Synthetic lipid membranes in the absence of proteins can display quantized conduction events for ions that are virtually indistinguishable from those of protein channel. By indistinguishable we mean that one cannot decide based on the current trace alone whether conductance events originate from a membrane, which does or does not contain channel proteins. Additional evidence is required to distinguish between the two cases, and it is not always certain that such evidence can be provided. The phenomenological similarities are striking and span a wide range of phenomena: The typical conductances are of equal order and both lifetime distributions and current histograms are similar. One finds conduction bursts, flickering, and multistep-conductance. Lipid channels can be gated by voltage, and can be blocked by drugs. They respond to changes in lateral membrane tension and temperature. Thus, they behave like voltage-gated, temperature-gated and mechano-sensitive protein channels, or like receptors. Lipid channels are remarkably under-appreciated. However, the similarity between lipid and protein channels poses an eminent problem for the interpretation of protein channel data. For instance, the Hodgkin-Huxley theory for nerve pulse conduction requires a selective mechanism for the conduction of sodium and potassium ions. To this end, the lipid membrane must act both as a capacitor and as an insulator. Non-selective ion conductance by mechanisms other than the gated protein-channels challenges the proposed mechanism for pulse propagation. ... Some important questions arise: Are lipid and protein channels similar due a common mechanism, or are these similarities fortuitous? Is it possible that both phenomena are different aspects of the same phenomenon? Are lipid and protein channels different at all? ... (abbreviated)
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…
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…
Lipid rafts are heterogeneous dynamic lipid domains of the cell membranes that are involved in several biological processes, like protein and lipids specific transport and signaling. Our understanding of lipid raft formation is still limited, due to the transient and elusive nature of these domains {\it in vivo}, in contrast to the stable phase-separated domains observed in artificial membranes. Inspired by experimental findings highlighting the relevance of transmembrane proteins for lipid rafts, we investigate lipid domain nucleation by coarse-grained molecular dynamics and Ising model simul…
Membrane proteins typically deform the surrounding lipid bilayer membrane, which can play an important role in the function, regulation, and organization of membrane proteins. Membrane elasticity theory provides a beautiful description of protein-induced lipid bilayer deformations, in which all physical parameters can be directly determined from experiments. Analytic treatments of the membrane elasticity theory of protein-induced lipid bilayer deformations have largely focused on idealized protein shapes with circular cross section, and on perturbative solutions for proteins with non-circular …
The spatio-temporal organization of proteins and the associated morphological changes in membranes are of importance in cell signaling. Several mechanisms that promote the aggregation of proteins at low cell surface concentrations have been investigated in the past. We show, using Monte Carlo simulations, that the affinity of proteins for specific lipids can hasten its aggregation kinetics. The lipid membrane is modeled as a dynamically triangulated surface with the proteins defined as in-plane fields at the vertices. We show that, even at low protein concentrations, strong lipid-protein inter…
Hydrophobic thickness mismatch between integral membrane proteins and the surrounding lipid bilayer can produce lipid bilayer thickness deformations. Experiment and theory have shown that protein-induced lipid bilayer thickness deformations can yield energetically favorable bilayer-mediated interactions between integral membrane proteins, and large-scale organization of integral membrane proteins into protein clusters in cell membranes. Within the continuum elasticity theory of membranes, the energy cost of protein-induced bilayer thickness deformations can be captured by considering compressi…
In recent experiments [T. Basta et al., Proc. Natl. Acad. Sci. U.S.A. 111, 670 (2014)] lipids and membrane proteins were observed to self-assemble into membrane protein polyhedral nanoparticles (MPPNs) with a well-defined polyhedral protein arrangement and characteristic size. We develop a model of MPPN self-assembly in which the preferred symmetry and size of MPPNs emerge from the interplay of protein-induced lipid bilayer deformations, topological defects in protein packing, and thermal effects. With all model parameters determined directly from experiments, our model correctly predicts the …
A simple model for conserved intracellular dynamics exhibits multiscale pattern formation, traveling protein domains and arrested coarsening of lipid domains
Physikalisch-Technische Bundesanstalt（德国联邦物理技术研究院）；Freie Universität Berlin（柏林自由大学）；Universitat Politècnica de Catalunya (UPC)（加泰罗尼亚理工大学）
BAR superfamily proteins have a banana-shaped domain that causes the local bending of lipid membranes. We study as to how such a local anisotropic curvature induces effective interaction between proteins and changes the global shape of vesicles and membrane tubes using meshless membrane simulations. The proteins are modeled as banana-shaped rods strongly adhered to the membrane. Our study reveals that the rods assemble via two continuous directional phase separations unlike a conventional two-dimensional phase separation. As the rod curvature increases, in the membrane tube the rods assemble a…
