Shapes of planar lipid monolayer domains at the air-water interface are theoretically and numerically investigated by minimizing the formation energy of the domains which consist of the surface energy, line tension energy, and dipole electrostatic energy. The shape equation which describes boundary curves of the domains at equilibrium state is derived from the first order variation of the formation energy. A relaxation method is proposed to find the numerical solutions of the shape equation. The theoretical and numerical results are in good agreement with previous experimental observation. Some new shapes not observed in previous experiments are also obtained, which awaits experimental confirmation in the future.
Sound waves are excited on lipid monolayers using a set of planar electrodes aligned in parallel with the excitable medium. By measuring the frequency dependent change in the lateral pressure we are able to extract the sound velocity for the entire monolayer phase diagram. We demonstrate that this velocity can also be directly derived from the lipid monolayer compressibility and consequently displays a minimum in the phase transition regime. This minimum decreases from v0=170m/s for one component lipid monolayers down to vm=50m/s for lipid mixtures. No significant attenuation can be detected c…
We study phase separation in mixed monolayers of neutral and highly negatively charged lipids, induced by the addition of divalent positively charged counterions. We find good agreement between experiments on mixtures of pip2 and sopc and simulations of a simplified model in which only the essential electrostatic interactions are retained. Thus, our results support an interpretation of pip2 clustering as governed primarily by electrostatic interactions, in which divalent ions such as calcium mediate an effective attraction between like-charged lipids. Surprisingly, the mediated attractions are…
We formulate a simple effective model to describe molecular interactions in a lipid monolayer. The model represents lipid molecules in terms of two-dimensional anisotropic particles on the plane of the monolayer. These particles interact through forces that are believed to be relevant for the understanding of fundamental properties of the monolayer: van der Waals interactions originating from lipid chain interaction, and dipolar forces between the dipole groups of the molecular heads. Thermodynamic and phase behaviour properties of the model are explored using density-functional theory. Interf…
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…
The existence of acoustic pulse propagation in lipid monolayers at the air-water interface is well known. These pulses are controlled by the thermodynamic state of the lipid membrane. Nevertheless, the role of acoustic pulses for intra- and intercellular communication are still a matter of debate. Herein, we used the dye di 4- -ANEPPDHQ, which is known to be sensitive to the physical state and transmembrane potential of membranes, in order to gain insight into compression waves in lipid-based membrane interfaces. The dye was incorporated into lipid monolayers made of phosphatidylserine or phos…
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…
A great variety of biologically relevant monolayers present phase coexistence characterized by domains formed by lipids in an ordered phase state dispersed in a continuous, disordered phase. The difference in surface densities between these phases originates inter-domain dipolar interactions, which are relevant for the determination of the spacial distribution of domains, as well as their dynamics. In this work, we propose a novel manner of estimating the dipolar repulsion using a passive method that involves the analysis of images of the monolayer with phase coexistence. The method is based o…
We re-examine previous observations of folding kinetics of compressed lipid monolayers in light of the accepted mechanical buckling mechanism recently proposed [L. Pocivavsek et al., Soft Matter, 2008, 4, 2019]. Using simple models, we set conservative limits on a) the energy released in the mechanical buckling process and b) the kinetic energy entailed by the observed folding motion. These limits imply a kinetic energy at least thirty times greater than the energy supplied by the buckling instability. We discuss possible extensions of the accepted picture that might resolve this discrepancy.
