Simulations of edge behavior in a mixed-lipid bilayer: fluctuation analysis

Coarse-grained molecular dynamics simulations of lipid bilayer ribbons consisting of a mixture of lipids of different tail lengths have been performed to gain insight into bicelle mixtures. The line tension of the bilayer edge decreases as the mole fraction of short-chain lipids in the system is increased, dropping below zero between 30% and 35%. The mole fraction of short-chain lipids in the ribbon interior is lower than the total mole fraction, as the short-chain lipids segregate towards the edge, but continues to rise even after the line tension vanishes, in contrast to predictions of a two-component two-phase model. The fluctuations of the bilayer edge in both high and low line tension regimes have been analyzed to extract information about the factors that influence the length and shape of the edge. At high line tension the wavelength-dependent in-plane fluctuations of the edge are predicted quantitatively using a simple analytical model using only the line tension as input. Where line tension is vanishing, the fluctuations can be modeled as arising from a combination of harmonic fluctuations around a minimum energy contour length and an in-plane bending elasticity. The estimated value of the in-plane bending modulus is of order 10(-29) J m, placing the intrinsic persistence length for the edge near the bilayer thickness of 4 nm.     

Determination of the line tension of giant vesicles from pore-closing dynamics

Giant vesicles generated from synthetic and natural lipids such as phosphatidylcholines are useful models for understanding mechanical properties of cell membranes. Line tension is the one-dimensional force enabling the closing of transient pores on cell membranes. Transient pores were repeatedly and reproducibly formed on the membrane edge of giant vesicles generated from synthetic and natural phosphatidylcholines employing a nitrogen-pumped coumarin dye laser (440 nm). Line tension was determined at room temperature from closing of these pores that occurred over several seconds when the radius of the vesicle could be considered to be constant. The value of line tension depends on the nature of the lipid for single lipid systems, which, at room temperature, yielded a vesicle bilayer region in the gel, fluid, or mixed gel and fluid phases. The line tension for vesicles generated from phosphatidylcholines with saturated acyl chains of lengths of 12-18 carbon atoms ranges from 1 to 12 pN, exhibiting an increase with chain length. Vesicles generated from the natural Egg-PC, which is a mixture of lipids, are devoid of phase transition and exhibited the largest value of line tension (32 pN). This value is much larger than that estimated from the line tensions of vesicles obtained from lipids with homologous acyl chains. This study, to our knowledge, is the first to employ laser ablation to generate transient pores and determine line tension from the rate of pore closure and demonstrate a relationship between line tension and acyl chain length.     

Composition dependence of bilayer elasticity

A previously developed molecular level model for homogeneous lipid bilayers [Brannigan and Brown, J. Chem. Phys 120, 1059 (2004)] is extended to allow for multiple lipid species. Monte Carlo simulations (including species exchange moves for efficient sampling) reveal a variety of mixing behaviors in binary systems. Two species are identified that maintain stable, randomly mixed fluid membranes at vanishing tension over all possible binary compositions. The thermal and elastic properties of membranes formed by these lipids are characterized over the full composition range. Equilibrium area at constant tension is nonmonotonic with respect to composition, but consistent with that of a quadratic mixture. In the constant tension ensemble, the bending rigidity of the bilayer is minimized at an intermediate composition. The observed functional form of bending rigidity vs composition is fit to a simple expression motivated by linear elasticity theory; this expression accounts for membrane heterogeneity through a single parameter.     

