We have constructed a model for the kinetics of rupture of membranes under tension, applying physical principles relevant to lipid bilayers held together by hydrophobic interactions. The membrane is characterized by the bulk compressibility (for expansion), the thickness of the hydrophobic part of the bilayer, the hydrophobicity and a parameter characterizing the tail rigidity of the lipids. The model is a lattice model which incorporates strain relaxation, and considers the nucleation of pores at constant area, constant temperature, and constant particle number. The particle number is conserved by allowing multiple occupancy of the sites. An equilibrium ``phase diagram'' is constructed as a function of temperature and strain with the total pore surface and distribution as the order parameters. A first order rupture line is found with increasing tension, and a continuous increase in proto-pore concentration with rising temperature till instability. The model explains current results on saturated and unsaturated PC lipid bilayers and thicker artificial bilayers made of diblock copolymers. Pore size distributions are presented for various values of area expansion and temperature, and the fractal dimension of the pore edge is evaluated.
The assembly of curved protein rods on fluid membranes is studied using implicit-solvent meshless membrane simulations. As the rod curvature increases, the rods on a membrane tube assemble along the azimuthal direction first and subsequently along the longitudinal direction. Here, we show that both transition curvatures decrease with increasing rod stiffness. For comparison, curvature-inducing isotropic inclusions are also simulated. When the isotropic inclusions have the same bending rigidity as the other membrane regions, the inclusions are uniformly distributed on the membrane tubes and ves…
The elastic properties of a self-assembled bilayer membrane are studied using the self-consistent field theory, applied to a model system composed of flexible amphiphilic chains dissolved in hydrophilic polymeric solvents. Examining the free energy of bilayer membranes with different geometries allows us to calculate their bending modulus, Gaussian modulus, two fourth-order membrane moduli, and the line tension. The dependence of these parameters on the microscopic characteristics of the amphiphilic chain, characterized by the volume fraction of the hydrophilic component, is systematically stu…
Hydrophobic thickness mismatch between integral membrane proteins and the surrounding lipid bilayer can produce lipid bilayer thickness deformations. Experiment and theory have shown that protein-induced lipid bilayer thickness deformations can yield energetically favorable bilayer-mediated interactions between integral membrane proteins, and large-scale organization of integral membrane proteins into protein clusters in cell membranes. Within the continuum elasticity theory of membranes, the energy cost of protein-induced bilayer thickness deformations can be captured by considering compressi…
Formation of membrane necks is crucial for fission and fusion in lipid bilayers. In this work, we seek to answer the following fundamental question: what is the relationship between protein-induced spontaneous mean curvature and the Gaussian curvature at a membrane neck? Using an augmented Helfrich model for lipid bilayers to include membrane-protein interaction, we solve the shape equation on catenoids to find the field of spontaneous curvature that satisfies mechanical equilibrium of membrane necks. In this case, the shape equation reduces to a variable coefficient Helmholtz equation for spo…
We report a new 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 the latter with cholesterol and dioleoylphosphatidylethanolamine (DOPE). 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 …
It is well known that at the gel-liquid phase transition temperature a lipid bilayer membrane exhibits an increased ion permeability. We analyze the quantized currents in which the increased permeability presents itself. The open time histogram shows a "-3/2" power law which implies an open-closed transition rate that decreases like $k(t) \propto t^{-1}$ as time evolves. We propose a "pore freezing" model to explain the observations. We discuss how this model also leads to the $1/f^α$ noise that is commonly observed in currents across biological and artificial membranes.
