The morphology of spherically confined flexoelectric fluid membrane vesicles in an external uniform electric field is studied numerically. Due to the deformations induced by the confinement, the membrane becomes polarized resulting in an interaction with the external field. The equilibrium shapes of the vesicle without electric field can be classified in a geometrical phase diagram as a function of scaled area and reduced volume [1,2]. When the area of the membrane is only slightly larger than the area of the confining sphere, a single axisymmetric invagination appears. A non-vanishing electric field induces an additional elongation of the confined vesicle which is either perpendicular or parallel depending on the sign of the electric field parameter. Higher values of the surface area or the electric field parameter can reduce the symmetry of the system leading to more complex folding. We present the resulting shapes and show that transition lines are shifted in the presence of an electric field. The obtained folding patterns could be of interest for biophysical and technological applications alike.
The disk-to-vesicle transition of a fluid membrane with no spontaneous curvature is well described by the competition between edge line and curvature energies. However, the transition of asymmetric membranes with spontaneous curvatures is not yet understood. In this study, the shape of the fluid membrane patch with a constant spontaneous curvature and its closing transition to a vesicle is investigated using theory and meshless membrane simulations. It is confirmed that the (meta)stable and transient membranes are well approximated by spherical caps. The membrane Gaussian modulus can be estima…
The shape transformations of fluid membranes induced by curved protein rods are studied using meshless membrane simulations. The rod assembly at low rod density induces a flat membrane tube and oblate vesicle. It is found that the polyhedral shapes are stabilized at high rod densities. The discrete shape transition between triangular and buckled discoidal tubes is obtained and their curvature energies are analyzed by a simple geometric model. For vesicles, triangular hosohedron and elliptic-disk shapes are formed in equilibrium, whereas tetrahedral and triangular prism shapes are obtained as m…
We investigate the morphology of a toroidal fluid membrane vesicle confined inside a spherical container. The equilibrium shapes are assembled in a geometrical phase diagram as a function of scaled area and reduced volume of the membrane. For small area the vesicle can adopt its free form. When increasing the area, the membrane cannot avoid contact and touches the confining sphere along a circular contact line, which extends to a zone of contact for higher area. The elastic energies of the equilibrium shapes are compared to those of their confined counterparts of spherical topology to predict …
Narrow membrane tubes are commonly pulled out from the surface of phospholipid vesicles using forces applied either through laser or magnetic tweezers or through the action of processive motor proteins. Recent examples have emerged where such tubes spontaneously grow from vesicles coated with bioactive cytoskeletal filaments (e.g. FtsZ, microtubule) in the presence GTP. We show how a soft vesicle deforms due to the interplay between its topology, local curvature and the forces due to the active filaments. We present results from Dynamically Triangulated Monte Carlo simulations of a spherical c…
Cellular membranes exhibit a large variety of shapes, strongly coupled to their function. Many biological processes involve dynamic reshaping of membranes, usually mediated by proteins. This interaction works both ways: while proteins influence the membrane shape, the membrane shape affects the interactions between the proteins. To study these membrane-mediated interactions on closed and anisotropically curved membranes, we use colloids adhered to ellipsoidal membrane vesicles as a model system. We find that two particles on a closed system always attract each other, and tend to align with the…
We analyze the non-equilibrium shape fluctuations of giant unilamellar vesicles encapsulating motile bacteria. Owing to bacteria--membrane collisions, we experimentally observe a significant increase in the magnitude of membrane fluctuations at low wave numbers, compared to the well-known thermal fluctuation spectrum. We interrogate these results by numerically simulating membrane height fluctuations via a modified Langevin equation, which includes bacteria--membrane contact forces. Taking advantage of the length and time scale separation of these contact forces and thermal noise, we further c…
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…
Motivated by a long-standing debate concerning the nature and interrelations of surface-tension variables in fluid membranes, we reformulate the thermodynamics of a membrane vesicle as a generic two-dimensional finite system enclosing a three-dimensional volume. The formulation is shown to require two tension variables, conjugate to the intensive constraints of area per molecule and volume-to-area ratio. We obtain the relation between these two variables in various scenarios, as well as their correspondence to other definitions of tension variables for membranes. Several controversies related …
