Tension-stabilized pores in giant vesicles: determination of pore size and pore line tension

Kinetics of Hole Nucleation in Biomembrane Rupture

The core component of a biological membrane is a fluid-lipid bilayer held together by interfacial-hydrophobic and van der Waals interactions, which are balanced for the most part by acyl chain entropy confinement. If biomembranes are subjected to persistent tensions, an unstable (nanoscale) hole will emerge at some time to cause rupture. Because of the large energy required to create a hole, thermal activation appears to be requisite for initiating a hole and the activation energy is expected to depend significantly on mechanical tension. Although models exist for the kinetic process of hole nucleation in tense membranes, studies of membrane survival have failed to cover the ranges of tension and lifetime needed to critically examine nucleation theory. Hence, rupturing giant (~20 μm) membrane vesicles ultra-slowly to ultra-quickly with slow to fast ramps of tension, we demonstrate a method to directly quantify kinetic rates at which unstable holes form in fluid membranes, at the same time providing a range of kinetic rates from < 0.01 s(-1) to > 100 s(-1). Measuring lifetimes of many hundreds of vesicles, each tensed by precision control of micropipet suction, we have determined the rates of failure for vesicles made from several synthetic phospholipids plus 1:1 mixtures of phospho- and sphingo-lipids with cholesterol, all of which represent prominent constituents of eukaryotic cell membranes. Plotted on a logarithmic scale, the failure rates for vesicles are found to rise dramatically with increase of tension. Converting the experimental profiles of kinetic rates into changes of activation energy versus tension, we show that the results closely match expressions for thermal activation derived from a combination of meso-scale theory and molecular-scale simulations of hole formation. Moreover, we demonstrate a generic approach to transform analytical fits of activation energies obtained from rupture experiments into energy landscapes characterizing the process hole nucleation along the reaction coordinate defined by hole size.

Toward understanding protocell mechanosensation

Mechanosensitive (MS) channels can prevent bacterial bursting during hypo-osmotic shocks by responding to increases in lateral tension at the membrane level through an integrated and coordinated opening mechanism. Mechanical regulation in protocells could have been one of the first mechanisms to evolve in order to preserve their integrity against changing environmental conditions. How has the rich functional diversity found in present cells been created throughout evolution, and what did the primordial MS channels look like? This review has been written with the aim of identifying which factors may have been important for the appearance of the first osmotic valve in a prebiotic context, and what this valve may have been like. It highlights the mechanical properties of lipid bilayers, the association of peptides as aggregates in membranes, and the conservation of sequence motifs as central aspects to understand the evolution of proteins that gate below the tension required for spontaneous pore formation and membrane rupture. The arguments developed here apply to both MscL and MscS homologs, but could be valid to mechano-susceptible proteins in general.

Minimum energy path to membrane pore formation and rupture

We combine dynamic self-consistent field theory with the string method to calculate the minimum energy path to membrane pore formation and rupture. In the regime where nucleation can occur on experimentally relevant time scales, the structure of the critical nucleus is between a solvophilic stalk and a locally thinned membrane. Classical nucleation theory fails to capture these molecular details and significantly overestimates the free energy barrier. Our results suggest that thermally nucleated rupture may be an important factor for the low rupture strains observed in lipid membranes.

Adhesion and merging of lipid bilayers: a method for measuring the free energy of adhesion and hemifusion

Lipid bilayers can be induced to adhere to each other by molecular mediators, and, depending on the lipid composition, such adhesion can lead to merging of the contacting monolayers in a process known as hemifusion. Such bilayer-bilayer reactions have never been systematically studied. In the course of our studies of membrane-active molecules, we encountered such reactions. We believe that they need to be understood whenever bilayer-bilayer interactions take place, such as during membrane fusion. For illustration, we discuss three examples: spontaneous adhesion between phospholipid bilayers induced by low pH, polymer-induced osmotic depletion attraction between lipid bilayers, and anionic lipid bilayers cross-bridged by multicationic peptides. Our purpose here is to describe a general method for studying such interactions. We used giant unilamellar vesicles, each of which was aspirated in a micropipette so that we could monitor the tension of the membrane and the membrane area changes during the bilayer-bilayer interaction. We devised a general method for measuring the free energy of adhesion or hemifusion. The results show that the energies of adhesion or hemifusion of lipid bilayers could vary over 2 orders of magnitude from -1 to -50 × 10(-5) J/m(2) in these examples alone. Our method can be used to measure the energy of transition in each step of lipid transformation during membrane fusion. This is relevant for current research on membrane fusion, which focuses on how fusion proteins induce lipid transformations.