An interfacial regularized Stokeslet scheme is presented to predict the motion of solid bodies (e.g. proteins or gel-phase domains) embedded within flowing lipid bilayer membranes. The approach provides a numerical route to calculate velocities and angular velocities in complex flow fields that are not amenable to simple Faxén-like approximations. Additionally, when applied to shearing motions, the calculations yield predictions for the effective surface viscosity of dilute rigid body-laden membranes. In the case of cylindrical proteins, effective viscosity calculations are compared to two pri…
For many biotechnological applications it would be useful to better understand the effects produced by electric fields on lipid membranes. This review discusses several aspects of the electrostatic properties of a planar lipid membrane with its surrounding electrolyte in a normal DC or AC electric field. In the planar geometry, the analysis of electrokinetic equations can be carried out quite far, allowing to characterize analytically the steady state and the dynamics of the charge accumulation in the Debye layers, which results from the application of the electric field. For a conductive memb…
Bilayer lipid membranes [BLMs] are an essential component of all biological systems, forming a functional barrier for cells and organelles from the surrounding environment. The lipid molecules that form membranes contain both permanent and induced dipoles, and an electric field can induce the formation of pores when the transverse field is sufficiently strong (electroporation). Here, a phenomenological free energy is constructed to model the response of a BLM to a transverse static electric field. The model contains a continuum description of the membrane dipoles and a coupling between the hea…
By reverting to spectroscopy, changes in the biological environment of a fluorescent probe can be monitored and the presence of various phases of the surrounding lipid bilayer membranes can be detected. This study highlights the important differences in orientation and location and therefore in efficiency between the probes when they are used in fluorescence microscopy to screen various lipid bilayer membrane phases. Dependent on the lipid composition, the angle between the transition state dipole moments of both probes and the normal to the membrane are found to deviate clearly from 90°. It i…
Colloids and proteins alike can bind to lipid bilayers and move laterally in these two-dimensional fluids. Inspired by proteins that generate membrane curvature, sense the underlying membrane geometry, and migrate to high curvature sites, we explore the question: Can colloids, adhered to lipid bilayers, also sense and respond to membrane geometry? We report the curvature migration of Janus microparticles adhered to giant unilamellar vesicles elongated to present well defined curvature fields. However, unlike proteins, which migrate to minimize membrane bending energy, colloids migrate by an en…
Bilayer lipid membranes (BLMs) are an essential component of many biological systems, forming a functional barrier between the cell and the surrounding environment. When the membrane relaxes from a structural perturbation, the dynamics of the relaxation depends on the bilayer structure. We present a model of a BLM in a viscous solvent, including an explicit description of a 'thick' membrane, where the fluctuations in the thickness of a monolayer leaflet are coupled to changes in the lipid density within that monolayer. We find dispersion relations describing three intuitive forms of bilayer mo…
We review recent computer simulation studies of undulating lipid bilayers. Theoretical interpretations of such fluctuating membranes are most commonly based on generalized Helfrich-type elastic models, with additional contributions of local "protrusions" and/or density fluctuations. Such models provide an excellent basis for describing the fluctuations of tensionless bilayers in the fluid phase at a quantitative level. However, this description is found to fail for membranes in the gel phase and for membranes subject to high tensions. The fluctuations of tilted gel membranes show a signature o…
We outline a concept of self-assembled soft matter devices based on micro-fluidics, which use surfactant bilayer membranes as their main building blocks, arrested in geometric structures provided by top-down lithography. Membranes form spontaneously when suitable water-in-oil emulsions are forced into micro-fluidic channels at high dispersed-phase volume fractions. They turn out to be remarkably stable even when pumped through the micro-fluidic channel system. Their geometric arrangement is self-assembling, driven by interfacial energy and wetting forces. The ordered membrane arrays thus emerg…
We report the self-assembly of thin actin shells beneath the membranes of giant vesicles. Ion-carrier mediated influx of Mg2+ induces actin polymerization in the initially spherical vesicles. Buckling of the vesicles and the formation of blisters after thermally induced bilayer expansion is demonstrated. Bilayer flickering is dominated by tension generated by its coupling to the actin cortex. Quantitative flicker analysis suggests the bilayer and the actin cortex are separated by 0.4 \mum to 0.5 \mum due to undulation forces.
