We study a model of a lipid bilayer membrane described by two order parameters: the chemical composition described using the Gaussian model and the spatial configuration described with the elastic deformation model of a membrane with a finite thickness, or equivalently, for an adherent membrane. We assume and explain on physical grounds the linear coupling between the two order parameters. Using the exact solution, we calculate the correlation functions and order parameters profiles. We also study the domains that form around inclusions on the membrane. We propose and compare six distinct ways to quantify the size of such domains. Despite of its simplicity, the model has many interesting features like Fisher-Widom line or two distinct critical regions.
Critical lateral pressure for a pore formation and phase diagram of porous membrane are derived analytically as functions of the microscopic parameters of the lipid chains. The derivation exploits path-integral calculation of the free energy of the ensembles of semi-flexible strings and rigid rods that mimic the hydrophobic tails of lipids in the lipid bilayers and bolalipid membranes respectively. Analytical expressions for the area stretch/compressibility moduli of the membranes are derived in both models.
The eukaryotic cell membrane is connected to a dense actin rich cortex. We present FCS and STED experiments showing that dense membrane bound actin networks have severe influence on lipid phase separation. A minimal actin cortex was bound to a supported lipid bilayer via biotinylated lipid streptavidin complexes (pinning sites). In general, actin binding to ternary membranes prevented macroscopic liquid-ordered and liquid-disordered domain formation, even at low temperature. Instead, depending on the type of pinning lipid, an actin correlated multi-domain pattern was observed. FCS measurements…
The behavior of lipid membranes in the presence of an external electric field is studied and used to examine the influence of such fields on membrane parameters such as roughness and show that for a micro sized membrane, roughness grows as the field increases. The dependence of bending rigidity on the electric field is also studied and an estimation of thickness of the accumulated charges around lipid membranes in a free-salt solution is presented.
Tension in lipid membranes is often controlled externally, by pulling on the boundary of the membrane or changing osmotic pressure across a curved membrane. But modifications of the tension can also be induced in an internal fashion, for instance as a byproduct of changing a membranes electric potential or, as observed experimentally, by activity of membrane proteins. Here we develop a theory which demonstrate how such internal contributions to the tension are moderated through elastic stretching of the membrane when the membrane is initially in a low tension floppy state.
Using integral equation theory of liquids to a binary mixed fluid lipid membrane, we study the membrane-mediated interactions between the macroions and the redistribution of neutral and charged lipids due to binding macroions. We find that when the concentration of binding macroions is infinitely dilute, the main contribution to the attractive potential between macroions is the line tension between neutral and charged lipids of the membrane, and the bridging effect also contributes to the attraction. As the relative concentration of charged lipids is increased, we observe a repulsive - attract…
The membrane curvature of cells and intracellular compartments continuously adapts to enable cells to perform vital functions, from cell division to signal trafficking. Understanding how membrane geometry affects these processes in vivo is challenging because of the membrane complexity as well as the short time and small length scales involved. By contrast, in vitro model membranes with engineered curvature provide a versatile platform for this investigation and applications to biosensing and biocomputing. However, a general route to the fabrication of lipid membranes with prescribed curvature…
We study, using dissipative particle dynamics simulations, the effect of active lipid flip-flop on model fluid bilayer membranes. We consider both cases of symmetric as well as asymmetric flip-flops. Symmetric flip-flop leads to a steady state of the membrane with an effective temperature higher than that of the equilibrium membrane and an effective surface tension lower than that of the equilibrium membrane. Asymmetric flip-flop leads to transient conformational changes of the membrane in the form of bud or blister formation, depending on the flip rate.
The phase separation in lipid bilayers that include negatively charged lipids is examined experimentally. We observed phase-separated structures and determined the membrane miscibility temperatures in several binary and ternary lipid mixtures of unsaturated neutral lipid, dioleoylphosphatidylcholine (DOPC), saturated neutral lipid, dipalmitoylphosphatidylcholine (DPPC), unsaturated charged lipid, dioleoylphosphatidylglycerol (DOPG$^{\scriptsize{(-)}}$), saturated charged lipid, dipalmitoylphosphatidylglycerol (DPPG$^{\scriptsize{(-)}}$), and cholesterol. In binary mixtures of saturated and uns…
We report a combined dynamic light scattering and neutron spin-echo (NSE) study on vesicles composed of the phospholipid 1,2-dimyristoyl-sn-glycero-3-phosphatidylcholine under the influence of varying amounts of perfluorooctanoic acid. We study local lipid bilayer undulations using NSE on time scales up to 200 ns. Similar to the effect evoked by cholesterol, we attribute the observed lipid bilayer stiffening to a condensing effect of the perfluorinated compound on the membrane.