A lipocentric view of peptide-induced pores

Although lipid membranes serve as effective sealing barriers for the passage of most polar solutes, nonmediated leakage is not completely improbable. A high activation energy normally keeps unassisted bilayer permeation at a very low frequency, but lipids are able to self-organize as pores even in peptide-free and protein-free membranes. The probability of leakage phenomena increases under conditions such as phase coexistence, external stress or perturbation associated to binding of nonlipidic molecules. Here, we argue that pore formation can be viewed as an intrinsic property of lipid bilayers, with strong similarities in the structure and mechanism between pores formed with participation of peptides, lipidic pores induced by different types of stress, and spontaneous transient bilayer defects driven by thermal fluctuations. Within such a lipocentric framework, amphipathic peptides are best described as pore-inducing rather than pore-forming elements. Active peptides bound to membranes can be understood as a source of internal surface tension which facilitates pore formation by diminishing the high activation energy barrier. This first or immediate action of the peptide has some resemblance to catalysis. However, the presence of membrane-active peptides has the additional effect of displacing the equilibrium towards the pore-open state, which is then maintained over long times, and reducing the size of initial individual pores. Thus, pore-inducing peptides, regardless of their sequence and oligomeric organization, can be assigned a double role of increasing the probability of pore formation in membranes to high levels as well as stabilizing these pores after they appear.

Effects of surface pressure and internal friction on the dynamics of shear-driven supported lipid bilayers

Supported lipid bilayers (SLBs) are one of the most common model systems for cell membrane studies. We have previously found that when applying a bulk flow of liquid above an SLB the lipid bilayer and its constituents move in the direction of the bulk flow in a rolling type of motion, with the lower monolayer being essentially stationary. In this study, a theoretical platform is developed to model the dynamic behavior of a shear-driven SLB. In most regions of the moving SLB, the dynamics of the lipid bilayer is well explained by a balance between the hydrodynamic shear force arising from the bulk flow above the lipid bilayer and the friction between the upper and lower monolayers of the SLB. These two forces result in a drift velocity profile for the lipids in the upper monolayer of the SLB that is highest at the center of the channel and decreases to almost zero at the corners of the channel. However, near the front of an advancing SLB a very different flow behavior is observed, showing an almost constant drift velocity of the lipids over the entire bilayer front. In this region, the motion of the SLB is significantly influenced by gradients in the surface pressure as well as internal friction due to molecules that have accumulated at the front of the SLB. It is shown that even a modest surface fraction of accumulated molecules (∼1%) can drastically affect the behavior of the SLB near the bilayer front, forcing the advancing lipids in the SLB away from the center of the channel out toward the sides.

Nanoscale patterning controls inorganic-membrane interface structure

The ability to non-destructively integrate inorganic structures into or through biological membranes is essential to realizing full bio-inorganic integration, including arrayed on-chip patch-clamps, drug delivery, and biosensors. Here we explore the role of nanoscale patterning on the strength of biomembrane-inorganic interfaces. AFM measurements show that inorganic probes functionalized with hydrophobic bands with thicknesses complimentary to the hydrophobic lipid bilayer core exhibit strong attachment in the bilayer. As hydrophobic band thickness increases to 2-3 times the bilayer core the interfacial strength decreases, comparable to homogeneously hydrophobic probes. Analytical calculations and molecular dynamics simulations predict a transition between a 'fused' interface and a 'T-junction' that matches the experimental results, showing lipid disorder and defect formation for thicker bands. These results show that matching biological length scales leads to more intimate bio-inorganic junctions, enabling rational design of non-destructive membrane interfaces.

A new method for measuring edge tensions and stability of lipid bilayers: effect of membrane composition

We report a novel and facile method for measuring edge tensions of lipid membranes. The approach is based on electroporation of giant unilamellar vesicles and analysis of the pore closure dynamics. We applied this method to evaluate the edge tension in membranes with four different compositions: egg phosphatidylcholine (eggPC), dioleoylphosphatidylcholine (DOPC), and mixtures of DOPC with cholesterol and dioleoylphosphatidylethanolamine. Our data confirm previous results for eggPC and DOPC. The addition of 17 mol % cholesterol to the DOPC membrane causes an increase in the membrane edge tension. On the contrary, when the same fraction of dioleoylphosphatidylethanolamine is added to the membrane, a decrease in the edge tension is observed, which is an unexpected result considering the inverted-cone shape geometry of the molecule. It is presumed that interlipid hydrogen bonding is the origin of this behavior. Furthermore, cholesterol was found to lower the lysis tension of DOPC bilayers. This behavior differs from that observed on bilayers made of stearoyloleoylphosphatidylcholine, suggesting that cholesterol influences the membrane mechanical stability in a lipid-specific manner.