We study membrane-protein interactions and membrane-mediated protein-protein interactions by Monte Carlo simulations of a generic coarse-grained model for lipid bilayers with cylindrical hydrophobic inclusions. The strength of the hydrophobic force and the hydrophobic thickness of the proteins are systematically varied. The results are compared with analytical predictions of two popular analytical theories: The Landau-de Gennes theory and the elastic theory. The elastic theory provides an excellent description of the fluctuation spectra of pure membranes and successfully reproduces the deforma…
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…
Analysis of fluorescent spectra from complex biological systems containing various fluorescent probes with overlapping emission bands is a challenging task. Valuable information can be extracted from the full spectra, however, by using multivariate analysis (MA) of measurements at different wavelengths. We applied MA to spectral data of purified Torpedo nicotinic acetylcholine receptor (AChR) protein reconstituted into liposomes made up of dioleoylphosphatidic acid (DOPA) and dioleoylphosphatidylcholine (DOPC) doped with two extrinsic fluorescent probes (NBD-cholesterol/pyrene-PC). Forster res…
Protein aggregation in cell membrane is vital for the majority of biological functions. Recent experimental results suggest that transmembrane domains of proteins such as $α$-helices and $β$-sheets have different structural rigidities. We use molecular dynamics simulation of a coarse-grained model of protein-embedded lipid membranes to investigate the mechanisms of protein clustering. For a variety of protein concentrations, our simulations under thermal equilibrium conditions reveal that the structural rigidity of transmembrane domains dramatically affects interactions and changes the shape o…
The spatiotemporal organisation of proteins and lipids on the cell surface has direct functional consequences for signaling, sorting and endocytosis. Earlier studies have shown that multiple types of membrane proteins including transmembrane proteins that have cytoplasmic actin binding capacity and lipid-tethered GPI-anchored proteins (GPI-APs) form nanoscale clusters driven by active contractile flows generated by the actin cortex. To gain insight into the role of lipids in organizing membrane domains in living cells, we study the molecular interactions that promote the actively generated nan…
By performing molecular dynamics simulations with up to 132 million coarse-grained particles in half-micron sized boxes, we show that hydrodynamics quantitatively explains the finite-size effects on diffusion of lipids, proteins, and carbon nanotubes in membranes. The resulting Oseen correction allows us to extract infinite-system diffusion coefficients and membrane surface viscosities from membrane simulations despite the logarithmic divergence of apparent diffusivities with increasing box width. The hydrodynamic theory of diffusion applies also to membranes with asymmetric leaflets and embed…
Organic Electrochemical Transistor Arrays with Integrated Lipid-Sealed Femtolitre Chambers for Simultaneous Electrical and Optical Detection of Membrane Protein Activity
University of New South Wales（新南威尔士大学）；The University of Tokyo（东京大学）
In this article we compare electrical conductance events from single channel recordings of three TRP channel proteins (TRPA1, TRPM2 and TRPM8) expressed in human embryonic kidney cells with channel events recorded on synthetic lipid membranes close to melting transitions. Ion channels from the TRP family are involved in a variety of sensory processes including thermo- and mechano-reception. Synthetic lipid membranes close to phase transitions display channel-like events that respond to stimuli related to changes in intensive thermodynamic variables such as pressure and temperature. TRP channel…
The interaction between the bacterial S-protein SbpA on different types of lipid membranes has been studied using atomic force microscopy, transmission electron microscopy, and quartz crystal microbalance with dissipation. On one hand, It has been found that the bacterial forms two dimensional nanocrystals on zwitterionic DOPC bilayers and negatively charged DMPG vesicles adsorbed on mica, on zwitterionic DPPC and charged DPPC/DMPG (1:1) monolayers adsorbed on carbon grids. On the other hand, SbpA protein adsorption took place on zwitterionic DOPC bilayers and DOPC/DOPS (4:1) bilayers, previou…
Random lateral translocation of lipids and proteins is a universal process on membrane surfaces. Local aggregation or organization of lipids and proteins can be induced when this lateral random diffusion is mediated by the electrostatic interactions and membrane curvature. Though the lateral diffusion rates of lipids on membrane of various compositions are measured and the electrostatic free energies of predetermined protein-membrane-lipid systems can be computed, the process of the aggregation and the evolution to the electrostatically favorable states remain undetermined. Here we propose an …
Lipid bilayers forming biological membranes are known to behave as viscous 2D fluids on submicrometer scales; usually they contain a large number of active protein inclusions. Recently, it has been shown [Proc. Nat. Acad. Sci. USA 112, E3639 (2015)] that such active proteins should in- duce non-thermal fluctuating lipid flows leading to diffusion enhancement and chemotaxis-like drift for passive inclusions in biomembranes. Here, a detailed analytical and numerical investigation of such effects is performed. The attention is focused on the situations when proteins are concentrated within lipid …