The computational study of the interaction between charged, ligand-protected metal nanoparticles and model lipid membranes has been recently addressed both at atomistic and coarse grained level. Here we compare the performance of three versions of the coarse grained Martini force field at describing the nanoparticle-membrane interaction. The three coarse-grained models differ in terms of treatment of long-range electrostatic interactions and water polarizability. The NP-membrane interaction consists in the transition from a metastable NP- membrane complex, in which the NP is only partially emb…
We propose a model that accounts for budding behavior of domains in lipid bilayers, where each of the bilayer leaflets has a coupling between its local curvature and local lipid composition. The compositional asymmetry between the two monolayers leads to an overall spontaneous curvature. The membrane free-energy contains three contributions: bending energy, line tension, and a Landau free-energy for a lateral phase separation. Within a mean-field treatment, we obtain various phase diagrams which contain fully-budded, dimpled and flat states. In particular, for some range of membrane parameters…
We formulate a theory of electrostatic interactions in lipid bilayer membranes where both monolayer leaflets contain dissociable moieties that are subject to charge regulation. We specifically investigate the coupling between membrane curvature and charge regulation of a lipid bilayer vesicle using both the linear Debye-Hückel (DH) and the non-linear Poisson-Boltzmann (PB) theory. We find that charge regulation of an otherwise symmetric bilayer membrane can induce charge symmetry breaking, non-linear flexoelectricity and anomalous curvature dependence of free energy. The pH effects investigate…
We simulate a phase-separating a bilayer in which the leaflets experience a direct coupling favouring local compositional symmetry ("registered" bilayer phases), and an indirect coupling due to hydrophobic mismatch that favours strong local asymmetry ("antiregistered" bilayer phases). For wide ranges of overall leaflet compositions, multiple competing states are possible. For estimated physical parameters, a quenched bilayer may first evolve toward a metastable state more asymmetric than if the leaflets were uncorrelated;\ subsequently, it must nucleate to reach its equilibrium, more symmetric…
Curvature-sensing and curvature-remodeling proteins are known to reshape cell membranes, and this remodeling event is essential for key biophysical processes such as tubulation, exocytosis, and endocytosis. Curvature-inducing proteins can act as curvature sensors as well as induce curvature in cell membranes to stabilize emergent high curvature, non-spherical, structures such as tubules, discs, and caveolae. A definitive understanding of the interplay between protein recruitment and migration, the evolution of membrane curvature, and membrane morphological transitions is emerging but remains i…
A question of considerable interest to cell membrane biology is whether phase segregated domains across an asymmetric bilayer are strongly correlated with each other and whether phase segregation in one leaflet can induce segregation in the other. We answer both these questions in the affirmative, using an atomistic molecular dynamics simulation to study the equilibrium statistical properties of a 3-component {\em asymmetric} lipid bilayer comprising an unsaturated POPC (palmitoyl-oleoyl-phosphatidyl-choline), a saturated SM (sphingomyelin) and cholesterol with different composition ratios. Ou…
Engineering the synthetic nanopores through lipid bilayer membrane to access the interior of a cell is a long persisting challenge in biotechnology. Here, we demonstrate the stability and dynamics of a tile-based 6-helix DNA nanotube (DNT) embedded in POPC lipid bilayer using the analysis of 0.2 microsecond long equilibrium MD simulation trajectories. We observe that the head groups of the lipid molecules close to the lumen cooperatively tilt towards the hydrophilic sugar-phosphate backbone of DNA and form a toroidal structure around the patch of DNT protruding in the membrane. Further, we exp…
Under dehydration conditions, amphipathic Late Embryogenesis Abundant (LEA) proteins fold spontaneously from a random conformation into alpha-helical structures and this transition is promoted by the presence of membranes. To gain insight into the thermodynamics of membrane association we model the resulting alpha-helical structures as infinite rigid cylinders patterned with hydrophobic and hydrophilic stripes oriented parallel to their axis. Statistical thermodynamic calculations using Single Chain Mean Field (SCMF) theory show that the relative thickness of the stripes controls the free ener…
A coarse-grained molecular model, which consists of a spherical particle and an orientation vector, is proposed to simulate lipid membrane on a large length scale. The solvent is implicitly represented by an effective attractive interaction between particles. A bilayer structure is formed by orientation-dependent (tilt and bending) potentials. In this model, the membrane properties (bending rigidity, line tension of membrane edge, area compression modulus, lateral diffusion coefficient, and flip-flop rate) can be varied over broad ranges. The stability of the bilayer membrane is investigated v…