Fractal avalanche ruptures in biological membranes

Bilayer membranes envelope cells as well as organelles, and constitute the most ubiquitous biological material found in all branches of the phylogenetic tree. Cell membrane rupture is an important biological process, and substantial rupture rates are found in skeletal and cardiac muscle cells under a mechanical load. Rupture can also be induced by processes such as cell death, and active cell membrane repair mechanisms are essential to preserve cell integrity. Pore formation in cell membranes is also at the heart of many biomedical applications such as in drug, gene and short interfering RNA delivery. Membrane rupture dynamics has been studied in bilayer vesicles under tensile stress, which consistently produce circular pores. We observed very different rupture mechanics in bilayer membranes spreading on solid supports: in one instance fingering instabilities were seen resulting in floral-like pores and in another, the rupture proceeded in a series of rapid avalanches causing fractal membrane fragmentation. The intermittent character of rupture evolution and the broad distribution in avalanche sizes is consistent with crackling-noise dynamics. Such noisy dynamics appear in fracture of solid disordered materials, in dislocation avalanches in plastic deformations and domain wall magnetization avalanches. We also observed similar fractal rupture mechanics in spreading cell membranes.

A systematically coarse-grained solvent-free model for quantitative phospholipid bilayer simulations

We present an implicit solvent coarse-grained (CG) model for quantitative simulations of 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC) bilayers. The absence of explicit solvent enables membrane simulations on large length and time scales at moderate computational expense. Despite improved computational efficiency, the model preserves chemical specificity and quantitative accuracy. The bonded and nonbonded interactions together with the effective cohesion mimicking the hydrophobic effect were systematically tuned by matching structural and mechanical properties from experiments and all-atom bilayer simulations, such as saturated area per lipid, radial distribution functions, density and pressure profiles across the bilayer, P(2) order, etc. The CG lipid model is shown to self-assemble into a bilayer starting from a random dispersion. Its line tension and elastic properties, such as bending and stretching modulus, are semiquantitatively consistent with experiments. The effects of (i) reduced molecular friction and (ii) more efficient integration combine to an overall speed-up of 3-4 orders of magnitude compared to all-atom bilayer simulations. Our CG lipid model is especially useful for studies of large-scale phenomena in membranes that nevertheless require a fair description of chemical specificity, e.g., membrane patches interacting with movable and transformable membrane proteins and peptides.

Systematic implicit solvent coarse-graining of bilayer membranes: lipid and phase transferability of the force field

We study the lipid and phase transferability of our recently developed systematically coarse-grained solvent-free membrane model. The force field was explicitly parameterized to describe a fluid 1-palmitoyl-2-oleoyl-phosphatidylcholine (POPC) bilayer at 310 K with correct structure and area per lipid, while gaining at least three orders of magnitude in computational efficiency (see Wang and Deserno 2010 J. Phys. Chem. B 114 11207-20). Here, we show that exchanging CG tails, without any subsequent re-parameterization, creates reliable models of 1,2-dioleoylphosphatidylcholine (DOPC) and 1,2-dipalmitoylphosphatidylcholine (DPPC) lipids in terms of structure and area per lipid. Furthermore, all CG lipids undergo a liquid-gel transition upon cooling, with characteristics like those observed in experiments and all-atom simulations during phase transformation. These studies suggest a promising transferability of our force field parameters to different lipid species and thermodynamic state points, properties that are a prerequisite for even more complex systems, such as mixtures.

Free energies of stable and metastable pores in lipid membranes under tension

The free energy profile of pore formation in a lipid membrane, covering the entire range from a density fluctuation in an intact bilayer to a large tension-stabilized pore, has been calculated by molecular dynamics simulations with a coarse-grained lipid model. Several fixed elongations are used to obtain the Helmholtz free energy as a function of pore size for thermodynamically stable, metastable, and unstable pores, and the system-size dependence of these elongations is discussed. A link to the Gibbs free energy at constant tension, commonly known as the Litster model, is established by a Legendre transformation. The change of genus upon pore formation is exploited to estimate the saddle-splay modulus or Gaussian curvature modulus of the membrane leaflets. Details are provided of the simulation approach, which combines the potential of mean constraint force method with a reaction coordinate based on the local lipid density.

