, we demonstrate how this method can be applied to identify plasma membrane-derived vesicle maturation, determine RET’s presence within these structures, and monitor RET’s recycling to the cell surface. This method improves on static and less discriminatory methods, providing a tool for analysis of real-time vesicle trafficking that is applicable to many systems.     

Analytical expressions for the shape of axisymmetric membranes with multiple domains

Based on the Canham-Helfrich free energy, we derive analytical expressions for the shapes of axisymmetric membranes consisting of multiple domains. We give explicit equations for both closed vesicles and almost cylindrical tubes. Using these expressions, we also find the shape of a tube attached to a spherical vesicle. The resulting shapes compare well to numerical data, and our expressions can be used to easily determine membrane parameters from experimentally obtained shapes.     

tBid蛋白引发磷脂膜透化过程的研究

Bid蛋白是仅有BH3结构域的Bcl-2家族蛋白,在溶酶体膜透化以及线粒体外膜透化引发的细胞凋亡过程中起着非常重要的调控作用,但是Bid蛋白与生物膜之间的相互作用导致脂膜透化的确切机制尚不十分清楚.本文利用激光扫描共聚焦显微成像技术及基于氧化石墨烯表面诱导荧光衰逝的单分子荧光技术,分别从单囊泡及单分子水平对tBid蛋白与磷脂膜之间的相互作用进行了系统的研究.结果表明,tBid蛋白在膜上聚集后可引起脂膜的透化,且脂膜透化的发生源于聚集体中一些tBid蛋白更深入地插入了脂膜中.     

Bending energy of a vesicle to which a small spherical particle adhere:An analytical study

On the basis of Helfrich's bending energy model, we show that the adsorption process of a small spherical particle to a closed vesicle can be analytically studied by retaining the leading terms in an expansion of the shape equation. Our general derivation predicts the optimal binding sites on a vesicle, where the local membrane shape of the binding site could be non-axisymmetric before the continuous adhesion transition takes place. Our derivation avoids directly solving the shape equation and depends on an integration of the contact-line condition. The results are verified by several examples of independent numerical solutions.     

Gel phase vesicles buckle into specific shapes

Osmotic deflation of giant vesicles in the rippled gel phase P(β') gives rise to a large variety of novel faceted shapes. These shapes are also found from a numerical approach by using an elastic surface model. A shape diagram is proposed based on the model that accounts for the vesicle size and ratios of three mechanical constants: in-plane shear elasticity and compressibility (usually neglected) and out-of-plane bending of the membrane. The comparison between experimental and simulated vesicle morphologies reveals that they are governed by a typical elasticity length, of the order of 1 μm, and must be described with a large Poisson's ratio.     

Shape instabilities in vesicles: A phase-field model

A phase field model for dealing with shape instabilities in fluid membrane vesicles is presented. This model takes into account the Canham-Helfrich bending energy with spontaneous curvature. A dynamic equation for the phase-field is also derived. With this model it is possible to see the vesicle shape deformation dynamically, when some external agent instabilizes the membrane, for instance, inducing an inhomogeneous spontaneous curvature. The numerical scheme used is detailed and some stationary shapes are shown together with a shape diagram for vesicles of spherical topology and no spontaneous curvature, in agreement with known results.     

Shape deformation of ternary vesicles coupled with phase separation

We report an experimental study on shape deformations of ternary vesicles undergoing phase separation under an osmotic pressure difference. The phase separation on various shape vesicles causes unique shape-deformation branches. In the domain coarsening stage, prolate, discocyte, and starfish vesicles show a shape convergence to discocytes, whereas a pearling instability is observed in tube vesicles. In late stages, the domains start to bud towards the inside or outside of the vesicle depending on the excess area. We discuss the deformation branches based on the membrane elasticity model.     

