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 strong enough to give nearly complete phase separation, so that clusters can even form when the overall concentration of pip2 is low, as is the case in the cell membrane.
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…
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. Som…
We study the influence of truncating the electrostatic interactions in a fully hydrated pure dipalmitoylphosphatidylcholine (DPPC) bilayer through 20 ns molecular dynamics simulations. The computations in which the electrostatic interactions were truncated are compared to similar simulations using the Particle-Mesh Ewald (PME) technique. All examined truncation distances (1.8 to 2.5 nm) lead to major effects on the bilayer properties, such as enhanced order of acyl chains together with decreased areas per lipid. The results obtained using PME, on the other hand, are consistent with experiments…
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…
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…
We present theoretical work in which the degree of electrostatic coupling across a charged lipid bilayer in aqueous solution is analyzed on the basis of nonlinear Poisson-Boltzmann theory. In particular, we consider the electrostatic interaction of a single, large macroion with the two apposed leaflets of an oppositely charged lipid bilayer where the macroion is allowed to optimize its distance to the membrane. Three regimes are identified: a weak and a high macroion charge regime, separated by a regime of close macroion-membrane contact for intermediate charge densities. The corresponding fre…
We consider DNA-cationic lipid complexes that form lamellar stacks of lipid bilayers with parallel DNA strands intercalated in between. We calculate the electrostatically induced elastic deformations of the lipid bilayers. It is found that the membranes undulate with a periodicity that is set by the DNA interaxial distance. As a consequence the lamellar repeat distance changes resulting in a swelling or compression of the lamellar stack. Such undulations may be responsible for the intermembrane coupling between DNA strands in different layers as it is observed experimentally.
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…
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…
Biomembranes, which are mainly composed of neutral and charged lipids, exhibit a large variety of functional structures and dynamics. Here, we report a coarse-grained molecular dynamics (MD) simulation of the phase separation and morphological dynamics in charged lipid bilayer vesicles. The screened long-range electrostatic repulsion among charged head groups delays or inhibits the lateral phase separation in charged vesicles compared with neutral vesicles, suggesting the transition of the phase-separation mechanism from spinodal decomposition to nucleation or homogeneous dispersion. Moreover,…
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…
This paper considers the effect of electrostatics on the stability of a charged membrane. We show that at low ionic strength and high surface charge density, repulsion between charges on the membrane renders it unstable to the formation of holes. A free straight edge is unstable to modulations with wavelength longer than the Debye screening length. Hence at low ionic strength, membranes will disintegrate into vesicles. We use these results to interpret stable holes in red blood cell ghosts (Steck et. al., Science 168:255(1970)).
We investigated the phase separation of dioleoylphosphatidylserine (DOPS) and dipalmitoylphosphatidylcholine (DPPC) in giant unilamellar vesicles in hypotonic solution using fluorescence and confocal laser scanning microscopy. Although phase separation in charged lipid membranes is generally suppressed by the electrostatic repulsion between the charged headgroups, osmotic stress can promote the formation of charged lipid domains. Interestingly, we observed three-phase coexistence even in DOPS/DPPC binary lipid mixtures. The three phases were DPPC-rich, dissociated DOPS-rich, and nondissociated…
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 …
Cationic lipid membranes are known to form compact complexes with DNA and to be effective as gene delivery agents both in vitro and in vivo. Here we employ molecular dynamics simulations for a detailed atomistic study of lipid bilayers consisting of a mixture of cationic dimyristoyltrimethylammonium propane (DMTAP) and zwitterionic dimyristoylphosphatidylcholine (DMPC). Our main objective is to examine how the composition of the bilayers affects their structural and electrostatic properties in the liquid-crystalline phase. By varying the mole fraction of DMTAP, we have found that the area per …
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…
We formulate a theory of electrostatic interactions in lipid bilayer membranes where both monolayer leaflets contain dissociable moieties that are subject to charge regulation. We specifically investigate the coupling between membrane curvature and charge regulation of a lipid bilayer vesicle using both the linear Debye-Hückel (DH) and the non-linear Poisson-Boltzmann (PB) theory. We find that charge regulation of an otherwise symmetric bilayer membrane can induce charge symmetry breaking, non-linear flexoelectricity and anomalous curvature dependence of free energy. The pH effects investigate…
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 impact of nanomaterials on lung fluids or on the plasma membrane of living cells has prompted researchers to examine the interactions between nanoparticles and lipid vesicles. Recent studies have shown that nanoparticle-lipid interaction leads to a broad range of structures including supported lipid bilayers (SLB), particles adsorbed at the surface or internalized inside vesicles, and mixed aggregates. Today, there is a need to have simple protocols that can readily assess the nature of structures obtained from particles and vesicles. Here we apply the method of continuous variation for me…