Release of cationic polymer-DNA complexes from the endosome: A theoretical investigation of the proton sponge hypothesis

Polyplexes are complexes composed of DNA and cationic polymers; they are promising transport vehicles for nonviral gene delivery. Cationic polymers that contain protonatable groups, such as polyethylenimine, have been suggested to trigger endosomal escape of polyplexes according to the "proton sponge hypothesis." Here, osmotic swelling is induced by a decrease in the endosomal pH value, leading to an accumulation of polymer charge accompanied by the influx of Cl(-) ions to maintain overall electroneutrality. We study a theoretical model of the proton sponge mechanism. The model is based on the familiar Poisson-Boltzmann approach, modified so as to account for the presence of ionizable polyelectrolytes within self-consistent field theory with assumed ground state dominance. We consider polyplexes, composed of fixed amounts of DNA and cationic polymer, to coexist with uncomplexed cationic polymer in an enclosing vesicle of fixed volume. For such a system, we calculate the increase in osmotic pressure upon moderately decreasing the pH value and relate that pressure to the rupture tension of the enclosing membrane. Our model predicts membrane rupture upon pH decrease only within a certain range of free polymer content in the vesicle. That range narrows with increasing amount of DNA. Consequently, there exists a maximal amount of DNA that can be incorporated into a vesicle while maintaining the ability of content release through the proton sponge mechanism.

Simulations of skin barrier function: free energies of hydrophobic and hydrophilic transmembrane pores in ceramide bilayers

Transmembrane pore formation is central to many biological processes such as ion transport, cell fusion, and viral infection. Furthermore, pore formation in the ceramide bilayers of the stratum corneum may be an important mechanism by which penetration enhancers such as dimethylsulfoxide (DMSO) weaken the barrier function of the skin. We have used the potential of mean constraint force (PMCF) method to calculate the free energy of pore formation in ceramide bilayers in both the innate gel phase and in the DMSO-induced fluidized state. Our simulations show that the fluid phase bilayers form archetypal water-filled hydrophilic pores similar to those observed in phospholipid bilayers. In contrast, the rigid gel-phase bilayers develop hydrophobic pores. At the relatively small pore diameters studied here, the hydrophobic pores are empty rather than filled with bulk water, suggesting that they do not compromise the barrier function of ceramide membranes. A phenomenological analysis suggests that these vapor pores are stable, below a critical radius, because the penalty of creating water-vapor and tail-vapor interfaces is lower than that of directly exposing the strongly hydrophobic tails to water. The PMCF free energy profile of the vapor pore supports this analysis. The simulations indicate that high DMSO concentrations drastically impair the barrier function of the skin by strongly reducing the free energy required for pore opening.

Pore structure, thinning effect, and lateral diffusive dynamics of oriented lipid membranes interacting with antimicrobial peptide protegrin-1: 31P and 2H solid-state NMR study

Membrane pores that are induced in oriented membranes by an antimicrobial peptide (AMP), protegrin-1 (PG-1), are investigated by (31)P and (2)H solid state NMR spectroscopy. We incorporated a well-studied peptide, protegrin-1 (PG-1), a beta-sheet AMP, to investigate AMP-induced dynamic supramolecular lipid assemblies at different peptide concentrations and membrane compositions. Anisotropic NMR line shapes specifying toroidal pores and thinned membranes, which are formed in membrane bilayers by the binding of AMPs, have been analyzed for the first time. Theoretical NMR line shapes of lipids distributed on the surface of toroidal pores and thinned membranes reproduce reasonably well the line shape characteristics of our experimentally measured (31)P and (2)H solid-state NMR spectra of oriented lipids binding with PG-1. The lateral diffusions of lipids are also analyzed from the motionally averaged one- and two-dimensional (31)P and (2)H solid-state NMR spectra of oriented lipids that are binding with AMPs.

The bound states of amphipathic drugs in lipid bilayers: study of curcumin

Drug-membrane interactions are well known but poorly understood. Here we describe dual measurements of membrane thickness change and membrane area change due to the binding of the amphipathic drug curcumin. The combined results allowed us to analyze the binding states of a drug to lipid bilayers, one on the water-membrane interface and another in the hydrocarbon region of the bilayer. The transition between the two states is strongly affected by the elastic energy of membrane thinning (or, equivalently, area stretching) caused by interfacial binding. The data are well described by a two-state model including this elastic energy. The binding of curcumin follows a common pattern of amphipathic peptides binding to membranes, suggesting that the binding states of curcumin are typical for amphipathic drugs.

Mechanosensitive membrane channels in action

The tension-driven gating process of MscL from Mycobacterium tuberculosis, Tb-MscL, has been addressed at near-atomic detail using coarse-grained molecular dynamics simulations. To perform the simulations, a novel coarse-grained peptide model based on a thermodynamic parameterization of the amino-acid side chains has been applied. Both the wild-type Tb-MscL and its gain-of-function mutant V21D embedded in a solvated lipid bilayer have been studied. To mimic hypoosmotic shock conditions, simulations were performed at increasing levels of membrane tension approaching the rupture threshold of the lipid bilayer. Both the wild-type and the mutant channel are found to undergo significant conformational changes in accordance with an irislike expansion mechanism, reaching a conducting state on a microsecond timescale. The most pronounced expansion of the pore has been observed for the V21D mutant, which is consistent with the experimentally shown gain-of-function phenotype of the V21D mutant.