Shapes of nearly cylindrical, axisymmetric bilayer membranes

Shapes of nearly cylindrical sections of axisymmetric phospholipid membranes are studied theoretically. Describing the shape of such sections by their deviation from a reference cylinder, the well-established shape equation for axisymmetric bilayer membranes is expanded in terms of this deviation, and it is then solved analytically. The phase diagram shows the resulting stationary shapes as functions of system parameters and external conditions, i.e., the pressure difference across the membrane, the membrane tension, the difference between the tensions of the two monolayers, and the axial force acting on the vesicle. The accuracy of the approximate analytical solution is demonstrated by comparison with numerical results. The obtained analytical solution allows to extend the analysis to include shapes where numerical methods have failed. Received 27 September 2000 and Received in final form 26 March 2001     

Vesicle dynamics in time-dependent elongation flow: wrinkling instability

We present experimental results on the relaxation dynamics of vesicles subjected to a time-dependent elongation flow. We observed and characterized a new instability, which results in the formation of higher-order modes of the vesicle shape (wrinkles), after a switch in the direction of the velocity gradient. This surprising generation of membrane wrinkles can be explained by the appearance of a negative surface tension during the vesicle deflation, which tunes itself to alternating stress. Moreover, the formation of buds in the vesicle membrane was observed in the vicinity of the dynamical transition point.     

Transport of ions and solvent in confined media

A new theoretical approach is used to model the transport properties of a cation-exchange membrane. By using the Navier-Stokes equation related to the Poisson-Boltzmann relation, it is thus possible to determine the solvent velocity in a membrane pore, and the influence of electroosmosis on the transport properties of the polymer. The variation of the transport coefficients with salt concentration in the membrane pore was modeled as for simple electrolytes: taking electrophoretic interactions and relaxation effect into account, we used MSA analytical expressions. We have investigated membrane conductivity and electrophoretic sodium mobility measurements when the membrane was equilibrated with NaCl solution. Good agreement was found between the experimental results and our theoretical model.     

Coarse-Grained Molecular Dynamics Simulation of a Red Blood Cell

A worm-like chain model based on a spectrin network is employed to study the biomechanics of red blood cells. Coarse-grained molecular dynamics simulations are performed to obtain a stable configuration free of external loadings. We also discuss the influence of two parameters： the average bending modulus and the persistence length. The change in shape of a malaria-infected red blood cell can contribute to the change in its molecular-based structure. As the persistence length of the membrane network in the infected red blood cell decreases, the deformability decreases and the biconcave shape is destroyed. The numerical results are comparable with previously reported experimental results. The coarse-grained model can be used to study the relationship between macro-mechanical properties and molecular-scale structures of cells.     

Curvature-dependent elastic properties of liquid-ordered domains result in inverted domain sorting on uniaxially compressed vesicles

Using a coarse-grained molecular model we study the spatial distribution of lipid domains on a 20-nm-sized vesicle. The lipid mixture laterally phase separates into a raftlike, liquid-ordered (l(o)) phase and a liquid-disordered phase. As we uniaxially compress the mixed vesicle keeping the enclosed volume constant, we impart tension onto the membrane. The vesicle adopts a barrel shape, which is composed of two flat contact zones and a curved edge. The l(o) domain, which exhibits a higher bending rigidity, segregates to the highly curved edge. This inverted domain sorting switches to normal domain sorting, where the l(o) domain prefers the flat contact zone, when we release the contents of the vesicle. We rationalize this domain sorting by a pronounced reduction of the bending rigidity and area compressibility of the l(o) phase upon bending.     

流场环境下复杂囊泡的动力学行为

采用非平衡态分子动力学方法研究了二维复杂囊泡在剪切流中的动力学行为. 模拟发现了复杂囊泡经典的翻滚(tumbling)、摇摆(trembling)和坦克履(tank-treading)行为, 还观察到由坦克履行为向平动行为(translating)的转变. 囊泡的平动行为与剪切率大小、复杂囊泡的形状密切相关. 当大囊泡均匀嫁接较多数目的小囊泡后, 其平动方式消失. 该研究有益于加深对囊泡在剪切流场中复杂性行为的理解.