Equilibrium budding and vesiculation in the curvature model of fluid lipid vesicles

Investigation of Shape Transformations of Vesicles, Induced by Their Adhesion to Flat Substrates Characterized by Different Adhesion Strength

The adhesion of lipid vesicles to a rigid flat surface is investigated. We examine the influence of the membrane spontaneous curvature, adhesion strength, and the reduced volume on the stability and shape transformations of adhered vesicles. The minimal strength of the adhesion necessary to stabilize the shapes of adhered vesicles belonging to different shape classes is determined. It is shown that the budding of an adhered vesicle may be induced by the change of the adhesion strength. The importance of the free vesicle shape for its susceptibility to adhesion is discussed.

Biomembranes undergo complex, non-axisymmetric deformations governed by Kirchhoff-Love kinematicsand revealed by a three-dimensional computational framework

Biomembranes play a central role in various phenomena like locomotion of cells, cell-cell interactions, packaging and transport of nutrients, transmission of nerve impulses, and in maintaining organelle morphology and functionality. During these processes, the membranes undergo significant morphological changes through deformation, scission, and fusion. Modelling the underlying mechanics of such morphological changes has traditionally relied on reduced order axisymmetric representations of membrane geometry and deformation. Axisymmetric representations, while robust and extensively deployed, suffer from their inability to model-symmetry breaking deformations and structural bifurcations. To address this limitation, a three-dimensional computational mechanics framework for high fidelity modelling of biomembrane deformation is presented. The proposed framework brings together Kirchhoff–Love thin-shell kinematics, Helfrich-energy-based mechanics, and state-of-the-art numerical techniques for modelling deformation of surface geometries. Lipid bilayers are represented as spline-based surface discretizations immersed in a three-dimensional space; this enables modelling of a wide spectrum of membrane geometries, boundary conditions, and deformations that are physically admissible in a three-dimensional space. The mathematical basis of the framework and its numerical machinery are presented, and their utility is demonstrated by modelling three classical, yet non-trivial, membrane deformation problems: formation of tubular shapes and their lateral constriction, Piezo1-induced membrane footprint generation and gating response, and the budding of membranes by protein coats during endocytosis. For each problem, the full three-dimensional membrane deformation is captured, potential symmetry-breaking deformation paths identified, and various case studies of boundary and load conditions are presented. Using the endocytic vesicle budding as a case study, we also present a ‘phase diagram’ for its symmetric and broken-symmetry states.

Shape Transformations of Vesicles Induced by Their Adhesion to Flat Surfaces

The shape transformations of lipid vesicles induced by the adhesion to a flat surface is investigated. We perform the calculations within the framework of the Helfrich spontaneous curvature model. The calculations were performed for a few values of the reduced volume and the spontaneous curvature. The range of stability for different shapes (oblate, prolate, and stomatocyte) of adhered vesicles is determined. New physical phenomena such as budding induced by the adhesion of vesicles are reported.

Fluctuations and conformational stability of a membrane patch with curvature inducing inclusions

Membranes with curvature inducing inclusions display a range of cooperative phenomena, which can be linked to biomembrane function, e.g. membrane tubulation, vesiculation, softening and spontaneous tension. We investigate how these phenomena are related for a fluctuating, framed membrane through analysis of a descretized membrane model by Monte Carlo simulation techniques. The membrane model is based on a dynamically triangulated surface equipped with non-interacting, up-down symmetry breaking inclusions where only terms coupled linearly to mean-curvature are maintained. We show that the lateral configurational entropy plays a key role for the mechanical properties of the semi-flexible membrane, e.g. a pronounced softening at intermediate inclusion coverages of the membrane and generation of membrane tension. Tensionless framed membranes will remain quasi-flat up to some threshold coverage, where a shape instability occurs with formation of pearling or tubular membranes, which below full coverage is associated with segregation of inclusions between the curved and flat membrane geometries. For inclusions with preference for highly curved membranes the instability appears at dilute inclusion coverages and is accompanied by strong configurational fluctuations.