Population study of sizes and components of self-reproducing giant multilamellar vesicles

Population analysis of a system of self-reproducing giant multilamellar vesicles (GMVs) was carried out by means of flow cytometry. The multidimensional distribution of forward light scattering (FS), side light scattering (SS), and fluorescence (FL) intensities originating from each GMV provided information about changes in a population composed of 104 vesicles. FS-FL dot plots indicated that, after the addition of the membrane precursor, the size distribution of the newly generated vesicles was nearly the same as that of the original, but the catalyst content was reduced. This result can be interpreted as evidence for the occurrence of the self-reproduction of GMVs. Moreover, the new GMVs recovered the amount of catalyst to the initial value, keeping their size distribution constant, when a solution of the catalyst was added to the new GMVs. These results are the first experimental evidence for a novel phenomenon on GMV size distribution during their self-reproducing cycle.

Sub-100 nm patterning of supported bilayers by nanoshaving lithography

Sub-100 nm wide supported phospholipid bilayers (SLBs) were patterned on a planar borosilicate substrate by AFM-based nanoshaving lithography. First, a bovine serum albumin monolayer was coated on the glass and then selectively removed in long strips by an AFM tip. The width of vacant strips could be controlled down to 15 nm. Bilayer lines could be formed within the vacant strips by vesicle fusion. It was found that stable bilayers formed by this method had a lower size limit of approximately 55 nm in width. This size limit stems from a balance between a favorable bilayer adhesion energy and an unfavorable bilayer edge energy.

Flicker spectroscopy of thermal lipid bilayer domain boundary fluctuations

This contribution describes measurements of lipid bilayer domain line tension based on two-dimensional thermal undulations of membranes with liquid ordered/liquid disordered phase coexistence and near-critical composition at room temperature. Lateral inhomogeneity of lipid and protein composition is currently a subject of avid research aimed at determining both fundamental properties and biological relevance of membrane domains. Line tension at fluid lipid bilayer membrane domain boundaries controls the kinetics of domain growth and therefore regulates the size of compositional heterogeneities. High line tension promotes membrane domain budding and fission. Line tension could therefore be an important control parameter regulating functional aspects of biological membranes. Here the established method of fluid domain flicker spectroscopy is applied to examine thermal domain wall fluctuations of phase-separated bilayer membranes. We find a Gaussian probability distribution for the first few excited mode amplitudes, which permits an analysis by means of appropriately specialized capillary wave theory. Time autocorrelation functions are found to decay exponentially, and relaxation times are fitted by means of a hydrodynamic theory relating line tensions and excited mode relaxation kinetics. Line tensions below 1 pN are obtained, with these two approaches yielding similar results. We examine experimental artifacts that perturb the Fourier spectrum of domain traces and discuss ways to identify the number of modes that yield reliable line tension information.

Antimicrobial peptides in action

Molecular dynamics simulations of the magainin MG-H2 peptide interacting with a model phospholipid membrane have been used to investigate the mechanism by which antimicrobial peptides act. Multiple copies of the peptide were randomly placed in solution close to the membrane. The peptide readily bound to the membrane, and above a certain concentration, the peptide was observed to cooperatively induce the formation of a nanometer-sized, toroidally shaped pore in the bilayer. In sharp contrast with the commonly accepted model of a toroidal pore, only one peptide was typically found near the center of the pore. The remaining peptides lay close to the edge of the pore, maintaining a predominantly parallel orientation with respect to the membrane.

Finite element analysis of microelectrotension of cell membranes

Electric fields can be focused by micropipette-based electrodes to induce stresses on cell membranes leading to tension and poration. To date, however, these membrane stress distributions have not been quantified. In this study, we determine membrane tension, stress, and strain distributions in the vicinity of a microelectrode using finite element analysis of a multiscale electro-mechanical model of pipette, media, membrane, actin cortex, and cytoplasm. Electric field forces are coupled to membranes using the Maxwell stress tensor and membrane electrocompression theory. Results suggest that micropipette electrodes provide a new non-contact method to deliver physiological stresses directly to membranes in a focused and controlled manner, thus providing the quantitative foundation for micreoelectrotension, a new technique for membrane mechanobiology.

