Implicit-solvent mesoscale model based on soft-core potentials for self-assembled lipid membranes

An efficient implicit-solvent model for self-assembled lipid bilayers is presented and analyzed using Langevin molecular dynamics simulations. The model is based on soft interactions between particles and short-range attractive interaction between lipid tails, leading for the self-assembly of a lipid bilayer without an explicit solvent. This allows for efficient simulations of large membranes over long times. The model exhibits a fluid phase at high temperatures and a gel phase at low temperatures, identified with the Lbeta-phase. The melting transition is investigated via analysis of the diffusivity of the lipid molecules, the chain-orientational order parameter, the sixfold bond-orientational order parameter, and the positional and bond-orientational correlation functions. The analysis suggests the existence of a hexatic phase over a narrow range of temperatures around the melting transition. The elastic properties of the membrane in the fluid phase are also investigated.     

Effective attraction interactions between like-charge macroions bound to binary fluid lipid membranes

Using integral equation theory of liquids to a binary mixed fluid lipid membrane, the authors study the membrane-mediated interactions between binding macroions and the redistribution of neutral and charged lipids due to the macroions. The authors 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. As the relative concentration of charged lipids is increased, the authors observe a repulsive-attractive-repulsive potential transition due to the competition between the line tension of mixed lipids and screened electrostatic macroion-macroion interactions. For the finite concentration of macroions, the main feature of the attraction is similar to the infinite-diluted case. However, the corresponding line tension of binary lipids under single macroion is lowered with the formation of multicomplexes by the charged lipids and the macroions, and the maximum of attractive potential will shift toward the higher values of charged lipid concentration.     

Simulation of domain formation in DLPC-DSPC mixed bilayers

Binary mixtures of two phosphatidylcholines of different chain lengths are simulated in the bilayer state. We find a phase transition between a liquid state and a gel state at all concentrations. This phase transition is characterized by the area per lipid headgroup, the order parameter, and a change in dynamics. At concentrations with a majority of the longer lipid, we find phase separation into a gel and a liquid state in a small temperature window. This leads to a strong dynamic heterogeneity. Experimental phase transition temperatures are reproduced semiquantitatively. We see a clear shift in the phase transition to higher temperatures with increasing concentration of the longer lipid.     

Modeling flexible amphiphilic bilayers: a solvent-free off-lattice Monte Carlo study

We present a simple, implicit-solvent model for fluid bilayer membranes. The model was designed to reproduce the elastic properties of real bilayer membranes. For this model, we observed the solid-fluid transition and studied the in-plane diffusivity of the fluid phase. As a test, we compute the elastic-bending and area-compressing moduli of fluid bilayer membranes. We find that the computed elastic properties are consistent with the available experimental data.     

Structure, phase behavior, and inhomogeneous fluid properties of binary dendrimer mixtures

The effective pair potentials between different kinds of dendrimers in solution can be well approximated by appropriate Gaussian functions. We find that in binary dendrimer mixtures the range and strength of the effective interactions depend strongly upon the specific dendrimer architecture. We consider two different types of dendrimer mixtures, employing the Gaussian effective pair potentials, to determine the bulk fluid structure and phase behavior. Using a simple mean field density functional theory (DFT) we find good agreement between theory and simulation results for the bulk fluid structure. Depending on the mixture, we find bulk fluid-fluid phase separation (macrophase separation) or microphase separation, i.e., a transition to a state characterized by undamped periodic concentration fluctuations. We also determine the inhomogeneous fluid structure for confinement in spherical cavities. Again, we find good agreement between the DFT and simulation results. For the dendrimer mixture exhibiting microphase separation, we observe a rather striking pattern formation under confinement.     

Attraction-driven disorder in a hard-core colloidal monolayer

Monte Carlo simulation techniques were employed to explore the effect of short-range attraction on the orientational ordering in a two-dimensional assembly of monodisperse spherical particles. We find that if the range of square-well attraction is approximately 15% of the particle diameter, the dense attractive fluid shows the same ordering behavior as the same density fluid composed of purely repulsive hard spheres. Fluids with an attraction range larger than 15% show an enhanced tendency to crystallization, while disorder occurs for fluids with an attractive range shorter than 15% of the particle diameter. A possible link with the existence of "repulsive" and "attractive" states in dense colloidal systems is discussed.     

