Dynamin: functional design of a membrane fission catalyst

Dynamin, best studied for its role in clathrin-mediated endocytosis, is the prototypical member of a family of multidomain GTPases involved in fission and remodeling of multiple organelles. Recent studies have shown that dynamin alone can catalyze fission of membrane tubules and vesicle formation from planar lipid templates. Thus, dynamin appears to be a self-sufficient fission machine. Here we review the biochemical activities and structural features of dynamin required for fission activity. As all changes in membrane topology require energetically unfavorable rearrangements of the lipid bilayer, we discuss the interplay between dynamin and its lipid substrates that are critical to defining a nonleaky pathway to membrane fission. We propose a two-stage model for dynamin-catalyzed fission. In stage one, dynamin's mechanochemical activities induce localized curvature stress and position its lipid-interacting pleckstrin homology domains to create a catalytic center that, in stage two, guides lipid remodeling through hemifission intermediates to drive membrane fission.

Mechanics and dynamics of triglyceride-phospholipid model membranes: Implications for cellular properties and function

We demonstrate here that triolein alters the mechanical properties of phospholipid membranes and induces extraordinary conformational dynamics. Triolein containing membranes exhibit fluctuations up to size range of 100μm and with the help of these are e.g. able to squeeze through narrow passages between neighbouring structures. Triolein-phosphatidylcholine membranes were found to have bending rigidity significantly lower than that of corresponding pure phosphatidylcholine membrane. Moreover, the triolein containing membranes were found to be reluctant to fuse, which is in good accordance with larger lamellar distances observed in the TOPOPC membranes. These findings suggest repulsion between adjacent membranes. We provide a comprehensive discussion on the possible explanations for the observed mechanics and dynamics in the TOPOPC system and on their potential cellular implications.

Effect of the HIV-1 fusion peptide on the mechanical properties and leaflet coupling of lipid bilayers

The fusion peptide (FP) of the human immunodeficiency virus (HIV) is part of the N-terminus of the viral envelope glycoprotein gp41 and is believed to play an important role in the viral entry process. To understand the immediate effect of this peptide on the cell membrane, we have studied the influence of the synthetic FP sequence FP23 on the mechanical properties of model lipid bilayers. For this purpose, giant unilamellar vesicles were prepared from the unsaturated lipid dioleoylphosphatidylcholine mixed in various molar ratios with FP23. The bending stiffness of the vesicles was measured with two different methods: fluctuation analysis and aspiration with micropipettes. The data obtained from both of these approaches show that the bending stiffness of the membrane decreases gradually with increasing concentration of the FP23 in the bilayer. Low concentrations of only a few mol% FP23 are sufficient to decrease the bending stiffness of the lipid bilayer by about a factor of 2. Finally, data obtained for the stretching elasticity modulus of the membrane suggest that the peptide insertion decreases the coupling between the two leaflets of the bilayer.

Effective line tension and contact angles between membrane domains in biphasic vesicles

Inhomogeneities in membranes give rise to localized interactions at the interface between domains in two-component vesicles. The corresponding energy is expressed as a line tension between the two phases. In this paper we study the implications of the thickness mismatch between domains which has been experimentally reported to be of order 20-30% and the conditions under which the induced line tension can destabilize the domains in inhomogeneous vesicles. For asymmetric lipidic membranes we prove an increase of the line tension and the existence of a contact angle. Adsorption of impurities is also examined, our scope being the extension of the Canham-Helfrich model to describe elastic deformations and chemical interactions arising at microscopic scales. This mismatch effect may have important consequences for the stability of very small domains.

The vesicle-to-micelle transformation of phospholipid-cholate mixed aggregates: a state of the art analysis including membrane curvature effects

We revisited the vesicle-to-micelle transformation in phosphatidylcholine-cholate mixtures paying special attention to the lipid bilayer curvature effects. For this purpose, we prepared unilamellar vesicles with different starting sizes (2r(v)=45-120nm). We then studied mixtures of the unilamellar vesicles (1-8mmol kg(-1)) and sodium cholate (0-11.75mmolkg(-1)) by static and dynamic light scattering. The transformation generally comprises at least two, largely parallel phenomena; one increases and the other decreases the average mixed aggregate size. In our view, cholate first induces bilayer fluctuations that lead to vesicle asphericity, and then to lipid bilayer poration followed by sealing/reformation (or fusion). The cholate-containing mixed bilayers, whether in vesicular or open form, project thread-like protrusions with surfactant enriched ends even before complete bilayer solubilisation. Increasing cholate concentration promotes detachment of such protrusions (i.e. mixed micelles formation), in parallel to further softening/destabilising of mixed amphipat bilayers over a broad range of concentrations. Vesicles ultimately fragment into mixed thread-like micelles. Higher cholate relative concentrations yield shorter thread-like mixed micelles. Most noteworthy, the cholate-induced bilayer fluctuations, the propensity for large aggregate formation, the transformation kinetics, and the cholate concentration ensuring complete lipid solubilisation all depend on the starting mean vesicle size. The smallest tested vesicles (2r(v)=45nm), with the highest bilayer curvature, require ~30% less cholate for complete solubilisation than the largest tested vesicles (2r(v)=120nm).