Equilibrium distributions of dipalmitoyl phosphatidylcholine and dilauroyl phosphatidylcholine in a mixed lipid bilayer: atomistic semigrand canonical ensemble simulations

Conventional molecular dynamics (MD) simulations are seriously limited by the slow rate of diffusive mixing in their ability to predict lateral distributions of different lipid types within mixed-lipid bilayers using atomistic models. A method to overcome this limitation, using configuration-bias Monte Carlo (MC) "mutation" moves to transform lipids from one type to another in dynamic equilibrium, is demonstrated in binary fluid-phase mixtures of lipids whose tails differ in length by four carbons. The hybrid MC-MD method operates within a semigrand canonical ensemble, so that an equilibrium composition of the mixture is determined by a constant difference in chemical potential (Delta(mu)) chosen for the components. Within several nanoseconds, bilayer structures initiated as pure dipalmitoyl phosphatidylcholine (DPPC) or pure dilauroyl phosphatidylcholine (DLPC) converge to a common composition and structure in independent simulations conducted at the same Delta(mu). Trends in bilayer thickness, area per lipid, density distributions across the bilayer, and order parameters have been investigated at three mixture compositions and compared with results from the pure bilayers at 323 K. The mixtures showed a moderate increase in DPPC acyl tail sites crossing the bilayer midplane relative to pure DPPC. Correlations between lateral positions of the two lipid types within or across the bilayer were found to be weak or absent. While the lateral distribution is consistent with nearly ideal mixing, the dependence of composition on Delta(mu) indicates a positive excess free energy of mixing.     

Perturbation of phospholipid bilayer properties by ethanol at a high concentration

Atomistic molecular dynamics (MD) simulations have been carried out at 30 degrees C on a fully hydrated liquid crystalline lamellar phase of dimyrystoylphosphatidylcholine (DMPC) lipid bilayer with embedded ethanol molecules at 1:1 composition, as well as on the pure bilayer phase. The ethanol molecules are found to exhibit a preference to occupy regions near the upper part of the lipid acyl chains and the phosphocholine headgroups. The calculations revealed that the phosphocholine headgroup dipoles (P- --> N+) of the lipids prefer to orient more toward the aqueous layer in the presence of ethanol. It is noticed that the ethanol molecules modify the dynamic properties of both lipids as well as the water molecules in the hydration layer of the lipid headgroups. Both the in-plane "rattling" and out-of-plane "protrusion" motions of the lipids have been found to increase in the presence of ethanol. Most importantly, it is observed that the water molecules within the hydration layer of the lipid headgroups exhibit faster translational and rotational motions in the presence of ethanol. This arises due to faster dynamics of hydrogen bonds between lipid headgroups and water in the presence of ethanol.     

Surface tension effect on transmembrane channel stability in a model membrane

The effect of surface tension on the lipid bilayer membrane is a question that has drawn considerable research effort. This interest has been driven both by the desire to determine the surface tension effects on the lipid bilayer and from the suggestion that adding finite surface tension to a small membrane system may provide more realistic lipid properties in molecular dynamics simulations. Here, the effect of surface tension on a palmitololelylphosphatidylcholine (POPC) bilayer membrane containing a four-helix transmembrane alamethicin peptide bundle is investigated. Simulations of 10 ns were undertaken for two different ensembles, NPT and NP(z)gammaT with a surface tension, gamma, of 20 mN m(-1) per interface, which is near the pore-forming region. The significance of differences between the tension-free and surface tension simulations was determined using nonparametric statistical analysis on replicate simulations with different initial conditions. The results suggest that, when the membrane is under surface tension, the peptide helical structure is perturbed from that in the tension-free state but that the bundle conformation is more stable than that in the tension-free state, with hydrogen bonding playing an important stabilizing role. Surface tension counteracts the influence of the transmembrane helix bundle on nearby lipid order, making the lipid order more uniform throughout the membrane in the tension state. Conversely, the lipid mobility was less uniform in the tension state, with lipids far from the bundle being significantly more mobile than those near the bundle. One general implication of the results is that surface tension can affect the membrane nonuniformly, in that the properties of lipids near the peptide are different from those further away.     