Membrane perturbation by an external electric field: a mechanism to permit molecular uptake

Electropermeabilisation is a well established physical method, based on the application of electric pulses, which induces the transient permeabilisation of the cell membrane. External molecules, otherwise nonpermeant, can enter the cell. Electropermeabilisation is now in use for the delivery of a large variety of molecules, as drugs and nucleic acids. Therefore, the method has great potential in the fields of cancer treatment and gene therapy. However many open questions about the underlying physical mechanisms involved remain to be answered or fully elucidated. In particular, the induced changes by the effects of the applied field on the membrane structure are still far from being fully understood. The present review focuses on questions related to the current theories, i.e. the basic physical processes responsible for the electropermeabilisation of lipid membranes. It also addresses recent findings using molecular dynamics simulations as well as experimental studies of the effect of the field on membrane components.

Giant vesicles in electric fields

This review is dedicated to electric field effects on giant unilamellar vesicles, a cell-size membrane system. We summarize various types of behavior observed when vesicles are subjected either to weak AC fields at various frequency, or to strong DC pulses. Different processes such as electro-deformation, -poration and -fusion of giant vesicles are considered. We describe some recent developments, which allowed us to detect the dynamics of the vesicle response with a resolution below milliseconds for all of these processes. Novel aspects on electric field effects on vesicles in the gel phase are introduced.

Ion transport across transmembrane pores

To study the pore-mediated transport of ionic species across a lipid membrane, a series of molecular dynamics simulations have been performed of a dipalmitoyl-phosphatidyl-choline bilayer containing a preformed water pore in the presence of sodium and chloride ions. It is found that the stability of the transient water pores is greatly reduced in the presence of the ions. Specifically, the binding of sodium cations at the lipid/water interface increases the pore line tension, resulting in a destabilization of the pore. However, the application of mechanical stress opposes this effect. The flux of ions through these mechanically stabilized pores has been analyzed. Simulations indicate that the transport of the ions through the pores depends strongly on the size of the water channel. In the presence of small pores (radius <1.5 nm) permeation is slow, with both sodium and chloride permeating at similar rates. In the case in which the pores are larger (radius >1.5 nm), a crossover is observed to a regime where the anion flux is greatly enhanced. Based on these observations, a mechanism for the basal membrane permeability of ions is discussed.

Line tension at fluid membrane domain boundaries measured by micropipette aspiration

Line tension is a determinant of fluid phase domain formation kinetics and morphology in lipid bilayer membranes, which are models for biological membrane heterogeneity. We describe the first direct measurement of this line tension by micropipette aspiration. Our data are analyzed with a model that does not rely on independently measured (and composition dependent) secondary parameters, such as bending stiffness or membrane viscosities. Line tension is strongly composition dependent and decreases towards a critical consolute point in a quasiternary room temperature phase diagram.

Nuclear pores and membrane holes: generic models for confined chains and entropic barriers in pore stabilization

The lumen of the nuclear pore complex is increasingly understood to be lined by a polymer brush that entropically regulates transport in and out of the nucleus-and it seems likely that similar effects probably arise with glycocalyx-lined holes in cell membranes. Here we mimic such pore-confined brushes with self-assembled polymer membranes imbued with nano-holes. Experiment and theory help elucidate the entropic origin and stabilization of the pores, which appear to have a similar basis as steric stabilization of colloids bearing polymer brushes. Free energies of interacting brushes reveal stable minima at pore sizes smaller than the classical metastable point, with little effect of the particular pore geometry. Such entropic forces have potential implications for lock and key mechanisms of nuclear pore assembly as well as transient poration of cells and synthetic nano-pores with regulatory mechanisms for transport.

Simulations of edge behavior in a mixed-lipid bilayer: Fluctuation analysis

Coarse-grained molecular dynamics simulations of lipid bilayer ribbons consisting of a mixture of lipids of different tail lengths have been performed to gain insight into bicelle mixtures. The line tension of the bilayer edge decreases as the mole fraction of short-chain lipids in the system is increased, dropping below zero between 30% and 35%. The mole fraction of short-chain lipids in the ribbon interior is lower than the total mole fraction, as the short-chain lipids segregate towards the edge, but continues to rise even after the line tension vanishes, in contrast to predictions of a two-component two-phase model. The fluctuations of the bilayer edge in both high and low line tension regimes have been analyzed to extract information about the factors that influence the length and shape of the edge. At high line tension the wavelength-dependent in-plane fluctuations of the edge are predicted quantitatively using a simple analytical model using only the line tension as input. Where line tension is vanishing, the fluctuations can be modeled as arising from a combination of harmonic fluctuations around a minimum energy contour length and an in-plane bending elasticity. The estimated value of the in-plane bending modulus is of order 10(-29) J m, placing the intrinsic persistence length for the edge near the bilayer thickness of 4 nm.