Fission of Lipid-Vesicles by Membrane Phase Transitions in Thermal Convection

Unilamellar lipid vesicles can serve as model for protocells. We present a vesicle fission mechanism in a thermal gradient under flow in a convection chamber, where vesicles cycle cold and hot regions periodically. Crucial to obtain fission of the vesicles in this scenario is a temperature-induced membrane phase transition that vesicles experience multiple times. We model the temperature gradient of the chamber with a capillary to study single vesicles on their way through the temperature gradient in an external field of shear forces. Starting in the gel-like phase the spherical vesicles are heated above their main melting temperature resulting in a dumbbell-deformation. Further downstream a temperature drop below the transition temperature induces splitting of the vesicles without further physical or chemical intervention. This mechanism also holds for less cooperative systems, as shown here for a lipid alloy with a broad transition temperature width of 8 K. We find a critical tether length that can be understood from the transition width and the locally applied temperature gradient. This combination of a temperature-induced membrane phase transition and realistic flow scenarios as given e.g. in a white smoker enable a fission mechanism that can contribute to the understanding of more advanced protocell cycles.

Modeling the Mechanics of Cell Division: Influence of Spontaneous Membrane Curvature, Surface Tension, and Osmotic Pressure

Many cell division processes have been conserved throughout evolution and are being revealed by studies on model organisms such as bacteria, yeasts, and protozoa. Cellular membrane constriction is one of these processes, observed almost universally during cell division. It happens similarly in all organisms through a mechanical pathway synchronized with the sequence of cytokinetic events in the cell interior. Arguably, such a mechanical process is mastered by the coordinated action of a constriction machinery fueled by biochemical energy in conjunction with the passive mechanics of the cellular membrane. Independently of the details of the constriction engine, the membrane component responds against deformation by minimizing the elastic energy at every constriction state following a pathway still unknown. In this paper, we address a theoretical study of the mechanics of membrane constriction in a simplified model that describes a homogeneous membrane vesicle in the regime where mechanical work due to osmotic pressure, surface tension, and bending energy are comparable. We develop a general method to find approximate analytical expressions for the main descriptors of a symmetrically constricted vesicle. Analytical solutions are obtained by combining a perturbative expansion for small deformations with a variational approach that was previously demonstrated valid at the reference state of an initially spherical vesicle at isotonic conditions. The analytic approximate results are compared with the exact solution obtained from numerical computations, getting a good agreement for all the computed quantities (energy, area, volume, constriction force). We analyze the effects of the spontaneous curvature, the surface tension and the osmotic pressure in these quantities, focusing especially on the constriction force. The more favorable conditions for vesicle constriction are determined, obtaining that smaller constriction forces are required for positive spontaneous curvatures, low or negative membrane tension and hypertonic media. Conditions for spontaneous constriction at a given constriction force are also determined. The implications of these results for biological cell division are discussed. This work contributes to a better quantitative understanding of the mechanical pathway of cellular division, and could assist the design of artificial divisomes in vesicle-based self-actuated microsystems obtained from synthetic biology approaches.

Sphingomyelin metabolism controls the shape and function of the Golgi cisternae

The flat Golgi cisterna is a highly conserved feature of eukaryotic cells, but how is this morphology achieved and is it related to its function in cargo sorting and export? A physical model of cisterna morphology led us to propose that sphingomyelin (SM) metabolism at the trans-Golgi membranes in mammalian cells essentially controls the structural features of a Golgi cisterna by regulating its association to curvature-generating proteins. An experimental test of this hypothesis revealed that affecting SM homeostasis converted flat cisternae into highly curled membranes with a concomitant dissociation of membrane curvature-generating proteins. These data lend support to our hypothesis that SM metabolism controls the structural organization of a Golgi cisterna. Together with our previously presented role of SM in controlling the location of proteins involved in glycosylation and vesicle formation, our data reveal the significance of SM metabolism in the structural organization and function of Golgi cisternae.

DOI:http://dx.doi.org/10.7554/eLife.24603.001

The Golgi complex is a hub inside cells that transports many proteins to various parts of the cell. It also receives freshly made proteins and modifies them to help them mature into their final active forms. The complex is made up of a stack of disc-like membrane structures called cisternae.

