Shape transformation of lipid vesicles induced by diffusing macromolecules

The attachment of macromolecules to the surface of a lipid vesicle may cause its deformations such as budding or creation of cylindrical protrusions. Diffusion of the macromolecules in the membranes may cause its shape transformations. The process of shrinking the protrusions due to diffusion of the macromolecules is investigated. It is assumed that macromolecules modify locally the spontaneous curvature and bending rigidity of the lipid membrane. Both spontaneous curvature and bending rigidities depend on the concentration of membrane components. It has been shown that cylindrical protrusions are created when the macromolecules which induce large spontaneous curvature are accumulated at a piece of the vesicle surface. It has been observed that here the elastic constants influence very little the evolution of the vesicle shape caused by diffusing macromolecules and the most important is the value the spontaneous curvature imposed by the macromolecules.     

Metabolic control of elastic properties of the inner mitochondrial membrane

A possible physical mechanism for inner mitochondrial membrane shape rearrangements is given. This analytical study shows that high transmembrane potential at the inner mitochondrial membrane brings about specific, substantial, and dynamic electrochemical contributions to lateral tension, bending rigidity constant, and elastic modulus of Gaussian curvature of the membrane. Changes in mitochondrial metabolism dramatically affect the magnitude of these elastic parameters but not necessarily that of proton-motive force. Metabolic-driven variation of mechanical properties of the inner mitochondrial membrane can promote the membrane remodeling between its principal geometric shapes and serve as a negative feedback in control of the oxidative phosphorylation.     

Instability of thin liquid films between membranes

The conditions for instability of the thin liquid film between two plane-parallel membranes were derived taking into account the influence of the membrane tension, the membrane bending elasticity, the film viscosity and the disjoining pressure. It was shown that the liquid film could be unstable if the negative (attractive) disjoining pressure is predominant. The characteristic timeτ _m of growth of perturbation due to thermal or other fluctuations of the membrane shape increases with increasing the film viscosity, the membrane tension and the membrane bending elasticity, and decreasing the film thickness and the negative disjoining pressure. It is of the order of 10^?2÷10³ sec. When the membranes approach each other at certain value of the average film thicknessh _cr called critical, the fastest growing perturbations lead to formation of a liquid film with smaller (or zero) thickness. It was found that the critical thickness increases with increasing the negative disjoining pressure and the membrane area and decreasing the membrane tension and the bending elasticity having typical values of the order of 10^?6÷10^?5 cm. The case of a membrane approaching a solid plane was also considered. Excluding the small differences in numerical coefficients the results are similar to the case of two identical membranes.     

Vesicle shapes from molecular dynamics simulations

Lipid bilayer membranes are known to form various structures such as large sheets or vesicles. When the two leaflets of the bilayer have an equal composition, the membrane preferentially forms a flat sheet or a spherical vesicle. However, a difference in the composition of the two leaflets may result in a curved bilayer or in a wide variety of vesicle shapes. Vesicles with different shapes have already been shown in experiments and diverse vesicle shapes have been predicted theoretically from energy minimization of continuous curves. Here we present a molecular dynamics study of the effect of small changes in the phospholipid headgroups on the spontaneous curvature of the bilayer and on the resulting vesicle shape transformations. Small asymmetries in the bilayers already result in high spontaneous curvature and large vesicle deformations. Vesicle shapes that are formed include ellipsoids, discoids, pear-shaped vesicles, cup-shaped vesicles, as well as budded vesicles. Comparison of these vesicles with theoretically derived vesicle shapes shows both resemblances and differences.     

“Electrocapillary” curve on solid metal obtained by holographic interferometry

A new very sensitive method was developed for obtaining the “electrocapillary” curve of a solid metal. The method is based on the measurement of small elastic deformations of a strip caused by the changes of the surface tension forces. For the precise measurement of the strip bending (the radius of curvature) holographic interferometry was applied. It is shown that a change of the surface tension ±0.1 mN m^?1 can be registered. The “electrocapillary” curve of platinum in 0.05 M H₂SO₄ solution was obtained. It was found that the zero charge potential is +0.25 V versus normal hydrogen electrode. The double layer capacity was evaluated. The method is not very sensitive to temperature changes and can be applied in any case when the working electrode (metal strip) is mounted in a transparent glass cell.     