Dynamic Light Scattering (DLS), Small Angle X-ray Scattering (SAXS) and Transmission Electron Microscopy (TEM) are physical techniques widely employed to characterize the morphology and the structure of vesicles such as liposomes or human extracellular vesicles (exosomes). Bacterial extracellular vesicles are similar in size to human exosomes, although their function and membrane properties have not been elucidated in such detail as in the case of exosomes. Here, we applied the above cited techniques, in synergy with the thermodynamic characterization of the vesicles lipid membrane using a tur…
Renormalized mechanics and stochastic thermodynamics of growing vesicles
The James Franck Institute, University of Chicago（芝加哥大学詹姆斯·弗兰克研究所）；Department of Chemistry, University of Chicago（芝加哥大学化学系）；Engineering Sciences and Applied Mathematics, Northwestern University（西北大学工程科学与应用数学系）
We study a synthetic system of motile Escherichia coli bacteria encapsulated inside giant lipid vesicles. Forces exerted by the bacteria on the inner side of the membrane are sufficient to extrude membrane tubes filled with one or several bacteria. We show that a physical coupling between the membrane tube and the flagella of the enclosed cells transforms the tube into an effective helical flagellum propelling the vesicle. We develop a simple theoretical model to estimate the propulsive force from the speed of the vesicles, and demonstrate the good efficiency of this coupling mechanism. Togeth…
Eukaryote cells have a flexible shape, which dynamically changes according to the function performed by the cell. One mechanism for deforming the cell membrane into the desired shape is through the expression of curved membrane proteins. Furthermore, these curved membrane proteins are often associated with the recruitment of the cytoskeleton, which then applies active forces that deform the membrane. This coupling between curvature and activity was previously explored theoretically in the linear limit of small deformations, and low dimensionality. Here we explore the unrestricted shapes of ves…
A tethered vesicle, which consists of a cylindrical membrane tube and a spherical vesicle, is produced by a mechanical force that is experimentally imposed by optical tweezers and a micropipette. This tethered vesicle is employed for examining the curvature sensing of curvature-inducing proteins. In this study, we clarify how the binding of proteins with a laterally isotropic spontaneous curvature senses and generates the membrane curvatures of the tethered vesicle using mean-field theory and meshless membrane simulation. The force-dependence curves of the protein density in the membrane tube …
A widely used method to measure the bending rigidity of bilayer membranes is fluctuation spectroscopy, which analyses the thermally-driven membrane undulations of giant unilamellar vesicles recorded with either phase-contrast or confocal microscopy. Here, we analyze the fluctuations of the same vesicle using both techniques and obtain consistent values for the bending modulus. We discuss the factors that may lead to discrepancies.
Unravelling the physical mechanisms behind the organisation of lipid domains is a central goal in cell biology and membrane biophysics. Previous studies on cells and model lipid bilayers featuring phase-separated domains found an intricate interplay between the membrane geometry and its chemical composition. However, the lack of a model system with simultaneous control over the membrane shape and conservation of its composition precluded a fundamental understanding of curvature-induced effects. Here, we present a new class of multicomponent vesicles supported by colloidal scaffolds of designed…
The viscosity of lipid bilayer membranes plays an important role in determining the diffusion constant of embedded proteins and the dynamics of membrane deformations, yet it has historically proven very difficult to measure. Here we introduce a new method based on quantification of the large-scale circulation patterns induced inside vesicles adhered to a solid surface and subjected to simple shear flow in a microfluidic device. Particle Image Velocimetry based on spinning disk confocal imaging of tracer particles inside and outside of the vesicle, and tracking of phase-separated membrane domai…
Many biological systems fold thin sheets of lipid membrane into complex three-dimensional structures. This microscopic origami is often mediated by the adsorption and self-assembly of proteins on a membrane. As a model system to study adsorption-mediated interactions, we study the collective behavior of micrometric particles adhered to a lipid vesicle. We estimate the colloidal interactions using a maximum likelihood analysis of particle trajectories. When the particles are highly wrapped by a tense membrane, we observe strong long-range attractions with a typical binding energy of 150 $k_B T$…
We study the effect of permeabilizing electric fields applied to two different types of giant unilamellar vesicles, the first formed from EggPC lipids and the second formed from DOPC lipids. Experiments on vesicles of both lipid types show a decrease in vesicle radius which is interpreted as being due to lipid loss during the permeabilization process. We show that the decrease in size can be qualitatively explained as a loss of lipid area which is proportional to the area of the vesicle which is permeabilized. Three possible mechanisms responsible for lipid loss were directly observed: pore fo…