A one-dimensional model with water-like anomalies and two phase transitions

We investigate a one-dimensional model that shows several properties of water. The model combines the long-range attraction of the van der Waals model with the nearest-neighbor interaction potential by Ben-Naim, which is a step potential that includes a hard core and a potential well. Starting from the analytical expression for the partition function, we determine numerically the Gibbs energy and other thermodynamic quantities. The model shows two phase transitions, which can be interpreted as the liquid-gas transition and a transition between a high-density and a low-density liquid. At zero temperature, the low-density liquid goes into the crystalline phase. Furthermore, we find several anomalies that are considered characteristic for water. We explore a wide range of pressure and temperature values and the dependence of the results on the depth and width of the potential well.     

Solvent mediated interactions close to fluid-fluid phase separation: microscopic treatment of bridging in a soft-core fluid

Using density functional theory we calculate the density profiles of a binary solvent adsorbed around a pair of big solute particles. All species interact via repulsive Gaussian potentials. The solvent exhibits fluid-fluid phase separation, and for thermodynamic states near to coexistence the big particles can be surrounded by a thick adsorbed "wetting" film of the coexisting solvent phase. On reducing the separation between the two big particles we find there can be a "bridging" transition as the wetting films join to form a fluid bridge. The effective (solvent mediated) potential between the two big particles becomes long ranged and strongly attractive in the bridged configuration. Within our mean-field treatment the bridging transition results in a discontinuity in the solvent mediated force. We demonstrate that accounting for the phenomenon of bridging requires the presence of a nonzero bridge function in the correlations between the solute particles when our model fluid is described within a full mixture theory based upon the Ornstein-Zernike equations.     

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.     

Dynamics of a bilayer membrane with membrane-solvent partial slip boundary conditions

We discuss the dynamics of a bilayer membrane with partial slip boundary conditions between the monolayers and the bulk fluid. Using Onsager’s variational principle to account for the associated dissipations, we derive the coupled dynamic equations for the membrane height and the excess lipid density. The newly introduced friction coe?cients appear in the renormalized fluid viscosities. For ordinary lipid bilayer membranes, we find that it is generally justified to ignore the e?ects of permeation and parallel slip at the membrane surface.     

Modeling of confinement-induced phase transitions for surfactant layers on amphiphilic surfaces

A self-consistent field model is used to consider a solution of positively charged surfactants up to its critical micellization concentration adsorbing onto two surfaces in close proximity. Each surface mimics a polystyrene sulfonate interface; that is, hydrophobic properties are combined with a (fixed) negative charge. We observe large and sudden changes in adsorption as a function of separation, which are not normally considered when interpreting surface force measurements. The parameters are chosen such that the adsorbed surfactant layer is of a monolayer type when the surfaces are far apart. A typical interaction curve is presented for a fixed surfactant chemical potential, which is extracted from the set of adsorption isotherms each with a fixed slit width. When the slit width approaches the thickness of the two surfactant layers, a first-order phase transition takes place, which is driven by the unfavorable hydrophobic-water contacts. At the transition, the average orientation of the surfactants switches from a high concentration of tails at the surface to a bilayer configuration where tail profiles from both sides merge in the center. The headgroups are pulled slightly away from the surface. The interaction force jumps from a weak electrostatic repulsion at large distances (two effectively positively charged surface layers repel each other) to a strong electrostatic attraction at short distances (the central surfactant bilayer is attracted to the oppositely charged surfaces). The amount of adsorbed surfactants tend to decrease with decreasing distance between the surfaces but suddenly increases at the transition. Because of this, we anticipate that in surface force experiments, for example, there is a hysteresis associated with this transition: the forces and also the adsorbed amounts depend not only on the distance between the surfaces but also on the history if nonsufficient equilibration times are implemented.     

Influence of pyrene-labeling on fluid lipid membranes

We elucidate the influence of pyrene-labeled phospholipids on the structural properties of a fluid dipalmitoylphosphatidylcholine lipid membrane. To this end, we employ extensive atomic-scale molecular dynamics simulations with varying concentrations of pyrene-linked lipids. We find pyrene labeling to perturb the membrane structure significantly in the vicinity of the probe, the correlation length in the bilayer plane being about 1.0-1.5 nm. The local perturbations lead to enhanced ordering and packing of lipid acyl chains located in the vicinity of the probe. Surprisingly, this holds true not only for lipids that reside in the same leaflet as the pyrene-labeled probe but also for lipids in the opposite monolayer. The latter is due to substantial interdigitation of the pyrene moiety into the opposite leaflet, suggesting that occasional excimer formation may take place for probes in different leaflets. As a related issue, we also discuss the location and conformational orientation of the pyrene moieties. In particular, the orientational distribution of pyrene turns out to be more broad and diverse than the distribution of the corresponding acyl tails of nonlabeled lipids.     