Are the shapes of the cisternae important for the Golgi complex to work properly? Membranes are made of mixtures of molecules known as lipids and proteins. Previous experiments show that when the mixture of lipids in the Golgi membranes changes in a specific manner, the cisternae curl into an onion-like shape and the Golgi cannot process or send out proteins anymore.

Campelo et al. used mathematics and experimental approaches to investigate what causes the Golgi to change shape when the lipid mixture of the cisternae changes. A mathematical description of the shape of the Golgi predicted that some proteins keep the cisternae flat by holding the membrane rim that connects the two faces of a cisterna. To test this prediction, Campelo et al. performed experiments in human cells, which showed that when the mixture of lipids in the Golgi membranes changes, certain proteins jump from the rim, causing the cisternae to curl. These same proteins are also needed to transport cargo proteins out of the Golgi, meaning that there is a connection between the shape of the Golgi and the tasks it carries out.

The shape of the Golgi complex is altered in Alzheimer’s disease and many other neurodegenerative diseases. The next challenges are to understand how these shape changes happen, how this affects cells, and if it could be possible to develop drugs that prevent these changes from occurring in patients.

DOI:http://dx.doi.org/10.7554/eLife.24603.002

Stabilization of membrane necks by adhesive particles, substrate surfaces, and constriction forces

Membrane remodelling processes involving the formation and fission of small buds require the formation and closure of narrow membrane necks, both for biological membranes and for model membranes such as lipid bilayers. The conditions required for the stability of such necks are well understood in the context of budding of vesicles with bilayer asymmetry and/or intramembrane domains. In many cases, however, the necks form in the presence of an adhesive surface, such as a solid particle or substrate, or the cellular cortex itself. Examples of such processes in biological cells include endocytosis, exocytosis and phagocytosis of solid particles, the formation of extracellular and outer membrane vesicles by eukaryotic and prokaryotic cells, as well as the closure of the cleavage furrow in cytokinesis. Here, we study the interplay of curvature elasticity, membrane-substrate adhesion, and constriction forces to obtain generalized stability conditions for closed necks which we validate by numerical energy minimization. We then explore the consequences of these stability conditions in several experimentally accessible systems such as particle-filled membrane tubes, supported lipid bilayers, giant plasma membrane vesicles, bacterial outer membrane vesicles, and contractile rings around necks. At the end, we introduce an intrinsic engulfment force that directly describes the interplay between curvature elasticity and membrane-substrate adhesion.

A model of vesicle tubulation and pearling induced by adsorbing particles

We study the basic theoretical model of a deformable vesicle immersed in a solution of particles that can adsorb onto one of the two surfaces of a membrane. The model consists of an adsorption energy gain for the adsorbing particles and the Canham-Helfrich membrane bending energy, in which the spontaneous curvature is coupled with the adsorption area. We demonstrate that bud, pearling, and tube conformations can be stabilized after minimizing the free energy and that the pearling-tubulation transition has the characteristics of an abrupt structural transition.

Coupling of bending and stretching deformations in vesicle membranes

Biomimetic membranes are fluid and can undergo two different elastic deformations, bending and stretching. The bending of a membrane is primarily governed by two elastic parameters: its spontaneous (or preferred) curvature m and its bending rigidity κ. These two parameters define an intrinsic tension scale, the spontaneous tension 2 κm². Membrane stretching and compression, on the other hand, are determined by the mechanical tension acting within the membrane. For vesicle membranes, the two elastic deformations are coupled via the enclosed vesicle volume even in the absence of mechanical forces as shown here by minimizing the combined bending and stretching energy with respect to membrane area for fixed vesicle volume. As a consequence, the mechanical tension within a vesicle membrane depends on the spontaneous curvature and on the bending rigidity. This interdependence, which is difficult to grasp intuitively, is then illustrated for a variety of simple vesicle shapes. Depending on the vesicle morphology, the magnitude of the mechanical tension can be comparable to or can be much smaller than the spontaneous tension.