The secretion of vesicles for intracellular transport often rely on the aggregation of specialized membrane-bound proteins into a coat able to curve cell membranes. The nucleation and growth of a protein coat is a kinetic process that competes with the energy-consuming turnover of coat components between the membrane and the cytosol. We propose a generic kinetic description of coat assembly and the formation of coated vesicles, and discuss its implication to the dynamics of COP vesicles that traffic within the Golgi and with the Endoplasmic Reticulum. We show that stationary coats of fixed are…
In this work, we study the adhesion of multi-component vesicle membrane to both flat and curved substrates, based on the conventional Helfrich bending energy for multi-component vesicles and adhesion potentials of different forms. A phase field formulation is used to describe the different components of the vesicle. For the axisymmetric case, a number of representative equilibrium vesicle shapes are computed and some energy diagrams are presented which reveal the dependence of the calculated shapes and solution branches on various parameters including both bending moduli and spontaneous curvat…
The morphologies of genus-2 to -8 fluid vesicles are studied by using dynamically triangulated membrane simulations with area-difference elasticity. It is revealed that the alignments of the membrane pores alter the vesicle shapes and the types of shape transitions for the genus $g \ge 3$. At a high reduced volume, a stomatocyte with a circular alignment of $g+1$ pores continuously transforms into a discocyte with a line of $g$ pores with increasing intrinsic area difference. In contrast, at a low volume, a stomatocyte transforms into a ($g+1$)-hedral shape and subsequently exhibits a discrete…
A transient analysis for vesicle deformation under DC electric fields is developed. The theory extends from a droplet model, with the additional consideration of a lipid membrane separating two fluids of arbitrary properties. For the latter, both a membrane-charging and a membrane-mechanical model are supplied. The vesicle is assumed to remain spheroidal in shape for all times. The main result is an ODE governing the evolution of the vesicle aspect ratio. The effects of initial membrane tension and pulse length are examined. The model prediction is extensively compared with experimental data, …
The study of vesicles in suspension is important to understand the complicated dynamics exhibited by cells in vivo and in vitro. We developed a computer simulation based on the boundary-integral method to model the three dimensional gravity-driven sedimentation of charged vesicles towards a flat surface. The membrane mechanical behavior was modeled using the Helfrich Hamiltonian and near incompressibility of the membrane was enforced via a model which accounts for the thermal fluctuations of the membrane. The simulations were verified and compared to experimental data obtained using suspended …
The growth, form, and division of prebiotic vesicles, membraneous bags of fluid of varying components and shapes is hypothesized to have served as the substrate for the origin of life. The dynamics of these out-of-equilibrium structures is controlled by physicochemical processes that include the intercalation of amphiphiles into the membrane, fluid flow across the membrane, and elastic deformations of the membrane. To understand prebiotic vesicular forms and their dynamics, we construct a minimal model that couples membrane growth, deformation, and fluid permeation, ultimately couched in terms…
Recent experiments have shown that when a near-hemispherical lipid vesicle attached to a solid surface is subjected to a simple shear flow it exhibits a pattern of membrane circulation much like a dipole vortex. This is in marked contrast to the toroidal circulation that would occur in the related problem of a drop of immiscible fluid attached to a surface and subjected to shear. This profound difference in flow patterns arises from the lateral incompressibility of the membrane, which restricts the observable flows to those in which the velocity field in the membrane is two-dimensionally diver…
Bilayer membranes self-assembled from simple amphiphiles in solution always have a planar ground-state shape. This is a consequence of several internal relaxation mechanisms of the membrane and prevents the straightforward control of vesicle size. Here, we show that this principle can be circumvented and that direct size control by molecular design is a realistic possibility. Using coarse-grained calculations, we design tetrablock copolymers that form membranes with a preferred curvature, and demonstrate how to form low-polydispersity vesicles while suppressing micellization.
We propose a free energy expression accounting for the formation of spherical vesicles from planar lipidic membranes and derive a Fokker-Planck equation for the probability distribution describing the dynamics of vesicle formation. We found that formation may occur as an activated process for small membranes and as a transport process for sufficiently large membranes. We give explicit expressions for the transition rates and the characteristic time of vesicle formation in terms of the relevant physical parameters.