Quantifying Membrane Curvature Generation of Drosophila Amphiphysin N-BAR Domains

Biological membrane functions are coupled to membrane curvature, the regulation of which often involves membrane-associated proteins. The membrane-binding N-terminal amphipathic helix-containing BIN/Amphiphysin/Rvs (N-BAR) domain of amphiphysin is implicated in curvature generation and maintenance. Improving the mechanistic understanding of membrane curvature regulation by N-BAR domains requires quantitative experimental characterization. We have measured tube pulling force modulation by the N-BAR domain of Drosophila amphiphysin (DA-N-BAR) bound to tubular membranes pulled from micropipette-aspirated giant vesicles. We observed that fluorescently-labeled DA-N-BAR showed significantly higher protein density on tubules compared to the connected low-curvature vesicle membrane. Furthermore, we found the equilibrium tube pulling force to be systematically dependent on the aqueous solution concentration of DA-N-BAR, thereby providing the first quantitative assessment of spontaneous curvature generation. At sufficiently high protein concentrations, pulled tubes required no external force to maintain mechanical equilibrium, in agreement with the qualitative spontaneous tubulation previously reported for amphiphysin.

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.

A Generalized System for Photo-Responsive Membrane Rupture in Polymersomes

Polymersomes are vesicles whose membranes are comprised of self-assembled block co-polymers. We recently showed that co-encapsulating conjugated multi-porphyrin dyes in a polymersome membrane with ferritin protein in the aqueous lumen confers photo-lability to the polymersome. In the present study, we illustrate that the photo-lability can be extended to vesicles containing dextran, an inert and inexpensive polysaccharide, as the luminal solute. Here we explore how structural features of the polymersome/porphyrin/dextran composite affect its photo-response. Increasing dextran molecular weight, decreasing block copolymer molecular weight, and altering fluorophore-membrane interactions results in increasing the photo-responsiveness of the polymersomes. Amphiphilic interactions of the luminal encapsulant with the membrane coupled with localized heat production in the hydrophobic bilayer likely cause differential thermal expansion in the membrane and the subsequent membrane rupture. This study suggests a general approach to impart photo-responsiveness to any biomimetic vesicle system without chemical modification, as well as a simple, bio-inert method for constructing photo-sensitive carriers for controlled release of encapsulants.

Understanding detergent effects on lipid membranes: a model study of lysolipids

Lysolipids and fatty acids are the natural products formed by the hydrolysis of phospholipids. Lysolipids and fatty acids form micelles in solution and acts as detergents in the presence of lipid membranes. In this study, we investigate the detergent strength of a homologous series of lyso-phosphatidylcholine lipids (LPCs) on 1-palmitoyl-2-oleyl-sn-glycerol-3-phosphatidylcholine (POPC) lipid membranes by use of isothermal titration calorimetry and vesicle fluctuation analysis. The membrane partition coefficient (K) and critical micelle concentration (cmc) are determined by isothermal titration calorimetry and found to obey an inverse proportionality relation (cmc.K approximately 0.05-0.3). The partition coefficient and critical micelle concentration are used for the analysis of the effect of LPCs on the membrane bending rigidity. The dependency of the bending rigidity on LPC membrane coverage has been analyzed in terms of a phenomenological model based on continuum elastic theory, which yields information about the curvature-inducing properties of the LPC molecule. The results reveal: 1), an increase in the partition coefficient with increasing LPC acyl-chain length; and 2), that the degree of acyl-chain mismatch between LPC and POPC determines the magnitude of the membrane mechanical perturbation per LPC molecule in the membrane. Finally, the three-stage model describing detergent membrane interaction has been extended by a parameter D(MCI), which governs the membrane curvature stability in the detergent concentration range below the cmc-value of the LPC molecule.

Dynamic sorting of lipids and proteins in membrane tubes with a moving phase boundary

Cellular organelle membranes maintain their integrity, global shape, and composition despite vigorous exchange among compartments of lipids and proteins during trafficking and signaling. Organelle homeostasis involves dynamic molecular sorting mechanisms that are far from being understood. In contrast, equilibrium thermodynamics of membrane mixing and sorting, particularly the phase behavior of binary and ternary model membrane mixtures and its coupling to membrane mechanics, is relatively well characterized. Elucidating the continuous turnover of live cell membranes, however, calls for experimental and theoretical membrane models enabling manipulation and investigation of directional mass transport. Here we introduce the phenomenon of curvature-induced domain nucleation and growth in membrane mixtures with fluid phase coexistence. Membrane domains were consistently observed to nucleate precisely at the junction between a strongly curved cylindrical (tube) membrane and a pipette-aspirated giant unilamellar vesicle. This experimental geometry mimics intracellular sorting compartments, because they often show tubular-vesicular membrane regions. Nucleated domains at tube necks were observed to present diffusion barriers to the transport of lipids and proteins. We find that curvature-nucleated domains grow with characteristic parabolic time dependence that is strongly curvature-dependent. We derive an analytical model that reflects the observed growth dynamics. Numerically calculated membrane shapes furthermore allow us to elucidate mechanical details underlying curvature-dependent directed lipid transport. Our observations suggest a novel dynamic membrane sorting principle that may contribute to intracellular protein and lipid sorting and trafficking.