Diffusion in cell membranes is not just simple two-dimensional Brownian motion, but typically depends on the timescale of the observation. The physical origins of this anomalous sub-diffusion are unresolved, and model systems capable of quantitative and reproducible control of membrane diffusion have been recognised as a key experimental bottleneck. Here we control anomalous dif- fusion using supported lipids bilayers containing lipids derivatized with polyethylene glycol (PEG) headgroups. Bilayers with specific excluded area fractions are formed by control of PEG-lipid mole fraction. These bi…
For endocytosis and exocytosis, membranes transition between planar, budding, and vesicular topographies through nanoscale reorganization of lipids, proteins, and carbohydrates. However, prior attempts to understand the initial stages of nanoscale bending have been limited by experimental resolution. Through the implementation of polarized localization microscopy (PLM), this manuscript reports the inherent membrane bending capability of cholera toxin subunit B (CTxB) in quasi-one component supported lipid bilayers. Membrane buds were first detected with <50 nm radius, grew to >200 nm radius, a…
We investigate the phenomenon of protein induced tubulation of lipid bilayer membranes within a continuum framework using Monte Carlo simulations coupled with the Widom insertion technique to compute excess chemical potentials. Tubular morphologies are spontaneously formed when the density and the curvature-field strength of the membrane bound proteins exceed their respective thresholds and this transition is marked by a sharp drop in the excess chemical potential. We find that the planar to tubular transition can be described by a micellar model and that the corresponding free energy barrier …
We use coarse-grained Monte Carlo simulations to study the elastic properties of charged membranes in solutions of monovalent and pentavalent counterions. The simulation results of the two cases reveal trends opposite to each other. The bending rigidity and projected area increase with the membrane charge density for monovalent counterions, while they decrease for the pentavalent ions. These observations can be related to the counterion screening of the lipid charges. While the monovalent counterions only weakly screen the Coulomb interactions, which implies a repulsive Coulomb system, the mul…
We study membrane-protein interactions and membrane-mediated protein-protein interactions by Monte Carlo simulations of a generic coarse-grained model for lipid bilayers with cylindrical hydrophobic inclusions. The strength of the hydrophobic force and the hydrophobic thickness of the proteins are systematically varied. The results are compared with analytical predictions of two popular analytical theories: The Landau-de Gennes theory and the elastic theory. The elastic theory provides an excellent description of the fluctuation spectra of pure membranes and successfully reproduces the deforma…
Most biological molecules contain acido-basic groups that modulate their structure and interactions. A consequence is that pH gradients, local heterogeneities and dynamic variations are used by cells and organisms to drive or regulate specific biological functions including energetic metabolism, vesicular traffic, migration and spatial patterning of tissues in development. While the direct or regulatory role of pH in protein function is well documented, the role of hydrogen and hydroxyl ions in modulating the properties of lipid assemblies such as bilayer membranes is only beginning to be unde…
We describe a simple coarse-grained model which is suited to study lipid layers and their phase transitions. Lipids are modeled by short semiflexible chains of beads with a solvophilic head and a solvophobic tail component. They are forced to self-assemble into bilayers by a computationally cheap `phantom solvent' environment. The model reproduces the most important phases and phase transitions of monolayers and bilayers. Technical issues such as Monte Carlo parallelization schemes are briefly discussed.
Biological membranes constitute boundaries of cells and cell organelles. Physico-chemical mechanisms at the atomic scale are dictated by protein-lipid interaction strength, lipid composition, lipid distribution in the vicinity of the protein, shape and amino acid composition of the protein, and its amino acid contents. The specificity of molecular interactions together with the cooperativity of multiple proteins induce and stabilize complex membrane shapes at the mesoscale. These shapes span a wide spectrum ranging from the spherical plasma membrane to the complex cisternae of the Golgi appara…
Continuum elastic models that account for membrane thickness variations are especially useful in the description of nanoscale deformations due to the presence of membrane proteins with hydrophobic mismatch. We show that terms involving the gradient and the Laplacian of the area per lipid are significant and must be retained in the effective Hamiltonian of the membrane. We reanalyze recent numerical data, as well as experimental data on gramicidin channels, in light of our model. This analysis yields consistent results for the term stemming from the gradient of the area per molecule. The order …