Pores in bilayer membranes of amphiphilic molecules: coarse-grained molecular dynamics simulations compared with simple mesoscopic models

We investigate pores in fluid membranes by molecular dynamics simulations of an amphiphile-solvent mixture, using a molecular coarse-grained model. The amphiphilic membranes self-assemble into a lamellar stack of amphiphilic bilayers separated by solvent layers. We focus on the particular case of tensionless membranes, in which pores spontaneously appear because of thermal fluctuations. Their spatial distribution is similar to that of a random set of repulsive hard disks. The size and shape distribution of individual pores can be described satisfactorily by a simple mesoscopic model, which accounts only for a pore independent core energy and a line tension penalty at the pore edges. In particular, the pores are not circular: their shapes are fractal and have the same characteristics as those of two-dimensional ring polymers. Finally, we study the size-fluctuation dynamics of the pores, and compare the time evolution of their contour length to a random walk in a linear potential.

Simulations of stable pores in membranes: system size dependence and line tension

Amphiphilic bilayers with a pore were simulated using a coarse grained model. By stretching the bilayer to 70% beyond its equilibrium surface area, we established the phase diagram of pores, identifying regions where pores are stable, metastable, or unstable. A simple theoretical model is proposed to explain the phase diagram, and to calculate the critical and equilibrium relative stretches. Interestingly, these are found to scale with the inverse cubic root of the number of amphiphiles in the bilayer, thus explaining the order of magnitude difference between the simulated and the measured values. Three different methods are used to calculate a line tension coefficient of (3.5-4.0) x 10(-11) J/m, in good agreement with experimental data.

The mechanisms of cell membrane repair: A tutorial guide to key experiments

The best way to approach a new area is to study closely a sample of the key papers, and spread out from there. In this tutorial paper I present my personal selection of papers introducing concepts in the study of the mechanisms of cell membrane repair. For a more comprehensive review up to 2003, I refer the student to McNeil and Steinhardt (2003).

Electric pulses induce cylindrical deformations on giant vesicles in salt solutions

In this article, we report for the first time unusual shape changes of vesicles subjected to strong electric pulses in salt solutions of low concentration. The electric field is created by two parallel electrodes between which the vesicle solution is located. Surprisingly, the vesicles assume cylindrical shapes during the pulse. These deformations are short-lived (their lifetime is approximately 1 ms) and occur only in the presence of salt outside the vesicles, irrespective of their content. When the solution conductivities inside and outside are the same, vesicles with square cross section are observed. Using a fast digital camera, we were able to record these deformations and study the vesicle shape dynamics. The aims of this article are to report the new vesicle morphologies and their dynamics and to provoke theoretical work in this direction.

Nucleation free energy of pore formation in an amphiphilic bilayer studied by molecular dynamics simulations

The formation of a pore in a membrane requires a considerable rearrangement of the amphiphilic molecules about to form the bilayer edge surrounding the pore, and hence is accompanied by a steep increase of the free energy. Recent rupture and conductance experiments suggest that this reshuffling process is also responsible for a small energy barrier that stabilizes "prepores" with diameters of less than 1 nm, rendering both the opening and closing of pores an activated process. We use the potential of mean constraint force method to study this free energy profile, as a function of pore radius, in a coarse grained bilayer model. The calculations show that the free energy rises by (15-20) kT during pore opening, making it an extremely rare nucleation event. Although we do not observe a barrier to pore closure, the results do make the existence of such a barrier plausible. For larger pores we find a smooth transition to Litster's model, from which a line tension coefficient of about 3.7 x 10(-11) J m(-1) is deduced.

A practical guide to giant vesicles. Probing the membrane nanoregime via optical microscopy

Research on giant vesicles is becoming increasingly popular. Giant vesicles provide model biomembrane systems for systematic measurements of mechanical and rheological properties of bilayers as a function of membrane composition and temperature, as well as hydrodynamic interactions. Membrane response to external factors (for example electric fields, ions and amphiphilic molecules) can be directly visualized under the microscope. In this paper we review our current understanding of lipid bilayers as obtained from studies on giant unilamellar vesicles. Because research on giant vesicles increasingly attracts the interest of scientists from various backgrounds, we also try to provide a concise introduction for newcomers in the field. Finally, we summarize some recent developments on curvature effects induced by polymers, domain formation in membranes and shape transitions induced by electric fields.