Diffusing proteins on a fluctuating membrane: analytical theory and simulations

Using analytical calculations and computer simulations, we consider both the lateral diffusion of a membrane protein and the fluctuation spectrum of the membrane in which the protein is embedded. The membrane protein interacts with the membrane shape through its spontaneous curvature and bending rigidity. The lateral motion of the protein may be viewed as diffusion in an effective potential, hence, the effective mobility is always reduced compared to the case of free diffusion. Using a rigorous path-integral approach, we derive an analytical expression for the effective diffusion coefficient for small ratios of temperature and bending rigidity, which is the biologically relevant limit. Simulations show very good quantitative agreement with our analytical result. The analysis of the correlation functions contributing to the diffusion coefficient shows that the correlations between the stochastic force of the protein and the response in the membrane shape are responsible for the reduction. Our quantitative analysis of the membrane height correlation spectrum shows an influence of the protein-membrane interaction causing a distinctly altered wave-vector dependence compared to a free membrane. Furthermore, the time correlations exhibit the two relevant time scales of the system: that of membrane fluctuations and that of lateral protein diffusion with the latter typically much longer than the former. We argue that the analysis of the long-time decay of membrane height correlations can thus provide a new means to determine the effective diffusion coefficient of proteins in the membrane.

Dynamics of multicomponent vesicles in a viscous fluid

We develop and investigate numerically a thermodynamically consistent model of two-dimensional multicomponent vesicles in an incompressible viscous fluid. The model is derived using an energy variation approach that accounts for different lipid surface phases, the excess energy (line energy) associated with surface phase domain boundaries, bending energy, spontaneous curvature, local inextensibility and fluid flow via the Stokes equations. The equations are high-order (fourth order) nonlinear and nonlocal due to incompressibil-ity of the fluid and the local inextensibility of the vesicle membrane. To solve the equations numerically, we develop a nonstiff, pseudo-spectral boundary integral method that relies on an analysis of the equations at small scales. The algorithm is closely related to that developed very recently by Veerapaneni et al. [81] for homogeneous vesicles although we use a different and more efficient time stepping algorithm and a reformulation of the inextensibility equation. We present simulations of multicomponent vesicles in an initially quiescent fluid and investigate the effect of varying the average surface concentration of an initially unstable mixture of lipid phases. The phases then redistribute and alter the morphology of the vesicle and its dynamics. When an applied shear is introduced, an initially elliptical vesicle tank-treads and attains a steady shape and surface phase distribution. A sufficiently elongated vesicle tumbles and the presence of different surface phases with different bending stiffnesses and spontaneous curvatures yields a complex evolution of the vesicle morphology as the vesicle bends in regions where the bending stiffness and spontaneous curvature are small.

Measurement of the membrane curvature preference of phospholipids reveals only weak coupling between lipid shape and leaflet curvature

In biological processes, such as fission, fusion and trafficking, it has been shown that lipids of different shapes are sorted into regions with different membrane curvatures. This lipid sorting has been hypothesized to be due to the coupling between the membrane curvature and the lipid's spontaneous curvature, which is related to the lipid's molecular shape. On the other hand, theoretical predictions and simulations suggest that the curvature preference of lipids, due to shape alone, is weaker than that observed in biological processes. To distinguish between these different views, we have directly measured the curvature preferences of several lipids by using a fluorescence-based method. We prepared small unilamellar vesicles of different sizes with a mixture of egg-PC and a small mole fraction of N-nitrobenzoxadiazole (NBD)-labeled phospholipids or lysophospholipids of different chain lengths and saturation, and measured the NBD equilibrium distribution across the bilayer. We observed that the transverse lipid distributions depended linearly on membrane curvature, allowing us to measure the curvature coupling coefficient. Our measurements are in quantitative agreement with predictions based on earlier measurements of the spontaneous curvatures of the corresponding nonfluorescent lipids using X-ray diffraction. We show that, though some lipids have high spontaneous curvatures, they nevertheless showed weak curvature preferences because of the low values of the lipid molecular areas. The weak curvature preference implies that the asymmetric lipid distributions found in biological membranes are not likely to be driven by the spontaneous curvature of the lipids, nor are lipids discriminating sensors of membrane curvature.