We discuss different mechanisms for curvature-induced domain formation in multicomponent lipid membranes and present a theoretical model that allows us to study the interplay between the domains. The model represents the membrane by two coupled monolayers, which each carry an additional order parameter field describing the local lipid composition. The spontaneous curvature of each monolayer is coupled to the local composition, moreover, the lipid compositions on opposing monolayers are coupled to each other. Using this model, we calculate the phase behavior of the bilayer in mean-field approxi…
Membrane proteins and lipids can self-assemble into membrane protein polyhedral nanoparticles (MPPNs). MPPNs have a closed spherical surface and a polyhedral protein arrangement, and may offer a new route for structure determination of membrane proteins and targeted drug delivery. We develop here a general analytic model of how MPPN self-assembly depends on bilayer-protein interactions and lipid bilayer mechanical properties. We find that the bilayer-protein hydrophobic thickness mismatch is a key molecular control parameter for MPPN shape that can be used to bias MPPN self-assembly towards hi…
Membrane proteins typically deform the surrounding lipid bilayer membrane, which can play an important role in the function, regulation, and organization of membrane proteins. Membrane elasticity theory provides a beautiful description of protein-induced lipid bilayer deformations, in which all physical parameters can be directly determined from experiments. Analytic treatments of the membrane elasticity theory of protein-induced lipid bilayer deformations have largely focused on idealized protein shapes with circular cross section, and on perturbative solutions for proteins with non-circular …
The conformational free energy landscape of a system is a fundamental thermodynamic quantity of importance particularly in the study of soft matter and biological systems, in which the entropic contributions play a dominant role. While computational methods to delineate the free energy landscape are routinely used to analyze the relative stability of conformational states, to determine phase boundaries, and to compute ligand-receptor binding energies its use in problems involving the cell membrane is limited. Here, we present an overview of four different free energy methods to study morpholog…
We have carried out extensive Monte Carlo simulations of the fusion of tense apposed bilayers formed by amphiphilic molecules within the framework of a coarse grained lattice model. The fusion pathway differs from the usual stalk mechanism. Stalks do form between the apposed bilayers, but rather than expand radially to form an axial-symmetric hemifusion diaphragm of the trans leaves of both bilayers, they promote in their vicinity the nucleation of small holes in the bilayers. Two subsequent paths are observed: (i) The stalk encircles a hole in one bilayer creating a diaphragm comprised of bot…
Since the pioneering works of the founder of membrane mimetic chemistry Janos H. Fendler it is known that a number of atomic or molecular clusters and films (including nanoscale ones) are capable of mimicking the membrane functions. Membrane mimetic materials can be either soft matter or solid state materials. Conducting films (including those with magnetic properties) and semiconductors are also known to possess membrane mimetic properties. If we consider the agent exchange through the membrane in the operator form, the chemical composition of the membranes and their models, as well as the di…
Artificial bilayer lipid membranes (BLMs), along with patch-clamped membranes, are frequently used for functional analyses of membrane proteins. In both methods, the electric properties of membranes are characterized by only one parameter, namely, transmembrane potential. Here the construction of a novel BLM system was reported, in which membrane voltages can be controlled in a lateral direction in addition to conventional transmembrane direction. A microaperture was fabricated in a Teflon film and Ti electrodes were evaporated around the aperture. BLMs were reproducibly formed in the aperture…
The adhesion bonds connecting a lipid bilayer to an underlying surface may undergo a condensation transition resulting from an interplay between a short range attractive potential between them, and a long range fluctuation-induced potential of mean force. Here, we use computer simulations of a coarse-grained molecular model of supported lipid bilayers to study this transition in confined membranes, and in membranes subjected to a non-vanishing surface tension. Our results show that confinement may alter significantly the condensation transition of the adhesion bonds, whereas the application of…
Water-phospholipid interactions at the lipid bilayer/water interfaces are of essential importance for the dynamics, stability and function of biological membrane, and are also strongly associated with numerous biological processes at the interfaces of lipid bilayers. Various force fields, such as the united-atom Berger force field, its two improved versions by Kukol and by Poger, and the all-atom Slipid force field developed recently, can be applied to simulating the structures of lipid bilayer, with their structural predictions in good agreement with experimental data. In this work, we show t…