Transbilayer Pores Induced by Thickness Fluctuations

Thermally-induced fluctuations of individual phospholipids in a bilayer lipid membrane (BLM) are converted into collective motions due to the intermolecular interactions. Here, we demonstrate that transbilayer stochastic pores can be generated via collective thermal movements (CTM). Using the elastic theory of continuous media applied to smectic-A liquid crystals, we estimate the pore radius and the energetic requirements for pore appearance. Three types of thermally-induced transbilayer pores could be formed through BLMs: open and stable, open and unstable, and closed. In most of the situations, two open and stable pores with different radii could be generated. Notably, the two pores have the same generation probability. Unstable pores are possible to appear across thin bilayers that contain phospholipids with a large polar headgroup. Closed pores are present throughout the cases that we have inspected. The effects of hydrophobic thickness, polar headgroup size of phospholipids, temperature, surface tension, and elastic compression on the pore formation and pore stability have been examined as well.

Free energy of a trans-membrane pore calculated from atomistic molecular dynamics simulations

Atomistic molecular dynamics simulations of a lipid bilayer were performed to calculate the free energy of a trans-membrane pore as a function of its radius. The free energy was calculated as a function of a reaction coordinate using a potential of mean constraint force. The pore radius was then calculated from the reaction coordinate using Monte Carlo particle insertions. The main characteristics of the free energy that comes out of the simulations are a quadratic shape for a radius less than about 0.3 nm, a linear shape for larger radii than this, and a rather abrupt change without local minima or maxima between the two regions. In the outer region, a line tension can be calculated, which is consistent with the experimentally measured values. Further, this line tension can be rationalized and understood in terms of the energetic cost for deforming a part of the lipid bilayer into a hydrophilic pore. The region with small radii can be described and understood in terms of statistical mechanics of density fluctuations. In the region of crossover between a quadratic and linear free energy there was some hysteresis associated with filling and evacuation of the pore with water. The metastable prepore state hypothesized to interpret the experiments was not observed in this region.

Fluorescence microscopic investigation on morphological changes of giant multilamellar vesicles induced by amphiphilic additives

Adding an artificial bolaamphiphile to a dispersion of giant multilamellar vesicles (GMVs) made of 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphatidylcholine (POPC) induced a cup-shaped deformation in GMVs accompanied by partial extrusion of the inner vesicle; thereafter, the deformed vesicles returned to their original shape. On the other hand, when the artificial bolaamphiphile together with a surfactant was added to the vesicular dispersion, these deformation and reformation dynamics were transmitted from the outer membranes in GMVs to the inner membranes until an intact inner vesicle was extruded out of the outer membrane. The microscopic aspects of these processes were investigated using amphiphiles tagged with individual fluorophores.

Field theoretic study of bilayer membrane fusion: II. Mechanism of a stalk-hole complex

We use self-consistent field theory to determine structural and energetic properties of intermediates and transition states involved in bilayer membrane fusion. In particular, we extend our original calculations from those of the standard hemifusion mechanism, which was studied in detail in the first article of this series, to consider a possible alternative to it. This mechanism involves non-axial stalk expansion, in contrast to the axially symmetric evolution postulated in the classical mechanism. Elongation of the initial stalk facilitates the nucleation of holes and leads to destabilization of the fusing membranes via the formation of a stalk-hole complex. We study properties of this complex in detail, and show how transient leakage during fusion, previously predicted and recently observed in experiment, should vary with lipid architecture and tension. We also show that the barrier to fusion in the alternative mechanism is lower than that of the standard mechanism by a few k(B)T over most of the relevant region of system parameters, so that this alternative mechanism is a viable alternative to the standard pathway. We emphasize that any mechanism, such as this alternative one, which affects, even modestly, the line tension of a hole in a membrane, affects greatly the ability of that membrane to undergo fusion.

Pore nucleation in mechanically stretched bilayer membranes

We report a computer-simulation study of the free-energy barrier for the nucleation of pores in the bilayer membrane under constant stretching lateral pressure. We find that incipient pores are hydrophobic but as the lateral size of the pore nucleus becomes comparable with the molecular length, the pore becomes hydrophilic. In agreement with previous investigations, we find that the dynamical process of growth and closure of hydrophilic pores is controlled by the competition between the surface tension of the membrane and the line tension associated with the rim of the pore. We estimate the line tension of a hydrophilic pore from the shape of the computed free-energy barriers. The line tension thus computed is in a good agreement with available experimental data. We also estimate the line tension of hydrophobic pores at both macroscopic and microscopic levels. The comparison of line tensions at these two different levels indicates that the "microscopic" line tension should be carefully distinguished from the "macroscopic" effective line tension used in the theoretical analysis of pore nucleation. The overall shape of the free-energy barrier for pore nucleation shows no indication for the existence of a metastable intermediate during pore nucleation.