Modulation of the spontaneous curvature and bending rigidity of lipid membranes by interfacially adsorbed amphipathic peptides

Amphipathic alpha-helical peptides are often ascribed an ability to induce curvature stress in lipid membranes. This may lead directly to a bending deformation of the host membrane, or it may promote the formation of defects that involve highly curved lipid layers present in membrane pores, fusion intermediates, and solubilized peptide-micelle complexes. The driving force is the same in all cases: peptides induce a spontaneous curvature in the host lipid layer, the sign of which depends sensitively on the peptide's structural properties. We provide a quantitative account for this observation on the basis of a molecular-level method. To this end, we consider a lipid membrane with peptides interfacially adsorbed onto one leaflet at high peptide-to-lipid ratio. The peptides are modeled generically as rigid cylinders that interact with the host membrane through a perturbation of the conformational properties of the lipid chains. Through the use of a molecular-level chain packing theory, we calculate the elastic properties, that is, the spontaneous curvature and bending stiffness, of the peptide-decorated lipid membrane as a function of the peptide's insertion depth. We find a positive spontaneous curvature (preferred bending of the membrane away from the peptide) for small penetration depths of the peptide. At a penetration depth roughly equal to half-insertion into the hydrocarbon core, the spontaneous curvature changes sign, implying negative spontaneous curvature (preferred bending of the membrane toward the peptide) for large penetration depths. Despite thinning of the membrane upon peptide insertion, we find an increase in the bending stiffness. We discuss these findings in terms of how the peptide induces elastic stress.     

Invited Lecture. Hats and saddles in lipid membranes

Abstract

Extrinsic or intrinsic defects in membranes may produce deformations resembling hats or saddles. It is shown that hats cannot absorb much area without reducing the bending rigidity of the membrane below 10^? erg. Estimates indicate that intrinsic saddles are promoted by the stress profile of electrically neutral biological model membranes. The saddle structures might warp the membrane if they cooperate.     

Separation of components in lipid membranes induced by shape transformation

Vesicles composed of a two component membrane with each component characterized by different spontaneous curvature are investigated by minimization of the free energy consisting of Helfrich elastic energy and entropy of mixing. The results show that mixing and demixing of membrane components can be induced by elongating a vesicle or changing its volume, if one of the components forms a complex with macromolecules on the outer monolayer. The influence of elastic coefficients on the separation of components is also examined.     

Surface tension in bilayer membranes with fixed projected area

We study the elastic response of bilayer membranes with fixed projected area to both the stretching and shape deformations. A surface tension is associated to each of these deformations. By using model amphiphilic membranes and computer simulations, we are able to observe both the types of deformation, and thus, both the surface tensions, related to each type of deformation, are measured for the same system. These surface tensions are found to assume different values in the same bilayer membrane, in particular, they vanish for different values of the projected area. We introduce a simple theory which relates the two quantities and successfully apply it to the data obtained with computer simulations.     

Spontaneous vesiculation

The thermodynamics of vesicle formation was analyzed by using the elastic bending energy approach. Several different possibilities of spontaneous vesiculation, due to soft bilayers, non-zero spontaneous curvature and Gaussian curvature, respectively, were presented and discussed. Intermediate structures in the closed vesicle–disklike mixed micelle phase transition could be either cup-like particles or open bilayers partially rolled into lipid tubules.     

耗散粒子动力学研究双层膜线张力与抗弯刚度的关系

利用耗散力粒子动力学模拟方法研究了拉伸状态下双层膜的抗弯刚度与膜孔线张力之间的关系.通过对双层膜在不同投影面积约束下的系统模拟,观察到3个区域:自由振动膜、伸展膜和穿孔膜.由前两个区域的应力张量计算得到的膜的面张力(σΣ)与拟合膜波动性质得到的面张力(σfluc)吻合的很好,除去在两区域的转变点附近σfluc略大于σΣ.当考虑在经典Helfrich弹性膜模型中被忽略的膜厚度时,线张力可以和抗弯刚度用一个简单的模型联系起来.通过对穿孔膜区域的数据进行分析,证明由本模型得到的抗弯刚度与拟合膜波动性质得到的抗弯刚度符合的很好.由此提出一种简便的测量方法,通过计算拉伸膜孔的面张力和统计膜厚度,拟合这个简单模型来测量膜的抗弯刚度.     