One of the most widely used methods for determination of the bending elasticity modulus of model lipid membranes is the analysis of the shape fluctuations of nearly spherical lipid vesicles. The theoretical basis of this analysis is given by Milner and Safran. In their theory the stretching effects are not considered. In the present study we generalized their approach including the stretching effects deduced after an application of statistical mechanics of vesicles.
Health concerns associated with the advent of nanotechnologies have risen sharply when it was found that particles of nanoscopic dimensions reach the cell lumina. Plasma and organelle lipid membranes, which are exposed to both the incoming and the engulfed nanoparticles, are the primary targets of possible disruptions. However, reported adhesion, invagination and embedment of nanoparticles (NPs) do not compromise the membrane integrity, precluding direct bilayer damage as a mechanism for toxicity. Here it is shown that a lipid membrane can be torn by small enough nanoparticles, thus unveiling …
We investigated the effect of charge on the membrane morphology of giant unilamellar vesicles (GUVs) composed of various mixtures containing charged lipids. We observed the membrane morphologies by fluorescent and confocal laser microscopy in lipid mixtures consisting of a neutral unsaturated lipid [dioleoylphosphatidylcholine (DOPC)], a neutral saturated lipid [dipalmitoylphosphatidylcholine (DPPC)], a charged unsaturated lipid [dioleoylphosphatidylglycerol (DOPG$^{\scriptsize{(-)}}$)], a charged saturated lipid [dipalmitoylphosphatidylglycerol (DPPG$^{\scriptsize{(-)}}$)], and cholesterol (C…
We present a stochastic phase-field model for multicomponent lipid bilayers that explicitly accounts for the quasi-two-dimensional hydrodynamic environment unique to a thin fluid membrane immersed in aqueous solution. Dynamics over a wide range of length scales (from nanometers to microns) for durations up to seconds and longer are readily accessed and provide a direct comparison to fluorescence microscopy measurements in ternary lipid/cholesterol mixtures. Simulations of phase separation kinetics agree with experiment and elucidate the importance of hydrodynamics in the coarsening process.
The behavior of a non-conductive quasi-planar lipid membrane in an electrolyte and in a static (DC) electric field is investigated theoretically in the nonlinear (Poisson-Boltzmann) regime. Electrostatic effects due to charges in the membrane lipids and in the double layers lead to corrections to the membrane elastic moduli which are analyzed here. We show that, especially in the low salt limit, i) the electrostatic contribution to the membrane's surface tension due to the Debye layers crosses over from a quadratic behavior in the externally applied voltage to a linear voltage regime. ii) the …
The nicotinic acetylcholine receptor (nAChR) and other pentameric ligand-gated ion channels (pLGICs) are native to neuronal membranes with an unusual lipid composition. While it is well-established that these receptors can be significantly modulated by lipids, the underlying mechanisms have been primarily studied in model membranes with only a few lipid species. Here we use coarse-grained molecular dynamics (MD) simulation to probe specific binding of lipids in a complex quasi-neuronal membrane. We ran a total of 50 microseconds of simulations of a single nAChR in a membrane composed of 36 spe…
Consider a lipid membrane with a free exposed edge. The energy describing this membrane is quadratic in the extrinsic curvature of its geometry; that describing the edge is proportional to its length. In this note we determine the boundary conditions satisfied by the equilibria of the membrane on this edge, exploiting variational principles. The derivation is free of any assumptions on the symmetry of the membrane geometry. With respect to earlier work for axially symmetric configurations, we discover the existence of an additional boundary condition which is identically satisfied in that limi…
The structure of membrane-active peptides and their interaction with lipid bilayers can be studied in oriented lipid membranes deposited on solid substrates. Such systems are desirable for a number of surface-sensitive techniques. Here we focus on structural characterization by x-ray and neutron reflectivity and give an account of recent progress in sample preparation and measurements. We show that the degree of mesoscopic disorder in the films can significantly influence the scattering curves. Static defects should be minimized by optimization of the preparation techniques and their presence …
Lipid membranes form the barrier between the inside and outside of cells and many of their subcompartments. As such, they bind to a wide variety of nano- and micrometer sized objects and, in the presence of strong adhesive forces, strongly deform and envelop particles. This wrapping plays a key role in many healthy and disease-related processes. So far, little work has focused on the dynamics of the wrapping process. Here, using a model system of micron-sized colloidal particles and giant unilamellar lipid vesicles with tunable adhesive forces, we measure the velocity of the particle during it…