Isolated domains in lipid monolayers exhibit shape transitions as a consequence of the competing effects of line tension and long-range dipolar interactions. Nontrivial integrals ultimately arise in instability analysis calculations of these domains. In this work we present a closed form evaluation of such integrals in terms of associated Legendre functions. Our approach is motivated by and extends the work of J. M. Deutch and F. E. Low (J. Phys. Chem., 1992, 96, 7097-7101). Our closed form solutions lead to simpler analytic expressions for stability thresholds, which are easier to evaluate ex…
The molecular arrangement of lipids and proteins within biomembranes and monolayers gives rise to complex film morphologies as well as regions of distinct electrical surface potential, topographical and electrostatic nanoscale domains. To probe these nanodomains in soft matter is a challenging task both experimentally and theoretically. This work addresses the effects of cholesterol, lipid composition, lipid charge, and lipid phase on the monolayer structure and the electrical surface potential distribution. Atomic Force Microscopy (AFM) was used to resolve topographical nanodomains and Kelvin…
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…
Grazing Incidence X-ray Diffraction (GIXD) studies of monolayers of biomolecules at the air-water interface give quantitative information of in-plane packing, coherence lengths of the ordered diffracting crystalline domains and the orientation of hydrocarbon chains. Rheo-GIXD measurements revel quantitative changes in the monolayer under shear. Here we report GIXD studies of monolayers of Alamethicin peptide, DPPC lipid and their mixtures at the air-water interface under the application of steady shear stresses. The Alamethicin monolayer and the mixed monolayer show flow jamming transition. On…
Lipid monolayers have been shown to represent a powerful tool in studying mechanical and thermodynamic properties of lipid membranes as well as their interaction with proteins. Using Einstein's theory of fluctuations we here demonstrate, that an experimentally derived linear relationship both between transition entropy S and area A as well as between transition entropy and charge q implies a linear relationships between compressibility κ_T, heat capacity c_π, thermal expansion coefficient α_T and electric capacity CT. We demonstrate that these couplings have strong predictive power as they all…
Monolayer spontaneous curvatures for cholesterol, DOPE, POPE, DOPC, DPPC, DSPC, POPC, SOPC, and egg sphingomyelin were obtained using small-angle X-ray scattering (SAXS) on inverted hexagonal phases (HII). Spontaneous curvatures of bilayer forming lipids were estimated by adding controlled amounts to a HII forming template following previously established protocols. Spontanous curvatures of both phosphatidylethanolamines and cholesterol were found to be at least a factor of two more negative than those of phosphatidylcholines, whose J0 are closer to zero. Interestingly, a significant positive …
We report on atomistic simulations of DPPC lipid monolayers using the CHARMM36 lipid force field and four-point OPC water model. The entire two-phase region where domains of the `liquid-condensed' (LC) phase coexist with domains of the `liquid-expanded' (LE) phase has been explored. The simulations are long enough that the complete phase-transition stage, with two domains coexisting in the monolayer, is reached in all cases. Also, system sizes used are larger than in previous works. As expected, domains of the minority phase are elongated, emphasizing the importance of anisotropic van der Waal…
Lipid monolayers and bilayers have been used as experimental models for the investigation of membrane thermal transitions. The main transition takes place near ambient temperatures for several lipids and reflects the order-disorder transition of lipid hydrocarbonic chains, which is accompanied by a small density gap. Equivalence between the transitions in the two systems has been argued by several authors. The two-state statistical model adopted by numerous authors for different properties of the membrane, such as permeability, diffusion, mixture or insertion of cholesterol or protein, is inad…
We report on the surface rheology of cross-linked F-actin networks associated with a lipid monolayer at the air-water interface of a Langmuir monolayer. The rheological measurements are made using a Couette cell. These data demonstrate that the network has a finite elastic modulus that grows as a function of the cross-linking concentration. We also note that under steady-state flow the system behaves as a power law fluid in which the effective viscosity decreases with imposed shear.