Bending stiffness depends on curvature of ternary lipid mixture tubular membranes

Lipid and protein sorting and trafficking in intracellular pathways maintain cellular function and contribute to organelle homeostasis. Biophysical aspects of membrane shape coupled to sorting have recently received increasing attention. Here we determine membrane tube bending stiffness through measurements of tube radii, and demonstrate that the stiffness of ternary lipid mixtures depends on membrane curvature for a large range of lipid compositions. This observation indicates amplification by curvature of cooperative lipid demixing. We show that curvature-induced demixing increases upon approaching the critical region of a ternary lipid mixture, with qualitative differences along two roughly orthogonal compositional trajectories. Adapting a thermodynamic theory earlier developed by M. Kozlov, we derive an expression that shows the renormalized bending stiffness of an amphiphile mixture membrane tube in contact with a flat reservoir to be a quadratic function of curvature. In this analytical model, the degree of sorting is determined by the ratio of two thermodynamic derivatives. These derivatives are individually interpreted as a driving force and a resistance to curvature sorting. We experimentally show this ratio to vary with composition, and compare the model to sorting by spontaneous curvature. Our results are likely to be relevant to the molecular sorting of membrane components in vivo.

Equilibrium theory and geometrical constraint equation for two-component lipid bilayer vesicles

This paper aims at the general mathematical framework for the equilibrium theory of two-component lipid bilayer vesicles. To take into account the influences of the local compositions together with the mean curvature and Gaussian curvature of the membrane surface, a general potential functional is constructed. We introduce two kinds of virtual displacement modes: the normal one and the tangential one. By minimizing the potential functional, the equilibrium differential equations and the boundary conditions of two-component lipid vesicles are derived. Additionally, the geometrical constraint equation and geometrically permissible condition for the two-component lipid vesicles are presented. The physical, mathematical, and biological meanings of the equilibrium differential equations and the geometrical constraint equations are discussed. The influences of physical parameters on the geometrically permissible phase diagrams are predicted. Numerical results can be used to explain recent experiments.

Emerging roles for lipids in shaping membrane-protein function

Studies of membrane proteins have revealed a direct link between the lipid environment and the structure and function of some of these proteins. Although some of these effects involve specific chemical interactions between lipids and protein residues, many can be understood in terms of protein-induced perturbations to the membrane shape. The free-energy cost of such perturbations can be estimated quantitatively, and measurements of channel gating in model systems of membrane proteins with their lipid partners are now confirming predictions of simple models.

Sorting of lipids and proteins in membrane curvature gradients

The sorting of lipids and proteins in cellular trafficking pathways is a process of central importance in maintaining compartmentalization in eukaryotic cells. However, the mechanisms behind these sorting phenomena are currently far from being understood. Among several mechanistic suggestions, membrane curvature has been invoked as a means to segregate lipids and proteins in cellular sorting centers. To assess this hypothesis, we investigate the sorting of lipid analog dye trace components between highly curved tubular membranes and essentially flat membranes of giant unilamellar vesicles. Our experimental findings indicate that intracellular lipid sorting, contrary to frequent assumptions, is unlikely to occur by lipids fitting into membrane regions of appropriate curvature. This observation is explained in the framework of statistical mechanical lattice models that show that entropy, rather than curvature energy, dominates lipid distribution in the absence of strongly preferential lateral intermolecular interactions. Combined with previous findings of curvature induced phase segregation, we conclude that lipid cooperativity is required to enable efficient sorting. In contrast to lipid analog dyes, the peripheral membrane binding protein Cholera toxin subunit B is effectively curvature-sorted. The sorting of Cholera toxin subunit B is rationalized by statistical models. We discuss the implications of our findings for intracellular sorting mechanisms.

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.

Curvature-driven lipid sorting needs proximity to a demixing point and is aided by proteins

Sorting of lipids and proteins is a key process allowing eukaryotic cells to execute efficient and accurate intracellular transport and to maintain membrane homeostasis. It occurs during the formation of highly curved transport intermediates that shuttle between cell compartments. Protein sorting is reasonably well described, but lipid sorting is much less understood. Lipid sorting has been proposed to be mediated by a physical mechanism based on the coupling between membrane composition and high curvature of the transport intermediates. To test this hypothesis, we have performed a combination of fluorescence and force measurements on membrane tubes of controlled diameters pulled from giant unilamellar vesicles. A model based on membrane elasticity and nonideal solution theory has also been developed to explain our results. We quantitatively show, using 2 independent approaches, that a difference in lipid composition can build up between a curved and a noncurved membrane. Importantly, and consistent with our theory, lipid sorting occurs only if the system is close to a demixing point. Remarkably, this process is amplified when even a low fraction of lipids is clustered upon cholera toxin binding. This can be explained by the reduction of the entropic penalty of lipid sorting when some lipids are bound together by the toxin. Our results show that curvature-induced lipid sorting results from the collective behavior of lipids and is even amplified in the presence of lipid-clustering proteins. In addition, they suggest a generic mechanism by which proteins can facilitate lipid segregation in vivo.