The interpretation electrical phenomena in biomembranes is usually based on the assumption that the experimentally found discrete ion conduction events are due to a particular class of proteins called ion channels while the lipid membrane is considered being an inert electrical insulator. The particular protein structure is thought to be related to ion specificity, specific recognition of drugs by receptors and to macroscopic phenomena as nerve pulse propagation. However, lipid membranes in their chain melting regime are known to be highly permeable to ions, water and small molecules, and are …
Cellular membranes are elastic lipid bilayers that contain a variety of proteins, including ion channels, receptors, and scaffolding proteins. These proteins are known to diffuse in the plane of the membrane and to influence the bending of the membrane. Experiments have shown that lipid flow in the plane of the membrane is closely coupled with the diffusion of proteins. Thus, there is a need for a comprehensive framework that accounts for the interplay between these processes. Here, we present a theory for the coupled in-plane viscous flow of lipids, diffusion of transmembrane proteins, and el…
Over the past thirty years, researchers have highlighted the role played by a class of proteins or polypeptides that forms pathogenic amyloid aggregates in vivo, including i) the amyloid Abeta peptide, which is known to form senile plaques in Alzheimer's disease; ii) alpha-synuclein, responsible for Lewy body formation in Parkinson's disease and iii) IAPP, which is the protein component of type 2 diabetes-associated islet amyloids. These proteins, known as intrinsically disordered proteins (IDPs), are present as highly dynamic conformational ensembles. IDPs can partially (mis) fold into (dys) …
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…
An interfacial regularized Stokeslet scheme is presented to predict the motion of solid bodies (e.g. proteins or gel-phase domains) embedded within flowing lipid bilayer membranes. The approach provides a numerical route to calculate velocities and angular velocities in complex flow fields that are not amenable to simple Faxén-like approximations. Additionally, when applied to shearing motions, the calculations yield predictions for the effective surface viscosity of dilute rigid body-laden membranes. In the case of cylindrical proteins, effective viscosity calculations are compared to two pri…
Biological membranes constitute boundaries of cells and cell organelles. Physico-chemical mechanisms at the atomic scale are dictated by protein-lipid interaction strength, lipid composition, lipid distribution in the vicinity of the protein, shape and amino acid composition of the protein, and its amino acid contents. The specificity of molecular interactions together with the cooperativity of multiple proteins induce and stabilize complex membrane shapes at the mesoscale. These shapes span a wide spectrum ranging from the spherical plasma membrane to the complex cisternae of the Golgi appara…
Colloids and proteins alike can bind to lipid bilayers and move laterally in these two-dimensional fluids. Inspired by proteins that generate membrane curvature, sense the underlying membrane geometry, and migrate to high curvature sites, we explore the question: Can colloids, adhered to lipid bilayers, also sense and respond to membrane geometry? We report the curvature migration of Janus microparticles adhered to giant unilamellar vesicles elongated to present well defined curvature fields. However, unlike proteins, which migrate to minimize membrane bending energy, colloids migrate by an en…
The assembly of curved protein rods on fluid membranes is studied using implicit-solvent meshless membrane simulations. As the rod curvature increases, the rods on a membrane tube assemble along the azimuthal direction first and subsequently along the longitudinal direction. Here, we show that both transition curvatures decrease with increasing rod stiffness. For comparison, curvature-inducing isotropic inclusions are also simulated. When the isotropic inclusions have the same bending rigidity as the other membrane regions, the inclusions are uniformly distributed on the membrane tubes and ves…
Intrinsically disordered proteins (IDPs), such as amyloid polypeptide (IAPP), beta-amyloid (A\b{eta}), and α-synuclein are linked to the insurgence of type 2 diabetes, Alzheimer's, and Parkinson's diseases, respectively. Common molecular mechanisms have been explored to elucidate the toxicity pathway of these proteins. For many years, the amyloid hypothesis was believed to explain the toxicity. According to this hypothesis, the misfolding of these proteins and the further aggregation into mature and insoluble fibrils rich in the \b{eta}-sheet lead to cell death. However, this theory fails to e…
At the neuromuscular junction (NMJ), the nicotinic acetylcholine receptor (nAChR) self-associates to give rise to rapid muscle movement. While lipid domains have maintained nAChR aggregates in-vitro, their specific roles in nAChR clustering are currently unknown. In the present study, we carried out coarse-grained molecular dynamics simulations (CG-MD) of 1-4 nAChR molecules in two membrane environments: One mixture containing domain-forming, homoacidic lipids, and a second mixture consisting of heteroacidic lipids. Spontaneous dimerization of nAChRs was up to ten times more likely in domain-f…