Mechanical Characterization of Micrometric Chitosan-Coated Vesicle by Atomic Force Microscopy

This article reports the main results obtained for the stabilization of DOPC liposomes by coating with chitosan. We investigated the compression between two planes of isolated GUV, combining force spectroscopy measurements with scanning probe microscopy (SPM) and epifluorescence microscopy observations. We obtained reproducible and reversible force-deformation curves for individual vesicles in the range of small deformation (relative deformation up to 0.3). Force-deformation curves were analyzed using a simple elastic model, which well describes the observed radius-dependency of the force response and allows determining the stretching modulus for bare vesicle and effective bending and stretching moduli for chitosan-coated membranes. Results first show that chitosan coating increases the effective stretching modulus of the lipid membranes, second, confirm that chitosan is adsorbed flat on the membrane, and finally lead us to assume that the chitosan coating structure can be regarded as a physical network of connected chitosan patches.     

Shape of fluid vesicles anchored by rigid rod

A method combined the self-consistent field theory (SCFT) for the rigid rod with the Helfrich curvature elasticity theory for the vesicle has been developed for studying the shape of vesicles anchored by rigid rod. Both the deformation of the vesicle and the density distribution of rod segments can be obtained. Because of the vesicle's impenetrability for the rod segments and the decrease of the available space for the rod orientational configurations, the anchored rod segments exert the inhomogeneous entropic pressure on the vesicle and induce the change of vesicle shape. The interaction between the rod segments and the vesicle membrane exerts an extra tension to the membrane. Thus the interaction between the vesicle membrane and the rod segments, the rod length, and the bending rigidity of vesicle are investigated as the important factors to the shape transformation of the vesicle and the density distribution of rod segments. This method can be extended to more complicated and real biological systems, such as polymers with different topological architectures/vesicle, multiple chains/vesicle, protein inclusions, etc.     

Solvent-free coarse-grained lipid model for large-scale simulations

A coarse-grained molecular model, which consists of a spherical particle and an orientation vector, is proposed to simulate lipid membrane on a large length scale. The solvent is implicitly represented by an effective attractive interaction between particles. A bilayer structure is formed by orientation-dependent (tilt and bending) potentials. In this model, the membrane properties (bending rigidity, line tension of membrane edge, area compression modulus, lateral diffusion coefficient, and flip-flop rate) can be varied over broad ranges. The stability of the bilayer membrane is investigated via droplet-vesicle transition. The rupture of the bilayer and worm-like micelle formation can be induced by an increase in the spontaneous curvature of the monolayer membrane.     

Curvature-modulated phase separation in lipid bilayer membranes

Cellular membranes exhibit a variety of controlled curvatures, with filopodia, microvilli, and mitotic cleavage furrows being only a few of many examples. Coupling between local curvature and chemical composition in membranes could provide a means of mechanically controlling the spatial organization of membrane components. Although this concept has surfaced repeatedly over the years, controlled experimental investigations have proven elusive. Here, we introduce an experimental platform, in which microfabricated surfaces impose specific curvature patterns onto lipid bilayers, that allows quantification of mechanochemical couplings in membranes. We find that, beyond a critical curvature value, membrane geometry governs the spatial ordering of phase-separated domain structures in membranes composed of cholesterol and phospholipids. The curvature-controlled ordering, a consequence of the distinct mechanical properties of the lipid phases, makes possible a determination of the bending rigidity difference between cholesterol-rich and cholesterol-poor lipid domains. These observations point to a strong coupling between mechanical bending and chemical organization that should have wide-reaching consequences for biological membranes. Curvature-mediated patterning may also be useful in controlling complex fluids other than biomembranes.     

Nonlocal membrane bending: A reflection,the facts and its relevance

About forty years ago it was realized that phospholipid membranes, because they are composed of two layers, exhibit particular, and specific mechanical properties [1–3]. This led to the concept of nonlocal membrane bending, often called area difference elasticity. We present a short history of the development of the concept, followed by arguments for a proper definition of the corresponding elastic constant. The effects of the nonlocal bending energy on vesicle shape are explained. It is demonstrated that lipid vesicles, cells and cellular aggregates exhibit phenomena that can only be described in a complete manner by considering nonlocal bending.     