We present a phenomenological theory of phase transitions in achiral lipid membranes in terms of two coupled order parameters -- a scalar order parameter describing lipid chain melting, and a vector order parameter describing the tilt of the hydrocarbon chains below the chain-melting transition. Existing theoretical models fail to account for all the observed features of the phase diagram, in particular the detailed microstructure of the asymmetric ripple phase lying between the fluid and the tilted gel phase. In contrast, our two-component theory reproduces all the salient structural features…
This review describes the analytical calculation of lateral pressure profile in lipid membrane with finite curvature. The derivation is based on the previously developed microscopic model of flexible strings [1,2]. According to this theory the energy per unit chain is considered as energy of flexible string (Euler's elastic beam of finite thickness) and interaction between chains is considered as an entropic repulsion. This microscopic theory allows to obtain expression for lateral pressure distribution in bent lipid membrane if treating a bending as a small deviation from the flat membrane co…
The structure of the ripple phase of phospholipid membranes remains poorly understood in spite of a large number of theoretical studies, with many experimentally established structural features of this phase unaccounted for. In this article we present a phenomenological theory of phase transitions in single- and two-component achiral lipid membranes in terms of two coupled order parameters -- a scalar order parameter describing {\it lipid chain melting}, and a vector order parameter describing the {\it tilt of the hydrocarbon chains} below the chain-melting transition. This model reproduces al…
Lipid membrane with freely exposed edge is regarded as smooth surface with curved boundary. Exterior differential forms are introduced to describe the surface and the boundary curve. The total free energy is defined as the sum of Helfrich's free energy and the surface and line tension energy. The equilibrium equation and boundary conditions of the membrane are derived by taking the variation of the total free energy. These equations can also be applied to the membrane with several freely exposed edges. Analytical and numerical solutions to these equations are obtained under the axisymmetric co…
Highly oriented solid-supported lipid membranes in stacks of controlled number $N \simeq 16$ (oligo-membranes) have been prepared by spin-coating using the uncharged lipid model system 1,2-dimyristoyl-sn-glycero-3-phosphocholine (DMPC). The samples have been immersed in aqueous polymer solutions for control of osmotic pressure and have been studied by X-ray reflectivity. The bilayer structure and fluctuations have been determined by modelling the data over the full q-range. Thermal fluctuations are described using the continuous smectic Hamiltonian with the appropriate boundary conditions at t…
A model of lipid bilayers made of a mixture of two lipids with different average compositions on both leaflets, is developed. A Landau hamiltonian describing the lipid-lipid interactions on each leaflet, with two lipidic fields $ψ_1$ and $ψ_2$, is coupled to a Helfrich one, accounting for the membrane elasticity, via both a local spontaneous curvature, which varies as $C_0+C_1(ψ_1-ψ_2)/2$, and a bending modulus equal to $κ_0+κ_1(ψ_1+ψ_2)/2$. This model allows us to define curved patches as membrane domains where the asymmetry in composition, $ψ_1-ψ_2$, is large, and thick and stiff patches whe…
The behavior of lipid bilayer is important to understand the functionality of cells like the trafficking of ions between cells. Standard procedures to explore the properties of lipid bilayer and hemifused states typically use either supported membranes or vesicles. Both techniques have several shortcoming in terms of bio relevance or accessibility for measurements. In this article the formation of individual free standing hemifused states between model cell membranes is studied using an optimized microfluidic scheme which allows for simultaneous optical and electrophysiological measurements. I…
We report results concerning the destabilisation of supported phospholipid bilayers in a well-defined geometry. When heating up supported phospholipid membranes deposited on highly hydrophilic glass slides from room temperature (i.e. with lipids in the gel phase), unbinding was observed around the main gel to fluid transition temperature of the lipids. It lead to the formation of relatively monodisperse vesicles, of which most remained tethered to the supported bilayer. We interpret these observations in terms of a sharp decrease of the bending rigidity modulus $κ$ in the transition region, co…
The organization of lipids in biological membranes is essential for cellular functions such as signal transduction and membrane trafficking. A major challenge is how to control lateral lipid composition in supported membranes which are crucial for the design of biosensors and investigation of cellular processes. Here, we undertake the first theoretical study of lateral organization of mixed lipids in bilayers induced by a geometrically patterned substrate, and examine the physical mechanism of patterned substrate-induced structural formation in the supported lipid bilayers. A rich variety of c…
Membrane bending is an extensively studied problem from both modeling and experimental perspectives because of the wide implications of curvature generation in cell biology. Many of the curvature generating aspects in membranes can be attributed to interactions between proteins and membranes. These interactions include protein diffusion and formation of aggregates due to protein-protein interactions in the plane of the membrane. Recently, we developed a model that couples the in-plane flow of lipids and diffusion of proteins with the out-of-plane bending of the membrane. Building on this work,…