Clathrin-mediated endocytosis (CME) is a key pathway for transporting cargo into cells via membrane vesicles. It plays an integral role in nutrient import, signal transduction, neurotransmission and cellular entry of pathogens and drug-carrying nanoparticles. As CME entails substantial local remodeling of the plasma membrane, the presence of membrane tension offers resistance to bending and hence, vesicle formation. Experiments show that in such high tension conditions, actin dynamics is required to carry out CME successfully. In this study, we build upon these pioneering experimental studies …
A method for determining permeability of phospholipid bilayer based on the osmotic swelling of micrometer-sized giant unilamellar vesicles (GUVs) is presented as an alternative to the two established techniques, dynamic light scattering on liposome suspension, and electrical measurements on planar lipid bilayers. In the described technique, an individual GUV is transferred using a micropipette from a sucrose/glucose solution into an isomolar solution containing the solute under investigation. Throughout the experiment, vesicle cross-section is monitored and recorded using a digital camera moun…
Lipid bilayer membranes are the fundamental biological barriers that permit life. The bilayer dynamics largely participates in orchestrating cellular workings and is characterized by substantial stability together with extreme plasticity that allows controlled morphological/topological changes. Modeling and understanding the topological change of vesicle-like membrane at the scale of a full cell has proved an elusive aim. We propose and discuss here a continuum model able to encompass the fusion/fission transition of a bilayer membrane at the scale of a Large Unilamellar Vesicle and evaluate t…
Small angle neutron scattering (SANS) on the unilamellar vesicle populations (diameter 500 and 1000 angstrom) was used to characterize lipid vesicles from dimyristoylphosphatidylcholine (DMPC) at three phases (gel, ripple, and liquid). Parameters of vesicle populations and internal structure of the DMPC bilayer were characterized on the basis of the Separated Form Factor (SFF) model. Parameters of the internal bilayer structure (thickness of the membrane and the hydrophobic core, hydration, and surface area of lipid molecule) were determined on the basis of the Hydrophobic-Hydrophilic (HH) app…
Salt is a very common molecule in aqueous environments but the question of whether the interactions of monovalent ions Na^+ and Cl^- ,with the neutral heads of phospholipids are impactful enough to change the membrane rigidity is still a mystery. To provide a resolution to this long simmering debate, we investigated the dynamics of DOPC vesicles in the fluid phase with increasing external salt concentration. At higher salt concentrations, we observe an increase in bending rigidity from neutron spin echo spectroscopy (NSE) and an increase in bilayer thickness from small-angle X-ray scattering (…
Vesicles and many biological membranes are made of two monolayers of lipid molecules and form closed lipid bilayers. The dynamical behaviour of vesicles is very complex and a variety of forms and shapes appear. Lipid bilayers can be considered as a surface fluid and hence the governing equations for the evolution include the surface (Navier--)Stokes equations, which in particular take the membrane viscosity into account. The evolution is driven by forces stemming from the curvature elasticity of the membrane. In addition, the surface fluid equations are coupled to bulk (Navier--)Stokes equatio…
As solute molecules permeate into a vesicle due to a concentration difference across its membrane, the vesicle swells through osmosis. The swelling can be divided into two stages: (a) an "ironing" stage, where the volume-to-area ratio of the vesicle increases without a significant change in its area; (b) a stretching stage, where the vesicle grows while remaining essentially spherical, until it ruptures. We show that the crossover between these two stages can be represented as a broadened continuous phase transition. Consequently, the swelling curves for different vesicles and different permea…
We develop an analytical theory to explain the experimentally-observed morphological transitions of giant vesicles induced by AC electric fields (1). The model treats the inner and suspending media as lossy dielectrics, while the membrane as an ion-impermeable flexible incompressible-fluid sheet. The vesicle shape is obtained by balancing electric, hydrodynamic, and bending stresses exerted on the membrane. Considering a nearly spherical vesicle, the solution to the electrohydrodynamic problem is obtained as a regular perturbation expansion in the excess area. The theory predicts that stationa…
Phospholipidic membranes and vesicles constitute a basic element in real biological functions. Vesicles are viewed as a model system to mimic basic viscoelastic behaviors of some cells, like red blood cells. Phase field and level-set models are powerful tools to tackle dynamics of membranes and their coupling to the flow. These two methods are somewhat similar, but to date no bridge between them has been made. This is a first focus of this paper. Furthermore, a constitutive viscoelastic law is derived for the composite fluid: the ambient fluid and the membranes. We present two different approa…