Phase-field modeling of the dynamics of multicomponent vesicles: Spinodal decomposition, coarsening, budding, and fission

We develop a thermodynamically consistent phase-field model to simulate the dynamics of multicomponent vesicles. The model accounts for bending stiffness, spontaneous curvature, excess (surface) energy, and a line tension between the coexisting surface phases. Our approach is similar to that recently used by Wang and Du [J. Math. Biol. 56, 347 (2008)] with a key difference. Here, we concentrate on the dynamic evolution and solve the surface mass conservation equation explicitly; this equation was not considered by Wang and Du. The resulting fourth-order strongly coupled system of nonlinear nonlocal equations are solved numerically using an adaptive finite element numerical method. Although the system is valid for three dimensions, we limit our studies here to two dimensions where the vesicle is a curve. Differences between the spontaneous curvatures and the bending rigidities of the surface phases are found numerically to lead to the formation of buds, asymmetric vesicle shapes and vesicle fission even in two dimensions. In addition, simulations of configurations far from equilibrium indicate that phase separation via spinodal decomposition and coarsening not only affect the vesicle shape but also that the vesicle shape affects the phase separation dynamics, especially the coarsening and may lead to lower energy states than might be achieved by evolving initially phase-separated configurations.

Diffusion of macromolecules on lipid vesicles

Diffusion of macromolecules on a surface of lipid vesicles of different reduced volume and geometry is investigated. It is assumed that the macromolecules deform the surface of the vesicles by inducing the spontaneous curvature which is proportional to their concentration. We study how nonuniform distribution of macromolecules is reflected in the shape of the vesicles and how the shape of the vesicles influences the diffusion process.

Biophysical approaches to protein-induced membrane deformations in trafficking

Membrane traffic requires membrane deformation to generate vesicles and tubules. Strong evidence suggests that assembly of curvature-active proteins can drive such membrane shape changes. Well-documented pathways often involve protein scaffolds, in particular coats (clathrin or COP). However, membrane curvature should, in principle, be influenced by any protein binding asymmetrically on a membrane; large membrane morphological changes could result from their aggregation. In the case of Shiga toxin or viral matrix proteins, tubules and buds appear to result from the cargo-driven formation of protein-lipid nanodomains, showing that collective protein behaviour is crucial in the process. We argue here that a combination of in vitro experiments on giant unilamellar vesicles and theoretical modelling based on statistical physics is ideally suited to tackle these collective effects.

Polymer-induced tubulation in lipid vesicles

A mechanism of extraction of tubular membranes from a lipid vesicle is presented. A concentration gradient of anchoring amphiphilic polymers generates tubes from budlike vesicle protrusions. We explain this mechanism in the framework of the Canham-Helfrich model. The energy profile is analytically calculated and a tube with a fixed length, corresponding to an energy minimum, is obtained in a certain regime of parameters. Further, using a phase-field model, we corroborate these results numerically. We obtain the growth of tubes when a polymer source is added, and the budlike shape after removal of the polymer source, in accordance with recent experimental results.

Path integrals for stiff polymers applied to membrane physics

Path integrals similar to those describing stiff polymers arise in the Helfrich model for membranes. We show how these types of path integrals can be evaluated and apply our results to study the thermodynamics of a minority stripe phase in a bulk membrane. The fluctuation induced contribution to the line tension between the stripe and the bulk phase is computed. Also the effective interaction between the interfaces of the two phases can be computed. Explicit forms are given for this Casmir-like interaction in the tensionless case where the two phases have differing bending rigidities.

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.

The interface width of separated two-component lipid membranes

We study two-component vesicles with coherent domains of the components, where the domains are separated by an interface. The components are characterized by different spontaneous curvatures. No line tension term or interactions between components are included in the model. The influence of the interface width and interface location on the bending energy and shape of the vesicles is studied. How the spontaneous curvature of one component influences the concentration profile is examined. The vesicles of oblate and prolate geometries are investigated.

Stability of biphasic vesicles with membrane embedded proteins

The basic physical properties of homogeneous membranes are relatively well known, while the effects of inhomogeneities with membranes are very much an active field of study. In this paper, a biphasic lipid vesicle with membrane embedded proteins is investigated. To take into account the influences of the proteins, a simple phenomenological coupling between the local fraction of proteins and the mean curvature square is suggested. By minimizing the energy of system, the E-L equations and boundary conditions are obtained and solved analytically for vesicle with a simple shape. Besides, stability phase diagrams and stability factor are put forward by linear perturbation analysis. Our results show two different situations which are strongly dependent on the nature of the proteins: a regime of easy instability when the proteins are strongly coupled to the membrane and a regime of difficult instability.

Domain registration in raft-mimicking lipid mixtures studied using polymer-tethered lipid bilayers

The degree of domain registration in a liquid-ordered/liquid-disordered phase-separating lipid mixture consisting of 1-stearoyl-2-oleoyl-sn-3-phosphocholine, egg sphingomyelin, and cholesterol (molar mixing ratio of 1:1:1) was studied using three different planar lipid bilayer architectures distinguished by their bilayer-substrate distance d using epifluorescence microscopy. The bilayer systems, which were built layer by layer using Langmuir-Blodgett/Schaefer film depositions, included a solid-supported bilayer (d approximately 15 A) and two polymer-supported bilayers with d approximately 30 A and d approximately 58 A, respectively. Complete domain registration between Langmuir-Blodgett and Schaefer monolayer domains was observed for d approximately 58 A but not in the cases when d approximately 15 A and d approximately 30 A. Building the bilayer layer by layer guaranteed that any preexisting domains were not in registration initially; our data show that the domain registration observed was not caused by lipid flip-flop or by lateral rearrangement of preexisting large-scale domains. Instead, additional studies on bilayer systems with asymmetric lipid composition indicate that preexisting domains in the Langmuir-Blodgett monolayer induce the formation of completely registered domains in the opposite Schaefer monolayer. This study provides insight into possible biophysical mechanisms of transbilayer domain coupling. Our findings support the concept that the formation of transbilayer signaling platforms based on registered raft domains may occur without the active involvement of membrane-spanning proteins.