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…
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…
We investigate the interaction between highly charged lipid bilayers in the presence of monovalent counterions. Neutron and X-ray reflectivity experiments show that the water layer between like-charged bilayers is thinner than for zwitterionic lipids, demonstrating the existence of counterintuitive electrostatic attractive interaction between bilayers. Such attraction can be explained by taking into account the correlations between counterions within the Strong Coupling limit, which falls beyond the classical Poisson-Boltzmann theory of electrostatics. Our results show the limit of the Strong …
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 use coarse-grained Monte Carlo simulations to study the elastic properties of charged membranes in solutions of monovalent and pentavalent counterions. The simulation results of the two cases reveal trends opposite to each other. The bending rigidity and projected area increase with the membrane charge density for monovalent counterions, while they decrease for the pentavalent ions. These observations can be related to the counterion screening of the lipid charges. While the monovalent counterions only weakly screen the Coulomb interactions, which implies a repulsive Coulomb system, the mul…
We 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…
We investigate the stability of seven inverse bicontinuous cubic phases ($G$, $D$, $P$, $C(P)$, $S$, $I-WP$, $F-RD$) in lipid-water mixtures based on a curvature model of membranes. Lipid monolayers are described by parallel surfaces to triply periodic minimal surfaces. The phase behavior is determined by the distribution of the Gaussian curvature on the minimal surface and the porosity of each structure. Only $G$, $D$ and $P$ are found to be stable, and to coexist along a triple line. The calculated phase diagram agrees very well with experimental results for 2:1 lauric acid/DLPC.
The computational study of the interaction between charged, ligand-protected metal nanoparticles and model lipid membranes has been recently addressed both at atomistic and coarse grained level. Here we compare the performance of three versions of the coarse grained Martini force field at describing the nanoparticle-membrane interaction. The three coarse-grained models differ in terms of treatment of long-range electrostatic interactions and water polarizability. The NP-membrane interaction consists in the transition from a metastable NP- membrane complex, in which the NP is only partially emb…
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…
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…
We have studied the electrostatic screening effect of NaCl solutions on the interactions between anionic lipid bilayers in the fluid lamellar phase using a Poisson-Boltzmann based mean-field approach with constant charge and constant potential limiting charge regulation boundary conditions. The full DLVO potential, including the electrostatic, hydration and van der Waals interactions, was coupled to thermal bending fluctuations of the membranes via a variational Gaussian Ansatz. This allowed us to analyze the coupling between the osmotic pressure and the fluctuation amplitudes and compare them…
Understanding interactions between membranes requires measurements on well-controlled systems close to natural conditions, in which fluctuations play an important role. We have determined, by grazing incidence X-ray scattering, the interaction potential between two lipid bilayers, one adsorbed on a solid surface and the other floating close by. We find that interactions in this highly hydrated model system are two orders of magnitude softer than in previously reported work on multilayer stacks. This is attributed to the weak electrostatic repulsion due to the small fraction of ionized lipids i…
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…
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 …
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…
The interaction potential between supported floating bilayers has been determined by grazing incidence specular and off-specular scattering using synchrotron radiation. Our measurements demonstrate that floating bilayers are significantly more hydrated than the usually studied multilayers, therefore giving access to more intrinsic properties of the membranes. At equilibrium, the interaction potential can be two orders of magnitude softer than previously reported, which can be explained by the weak electrostatic interaction due to the small fraction (sigma ~ 0.001 e$^-$/nm$^2$) of ionized lipid…
We studied the adsorption of a charged protein onto an oppositely charged membrane, composed of mobile phospholipids of differing valence, using a statistical-thermodynamical approach. A two-block model was employed, one block corresponding to the protein-affected region on the membrane, referred to as the adsorption domain, and the other to the unaffected remainder of the membrane. We calculated the protein-induced lipid rearrangement in the adsorption domain as arising from the interplay between the electrostatic interactions in the system and the mixing entropy of the lipids. Equating the e…
We consider the phase separation in an asymmetrically charged lipid bilayer membrane consisting of neutral and negatively charged lipids that are in contact with in/out ionic solutions having different ionic strengths. The two asymmetric leaflets are coupled through electrostatic interactions. Based on a free energy approach, the critical point and phase diagrams are calculated for different ionic strength of the two solutions and coupling parameter. An increase of the coupling constant or asymmetry in the salt concentration between the in/out solutions yields a higher phase separation tempera…