The role of cholesterol-sphingomyelin membrane nanodomains in the stability of intercellular membrane nanotubes

Intercellular membrane nanotubes (ICNs) are highly curved tubular structures that connect neighboring cells. The stability of these structures depends on the inner cytoskeleton and the cell membrane composition. Yet, due to the difficulty in the extraction of ICNs, the cell membrane composition remains elusive. In the present study, a raft marker, ostreolysin, revealed the enrichment of cholesterol-sphingomyelin membrane nanodomains along ICNs in a T24 (malignant) urothelial cancer cell line. Cholesterol depletion, due to the addition of methyl-β-cyclodextrin, caused the dispersion of cholesterol-sphingomyelin membrane nanodomains and the retraction of ICNs. The depletion of cholesterol also led to cytoskeleton reorganization and to formation of actin stress fibers. Live cell imaging data revealed the possible functional coupling between the change from polygonal to spherical shape, cell separation, and the disconnection of ICNs. The ICN was modeled as an axisymmetric tubular structure, enabling us to investigate the effects of cholesterol content on the ICN curvature. The removal of cholesterol was predicted to reduce the positive spontaneous curvature of the remaining membrane components, increasing their curvature mismatch with the tube curvature. The mechanisms by which the increased curvature mismatch could contribute to the disconnection of ICNs are discussed.

On the role of membrane anisotropy and BAR proteins in the stability of tubular membrane structures

Recent studies have demonstrated that actin filaments are not crucial for the short-term stability of tubular membrane protrusions originating from the cell surface. It has also been demonstrated that prominin nanodomains and curvature inducing I-BAR proteins could account for the stability of the membrane protrusion. Here we constructed an axisymmetric model of a membrane protrusion that excludes actin filaments in order to investigate the contributions of prominin nanodomains (rafts) and I-BAR proteins to the membrane protrusion stability. It was demonstrated that prominin nanodomains and I-BAR proteins can stabilize the membrane protrusion only over a specific range of spontaneous curvature. On the other hand, high spontaneous curvature and/or high density of I-BAR proteins could lead to system instability and to non-uniform contraction in the radial direction of the membrane protrusion. In agreement with previous studies, it was also shown that the isotropic bending energy of lipids is not sufficient to explain the stability of the observed tubular membrane protrusion without actin filaments.

SHAPE TRANSFORMATIONS OF VESICLES BUILT OF AMPHIPHILIC MOLECULES

We review our recent work on the shape transformations of vesicles subject to external stimuli. Possible shape transformations resulting from the change of the spontaneous curvature, volume, or composition of the components on the surface of a vesicle are examined within the framework of the spontaneus curvature model. The influence of encapsulated or adhered rigid object such as microtubules or colloidal particles on the shape transformation is also investigated. A few cases of shape transformations encountered in experiments are described.

Continuum simulations of biomembrane dynamics and the importance of hydrodynamic effects

Traditional particle-based simulation strategies are impractical for the study of lipid bilayers and biological membranes over the longest length and time scales (microns, seconds and longer) relevant to cellular biology. Continuum-based models developed within the frameworks of elasticity theory, fluid dynamics and statistical mechanics provide a framework for studying membrane biophysics over a range of mesoscopic to macroscopic length and time regimes, but the application of such ideas to simulation studies has occurred only relatively recently. We review some of our efforts in this direction with emphasis on the dynamics in model membrane systems. Several examples are presented that highlight the prominent role of hydrodynamics in membrane dynamics and we argue that careful consideration of fluid dynamics is key to understanding membrane biophysics at the cellular scale.

Observation of stable shapes and conformal diffusion in genus 2 vesicles

The observed equilibrium shapes of phospholipid vesicles of topological genus 2 (shapes with two holes) are found to be in agreement with theoretical predictions on the basis of a minimization of the elastic curvature energy for fluid membranes under the constraints of constant area, volume, and area difference (between the inner and outer layers of the membrane). For some particular geometrical characteristics, the shapes of the vesicles change continuously and randomly on a slow time scale (tens of seconds) and thus exhibit conformal diffusion. This phenomenon is a reflection of the conformal degeneracy of the elastic curvature energy. Its observation sets a limit (three constraints) on the number of physical constraints relevant to the determination of the shapes of vesicles.