Nonequilibrium patterns of cholesterol-rich chemical heterogenieties within single fluid supported phospholipid bilayer membranes

We have developed a simple method to introduce cholesterol- and sphingomyelin-rich chemical heterogeneities into controlled densities and concentrations within predetermined regions of another distinct fluid phospholipid bilayer supported on a solid substrate. A contiguous primary phase--a fluid POPC bilayer displaying a well-defined array of lipid-free voids (e.g., 20-100 microm squares)--was first prepared on a clean glass surface by microcontact printing under water using a poly(dimethylsiloxane) stamp. The aqueous-phase primary bilayer pattern was subsequently incubated with secondary-phase small unilamellar vesicles composed of independent chemical compositions. Backfilling by comparable vesicles resulted in gradual mixing between the primary- and secondary-phase lipids, effacing the pattern. When the secondary vesicles consisted of phase-separating mixtures of cholesterol, sphingomyelin, and a phospholipid (2:1:1 POPC/sphingomyelin/cholesterol or 1:1:1 DOPC/sphingomyelin/cholesterol), well-defined spatial patterns of fluorescence, chemical compositions, and fluidities emerged. We conjecture that these patterns form because of the differences in the equilibration rates of the secondary liquid-ordered and liquid-disordered phases with the primary fluid POPC phase. The pattern stability depended strongly on the ambient-phase temperature, cholesterol concentration, and miscibility contrast between the two phases. When cholesterol concentration in the secondary vesicles was below 20 mol %, secondary intercalants gradually diffused within the primary POPC bilayer phase, ultimately dissolving the pattern in several minutes and presumably forming a new quasi-equilibrated lipid mixture. These phase domain micropatterns retain some properties of biological rafts including detergent resistance and phase mixing induced by selective cholesterol extraction. These patterns enable direct comparisons of cholesterol- and sphingomyelin-rich phase domains and fluid phospholipid phases for their functional preferences and may be useful for developing simple, parallelized assays for phase and chemical composition-dependent membrane functionalities.     

Gauging the effect of impurities on lipid bilayer phase transition temperature

We report on the gel-to-fluid phase transition behavior of unilamellar vesicles formed with 1,2-dimyristoyl-sn-phosphatidylcholine (14:0 DMPC). We have interrogated the gel-to-fluid transition temperature of these bilayer structures using the chromophore perylene incorporated in their nonpolar region. We observe a discontinuous change in the reorientation time of perylene sequestered within the bilayer at the known melting transition temperature of 14:0 DMPC, 24 degrees C. The perylene reorientation data reveal a local viscosity of 14.5 +/- 2.5 cP in the gel phase, and 8.5 +/- 1.5 cP in the fluid phase. We have also incorporated small amounts of 1,2-dimyristoleoyl-sn-glycero-3-phosphocholine (14:1 DMPC) into these unilamellar vesicles and find that the melting transition temperature for these bilayers varies in a regular manner with the amount of 14:1 DMPC present. These data demonstrate that very little "contaminant" is required to cause a substantial change in the gel-to-fluid transition temperature, even though these contaminants do not alter the viscosity of the bilayer sensed by perylene, either above or below the melting transition.     

Membrane-forming properties of pseudoglyceryl backbone based gemini lipids possessing oxyethylene spacers

Five pseudoglyceryl backbone based gemini lipids possessing varying lengths of oxyethylene [(-CH2-O-CH2-)n] spacers between cationic ammonium head groups have been synthesized, where n varies from 1 to 5. The membrane-forming properties of these gemini cationic lipids have been investigated. All the gemini lipids formed stable suspensions in water. The presence of membranous aggregates in such lipid suspensions was evidenced by transmission electron microscopy. The membrane-forming characteristics of these gemini lipids were compared with those of the corresponding monomeric lipid with one head group to understand the effect of lipid dimerization. The lipid suspensions were further characterized by dynamic light scattering and zeta potential measurements. Except for the gemini lipid with -CH2-CH2-O-CH2-CH2- spacer (2a), zeta potential of aggregates of all other gemini lipids were significantly greater than that of monomeric lipid suspensions. X-ray diffraction studies with lipid cast films revealed the increase in membrane bilayer width with increase in the length of the spacer (-CH2-O-CH2-)n. Clear thermotropic phase transitions typical of membranous assemblies were observed for all the lipid suspensions by high sensitivity differential scanning calorimetry. Aggregates of gemini lipid 2a bearing one oxyethylene [-(CH2-CH2-O-CH2-CH2)-] unit between headgroups manifested the highest phase transition temperature as compared to other gemini analogues as well as that of monomeric lipid 1. The phase transitions were reversible and exhibited large hysteresis, indicating that the observed phase transitions were of first order. To probe the surface hydration of these membranous aggregates, Paldan fluorescence studies were performed. These studies indicated the high polarity of the vesicular surface of gemini lipid 2a both in the gel and fluid melted phase as compared to vesicles of other gemini lipids.     

