Balance of forces in simulated bilayers

Two kinds of simulated bilayers are described, and the results are reported for lateral tension and for partial contributions of intermolecular forces to it. Data for the widest possible range of areas per surfactant head, from tunnel formation through tensionless state, transition to floppy bilayer, and its disintegration, are reported and discussed. The significance of the tensionless state is discussed.     

Variation of lateral tension and a new transition in model bilayers made of chain molecules

Molecular dynamics simulations of model bilayers made of amphiphilic chain molecules dissolved in a Lennard-Jones solvent, reveal a new transition between a flat tensioned state and a foamy rough thick compressed bilayer. Variation of lateral tension with area per surfactant head undergoes unexpected and dramatic changes when the system size is substantially increased; a new transition is then found. Scaling is discussed and structure factor is reported.     

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.     

Investigation of finite system-size effects in molecular dynamics simulations of lipid bilayers

In the absence of external stress, the surface tension of a lipid membrane vanishes at equilibrium, and the membrane exhibits long wavelength undulations that can be described as elastic (as opposed to tension-dominated) deformations. These long wavelength fluctuations are generally suppressed in molecular dynamics simulations of membranes, which have typically been carried out on membrane patches with areas <100 nm2 that are replicated by periodic boundary conditions. As a result, finite system-size effects in molecular dynamics simulations of lipid bilayers have been subject to much discussion in the membrane simulation community for several years, and it has been argued that it is necessary to simulate small membrane patches under tension to properly model the tension-free state of macroscopic membranes. Recent hardware and software advances have made it possible to simulate larger, all-atom systems allowing us to directly address the question of whether the relatively small size of current membrane simulations affects their physical characteristics compared to real macroscopic bilayer systems. In this work, system-size effects on the structure of a DOPC bilayer at 5.4 H2O/lipid are investigated by performing molecular dynamics simulations at constant temperature and isotropic pressure (i.e., vanishing surface tension) of small and large single bilayer patches (72 and 288 lipids, respectively), as well as an explicitly multilamellar system consisting of a stack of five 72-lipid bilayers, all replicated in three dimensions by using periodic boundary conditions. The simulation results are compared to X-ray and neutron diffraction data by using a model-free, reciprocal space approach developed recently in our laboratories. Our analysis demonstrates that finite-size effects are negligible in simulations of DOPC bilayers at low hydration, and suggests that refinements are needed in the simulation force fields.     

The Role of Lateral Tension in Calcium-Induced DPPS Vesicle Rupture

We assess the role of lateral tension in rupturing anionic dipalmitoylphosphatidyserine (DPPS), neutral dipalmitoylphosphatidylcholine (DPPC), and mixed DPPS-DPPC vesicles. Binding of Ca(2+) is known to have a significant impact on the effective size of DPPS lipids and little effect on the size of DPPC lipids in bilayer structures. In the present work we utilized laser transmission spectroscopy (LTS) to assess the effect of Ca(2+)-induced stress on the stability of the DPPS and DPPC vesicles. The high sensitivity and resolution of LTS has permitted the determination of the size and shape of liposomes in solution. The results indicate a critical size after which DPPS single shell vesicles are no longer stable. Our measurements indicate Ca(2+) promotes bilayer fusion up to a maximum diameter of ca. 320 nm. These observations are consistent with a straightforward free-energy-based model of vesicle rupture involving lateral tension between lipids regulated by the binding of Ca(2+). Our results support a critical role of lateral interactions within lipid bilayers for controlling such processes as the formation of supported bilayer membranes and pore formation in vesicle fusion. Using this free energy model we are able to infer a lower bound for the area dilation modulus for DPPS (252 pN/nm) and demonstrate a substantial free energy increase associated with vesicle rupture.     

Semiflexible polymers confined in soft tubes

We discuss various conformations for a polymer (of persistent length l(p)) confined into a deformable tube (the wall being a lipid bilayer with a certain surface tension sigma and curvature energy K). Our study assumes that there is no adsorption of the chain on the wall. Three states are compared: (a) an unperturbed tube, plus a confined chain, (b) a tube swollen in all the region surrounding the chain (similar to a snake eating a sausage), (c) a globule, a roughly spherical coil surrounded by a strongly deformed tube. We construct a (qualitative) phase diagram for these systems with two variables: the surface tension sigma and the degree of polymerization N. Our main conclusion is that "globules" usually win over "snakes".     