Lipid domains are found in systems such as multi-component bilayer membranes and single component monolayers at the air-water interface. It was shown by Andelman et al. (Comptes Rendus 301, 675 (1985)) and McConnell et al. (Phys. Chem. {\bf 91}, 6417 (1987)) that in monolayers, the size of the domains results from balancing the line tension, which favors the formation of a large single circular domain, against the electrostatic cost of assembling the dipolar moments of the lipids. In this paper, we present an exact analytical expression for the electric potential, ion distribution and electros…
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…
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…
We investigate theoretically the behavior of proteins as well as other large macromolecules which are incorporated into amphiphilic monolayers at the air-water interface. We assume the monolayer to be in the coexistence region of the ``main'' transition, where domains of the liquid condensed phase coexist with the liquid expanded background. Using a simple mean-field free energy accounting for the interactions between proteins and amphiphilic molecules, we obtain the spatial protein distribution with the following characteristics. When the proteins preferentially interact with either the liqui…
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…
In this work, we present the first example of the self-assembly of phospholipid monolayers at the interface between air and an ionic solvent. Deep eutectic solvents are a novel class of environmentally friendly non-aqueous room temperature liquids with tunable properties, that have wide ranging potential applications and are capable of promoting the self-assembly of surfactant molecules. We use a chemically-consistent Bayesian modelling of X-ray and neutron reflectometry measurements to show that these monolayers broadly behave as they do on water. This method allows for the monolayer structur…
Stripe-like domains of Langmuir monolayers formed by surfactants with partially fluorinated lipid anchors (F-alkyl lipids) are observed at the gas-liquid phase coexistence. The average periodicity of the stripes, measured by fluorescence microscopy, is in the micrometer range, varying between 2 and 8 microns. The observed stripe-like patterns are stabilized due to dipole-dipole interactions between terminal -CF3 groups. These interactions are particularly strong as compared with non-fluorinated lipids due to the low dielectric constant of the surrounding media (air). These long-range dipolar i…
This article summarizes a variety of physical mechanisms proposed in the literature, which can generate micro- and nanodomains in multicomponent lipid bilayers and biomembranes. It mainly focusses on lipid-driven mechanisms that do not involve direct protein-protein interactions. Specifically, it considers (i) equilibrium mechanisms based on lipid-lipid phase separation such as critical cluster formation close to critical points, and multiple domain formation in curved geometries, (ii) equilibrium mechanisms that stabilize two-dimensional microemulsions, such as the effect of linactants and th…
Using molecular simulation to aid in the analysis of neutron reflectometry measurements is commonplace. However, reflectometry is a tool to probe large-scale structures, and therefore the use of all-atom simulation may be irrelevant. This work presents the first direct comparison between the reflectometry profiles obtained from different all-atom and coarse-grained molecular dynamics simulations. These are compared with a traditional model layer structure analysis method to determine the minimum simulation resolution required to accurately reproduce experimental data. We find that systematic l…
We consider the formation of finite-size domains in lipid bilayers consisting of saturated and hybrid lipids. First, we describe a monolayer model that includes a coupling between a compositional scalar field and a two-dimensional vectorial order-parameter. Such a coupling yields an effective two-dimensional microemulsion free-energy for the lipid monolayer, and its characteristic length of compositional modulations can be considered as the origin of finite-size domains in biological membranes. Next, we consider a coupled bilayer composed of two modulated monolayers, and discuss the static and…
We model cyclic voltammetry experiments on supported lipid films where a non-trivial dependence of the capacitance on the applied voltage is observed. Previously, based on a mean-field treatment of the Flory-Huggins type, under the assumption of strongly screened electrostatic interactions, it has been hypothesized that peaks in the capacitance-vs-voltage profiles correspond to a sequence of structural or phase transitions within the interface. To examine this hypothesis, in this study we use both mean-field calculations and Monte Carlo simulations where the electrostatic effects due to the va…