Domain-induced budding of fluid membranes

Domains within fluid membranes grow by the aggregation of molecules which diffuse laterally within the membrane matrix. A simple theoretical model is introduced which predicts that a flat or weakly curved domain becomes unstable at a certain limiting size and then undergoes a budding or invagination process. This instability is driven by the competition between the bending energy of the domain and the line tension of the domain edge. For lipid bilayers, the budding domain can rupture the membrane and then it pinches off from the matrix. The same mechanism should also drive the budding of non-coated domains in biomembranes, and could even be effective when these domains are covered by a coat of clathrin molecules.

Effect of counterions on the Rayleigh-Plateau instability of a charged cylinder

The effect of counterions on the instability of a charged cylinder is investigated. Both axisymmetric and asymmetric perturbations are considered. The analysis shows that the Rayleigh-Plateau instability is modified for a charged cylinder in the presence of counterions. For the axisymmetric instability, the counterions have a stabilizing effect at low values of kappa, the inverse Debye layer thickness. However, the effect is destabilizing at higher values of kappa . The asymmetric modes which are stable for an uncharged cylinder are rendered unstable at high values of kappa . The analysis should be important in pearling instability of charged cylindrical vesicles. The expression for the correlation time of thermally induced shape fluctuations of charged cylindrical vesicles is also derived.

Vesicle budding and the origin of cellular life

This Minireview provides an appropriate opportunity to demonstrate the connection between the results of some early experimental and theoretical investigations of vesicle budding and the more recent application of the concepts developed there to the process of vesicle self-reproduction. Herein, we also explain why vesicle budding could have preceded the establishment of cellular life.

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.

Interaction of tea catechin (-)-epigallocatechin gallate with lipid bilayers

A major component of green tea extracts, catechin (-)-Epigallocatechin gallate (EGCg), has been reported to be biologically active and interacting with membranes. A recent study reported drastic effects of EGCg on giant unilamellar vesicles (GUVs). In particular, EGCg above 30 microM caused GUVs to burst. Here we investigated the effect of EGCg on single GUVs at lower concentrations, believing that its molecular mechanism would be more clearly revealed. We used the micropipette aspiration method, by which the changes of surface area and volume of a GUV could be measured as a result of interaction with EGCg. We also used x-ray diffraction to measure the membrane thinning effect by EGCg. To understand the property of EGCg, we compared its effect with other membrane-active molecules, including pore-forming peptide magainin, the turmeric (curry) extract curcumin, and detergent Triton X100. We found the effect of EGCg somewhat unique. Although EGCg readily binds to lipid bilayers, its membrane area expansion effect is one order of magnitude smaller than curcumin. EGCg also solubilizes lipid molecules from lipid bilayers without forming pores, but its effect is different from that of Triton X100.

Actin is not required for nanotubular protrusions of primary astrocytes grown on metal nano-lawn

We used sub-micron metal rod decorated surfaces, 'nano-lawn' structures, as a substrate to study cell-to-cell and cell-to-surface interactions of primary murine astrocytes. These cells form thin membranous tubes with diameters of less than 100 nm and a length of several microns, which make contact to neighboring cells and the substrate during differentiation. While membrane protrusions grow on top of the nano-lawn pillars, nuclei sink to the bottom of the substrate. We observed gondola-like structures along those tubes, suggestive of their function as transport vehicles. Elements of the cytoskeleton such as actin fibers are commonly believed to be essential for triggering the onset and growth of tubular membrane protrusions. A rope-pulling mechanism along actin fibers has recently been proposed to account for the transport or exchange of cellular material between cells. We present evidence for a complementary mechanism that promotes growth and stabilization of the observed tubular protrusions of cell membranes. This mechanism does not require active involvement of actin fibers as the formation of membrane protrusions could not be prevented by suppressing polymerization of actin by latrunculin B. Also theoretically, actin fibers are not essential for the growing and stability of nanotubes since curvature-driven self-assembly of interacting anisotropic raft elements is sufficient for the spontaneous formation of thin nano-tubular membrane protrusions.