Annexins are a family of proteins that bind to anionic phospholipid membranes in a Ca2+-dependent manner. Annexin A2 forms heterotetramers (Anx A2t) with the S100A10 (p11) protein dimer. The tetramer is capable of bridging phospholipid membranes and it has been suggested to play a role in Ca2+-dependent exocytosis and cell-cell adhesion of metastatic cells. Here, we employ x-ray reflectivity measurements to resolve the conformation of Anx A2t upon Ca2+-dependent binding to single supported lipid bilayers (SLBs) composed of different mixtures of anionic (POPS) and neutral (POPC) phospholipids. …
The interplay of membrane proteins is vital for many biological processes, such as cellular transport, cell division, and signal transduction between nerve cells. Theoretical considerations have led to the idea that the membrane itself mediates protein self-organization in these processes through minimization of membrane curvature energy. Here, we present a combined experimental and numerical study in which we quantify these interactions directly for the first time. In our experimental model system we control the deformation of a lipid membrane by adhering colloidal particles. Using confocal m…
Artificial bilayer lipid membranes (BLMs), along with patch-clamped membranes, are frequently used for functional analyses of membrane proteins. In both methods, the electric properties of membranes are characterized by only one parameter, namely, transmembrane potential. Here the construction of a novel BLM system was reported, in which membrane voltages can be controlled in a lateral direction in addition to conventional transmembrane direction. A microaperture was fabricated in a Teflon film and Ti electrodes were evaporated around the aperture. BLMs were reproducibly formed in the aperture…
Membrane proteins and lipids can self-assemble into membrane protein polyhedral nanoparticles (MPPNs). MPPNs have a closed spherical surface and a polyhedral protein arrangement, and may offer a new route for structure determination of membrane proteins and targeted drug delivery. We develop here a general analytic model of how MPPN self-assembly depends on bilayer-protein interactions and lipid bilayer mechanical properties. We find that the bilayer-protein hydrophobic thickness mismatch is a key molecular control parameter for MPPN shape that can be used to bias MPPN self-assembly towards hi…
Integrin is an important transmembrane receptor protein which remodels the actin network and anchors the cell membrane towards the extracellular matrix via mechanochemical pathways. The clustering of specific lipids and lipid-anchored proteins, which is essential for a certain type of endocytosis process, is facilitated at integrin-mediated active regions. To study this, we propose a minimal exactly solvable model which includes the interplay of stochastic shuttling between integrin on and off states with the intrinsic dynamics of the membrane. We obtain an analytic expression for the deformat…
Synthetic lipid membranes can display channel-like ion conduction events even in the absence of proteins. We show here that these events are voltage-gated with a quadratic voltage dependence as expected from electrostatic theory of capacitors. To this end, we recorded channel traces and current histograms in patch-experiments on lipid membranes. We derived a theoretical current-voltage relationship for pores in lipid membranes that describes the experimental data very well when assuming an asymmetric membrane. We determined the equilibrium constant between closed and open state and the open pr…
Lipid phase heterogeneity in the plasma membrane is thought to be crucial for many aspects of cell signaling, but the physical basis of participating membrane domains such as "lipid rafts" remains controversial. Here we consider a lattice model yielding a phase diagram that includes several states proposed to be relevant for the cell membrane, including microemulsion - which can be related to membrane curvature - and Ising critical behavior. Using a neural network-based machine learning approach, we compute the full phase diagram of this lattice model. We analyze selected regions of this phase…
Many biological systems fold thin sheets of lipid membrane into complex three-dimensional structures. This microscopic origami is often mediated by the adsorption and self-assembly of proteins on a membrane. As a model system to study adsorption-mediated interactions, we study the collective behavior of micrometric particles adhered to a lipid vesicle. We estimate the colloidal interactions using a maximum likelihood analysis of particle trajectories. When the particles are highly wrapped by a tense membrane, we observe strong long-range attractions with a typical binding energy of 150 $k_B T$…
We show that lateral fluidity in membranes containing quenched protein obstacles belongs to the universality class of the two-dimensional random-field Ising model. The main feature of this class is the absence of a phase transition: there is no critical point, and macroscopic domain formation does not occur. Instead, there is only one phase. This phase is highly heterogeneous, with a structure consisting of micro-domains. The presence of quenched protein obstacles thus provides a mechanism to stabilize lipid rafts in equilibrium. Crucial for two-dimensional random-field Ising universality is t…
It is well known that at the gel-liquid phase transition temperature a lipid bilayer membrane exhibits an increased ion permeability. We analyze the quantized currents in which the increased permeability presents itself. The open time histogram shows a "-3/2" power law which implies an open-closed transition rate that decreases like $k(t) \propto t^{-1}$ as time evolves. We propose a "pore freezing" model to explain the observations. We discuss how this model also leads to the $1/f^α$ noise that is commonly observed in currents across biological and artificial membranes.