The effect of the adsorption of a polypeptide on the lateral interaction of dimyristoylphosphatidylserine molecules in different phase states on the surface of a 10\,mM KCl aqueous solution has been studied. Changes in the surface pressure and Volta potential induced by the adsorption of large poly-D-lysine molecules (about 200 links in a chain) have been determined at different areas per lipid molecule in a monolayer. The adsorption of macromolecules noticeably increases the elasticity of the monolayer under lateral compression in the liquid expanded state of lipid and reduces the effective d…
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…
Nanoparticles with hydrophobic capping ligands and amphiphilic phospholipids are both found to self-assemble into monolayer films when deposited on the air water interface. By separately measuring the anisotropic stress response of these films under uniaxial compression, we obtain both the 2D compressive and shear moduli of a range of different thin nanoparticle and phospholipid films. The compressive moduli of both nanoparticle and lipid films in the solid phase are on the same order of magnitude, whereas the shear moduli of the lipid films are found to be significantly lower. Additionally th…
Self-assembly dynamics in binary surfactant mixtures and structure changes of lipid vesicles induced by detergent solution are studied using coarse-grained molecular simulations. Disk-shaped micelles, the bicelles, are stabilized by detergents surrounding the rim of a bilayer disk of lipids. The self-assembled bicelles are considerably smaller than bicelles formed from vesicle rupture, and their size is determined by the concentrations of lipids and detergents and the interactions between the two species. The detergent-adsorption induces spontaneous curvature of the vesicle bilayer and results…
We propose a model that accounts for the budding transition of asymmetric two-component lipid domains, where the two monolayers (leaflets) have different average compositions controlled by independent chemical potentials. Assuming a coupling between the local curvature and local lipid composition in each of the leaflets, we discuss the morphology and thermodynamic behavior of asymmetric lipid domains. The membrane free-energy contains three contributions: the bending energy, the line tension, and a Landau free-energy for a lateral phase separation. Within a mean-field treatment, we obtain vari…
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…
A micelle consists of monolayer of lipid molecules containing hydrophilic head and hydrophobic tail. These amphiphilic molecules in aqueous environment aggregate spontaneously into monomolecular layer held together due to hydrophobic effect by weak non-covalent forces. Micelles are flexible surfaces that show variety of shapes of different topology, but remarkably in mechanical equilibrium conditions they are spherical in shape. The shape and size of a micelle are functions of many variables such as lipid concentration, temperature, ionic strength, etc. Addressing the question, why the shape o…
Inverse bicontinuous cubic phases are ubiquitous in lipid-water mixtures and consist of a lipid bilayer forming a cubic minimal surface, thereby dividing space into two cubic networks of water channels. For small hydrocarbon chain lengths, the monolayers can be modeled as parallel surfaces to a minimal midsurface. The bending energy of the cubic phases is determined by the distribution of Gaussian curvature over the minimal midsurfaces which we calculate for seven different structures (G, D, P, I-WP, C(P), S and F-RD). We show that the free-energy densities of the structures G, D and P are con…
Using the Parsons Lee theory we examined the effect of shape anisotropy and the wall to wall separation on the phase behavior of the hard parallelepiped rods with dimensions L, D, and D (L>D) in such narrow slitlike pores which only one homeotropic layer can form. The phase structures, including biaxiality, planar nematic layering transition as well as planar to homeotropic, were studied for some separations in the range 2.5D<H<10.0D for H-D<L<H.
We introduce a simple model for DNA-cationic-lipid complexes in which galleries between planar bilayer lipid lamellae contain DNA 2D smectic lattices that couple orientationally and positionally to lattices in neighboring galleries. We identify a new equilibrium phase in which there are long-range orientational but not positional correlations between DNA lattices. We discuss properties of this new phase such as its X-ray structure factor S(r), which exhibits unusual exp(- const.ln^2 r) behavior as a function of in-plane separation r.