Eukaryotic cells adhere to extracellular matrix during the normal development of the organism, forming static adhesion as well as during cell motility. We study this process by considering a simplified coarse-grained model of a vesicle that has uniform adhesion energy with a flat substrate, mobile curved membrane proteins and active forces. We find that a high concentration of curved proteins alone increases the spreading of the vesicle, by the self-organization of the curved proteins at the high curvature vesicle-substrate contact line, thereby reducing the bending energy penalty at the vesic…
Biological membranes constantly change their shape in response to external stimuli, and understanding the remodeling and stability of vesicles in heterogeneous environments is therefore of fundamental importance for a range of cellular processes. One crucial question is how vesicles respond to external osmotic stresses, imposed by differences in solute concentrations between the vesicle interior and exterior. Previous analyses of the membrane bending energy have predicted that micron-sized giant unilamellar vesicles (GUVs) should become globally deformed already for nanomolar concentration dif…
A technique for determining the permeability of a phospholipid membrane on a single giant unilamellar vesicle (GUV) is described, which complements the existing methods utilizing either a planar black lipid membrane or sub-micrometre-sized liposomes. A single GUV is transferred using a micropipette from a solution of a nonpermeable solute into an iso-osmolar solution of a solute with a higher membrane permeability. Osmotical swelling of the vesicle is monitored with a CCD camera mounted on a phase contrast microscope, and a sequence of images is obtained. On each image, the points on the vesic…
The presence of membrane tubules in living cells is essential to many biological processes. In cells, one mechanism to form nanosized lipid tubules is via molecular motor induced bilayer extraction. In this paper, we describe a simple experimental model to investigate the forces required for lipid tube formation using kinesin motors anchored to DOPC vesicles. Previous related studies have used molecular motors actively pulling on the membrane to extract a nanotube. Here, we invert the system geometry; molecular motors are used as static anchors linking DOPC vesicles to a two-dimensional microt…
Amphiphilic molecules such as surfactants, lipids and block copolymers can be assembled into bilayers and form vesicles. Fluorescent membrane labeling methods require the use of dye molecules that can be inserted in the bilayers at different stages of the synthesis. To our knowledge there is no generalized method for labeling preformed vesicles. Herein we develop a versatile protocol that is suitable to both surfactant and lipid preformed vesicles and requires no separation or purification steps. Based on the lipophilic carbocyanine green dye PKH67, the methodology is assessed on zwitterionic …
We present a method for simulating fluid vesicles with in-plane orientational ordering. The method involves computation of local curvature tensor and parallel transport of the orientational field on a randomly triangulated surface. It is shown that the model reproduces the known equilibrium conformation of fluid membranes and work well for a large range of bending rigidities. Introduction of nematic ordering leads to stiffening of the membrane. Nematic ordering can also result in anisotropic rigidity on the surface leading to formation of membrane tubes.
We establish a biophysical model for the dynamics of lipid vesicles exposed to surfactants. The solubilization of the lipid membrane due to the insertion of surfactant molecules induces a reduction of membrane surface area at almost constant vesicle volume. This results in a rate-dependent increase of membrane tension and leads to the opening of a micron-sized pore. We show that solubilization kinetics due to surfactants can determine the regimes of pore dynamics: either the pores open and reseal within a second (short-lived pore), or the pore stays open up to a few minutes (long-lived pore). …
A model of vesicle electrodeformation is described which obtains a parametrized vesicle shape by minimizing the sum of the membrane bending energy and the energy due to the electric field. Both the vesicle membrane and the aqueous media inside and outside the vesicle are treated as leaky dielectrics, and the vesicle itself is modelled as a nearly spherical shape enclosed within a thin membrane. It is demonstrated (a) that the model achieves a good quantitative agreement with the experimentally determined prolate-to-oblate transition frequencies in the kHz range, and (b) that the model can expl…
(200 words) Oxidation of unsaturated lipids is a fundamental process involved in cell bioenergetics as well as in cell death. Using giant unilamellar vesicles and a chlorin photosensitizer, we asymmetrically oxidized the outer or inner monolayers of lipid membranes. We observed different shape transitions such as oblate to prolate and budding, which are typical of membrane curvature modifications. The asymmetry of the shape transitions is in accordance with a lowered effective spontaneous curvature of the leaflet being targeted. We interpret this effect as a decrease in the preferred area of t…
We study a dynamical curvature instability caused by a local chemical modification of a phospholipid membrane. In our experiments, a basic solution is microinjected close to a giant unilamellar vesicle, which induces a local chemical modification of some lipids in the external monolayer of the membrane. This modification causes a local deformation of the vesicle, which then relaxes. We present a theoretical description of this instability, taking into account both the change of the equilibrium lipid density and the change of the spontaneous membrane curvature induced by the chemical modificati…