Model for curvature-driven pearling instability in membranes

A phase-field model for dealing with dynamic instabilities in membranes is presented. We use it to study curvature-driven pearling instability in vesicles induced by the anchorage of amphiphilic polymers on the membrane. Within this model, we obtain the morphological changes reported in recent experiments. The formation of a homogeneous pearled structure is achieved by consequent pearling of an initial cylindrical tube from the tip. For high enough concentration of anchors, we show theoretically that the homogeneous pearled shape is energetically less favorable than an inhomogeneous one, with a large sphere connected to an array of smaller spheres.

Inverted catenoid as a fluid membrane with two points pulled together

Under inversion in any (interior) point, a catenoid transforms into a deflated compact geometry which touches at two points (its poles). The catenoid is a minimal surface and, as such, is an equilibrium shape of a symmetric fluid membrane. The conformal symmetry of the Hamiltonian implies that inverted minimal surfaces are also equilibrium shapes. However, they will exhibit curvature singularities at their poles. Such singularities are the geometrical signature of the external forces required to pull the poles together. These forces will set up stresses in the inverted shapes. Tuning the force corresponds geometrically to the translation of the point of inversion. For any fixed surface area, there will be a maximum force. The associated shape is a symmetric discocyte. Lowering the external force will induce a transition from the discocyte to a cup-shaped stomatocyte.

Influence of spontaneous curvature and microtubules on the conformations of lipid vesicles

The conformations of vesicles deformed by microtubules are studied within the framework of the curvature energy. The phenomenon in which the destruction of a microtubule is followed by the formation of peristaltic shapes on a protrusion created by the microtubule is investigated. The influence of the spontaneous curvature on the conformations of vesicles is examined, and the results are compared to existing experiments. The elastic properties of a vesicle deformed by the microtubule are studied.

Possible role of flexible red blood cell membrane nanodomains in the growth and stability of membrane nanotubes

Tubular budding of the erythrocyte membrane may be induced by exogenously added substances. It is shown that tubular budding may be explained by self-assembly of anisotropic membrane nanodomains into larger domains forming nanotubular membrane protrusions. In contrast to some previously reported theories, no direct external mechanical force is needed to explain the observed tubular budding of the bilayer membrane. The mechanism that explains tubular budding may also be responsible for stabilization of the thin tubes that connect cells or cell organelles and which might be important for the transport of matter and information in cellular systems. It is shown that small carrier vesicles (gondolas), transporting enclosed material or the molecules composing their membrane, may travel over long distances along the nanotubes connecting two cells.

How to determine local elastic properties of lipid bilayer membranes from atomic-force-microscope measurements: a theoretical analysis

Measurements with an atomic force microscope (AFM) offer a direct way to probe elastic properties of lipid bilayer membranes locally: provided the underlying stress-strain relation is known, material parameters such as surface tension or bending rigidity may be deduced. In a recent experiment a pore-spanning membrane was poked with an AFM tip, yielding a linear behavior of the force-indentation curves. A theoretical model for this case is presented here which describes these curves in the framework of Helfrich theory. The linear behavior of the measurements is reproduced if one neglects the influence of adhesion between tip and membrane. Including it via an adhesion balance changes the situation significantly: force-distance curves cease to be linear, hysteresis and nonzero detachment forces can show up. The characteristics of this rich scenario are discussed in detail in this paper.

Mechanical properties of pore-spanning lipid bilayers probed by atomic force microscopy

We measure the elastic response of a free-standing lipid membrane to a local indentation by using an atomic force microscope. Starting point is a planar gold-coated alumina substrate with a chemisorbed 3-mercaptopropionic acid monolayer displaying circular pores of very well defined and tunable size, over which bilayers composed of N,N,-dimethyl-N,N,-dioctadecylammonium bromide or 1,2-dioleoyl-3-trimethylammonium-propane chloride were spread. Centrally indenting these "nanodrums" with an atomic force microscope tip yields force-indentation curves, which we quantitatively analyze by solving the corresponding shape equations of continuum curvature elasticity. Since the measured response depends in a known way on the system geometry (pore size, tip radius) and on material parameters (bending modulus, lateral tension), this opens the possibility to monitor local elastic properties of lipid membranes in a well-controlled setting.