In this article we compare electrical conductance events from single channel recordings of three TRP channel proteins (TRPA1, TRPM2 and TRPM8) expressed in human embryonic kidney cells with channel events recorded on synthetic lipid membranes close to melting transitions. Ion channels from the TRP family are involved in a variety of sensory processes including thermo- and mechano-reception. Synthetic lipid membranes close to phase transitions display channel-like events that respond to stimuli related to changes in intensive thermodynamic variables such as pressure and temperature. TRP channel…
In biological membranes, alpha-tocopherols (α-toc; vitamin E) protect polyunsaturated lipids from free radicals. Although the interactions of α-toc with non-oxidized lipid bilayers have been studied, their on oxidized bilayers remain unknown. In this study, atomistic molecular dynamics (MD) simulations of oxidized lipid bilayers were performed with varying concentrations of α-toc. Bilayers with 1-palmitoyl-2-lauroyl-sn-glycero-3-phosphocholine (PLPC) lipids and its aldehyde derivatives at 1:1 ratio were studied. Our simulations show that oxidized lipids self-assemble into aggregates with a wat…
Although promising for biomedicine, the clinical translation of inorganic nanoparticles (NPs) is limited by low biocompatibility and stability in biological fluids. A common strategy to circumvent this drawback consists in disguising the active inorganic core with a lipid bilayer coating, reminiscent of the structure of the cell membrane to redefine the chemical and biological identity of NPs. While recent reports introduced membrane coating procedures for NPs, a robust and accessible method to quantify the integrity of the bilayer coverage is not yet available. To fill this gap, we prepared S…
In this work, we develop a two-component coarse-grained molecular dynamics (CGMD) model for simulating the erythrocyte membrane. This proposed model possesses the key feature of combing the lipid bilayer and the erythrocyte cytoskeleton, thus showing both the fluidic behavior of the lipid bilayer and elastic properties of the erythrocyte cytoskeleton. The proposed model facilitates simulations that span large length-scales (~ micrometer) and time-scales (~ ms). By tuning the interaction potential parameters, diffusivity and bending rigidity of the membrane model can be controlled. In the study…
According to the lipid raft hypothesis, biological lipid membranes are laterally heterogeneous and filled with nanoscale ordered "raft" domains, which are believed to play an important role for the organization of proteins in membranes. However, the mechanisms stabilizing such small rafts are not clear, and even their existence is sometimes questioned. Here we report the observation of raft-like structures in a coarse-grained molecular model for multicomponent lipid bilayers. On small scales, our membranes demix into a liquid ordered (lo) and a liquid disordered (ld) phase. On large scales, ph…
Genesis of a Horizontal Electric Field within the Lipid Bilayer: A Bilayer-Embedded Actuation Platform
Laboratory for Nanoelectronics and Spintronics, Research Institute of Electrical Communication (RIEC), Tohoku University（东北大学电气通信研究所纳米电子与自旋电子学实验室）；Graduate School of Biomedical Engineering, Tohoku University（东北大学生物医学工程学院研究生院）；School of Mechatronical Engineering, Beijing Institute of Technology（北京理工大学机电学院）；Advanced Institute for Materials Research (WPI-AIMR), Tohoku University（东北大学材料研究高等研究院）；Department of Molecular Neuroscience, Faculty of Medical Sciences, University of Fukui（福井大学医学科学部分子神经科学系）；Life Science Innovation Center, University of Fukui（福井大学生命科学创新中心）
Blebs are balloon-shaped membrane protrusions that form during many physiological processes. Using computer simulation of a particle-based model for self-assembled lipid bilayers coupled to an elastic meshwork, we investigated the phase behavior and kinetics of blebbing. We found that blebs form for large values of the ratio between the areas of the bilayer and the cytoskeleton. We also found that blebbing can be induced when the cytoskeleton is subject to a localized ablation or a uniform compression. The results obtained are qualitatively in agreement with the experimental evidence and the m…
Diffusion in biological membranes is seldom simply Brownian motion; instead, the rate of diffusion is dependent on the timescale of observation and so is often described as anomalous. In order to help better understand this phenomenon, model systems are needed where the anomalous subdiffusion of the lipid bilayer can be tuned and quantified. We recently demonstrated one such model by controlling the excluded area fraction in supported lipid bilayers (SLBs) through the incorporation of lipids derivatised with polyethylene glycol. Here we extend this work, using urea to induce anomalous subdiffu…
We have carried out Monte Carlo simulation of the fusion of bilayers of single chain amphiphiles which show phase behavior similar to that of biological lipids. The fusion mechanism we observe is very different from the ``stalk'' hypothesis. Stalks do form on the first stage of fusion, but they do not grow radially to form a hemifused state. Instead, stalk formation destabilizes the membranes and results in hole formation in the vicinity of the stalks. When holes in each bilayer nucleate spontaneously next to the same stalk, an incomplete fusion pore is formed. The fusion process is completed …
