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.
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…
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…
Closed form results for shape transitions in lipid monolayer domains
孤立的结构域在脂质单层表现出形状转变的结果线张力和长程偶极相互作用的竞争效应。非平凡积分最终出现在这些领域的不稳定性分析计算。在这项工作中，我们提出了一个封闭的形式评估这样的积分相关的勒让德函数。我们的方法受到JM工作的启发并扩展了JM的工作。Deutch和F. E. Low（J. Phys. Chem.，1992，96，7097-7101）。我们的封闭形式的解决方案导致更简单的稳定性阈值的解析表达式，这是更容易显式地评估。相关的渐近行为计算在各种限制的利益。对于库仑相互作用的情况下，一个通用的封闭形式的表达得到的临界域半径。
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…
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…
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…
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…
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…
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…
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…
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…
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.
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 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…
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…