Structure and characteristics of the complexes between polyampholites and anionic liposomes

Polyampholites are synthesized by the alkylation of poly-4-vinylpyridine with ω-bromocarboxylic acids, and their interaction with the negatively charged bilayer lipid vesicles (liposomes) is studied. In the above polymers, quaternized pyridine units are zwitterion (betaine) groups, in which cationic and anionic groups are linked by the -(CH₂) _n -bridges. Via the methods of fluorescence, laser scattering, and DSC, the length of the ethylene spacer in the betaine group is shown to control the ability of the polymer to interact with anionic liposomes and induce structural rearrangements in the liposomal membrane. At n = 1, polybetaine is not linked to anionic liposomes. At n = 2, polybetaine is sorbed on the membrane, but it causes no dramatic structural rearrangements in the bilayer. At n = 3, the adsorption of polybetaine triggers the lateral segregation of lipids in the outer membrane layer. At n = 5, adsorption of polymer is accompanied by the lateral segregation and flip-flop of lipid molecules; as a result, all anionic membrane lipids are involved in the microphase separation. This evidence is of evident interest for the controlled design of polymers and related complexes and conjugates for biomedical applications.     

Membrane resistance to Triton X-100 explored by real-time atomic force microscopy

Lateral segregation of lipids and proteins in biological membranes leads to the formation of detergent-resistant domains, also called "rafts". Understanding the mechanisms governing the biomembrane's resistance to solubilization by detergents is crucial in biochemical research. Here, we used real-time atomic force microscopy (AFM) imaging to visualize the behavior of a model supported lipid bilayer in the presence of different Triton X-100 (TX-100) concentrations. Mixed dioleoylphosphatidylcholine/dipalmitoylphosphatidylcholine (DOPC/DPPC) supported bilayers were prepared by vesicle fusion. Real-time AFM imaging revealed that, at concentrations below the critical micelle concentration (CMC), TX-100 did not solubilize the bilayer, but the DPPC domains were eroded in a time-dependent manner. This effect was attributed to the DPPC molecular packing disorganization by the detergent starting from the DOPC/DPPC interface. Just above the CMC, the detergent led to a complete solubilization of the DOPC matrix, leaving the DPPC domains unaltered. At higher TX-100 concentrations, the DOPC was also immediately removed just after detergent addition, and the DPPC domains remaining on the mica surface appeared to be more swollen and were gradually solubilized. This progressive solubilization of the DPPC remaining phase did not start at the edge of the domains but from holes appearing and expanding at the center of DPPC patches. The swelling of the DPPC domains was directly correlated with TX-100 concentration above the CMC and with detergent intercalation between DPPC molecules. We are convinced that this approach will provide a key system to elucidate the physical mechanisms of membrane solubilization by nonionic detergents.     

Interfacial tension of bilayer lipid membranes

Interfacial tension is an important characteristic of a biological membrane because it determines its rigidity, thus affecting its stability. It is affected by factors such as medium pH and by the presence of certain substances, for example cholesterol, other lipids, fatty acids, amines, amino acids, or proteins, incorporated in the lipid bilayer. Here, the effects of various parameters to on interfacial tension values of bilayer lipid membranes are discussed.     

Phase separation of saturated and mono-unsaturated lipids as determined from a microscopic model

A molecular model is proposed of a bilayer consisting of fully saturated dipalmitoylphosphatidylcholine (DPPC) and mono-unsaturated dioleoylphosphatidylcholine (DOPC). The model not only encompasses the constant density within the hydrophobic core of the bilayer, but also the tendency of chain segments to align. It is solved within self-consistent field theory. A model bilayer of DPPC undergoes a main-chain transition to a gel phase, while a bilayer of DOPC does not do so above zero degrees centigrade because of the double bond which disrupts order. We examine structural and thermodynamic properties of these membranes and find our results in reasonable accord with experiment. In particular, order-parameter profiles are in good agreement with NMR experiments. A phase diagram is obtained for mixtures of these lipids in a membrane at zero tension. The system undergoes phase separation below the main-chain transition temperature of the saturated lipid. Extensions to the ternary DPPC, DOPC, and cholesterol system are outlined.     