Curvature-induced accumulation of anisotropic membrane components and raft formation in cylindrical membrane protrusions

Coupling between the area density of anisotropic membrane inclusions and local membrane curvature is considered theoretically for a simple case of nearly flat bilayer membrane with thin tubular membrane protrusions. Lateral phase separation, i.e. accumulation of membrane inclusions in tubular membrane protrusions was obtained for strongly anisotropic inclusions if the radius of tubular protrusions is small enough. In accordance with these theoretical predictions we observed persistence of long tubular membrane protrusions devoid of internal rod-like microtubular structure in cells. We suggest that the stability of the tubular membrane protrusions without the inner supporting rod-like cytoskeleton is a consequence of the accumulation of anisotropic membrane components in the bilayer membrane of these protrusions. Based on the presented theoretical and experimental results it is suggested that previously reported concentration of prominin rafts in thin tubular membrane protrusions may be caused by a curvature-induced accumulation of small prominin-lipid complexes (inclusions) in protrusions and their coalescence into larger rafts.

Implicit solvent simulation models for biomembranes

Fully atomic simulation strategies are infeasible for the study of many processes of interest to membrane biology, biophysics and biochemistry. We review various coarse-grained simulation methodologies with special emphasis on methods and models that do not require the explicit simulation of water. Examples from our own research demonstrate that such models have potential for simulating a variety of biologically relevant phenomena at the membrane surface.

Amphiphile-induced tubular budding of the bilayer membrane

Amphiphile-induced tubular budding of the erythrocyte membrane was studied using transmission electron microscopy. No chiral patterns of the intramembraneous particles were found, either on the cylindrical buds, or on the tubular nanoexovesicles. In agreement with these observations, the tubular budding may be explained by in-plane ordering of anisotropic membrane inclusions in the buds where the difference between the principal membrane curvatures is very large. In contrast to previously reported theories, no direct external mechanical force is needed to explain tubular budding of the bilayer membrane.

Spontaneous curvature induced shape transformations of tubular polymersomes

The behavior of tubular polymersomes is investigated within the framework of the elastic energy model. The transition from a cylindrical tube to a chain of beads connected by small necks is studied in detail. The evolution of a polymersome shape, resulting from a change of the temperature is modeled by the shape transformations caused by a change of the spontaneous curvature. Good agreement between the experiments and the theoretical calculations is found.

A relationship between membrane properties forms the basis of a selectivity mechanism for vesicle self-reproduction

Self-reproduction and the ability to regulate their composition are two essential properties of terrestrial biotic systems. The identification of non-living systems that possess these properties can therefore contribute not only to our understanding of their functioning but also hint at possible prebiotic processes that led to the emergence of life. Growing lipid vesicles have been previously established as having the capacity to self-reproduce. Here it is demonstrated that vesicle self-reproduction can occur only at selected values of vesicle properties. We treat as an example a simple vesicle with membrane elastic properties defined by a membrane bending modulus kappa and spontaneous curvature C0, whose volume variation depends on the membrane hydraulic permeability Lp and whose membrane area doubles in time Td. Vesicle self-reproduction is described as a process in which a growing vesicle first transforms its shape from a sphere into a budded shape of two spheres connected by a narrow neck, and then splits into two spherical daughter vesicles. We show that budded vesicle shapes can be reached only under the condition that Td Lpkappa C0(4)> or =1.85. Thus, in a growing vesicle population containing vesicles of different composition, only the vesicles for which this condition is fulfilled can increase their number in a self-reproducing manner. The obtained results also suggest that at times much longer than Td the number of vesicles with their properties near the "edge" in the system parameter space defined by the minimum value of the product Td Lpkappa C0(4), will greatly exceed the number of any other vesicles.

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.

Raspberry vesicles

We present a method to control the osmotic stress of giant unilamellar vesicles (GUV) and we report an original shrinkage mode of the vesicles: the volume reduction is accompanied by the formation of inverted daughter vesicles which gives the shrunk vesicles the appearance of raspberries. We analyze this peculiar shrinkage and we propose some physical origins for the observed phenomena.