Specific lipid environments are necessary for the establishment of protein signalling platforms in membranes, yet their origin has been highly debated. We present a continuum, exactly solvable model of protein induced local demixing of lipid membranes. The coupling between a local composition and a local thickness of the membrane induces lipid domains around inclusions with hydrophobic mismatch, even for temperatures above the miscibility critical point of the membrane. The model qualitatively explains the experimentally observed formation of lipid domains induced by anchoring of reconstituted…
We study the stress distribution profiles and the height and thickness fluctuations of lipid membranes in the tilted gel state by Monte Carlo simulations of a generic coarse-grained model for lipid membranes, which reproduces many known properties of DPPC bilayers. The results are related to the corresponding properties of fluid membranes, and to theoretical predictions for crystalline and hexatic membranes. One striking observation is that the spontaneous curvature of the monolayers changes sign from the fluid to the gel phase. In the gel phase, the long-wavelength height fluctuations are sup…
Caffeine (1,3,7-trimethylxanthine), an ingredient of coffee, is used worldwide as a psychostimulant, antioxidant, and adjuvant analgesic. To gain insights into the action mechanism of caffeine, we report on its effects on the phase behaviour and microscopic dynamics of a dioctadecyldimethylammonium bromide (DODAB) lipid membrane, as studied quasielastic neutron scattering (QENS). Tracking the elastic scattering intensity as a function of temperature showed that caffeine does not alter the phase behaviour of the DODAB membrane and that transition temperatures remain almost unaltered. However, Q…
Changes of external parameters in proximity of critical point can increase thermal fluctuations of tubular lipid membrane (TLM) and result in variation of the membrane shape. The phase transitions in the system are shown to be controlled by a single effective parameter, which depends on the pressure difference between inner and outer regions of membrane and the applied stretching force. We determine an interval of the parameter values corresponding to the stability region of the cylindrical shape of TLM and investigate the behavior of the system in the vicinity of critical instabilities, where…
We present a general and systematic theory of non-equilibrium dynamics of multi-component fluid membranes, in general, and membranes containing transmembrane proteins, in particular. Developed based on a minimal number of principles of statistical physics and designed to be a meso/macroscopic-scale effective description, the theory is formulated in terms of a set of equations of hydrodynamics and linear constitutive relations. As a particular emphasis of the theory, the equations and the constitutive relations address both the thermodynamic and the hydrodynamic consequences of the unconvention…
We study a model lipid bilayer composed of a mixture of two incompatible lipid types which have a natural tendency to segregate in the absence of membrane fluctuations. The membrane is mechanically characterized by a local bending rigidity $κ(ϕ)$ which varies with the average local lipid composition $ϕ$. We show, in the case where $κ$ varies weakly with $ϕ$, that the effective interaction between lipids of the same type can either be everywhere attractive or can have a repulsive component at intermediate distances greater than the typical lipid size. When this interaction has a repulsive compo…
A mesoscopic coarse-grain model for computationally-efficient simulations of biomembranes is presented. It combines molecular dynamics simulations for the lipids, modeled as elastic chains of beads, with multiparticle collision dynamics for the solvent. Self-assembly of a membrane from a uniform mixture of lipids is observed. Simulations at different temperatures demonstrate that it reproduces the gel and liquid phases of lipid bilayers. Investigations of lipid diffusion in different phases reveals a crossover from subdiffusion to normal diffusion at long times. Macroscopic membrane properties…
Lipid membranes, the barrier defining living cells and many of their sub-compartments, bind to a wide variety of nano- and micro-meter sized objects. In the presence of strong adhesive forces, membranes can strongly deform and wrap the particles, an essential step in crossing the membrane for a variety of health and disease-related processes. A large body of theoretical and numerical work has focused on identifying the physical properties that underly wrapping. Using a model system of micron-sized colloidal particles and giant unilamellar lipid vesicles with tunable adhesive forces, we measure…
We use a coarse-grained molecular dynamics simulation to investigate the interaction between neutral or charged nanoparticles (NPs) and a vesicle consisting of neutral and negatively charged lipids. We focus on the interaction strengths of hydrophilic and hydrophobic attraction and electrostatic interactions between a lipid molecule and an NP. A neutral NP passes through the lipid membrane when the hydrophobic interaction is sufficiently strong. As the valence of the positively charged NP increases, the membrane permeation speed of the NP is increased compared with the neutral NP and charged l…