An ionic polymer bead-supported lipid system

In this paper, we report on the preparation of an ionic polymer bead-supported lipid system several hundred micrometers in diameter. The electrostatic attractive interactions between anionic lipids and cationic polymer beads served as a "molecular glue" to immobilize the lipids on the beads, and then the immobilized lipids prompted the spontaneous formation of lipid bilayer membranes. Confocal fluorescence microscopic techniques revealed that the lipid bilayer membranes were located along the outline of the beads. In addition, the integrity of the lipid bilayer membranes was microscopically confirmed by a low-molecular-weight dye (trypan blue) exclusion test.     

Solvent-free coarse-grained lipid model for large-scale simulations

A coarse-grained molecular model, which consists of a spherical particle and an orientation vector, is proposed to simulate lipid membrane on a large length scale. The solvent is implicitly represented by an effective attractive interaction between particles. A bilayer structure is formed by orientation-dependent (tilt and bending) potentials. In this model, the membrane properties (bending rigidity, line tension of membrane edge, area compression modulus, lateral diffusion coefficient, and flip-flop rate) can be varied over broad ranges. The stability of the bilayer membrane is investigated via droplet-vesicle transition. The rupture of the bilayer and worm-like micelle formation can be induced by an increase in the spontaneous curvature of the monolayer membrane.     

Electrical surface potential of pulmonary surfactant

Pulmonary surfactant is a mixed lipid protein substance of defined composition that self-assembles at the air-lung interface into a molecular film and thus reduces the interfacial tension to close to zero. A very low surface tension is required for maintaining the alveolar structure. The pulmonary surfactant film is also the first barrier for airborne particles entering the lung upon breathing. We explored by frequency modulation Kelvin probe force microscopy (FM-KPFM) the structure and local electrical surface potential of bovine lipid extract surfactant (BLES) films. BLES is a clinically used surfactant replacement and here served as a realistic model surfactant system. The films were distinguished by a pattern of molecular monolayer areas, separated by patches of lipid bilayer stacks. The stacks were at positive electrical potential with respect to the surrounding monolayer areas. We propose a particular molecular arrangement of the lipids and proteins in the film to explain the topographic and surface potential maps. We also discuss how this locally variable surface potential may influence the retention of charged or polar airborne particles in the lung.     

Size-dependent properties of small unilamellar vesicles formed by model lipids

The size-dependent behavior of small unilamellar vesicles is explored by dissipative particle dynamics, including the membrane characteristics and mechanical properties. The spontaneously formed vesicles are in the metastable state and the vesicle size is controlled by the concentration of model lipids. As the vesicle size decreases, the bilayer gets thinner and the area density of heads declines. Nonetheless, the area density in the inner leaflet is higher than that in the outer. The packing parameters are calculated for both leaflets. The result indicates that the shape of lipid in the outer leaflet is like a truncated cone but that in the inner leaflet resembles an inverted truncated cone. Based on a local order parameter, our simulations indication that the orientation order of lipid molecules decreases as the size of the vesicle reduces and this fact reveals that the bilayer becoming thinner for smaller vesicle is mainly attributed to the orientation disorder of the lipids. The membrane tension can be obtained through the Young-Laplace equation. The tension is found to grow with reducing vesicle size. Therefore, small vesicles are less stable against fusion. Using the inflation method, the area stretching and bending moduli can be determined and those moduli are found to grow with reducing size. Nonetheless, a general equation with a single numerical constant can relate bending modulus, area stretching modulus, and bilayer thickness irrespective of the vesicle size. Finally, a simple metastable model is proposed to explain the size-dependent behavior of bilayer thickness, orientation, and tension.     