Morphology and phase behavior of two-component lipid membranes

The stability and shapes of domains with different bending rigidities in lipid membranes are investigated. These domains can be formed from the inclusion of an impurity in a lipid membrane or from the phase separation within the membrane. We show that, for weak line tensions, surface tensions and finite spontaneous curvatures, an equilibrium phase of protruding circular domains or striped domains may be obtained. We also predict a possible phase transition between the investigated morphologies.

Influence of rigid inclusions on the bending elasticity of a lipid membrane

We model the influence of rigid inclusions on the curvature elasticity of a lipid membrane. Our focus is on conelike transmembrane inclusions that are able to induce long-range deformations in the host bilayer membrane. The elastic properties of the membrane are described in terms of curvature and tilt elasticity. The latter adds an additional degree of freedom that allows the membrane to accommodate an inclusion not only through a curvature deformation but also via changes in lipid tilt. Using a (mean-field level) cell model for homogeneously distributed inclusions in a small membrane segment of prescribed (mesoscopic-scale) spherical shape, we calculate the optimal microscopic-scale deviation of the membrane shape around the intercalated inclusions and the corresponding free energy, analytically. We show that the lipid tilt degree of freedom can lead to local softening of the inclusion-containing lipid bilayer segment. The predicted softening requires a sufficiently small value of the tilt modulus; its origin lies in the reduction of the excess membrane-inclusion interaction energy. We compare our results to the case of suppressed microscopic shape relaxation. Here, too, local softening of the membrane is possible.

Effective creases and contact angles between membrane domains with high spontaneous curvature

We show that the short-scale elastic distortions that are excited in the vicinity of the joint between different lipidic membrane domains (at a scale of approximately 10nm) may produce a "crease" from the point of view of the standard elastic description of membranes, i.e., an effective discontinuity in the membrane slope at the level of Helfrich's theory. This "discontinuity" may be accounted for by introducing a line tension with an effective angular dependence. We show that domains bearing strong spontaneous curvatures, such as biological rafts, should exhibit creases with a finite contact angle, almost prescribed, corresponding to a steep extremum of the line energy. Finite contact angles might also occur in symmetric membranes from the recruitment of impurities at the boundary.

Budding and fission of a multiphase vesicle

We present a model of bi-phasic vesicles in the limit of large surface tension. In this regime, the vesicle is completely stretched and well described by two spherical caps with a fold, which concentrates the membrane stress. The conservation laws and geometric constraints restrict the space of possible shapes to a pair of solutions labeled by a parameter sigma given by line tension/pressure. For a given value of sigma, the two solutions differ by the length of the interface between domains. For a critical value, sigmac, the two vesicle shapes become identical and no connected solution exists above this critical value. This model sheds new light on two proposed mechanisms (osmotic shocks and molecule absorption) to explain the budding and the fission in recent experiments.

Fluctuation-induced interactions between domains in membranes

We study a model lipid bilayer composed of a mixture of two incompatible lipid types which have a natural tendency to segregate in the absence of membrane fluctuations. The membrane is mechanically characterized by a local bending rigidity kappa(phi) which varies with the average local lipid composition phi. We show, in the case where kappa varies weakly with phi, that the effective interaction between lipids of the same type either can be everywhere attractive or can have a repulsive component at intermediate distances greater than the typical lipid size. When this interaction has a repulsive component, it can prevent macrophase separation and lead to separation in mesophases with a finite domain size. This effect could be relevant to certain experimental and numerical observations of mesoscopic domains in such systems.

Coupling between vesicle shape and lateral distribution of mobile membrane inclusions

Membrane inclusions such as membrane-embedded peptides or proteins exhibit a curvature-dependent interaction with the surrounding lipid matrix due to the mismatch between their intrinsic curvature and the local membrane curvature. This interaction causes an inhomogeneous lateral distribution of the inclusions and a corresponding adjustment of the vesicle shape. We have studied theoretically the axisymmetric equilibrium shapes of lipid vesicles with mobile inclusions, taking into account that the membrane free energy includes the elastic energy of the lipid bilayer and a contribution due to an inclusion-membrane interaction. Equations describing the shape are derived by minimizing the total free energy at fixed membrane area, enclosed volume, and number of inclusions and are then solved numerically. It is shown that vesicle shape may assume a symmetry that differs from that of the vesicle with no inclusions. If the inclusion-membrane interaction exceeds a certain value, there is no axisymmetric solution of the equations with a continuous and derivable lateral density of inclusions over the whole area of the vesicle. When approaching the critical vesicle shape, the shapes obtained differ qualitatively from those described by the area difference elasticity model of the elastic properties of lipid membranes. In general, vesicle shapes adjust to the presence of inclusions by increasing regions with favorable curvature and decreasing regions of unfavorable curvature in a way such that the lateral distribution of inclusions becomes inhomogeneous.