Size-dependent properties of small unilamellar vesicles formed by model lipids

The size-dependent behavior of small unilamellar vesicles is explored by dissipative particle dynamics, including the membrane characteristics and mechanical properties. The spontaneously formed vesicles are in the metastable state and the vesicle size is controlled by the concentration of model lipids. As the vesicle size decreases, the bilayer gets thinner and the area density of heads declines. Nonetheless, the area density in the inner leaflet is higher than that in the outer. The packing parameters are calculated for both leaflets. The result indicates that the shape of lipid in the outer leaflet is like a truncated cone but that in the inner leaflet resembles an inverted truncated cone. Based on a local order parameter, our simulations indication that the orientation order of lipid molecules decreases as the size of the vesicle reduces and this fact reveals that the bilayer becoming thinner for smaller vesicle is mainly attributed to the orientation disorder of the lipids. The membrane tension can be obtained through the Young-Laplace equation. The tension is found to grow with reducing vesicle size. Therefore, small vesicles are less stable against fusion. Using the inflation method, the area stretching and bending moduli can be determined and those moduli are found to grow with reducing size. Nonetheless, a general equation with a single numerical constant can relate bending modulus, area stretching modulus, and bilayer thickness irrespective of the vesicle size. Finally, a simple metastable model is proposed to explain the size-dependent behavior of bilayer thickness, orientation, and tension.     

Composition dependence of bilayer elasticity

A previously developed molecular level model for homogeneous lipid bilayers [Brannigan and Brown, J. Chem. Phys 120, 1059 (2004)] is extended to allow for multiple lipid species. Monte Carlo simulations (including species exchange moves for efficient sampling) reveal a variety of mixing behaviors in binary systems. Two species are identified that maintain stable, randomly mixed fluid membranes at vanishing tension over all possible binary compositions. The thermal and elastic properties of membranes formed by these lipids are characterized over the full composition range. Equilibrium area at constant tension is nonmonotonic with respect to composition, but consistent with that of a quadratic mixture. In the constant tension ensemble, the bending rigidity of the bilayer is minimized at an intermediate composition. The observed functional form of bending rigidity vs composition is fit to a simple expression motivated by linear elasticity theory; this expression accounts for membrane heterogeneity through a single parameter.     

Lipid nanotube formation from streptavidin-membrane binding

A novel transformation of giant lipid vesicles to produce nanotubular structures was observed upon the binding of streptavidin to biotinylated membranes. Unlike membrane budding and tubulation processes caused by proteins involved with endocytosis and vesicle fusion, streptavidin is known to crystallize at near the isoelectric point (pI 5 to 6) into planar sheets against biotinylated films. We have found, however, that at neutral pH membranes of low bending rigidity (<10kT), such as 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC), spontaneously produce tubular structures with widths ranging from micrometers to below the diffraction limit (<250 nm) and lengths spanning up to hundreds of micrometers. The nanotubes were typically held taut between surface-bound vesicles suggesting high membrane tension, yet the lipid nanotubes exhibited a fluidic nature that enabled the transport of entrained vesicles. Confocal microscopy confirmed the uniform coating of streptavidin over the vesicles and nanotubes. Giant vesicles composed of lipid membranes of higher bending energy exhibited only aggregation in the presence of streptavidin. Routes toward the development of these highly curved membrane structures are discussed in terms of general protein-membrane interactions.     

The influence of anisotropic membrane inclusions on curvature elastic properties of lipid membranes

A membrane inclusion can be defined as a complex of protein or peptide and the surrounding significantly distorted lipids. We suggest a theoretical model that allows for the estimation of the influence of membrane inclusions on the curvature elastic properties of lipid membranes. Our treatment includes anisotropic inclusions whose energetics depends on their in-plane orientation within the membrane. On the basis of continuum elasticity theory, we calculate the inclusion-membrane interaction energy that reflects the protein or peptide-induced short-ranged elastic deformation of a bent lipid layer. A numerical estimate of the corresponding interaction constants indicates the ability of inclusions to sense membrane bending and to accumulate at regions of favorable curvature, matching the effective shape of the inclusions. Strongly anisotropic inclusions interact favorably with lipid layers that adopt saddlelike curvature; such structures may be stabilized energetically. We explore this possibility for the case of vesicle budding where we consider a shape sequence of closed, axisymmetric vesicles that form a (saddle-curvature adopting) membrane neck. It appears that not only isotropic but also strongly anisotropic inclusions can significantly contribute to the budding energetics, a finding that we discuss in terms of recent experiments.