533—Structure and transport properties of artificial bipolar lipid membranes

The membranes of thermophilic archaebacteria are characterized by the presence of unusual bipolar saturated isoprenoid lipids. In order to investigate their molecular arrangement in the membrane and a possible influence on transport properties, we studied black films made from lipids of Caldariella acidophila, one of the most thermophilic archaebacteria. Details on the kinetics of formation at various temperatures are presented.Capacitance, compressibility and valinomycin-induced conductance values are compared with the corresponding data for a glycerol-monooleate (GMO) bilayer. A very peculiar behavior is presented by the bipolar lipid films studied. In fact, the values of conductance are more than two orders of magnitude lower than those of a GMO bilayer, while the values of capacitance and compressibility do not depend appreciably on the solvent in which the lipid is dispersed (in contrast with a GMO bilayer, where there is a 100% change).The results are discussed in terms of a proposed model of a monolayer organization of bipolar lipids and of the unusual composition of the hydrophobic core of the membrane.     

Stability of DNA-tethered lipid membranes with mobile tethers

We recently introduced two approaches for tethering planar lipid bilayers as membrane patches to either a supported lipid bilayer or DNA-functionalized surface using DNA hybridization (Chung, M.; Lowe, R. D.; Chan, Y-H. M.; Ganesan, P. V.; Boxer, S. G. J. Struct. Biol.2009, 168, 190-9). When mobile DNA tethers are used, the tethered bilayer patches become unstable, while they are stable if the tethers are fixed on the surface. Because the mobile tethers between a patch and a supported lipid bilayer offer a particularly interesting architecture for studying the dynamics of membrane-membrane interactions, we have investigated the sources of instability, focusing on membrane composition. The most stable patches were made with a mixture of saturated lipids and cholesterol, suggesting an important role for membrane stiffness. Other factors such as the effect of tether length, lateral mobility, and patch membrane edge were also investigated. On the basis of these results, a model for the mechanism of patch destruction is developed.     

Atomistic simulation of lipid and DiI dynamics in membrane bilayers under tension

Membrane tension modulates cellular processes by initiating changes in the dynamics of its molecular constituents. To quantify the precise relationship between tension, structural properties of the membrane, and the dynamics of lipids and a lipophilic reporter dye, we performed atomistic molecular dynamics (MD) simulations of DiI-labeled dipalmitoylphosphatidylcholine (DPPC) lipid bilayers under physiological lateral tensions ranging from -2.6 mN m(-1) to 15.9 mN m(-1). Simulations showed that the bilayer thickness decreased linearly with tension consistent with volume-incompressibility, and this thinning was facilitated by a significant increase in acyl chain interdigitation at the bilayer midplane and spreading of the acyl chains. Tension caused a significant drop in the bilayer's peak electrostatic potential, which correlated with the strong reordering of water and lipid dipoles. For the low tension regime, the DPPC lateral diffusion coefficient increased with increasing tension in accordance with free-area theory. For larger tensions, free area theory broke down due to tension-induced changes in molecular shape and friction. Simulated DiI rotational and lateral diffusion coefficients were lower than those of DPPC but increased with tension in a manner similar to DPPC. Direct correlation of membrane order and viscosity near the DiI chromophore, which was just under the DPPC headgroup, indicated that measured DiI fluorescence lifetime, which is reported to decrease with decreasing lipid order, is likely to be a good reporter of tension-induced decreases in lipid headgroup viscosity. Together, these results offer new molecular-level insights into membrane tension-related mechanotransduction and into the utility of DiI in characterizing tension-induced changes in lipid packing.     