We use coarse grained molecular dynamics simulations to investigate diffusion properties of sheared lipid membranes with embedded transmembrane proteins. In membranes without proteins, we find normal in-plane diffusion of lipids in all flow conditions. Protein embedded membranes behave quite differently: by imposing a simple shear flow and sliding the monolayers of the membrane over each other, the motion of protein clusters becomes strongly superdiffusive in the shear direction. In such a circumstance, subdiffusion regime is predominant perpendicular to the flow. We show that superdiffusion i…
The cytoplasm and biomembranes in biological cells contain large numbers of proteins that cyclically change their shapes. They are molecular machines that can function as molecular motors or carry out many other tasks in the cell. We analyze the effects that hydrodynamic flows induced by active proteins have on other passive molecules in solution or membranes. We show that the diffusion constants of passive particles are enhanced substantially. Furthermore, when gradients of active proteins are present, a chemotaxis-like drift of passive particles takes place. In lipid bilayers, the effects ar…
The effect of AC electric fields on the elasticity of supported lipid bilayers has been investigated at the microscopic level using grazing incidence synchrotron x-ray scattering. A strong decrease in the membrane tension up to 1mN/m and a dramatic increase of its effective rigidity up to 300kBT are observed for local electric potentials seen by the membrane < 1V. The experimental results were analyzed using detailed electrokinetic modeling and non-linear Poisson-Boltzmann theory. Based on a modeling of the electromagnetic stress which provides an accurate description of bilayer separation vs …
Experiments on supported lipid bilayers featuring liquid ordered/disordered domains have shown that the spatial arrangement of the lipid domains and their chemical composition are strongly affected by the curvature of the substrate. Furthermore, theoretical predictions suggest that both these effects are intimately related with the closed topology of the bilayer. In this work, we test this hypothesis by fabricating supported membranes consisting of colloidal particles of various shapes lying on a flat substrate. A single lipid bilayer coats both colloids and substrate, allowing local lipid exc…
Over recent decades, lipid membranes have become standard models for examining the biophysics and biochemistry of cell membranes. Interrogation of lipid domains within biomembranes is generally done with fluorescence microscopy via exogenous chemical probes. However, most fluorophores have limited partitioning tunability, with the majority segregating in the least biologically relevant domains (i.e., low-density liquid domains). Therefore, a molecular-level picture of the majority of non-labeled lipids forming the membrane is still elusive. Here, we present simple, label-free imaging of domain…
Lipid membranes are abundant in living organisms, where they constitute a surrounding shell for cells and their organelles. There are many circumstances in which the deformations of lipid membranes are involved in living cells: fusion and fission, membrane-mediated interaction between membrane inclusions, lipid-protein interaction, formation of pores, etc. In all of these cases, elastic parameters of lipid membranes are important for the description of membrane deformations, as these parameters determine energy barriers and characteristic times of membrane-involved phenomena. Since the develop…
Doxorubicin (DOX) is one of the most efficient antitumor drugs employed in numerous cancer therapies. Its incorporation into lipid-based nanocarriers, such as liposomes, improves the drug targeting into tumor cells and reduces drug side effects. The carriers' lipid composition is expected to affect the interactions of DOX and its partitioning into liposomal membranes. To get a rational insight into this aspect and determine promising lipid compositions, we use numerical simulations, which provide unique information on DOX-membrane interactions at the atomic level of resolution. In particular, …
The propagation of sound waves on lipid monolayers supported on water has been studied during the melting transition. Since changes in volume, area, and compressibility in lipid membranes have biological relevance, the observed sound propagation is of paramount importance. However, it is unknown what would occur on a lipid bilayer, which is a more approximate model of a cell membrane. With the aim to answer this relevant question, we built an experimental setup to assemble long artificial lipid membranes. We found that if these membranes are heated in order to force local melting, a thermo-mec…
A novel two-leaflet description of lipid membranes is proposed. Within its framework, phase separation phenomena in multicomponent biological membranes are analyzed. As we show, interactions between the leaflets tend to suppress macroscopic phase segregation (i.e., complete demixing of lipids) in such systems. Instead, microphase separation characterized by formation of equilibrium nanoscale domains can take place. The phase diagram is constructed and numerical simulations revealing nanostructures of different morphology are performed.
Simulating Curved Lipid Membranes Using Anchored Frozen Patches
Department of Materials Science and Engineering, Grainger College of Engineering, University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校格雷恩工程学院材料科学与工程系）