The equilibrium properties of hard rod monolayers are investigated in a lattice model (where position and orientation of a rod are restricted to discrete values) as well as in an off--lattice model featuring spherocylinders with continuous positional and orientational degrees of freedom. Both models are treated using density functional theory and Monte Carlo simulations. Upon increasing the density of rods in the monolayer, there is a continuous ordering of the rods along the monolayer normal ("standing up" transition). The continuous transition also persists in the case of an external potenti…
In cell extrusion, a cell embedded in an epithelial monolayer loses its apical or basal surface and is subsequently squeezed out of the monolayer by neighboring cells. Cell extrusions occur during apoptosis, epithelial-mesenchymal transition, or pre-cancerous cell invasion. They play important roles in embryogenesis, homeostasis, carcinogenesis, and many other biological processes. Although many of the molecular factors involved in cell extrusion are known, little is known about the mechanical basis of cell extrusion. We used a three-dimensional (3D) vertex model to investigate the mechanical …
Lipid vesicles play a key role in fundamental biological processes. Despite recent progress, we lack a complete understanding of the non-equilibrium dynamics of vesicles due to challenges associated with long-time observation of shape fluctuations in strong flows. In this work, we present a flow-phase diagram for vesicle shape and conformational transitions in planar extensional flow using a Stokes trap, which enables control over the center-of-mass position of single or multiple vesicles in precisely defined flows [Shenoy, Rao, Schroeder, \textit{PNAS}, 113(15):3976-3981, 2016]. In this way, …
Growth of hard--rod monolayers via deposition is studied in a lattice model using rods with discrete orientations and in a continuum model with hard spherocylinders. The lattice model is treated with kinetic Monte Carlo simulations and dynamic density functional theory while the continuum model is studied by dynamic Monte Carlo simulations equivalent to diffusive dynamics. The evolution of nematic order (excess of upright particles, "standing--up" transition) is an entropic effect and is mainly governed by the equilibrium solution, {rendering a continuous transition} (paper I, J. Chem. Phys. 1…
We study the equilibrium conformations of a lipid domain on a planar fluid membrane where the domain is decorated by a vector field representing the tilt of the stiff fatty acid chains of the lipid molecules, while the surrounding membrane is fluid and structureless. The inclusion of chirality in the bulk of the domain induces a novel budding of the membrane, which preempts the budding induced by a decrease in interfacial tension.
We consider a model of bilayer lipid membrane with interdigitation, in which the lipid tails of the opposite monolayers interpenetrate. The interdigitation is modeled by linking tails of the hydrophobic chains in the opposite monolayers within bilayer as a first approximation. A number of thermodynamical characteristics are calculated analytically and compared with the ones of a regular membrane without interdigitation. Striking difference between lateral pressure profiles at the layers interface for linked and regular bilayer models is found. In the linked case, the lateral pressure mid-plane…
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 develop a theoretical model for the solubilization of phospholipid bilayers by micelle-forming surfactants. Cylindrical micelles, disc-like micelles and spherical micelles are considered as alternative resultant structures. The main question addressed is what kind of micelles can be expected under various thermodynamical conditions. Our analysis is based on a theoretical model that accounts for Helfrich energy of curvature of amphiphile monolayers and for the entropy of mixing of lipids and surfactants in mixed aggregates. We conclude that for usual values of the elastic parameters of amphi…
A planar colloidal monolayer exhibits anomalous collective diffusion due to the hydrodynamic interactions. We investigate how this behavior is affected by the curvature of the monolayer when it resides on the interface of a spherical droplet. It is found that the characteristic times of the dynamics still exhibit the same anomalous scaling as in the planar case. The spatial distribution, however, shows a difference due to the relevance of the radius of the droplet. Since for the droplet this is both a global magnitude, i.e., pertaining the spatial extent of the spherical surface, and a local o…
Domain growth in lipid membranes and the budding instability
Institut Charles Sadron, CNRS UPR22 & Université de Strasbourg（斯特拉斯堡大学）；University of Lyon, ENS-Lyon, CNRS UMR 5182, Chemistry Laboratory（里昂大学）；Center for Physics and Chemistry of Living Systems, Tel Aviv University（特拉维夫大学）；School of Chemistry & Center for Physics and Chemistry of Living Systems, Tel Aviv University（特拉维夫大学）；Zhejiang Key Laboratory of Soft Matter Biomedical Materials, Wenzhou Institute, University of Chinese Academy of Sciences（中国科学院大学温州研究所）
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…
We study coarse grained, continuum models for Langmuir monolayers by self consistent field theory and by Monte Carlo simulations. Amphiphilic molecules are represented by stiff chains of monomers with one end grafted to a planar surface. In particular, we discuss the origin of successive fluid-fluid transitions, the possible origin of tilt order and the factors which determine the direction of tilt.