Determination of the lipid bilayer breakdown voltage by means of linear rising signal

Electroporation is characterized by formation of structural changes within the cell membrane, which are caused by the presence of electrical field. It is believed that "pores" are mostly formed in lipid bilayer structure; if so, planar lipid bilayer represents a suitable model for experimental and theoretical studies of cell membrane electroporation. The breakdown voltage of the lipid bilayer is usually determined by repeatedly applying a rectangular voltage pulse. The amplitude of the voltage pulse is incremented in small steps until the breakdown of the bilayer is obtained. Using such a protocol each bilayer is exposed to a voltage pulse many times and the number of applied voltage pulses is not known in advance. Such a pre-treatment of the lipid bilayer affects its stability and consequently the breakdown voltage of the lipid bilayer. The aim of this study is to examine an alternative approach for determination of the lipid bilayer breakdown voltage by linear rising voltage signal. Different slopes of linear rising signal have been used in our experiments (POPC lipids; folding method for forming in the salt solution of 100 mM KCl). The breakdown voltage depends on the slope of the linear rising signal. Results show that gently sloping voltage signal electroporates the lipid bilayer at a lower voltage then steep voltage signal. Linear rising signal with gentle slope can be considered as having longer pre-treatment of the lipid bilayer; thus, the corresponding breakdown voltage is lower. With decreasing the slope of linear rising signal, minimal breakdown voltage for specific lipid bilayer can be determined. Based on our results, we suggest determination of lipid bilayer breakdown voltage by linear rising signal. Better reproducibility and lower scattering are obtained due to the fact that each bilayer is exposed to electroporation treatment only once. Moreover, minimal breakdown voltage for specific lipid bilayer can be determined.     

Mechanical stability of micropipet-aspirated giant vesicles with fluid phase coexistence

Micropipet aspiration of phase-separated lipid bilayer vesicles can elucidate physicochemical aspects of membrane fluid phase coexistence. Recently, we investigated the composition dependence of line tension at the boundary between liquid-ordered and liquid-disordered phases of giant unilamellar vesicles obtained from ternary lipid mixtures using this approach. Here we examine mechanical equilibria and stability of dumbbell-shaped vesicles deformed by line tension. We present a relationship between the pipet aspiration pressure and the aspiration length in vesicles with two coexisting phases. Using a strikingly simple mechanical model for the free energy of the vesicle, we predict a relation that is in almost quantitative agreement with experiment. The model considers the vesicle free energy to be proportional to line tension and assumes that the vesicle volume, domain area fraction, and total area are conserved during aspiration. We also examine a mechanical instability encountered when releasing a vesicle from the pipet. We find that this releasing instability is observed within the framework of our model that predicts a change of the compressibility of a pipet-aspirated membrane cylinder from positive (i.e., stable) to negative (unstable) values, at the experimental instability. The model furthermore includes an aspiration instability that has also previously been experimentally described. Our method of studying micropipet-induced shape transitions in giant vesicles with fluid domains could be useful for investigating vesicle shape transitions modulated by bending stiffness and line tension.     

Molecular dynamics simulations of phospholipid bilayers: Influence of artificial periodicity, system size, and simulation time

This article investigates the convergence of structural and dynamical properties with system size and with time in molecular dynamics simulations of solvated phospholipid bilayers performed at constant volume under periodic boundary conditions using lattice-sum electrostatics. The electron density profile across the bilayer, the carbon-deuterium order parameters, and the surface tension are shown to be converged for a bilayer containing 36 lipids per leaflet and simulated over a period of 3-4 ns. Reasonable estimates for these properties can already be obtained from a system containing 16 lipids per leaflet. The convergence limit of 36 lipids per leaflet and the investigation of the correlation between lipid headgroup dipoles suggest a correlation length of about 3-5 nm in the lateral directions for a hydrated DPPC bilayer in the liquid-crystalline phase. Although these (relatively small) system sizes and (relatively short) time scales appear sufficient to obtain converged collective structural properties at constant volume, two restrictions should be kept in mind: (i) the relaxation times associated with the motion of individual lipids may be much longer and (ii) simulated properties converge significantly faster under constant volume conditions as compared to constant pressure conditions. Therefore, an accurate assessment of the dynamical properties of the system or of the relaxation of the bilayer under constant pressure conditions may require longer simulation time scales.