Fission of biological membranes: interplay between dynamin and lipids

Membrane budding and fission are the key stages of ubiquitous processes of formation of intracellular transport vesicles. We present a theoretical consideration of one of the most important types of fission machinery, which is mediated by GTPase dynamin and controlled by lipid composition of the membrane. We suggest a mechanism for collapse of a membrane neck driven by interplay between the dynamin collar and the bending elastic energy of the neck membrane. The collar plays a role of a rigid external skeleton, which imposes mechanical constraints on the neck. We show that in certain conditions the membrane of the neck loses its stability and collapses. Collapse can result from: (i) shifting of the spontaneous curvature of the neck membrane towards negative values, (ii) stretching of the dynamin collar, (iii) tightening of the dynamin collar. The three factors can act separately or concertedly. The suggested model accounts for the major experimental knowledge on membrane fission mediated by dynamin. It includes the elements of all previous models of dynamin action based on different sets of experimental results [Sever et al., Traffic 2000; 1: 385-392]. It reconciles, at least partially, the apparent contradictions between the existing alternative views on biomembrane fission machinery.

Stable tubular microexovesicles of the erythrocyte membrane induced by dimeric amphiphiles

It is experimentally observed that adding a dimeric cationic amphiphile to the erythrocyte suspension results in a release of stable tubular microexovesicles from the erythrocyte membrane. Theoretical description starts from the single-inclusion energy, which takes into account anisotropic shape of the dimeric amphiphile. It is shown explicitly that the tubular shape of the microexovesicle is the extremal to the functional yielding the maximum of the average curvature deviator. It is derived for which intrinsic shapes of the membrane inclusions created by the intercalated amphiphiles the maximum of the average curvature deviator coincides with the minimum of the membrane free energy-thereby determining the stable tubular shape.

Method for efficient shape parametrization of fluid membranes and vesicles

In this paper we describe a method for the parametrization of the shapes adopted by fluid membranes and vesicles. The method is based upon a boundary-value approach to geometry description in which smooth surfaces are produced as the solution to an elliptic partial differential equations. Shape parameters are introduced through the boundary conditions, which control the shape of the vesicle models. In combination with a model for the surface energy and a method for numerical minimization, it is shown how the method can accurately approximate the shapes of both axisymmetric and nonaxisymmetric vesicles over a wide range of control parameters. The particular value of the method lies in its ability to parametrize complicated shapes efficiently, a feature that becomes especially valuable when seeking shapes of minimal energy using direct optimization techniques.

Modulated phases in multicomponent fluid membranes

We investigate the behavior of flexible two-component bilayer and three-component monolayer membranes. The components are assumed to have different spontaneous curvatures, and to mutually phase separate in planar membranes. As a function of temperature, lateral tension and bending rigidity, a rich phase behavior is obtained. In particular, we find three different types of modulated phases. In symmetric bilayers, the excess component assembles at the boundary between oppositely curved domains; in sufficiently asymmetric bilayers, the excess component is found to preferentially assemble in a single layer, with no tendency for segregation to the domain boundaries. We show that the phase behavior of three-component monolayer strongly resembles the behavior of two-component bilayers. In fact, in a certain, restricted region of parameter space, the two models can be shown to be equivalent.

Enhancement of endocytosis due to aminophospholipid transport across the plasma membrane of living cells

Formation of intracellular vesicles is initiated by membrane budding. Here we test the hypothesis that the plasma membrane surface area asymmetry could be a driving force for vesicle formation during endocytosis. The inner layer phospholipid number was therefore increased by adding exogenous aminophospholipids to living cells, which were then translocated from the outer to the inner layer of the membrane by the ubiquitous flippase. Addition of either phosphatidylserine or phosphatidylethanolamine led to an enhancement of endocytosis, showing that the observed acceleration does not depend on the lipid polar head group. Conversely, a closely related aminophospholipid that is not recognized by the flippase, lyso-alpha-phosphatidylserine, inhibited endocytosis, and similar results were obtained with a cholesterol derivative that also remains in the plasma membrane outer layer. Thus an increase of lipid concentration in the inner layer enhanced internalization, whereas an increase of the lipid concentration in the outer layer inhibited internalization. These experiments suggest that transient asymmetries in lipid concentration might contribute to the formation of endocytic vesicles.