Alamethicin influence on the membrane bending elasticity

We investigate the bending elasticity of lipid membranes with the increase of the alamethicin concentrations in the membrane via analysis of the thermally induced shape fluctuations of quasi-spherical giant vesicles. Our experimental results prove the strong influence of alamethicin molecules on the bending elasticity of diphytanoyl phosphatidylcholine and dilauroyl phosphatidylcholine membranes even in the range of very low peptide concentrations (less than 10(-3) mol/mol in the membrane). The results presented in this work, testify to the peripheral orientation of alamethicin molecules at low peptide concentrations in the membrane for both types of lipid bilayers. An upper limit of the concentration of the peptide in the membrane is determined below which the system behaves as an ideal two-dimensional solution and the peptide molecules have a planar orientation in the membrane.

Fluctuations and instability of a biological membrane induced by interaction with macromolecules

This paper studies the dynamics and fluctuations of a phospholipidic membrane in the presence of a diffusion field of foreign molecules, such as polymers, proteins, etc., which have the ability to adsorb on, and to desorb from, the membrane. We develop a model that includes, besides hydrodynamics, molecular diffusion in the surrounding fluid and lateral diffusion (i.e., diffusion along the membrane) as well as the kinetics of attachment and detachment to and from the membrane. This model is exploited here for the case of a free membrane which is globally at equilibrium while the nonequilibrium part will be presented in the future. We show that if the coupling between the membrane and the molecules is strong enough, the flat membrane can suffer a morphological instability. The numerical calculation in the nonlinear regime reveals budding, and an initial stage of spontaneous vesicle emission. When the condition of stability is satisfied we show how kinetic fluctuations lead to a rich variety of dynamical behaviors expressing the dominant dissipation mechanisms. We show that in the limit of well separated length scales related to the physical mechanisms that enter into play, the width of the membrane fluctuations exhibits various dynamical scalings with universal scaling exponents. It is shown that the usual behavior with time w approximately t(1/3) is altered in various time and length scales of interest. For example, we find that , w approximately t(1/4), w approximately t(1/2), and w approximately [t ln(t)](1/2), depending on which physical mechanism limits the membrane fluctuations on the time scale under consideration. The experimental study of the fluctuation spectrum can be viewed as a precious tool in order to have access to the underlying microscopic physical mechanisms.

Fluctuation spectrum of membranes with anchored linear and star polymers

The effect of linear homopolymers, diblock copolymers, and star polymers anchored to a membrane on the membrane's fluctuation spectrum is investigated for low grafting densities. Due to the nonlocality of the polymer-membrane interaction, the effective bending rigidity kappa(eff)(q) of the composite membrane is found to depend strongly on the wave vector q of the membrane undulations. Analytical calculations for ideal linear chains and simulations for ideal and self-avoiding linear chains as well as for star polymers are presented. The analytical calculations are based on the Green's function approach of Bickel and Marques [Eur. Phys. J. E 9, 349 (2002)]; for the simulations the Monte Carlo method is used. The functional form of kappa(eff)(q) differs for end-grafted chains and diblock copolymers. In general, the polymer effect is most pronounced for undulations on length scales larger than or comparable to the polymer size, and decreases rapidly for smaller undulation wavelengths. Anchored linear chains always increase kappa; anchored star polymers may increase as well as decrease kappa, depending on whether they are anchored symmetrically or asymmetrically to the membrane.

Shape equations and curvature bifurcations induced by inhomogeneous rigidities in cell membranes

This article aims at two objectives: one is the shape equation for the equilibrium configurations of biomembranes with heterogeneous rigidities; another is the possible mechanism for curvature bifurcations in various biomembranes such as human red blood cells (RBC). The shape equation is established by treating the inhomogeneous biomembrane as a lipid bilayer vesicle containing inclusions or impurities. After careful investigation of the equation, the rigidity gradient is found to be an initial "driving force" that may destabilize the biomembrane and stimulate shape transitions, and the concept (or mechanism) termed "curvature bifurcations induced by rigidity gradients" is suggested. Various post-bifurcation modes recording the new equilibrium configurations are disclosed. A few post-bifurcation modes are found to coincide well with some practical shape transitions in cells such as the cup-like shape (stomatocyte) transition and spiculated shape (echinocyte) transition in RBC.