Critical endpoint and analytical phase diagram of attractive hard-core Yukawa spheres

We analytically calculate the gas-liquid critical endpoint (cep) for hard spheres with a Yukawa attraction. This cep is a boundary condition for the existence of a liquid. We use an analytical Helmholtz energy expression for the attractive Yukawa (hard) spheres based on the first-order mean spherical approximation to the attractive Yukawa potential by Tang and Lu (J. Chem. Phys. 1993, 99, 9828). This theory and our analytical simplification of it predict the gas-liquid and fluid-solid phase behavior, as found from computer simulations, very accurately as long as the range 1/kappa of attraction is not too short. We find that the cep is situated at kappasigma approximately 6 and at a contact potential around 2 kT. It follows that a liquid state is only possible when the attraction range is longer than (1/6) of the particle diameter sigma, and the attraction strength is smaller than 2 kT. The liquid region does not span more than 0.6 kT in strength, and there is also a relatively narrow window for the attraction range.     

Asymmetry of lipid bilayers induced by monovalent salt: atomistic molecular-dynamics study

Interactions between salt ions and lipid components of biological membranes are essential for the structure, stability, and functions of the membranes. The specific ionic composition of aqueous buffers inside and outside of the cell is known to differ considerably. To model such a situation we perform atomistic molecular-dynamics (MD) simulations of a single-component phosphatidylcholine lipid bilayer which separates two aqueous reservoirs with and without NaCl salt. To implement the difference in electrolyte composition near two membrane sides, a double bilayer setup (i.e., two bilayers in a simulation box) is employed. It turns out that monovalent salt, being in contact with one leaflet only, induces a pronounced asymmetry in the structural, electrostatic, and dynamical properties of bilayer leaflets after 50 ns of MD simulations. Binding of sodium ions to the carbonyl region of the leaflet which is in contact with salt results in the formation of "Na-lipids" complexes and, correspondingly, reduces mobility of lipids of this leaflet. In turn, attractive interactions of chloride ions (mainly located in the aqueous phase close to the water-lipid interface) with choline lipid groups lead to a substantial (more vertical) reorientation of postphatidylcholine headgroups of the leaflet adjoined to salt. The difference in headgroup orientation on two sides of a bilayer, being coupled with salt-induced reorientation of water dipoles, leads to a notable asymmetry in the charge-density profiles and electrostatic potentials of bilayer constitutes of the two leaflets. Although the overall charge density of the bilayer is found to be almost insensitive to the presence of salt, a slight asymmetry in the charge distribution between the two bilayer leaflets results in a nonzero potential difference of about 85 mV between the two water phases. Thus, a transmembrane potential of the order of the membrane potential in a cell can arise without ionic charge imbalance between two aqueous compartments.     

Comparative studies on the crystalline to fluid phase transitions of two equimolar cationic/anionic surfactant mixtures containing dodecylsulfonate and dodecylsulfate

In this work, a cationic surfactant, dodecyltrimethylammonium bromide (DTAB), and an anionic surfactant, sodium dodecylsulfonate (SDSO(3)) or sodium dodecylsulfate (SDSO(4)), were mixed in an equimolar ratio to prepare SDSO(3)-DTAB and SDSO(4)-DTAB binary mixtures. The phase behavior, structure, and morphology of these two surfactant mixtures were investigated by differential scanning calorimetry, synchrotron X-ray scattering, freeze-fracture electron microscopy, and Fourier transform infrared spectroscopy. It was found that upon heating, both of the two systems transform from multilamellar crystalline phase to liquid crystalline (or fluid) phase. It is interesting to find that, although SDSO(3) has a lower molecular weight, the crystalline phase of SDSO(3)-DTAB shows much higher thermostability as compared with that of SDSO(4)-DTAB. Other than this, we observed a large difference in the repeat distances of the two crystalline phases. More interestingly, at 60 °C in the fluid phases, cylindrical micelles formed in the SDSO(3)-DTAB system, while spherical micelles were observed in the SDSO(4)-DTAB system. Our present work demonstrates that a subtle difference in the headgroup structure of the anionic component markedly affects the thermostability, packing structure, and morphology of the surfactant mixtures, which suggests the importance of the match of the head-head and tail-tail interactions between the cationic and anionic surfactants.