The theory of irreversible thermodynamics for arbitrarily curved lipid membranes is presented here. The coupling between elastic bending and irreversible processes such as intra-membrane lipid flow, intra-membrane phase transitions, and protein binding and diffusion is studied. The forms of the entropy production for the irreversible processes are obtained, and the corresponding thermodynamic forces and fluxes are identified. Employing the linear irreversible thermodynamic framework, the governing equations of motion along with appropriate boundary conditions are provided.
This chapter summarizes several approaches combining theory, simulation and experiment that aim for a better understanding of phenomena in lipid bilayers and membrane protein systems, covering topics such as lipid rafts, membrane mediated interactions, attraction between transmembrane proteins, and aggregation in biomembranes leading to large superstructures such as the light harvesting complex of green plants. After a general overview of theoretical considerations and continuum theory of lipid membranes we introduce different options for simulations of biomembrane systems, addressing question…
In this paper the problem of surface charge of the lipid membrane immersed in the physiological solution is considered. It is shown that both side of the bilayer phospholipid membrane surface are negatively charged. A self-consistent model of the potential in solution is developed, and a stationary charge density on the membrane surface is found. It is shown that the ions of the surface charge are in a relatively deep (as compared to kBT) potential wells, which are localized near the dipole heads of phospholipid membrane. It makes impossible for ions to slip along the membrane surface. Simple …
Self-assembly of protein monomers into distinct membrane protein oligomers provides a general mechanism for diversity in the molecular architectures, and resulting biological functions, of membrane proteins. We develop a general physical framework describing the thermodynamic competition between different oligomeric states of membrane proteins. Using the mechanosensitive channel of large conductance as a model system, we show how the dominant oligomeric states of membrane proteins emerge from the interplay of protein concentration in the cell membrane, protein-induced lipid bilayer deformation…
Supported lipid bilayers have been studied intensively over the past two decades. In this work, we study the diffusion of single gold nanoparticles (GNPs) with diameter of 20 nm attached to GM1 ganglioside or DOPE lipids at different concentrations in supported DOPC bilayers. The indefinite photostability of GNPs combined with the high sensitivity of interferometric scattering microscopy (iSCAT) allows us to achieve 1.9 nm spatial precision at 1 ms temporal resolution, while maintaining long recording times. Our trajectories visualize strong transient confinements within domains as small as 20…
Rafts, or functional domains, are transient nano- or mesoscopic structures in the plasma membrane and are thought to be essential for many cellular processes such as signal transduction, adhesion, trafficking and lipid/protein sorting. Observations of these membrane heterogeneities have proven challenging, as they are thought to be both small and short-lived. With a combination of coarse-grained molecular dynamics simulations and neutron diffraction using deuterium labeled cholesterol molecules we observe raft-like structures and determine the ordering of the cholesterol molecules in binary ch…
We describe simulations of Proteins and artificial pseudo-molecules interacting and shaping lipid bilayer membranes. We extract protein diffusion Parameters, membrane deformation profiles and the elastic properties of the used membrane models in preparation of calculations based on a large scale continuum model.
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…
While modern structural biology has provided us with a rich and diverse picture of membrane proteins, the biological function of membrane proteins is often influenced by the mechanical properties of the surrounding lipid bilayer. Here we explore the relation between the shape of membrane proteins and the cooperative function of membrane proteins induced by membrane-mediated elastic interactions. For the experimental model system of mechanosensitive ion channels we find that the sign and strength of elastic interactions depend on the protein shape, yielding distinct cooperative gating curves fo…
Membrane proteins deform the surrounding lipid bilayer, which can lead to membrane-mediated interactions between neighboring proteins. Using the mechanosensitive channel of large conductance (MscL) as a model system, we demonstrate how the observed differences in protein structure can affect membrane-mediated interactions and cooperativity among membrane proteins. We find that distinct oligomeric states of MscL lead to distinct gateway states for the clustering of MscL, and predict signatures of MscL structure and spatial organization in the cooperative gating of MscL. Our modeling approach es…
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 …