Budding and domain shape transformations in mixed lipid films and bilayer membranes

We study the stability and shapes of domains with spontaneous curvature in fluid films and membranes, embedded in a surrounding membrane with zero spontaneous curvature. These domains can result from the inclusion of an impurity in a fluid membrane or from phase separation within the membrane. We show that for small but finite line and surface tensions and for finite spontaneous curvatures, an equilibrium phase of protruding circular domains is obtained at low impurity concentrations. At higher concentrations, we predict a transition from circular domains, or caplets, to stripes. In both cases, we calculate the shapes of these domains within the Monge representation for the membrane shape. With increasing line tension, we show numerically that there is a budding transformation from stable protruding circular domains to spherical buds. We calculate the full phase diagram and demonstrate two triple points of, respectively, bud-flat-caplet and flat-stripe-caplet coexistence.

General Mathematical Frame for Open or Closed Biomembranes (Part I): Equilibrium Theory and Geometrically Constraint Equation

This paper aims at constructing a general mathematical frame for the equilibrium theory of open or closed biomembranes. Based on the generalized potential functional, the equilibrium differential equation for open biomembrane (with free edge) or closed one (without boundary) is derived. The boundary conditions for open biomembranes are obtained. Besides, the geometrically constraint equation for the existence, formation and disintegration of open or closed biomembranes is revealed. The physical and biological meanings of the equilibrium differential equation and the geometrically constraint equation are discussed. Numerical simulation results for axisymmetric open biomembranes show the effectiveness and convenience of the present theory.

Nonequilibrium patterns and shape fluctuations in reactive membranes

A simple kinetic model of a two-component deformable and reactive bilayer is presented. The two differently shaped components are interconverted by a nonequilibrium reaction, and a phenomenological coupling between local composition and curvature is proposed. When the two components are not miscible, linear stability analysis predicts, and numerical simulations show, the formation of stationary nonequilibrium composition/curvature patterns whose typical size is determined by the reactive process. For miscible components, a linearization of the dynamic equations is performed in order to evaluate the correlation function for shape fluctuations from which the behavior of these systems in micropipet aspiration experiments can be predicted.

Passive or active fluctuations in membranes containing proteins

We have experimentally investigated the effect of a transmembrane protein, the Ca2+-ATPase, on shape fluctuations of giant vesicles. By using the micropipette method, we have measured a substantial renormalization of the bending modulus due to the presence of proteins in the membrane. Moreover, we have produced the first quantitative measurement of the active force dipole associated with the amplification of the fluctuations when the proteins are activated by adenosine 5'-triphosphate (ATP).

Thermodynamics of membrane elasticity--a molecular level approach to one- and two-component fluid amphiphilic membranes, part II: applications

The theoretical framework developed in the accompanying publication is applied to a number of experimentally relevant amphiphilic systems. These include the influence of thermodynamic conditions and non-ideal mixing on bending elasticity, ellipsoidal modes of microemulsions and vesicles, hydrocarbon chain coupling in bilayers and the effect of osmotic and hydrostatic pressure on inverse hexagonal (H(II)) phases. It is found that the bending moduli at constant surface tension and constant chemical potentials are markedly different only for two-component membranes and non-ideal mixing with a tendency towards phase separation. The results indicate that non-ideal mixing is the main reason behind the experimentally observed strong compositional dependence of membrane elasticity. It is generally recommended to prefer the bending elastic moduli at constant chemical potentials to those at constant surface tension. A comparison between the area-difference-elasticity (ADE) model and explicit free energy calculations using a molecular model shows a good qualitative agreement for the sphere-to-ellipsoid transition of vesicles. Results for different free energy models of the hydrocarbon chains of amphiphilic molecules suggest that monolayer-monolayer chain coupling is responsible for the relatively higher bending stiffness of bilayers compared to single monolayers. For H(II)-phases an instability at negative pressure differences is predicted.

A new method for the reconstitution of membrane proteins into giant unilamellar vesicles

In this work, we have investigated a new and general method for the reconstitution of membrane proteins into giant unilamellar vesicles (GUVs). We have analyzed systematically the reconstitution of two radically different membrane proteins, the sarcoplasmic reticulum Ca(2+)-ATPase and the H(+) pump bacteriorhodopsin. In a first step, our method involved a detergent-mediated reconstitution of solubilized membrane proteins into proteoliposomes of 0.1-0.2 microm in size. In a second step, these preformed proteoliposomes were partially dried under controlled humidity followed, in a third step, by electroswelling of the partially dried film to give GUVs. The physical characteristics of GUVs were analyzed in terms of morphology, size, and lamellarity using phase-contrast and differential interference contrast microscopy. The reconstitution process was further characterized by analyzing protein incorporation and biological activity. Both membrane proteins could be homogeneously incorporated into GUVs at lipid/protein ratios ranging from 5 to 40 (w/w). After reconstitution, both proteins retained their biological activity as demonstrated by H(+) or Ca(2+) pumping driven by bacteriorhodopsin or Ca(2+)-ATPase, respectively. This constitutes an efficient new method of reconstitution, leading to the production of large unilamellar membrane protein-containing vesicles of more than 20 microm in diameter, which should prove useful for functional and structural studies through the use of optical microscopy, optical tweezers, microelectrodes, or atomic force microscopy.