Dielectric properties of aqueous zwitterionic liposome suspensions

The dielectric spectra of aqueous suspensions of unilamellar liposomial vesicles built up by zwitterionic phospholipids (dipalmitoylphosphatidyl-choline, DPPC) were measured over the frequency range extending from 1 kHz to 10 MHz, where the interfacial polarization effects, due to the highly heterogeneous properties of the system, prevail. The dielectric parameters, i.e., the permittivity epsilon'(omega) and the electrical conductivity sigma(omega), have been analyzed in terms of dielectric models based on the effective medium approximation theory, considering the contribution associated with the bulk ion diffusion on both sides of the aqueous interfaces. The zwitterionic character of the lipidic bilayer has been modeled by introducing an "apparent" surface charge density at both the inner and outer aqueous interface, which causes a tangential ion diffusion similar to the one occurring in charged colloidal particle suspensions. A good agreement with the experimental results has been found for all the liposomes investigated, with size ranging from 100 to 1000 nm in diameter, and the most relevant parameters have briefly discussed in the light of the effective medium approximation theory.     

Pore nucleation in mechanically stretched bilayer membranes

We report a computer-simulation study of the free-energy barrier for the nucleation of pores in the bilayer membrane under constant stretching lateral pressure. We find that incipient pores are hydrophobic but as the lateral size of the pore nucleus becomes comparable with the molecular length, the pore becomes hydrophilic. In agreement with previous investigations, we find that the dynamical process of growth and closure of hydrophilic pores is controlled by the competition between the surface tension of the membrane and the line tension associated with the rim of the pore. We estimate the line tension of a hydrophilic pore from the shape of the computed free-energy barriers. The line tension thus computed is in a good agreement with available experimental data. We also estimate the line tension of hydrophobic pores at both macroscopic and microscopic levels. The comparison of line tensions at these two different levels indicates that the "microscopic" line tension should be carefully distinguished from the "macroscopic" effective line tension used in the theoretical analysis of pore nucleation. The overall shape of the free-energy barrier for pore nucleation shows no indication for the existence of a metastable intermediate during pore nucleation.     

Improved dissipative particle dynamics simulations of lipid bilayers

The authors introduce a new parameterization for the dissipative particle dynamics simulations of lipid bilayers. In this parameterization, the conservative pairwise forces between beads of the same type in two different hydrophobic chains are chosen to be less repulsive than the water-water interaction, but the intrachain bead interactions are the same as the water-water interaction. For a certain range of parameters, the new bilayer can only be stretched up to 30% before it ruptures. Membrane tension, density profiles, and the in-plane lipid diffusion coefficient of the new bilayer are discussed in detail. They find two kinds of finite size effects that influence the membrane tension: lateral finite size effects, for which larger membranes rupture at a smaller stretch, and transverse finite size effects, for which tensionless bilayers are more compact in larger systems. These finite size effects become rather small when the simulation box is sufficiently large.     

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.     

Statistical mechanics of bilayer membrane with a fixed projected area

The equilibrium and fluctuation methods for determining the surface tension, sigma, and bending modulus, kappa, of a bilayer membrane with a fixed projected area are discussed. In the fluctuation method the elastic coefficients sigma and kappa are measured from the amplitude of thermal fluctuations of the planar membrane, while in the equilibrium method the free energy required to deform the membrane is considered. The latter approach is used to derive new expressions for sigma and kappa (as well as for the saddle-splay modulus), which relate them to the pair-interactions between the amphiphiles forming the membrane. We use linear response theory to argue that the two routes lead to similar values for sigma and kappa. This argument is confirmed by Monte Carlo simulations of a model membrane whose elastic coefficients are calculated using both methods.     

Structural, dynamic, and electrostatic properties of fully hydrated DMPC bilayers from molecular dynamics simulations accelerated with graphical processing units (GPUs)

We present results of molecular dynamics simulations of fully hydrated DMPC bilayers performed on graphics processing units (GPUs) using current state-of-the-art non-polarizable force fields and a local GPU-enabled molecular dynamics code named FEN ZI. We treat the conditionally convergent electrostatic interaction energy exactly using the particle mesh Ewald method (PME) for solution of Poisson's Equation for the electrostatic potential under periodic boundary conditions. We discuss elements of our implementation of the PME algorithm on GPUs as well as pertinent performance issues. We proceed to show results of simulations of extended lipid bilayer systems using our program, FEN ZI. We performed simulations of DMPC bilayer systems consisting of 17,004, 68,484, and 273,936 atoms in explicit solvent. We present bilayer structural properties (atomic number densities, electron density profiles), deuterium order parameters (S(CD)), electrostatic properties (dipole potential, water dipole moments), and orientational properties of water. Predicted properties demonstrate excellent agreement with experiment and previous all-atom molecular dynamics simulations. We observe no statistically significant differences in calculated structural or electrostatic properties for different system sizes, suggesting the small bilayer simulations (less than 100 lipid molecules) provide equivalent representation of structural and electrostatic properties associated with significantly larger systems (over 1000 lipid molecules). We stress that the three system size representations will have differences in other properties such as surface capillary wave dynamics or surface tension related effects that are not probed in the current study. The latter properties are inherently dependent on system size. This contribution suggests the suitability of applying emerging GPU technologies to studies of an important class of biological environments, that of lipid bilayers and their associated integral membrane proteins. We envision that this technology will push the boundaries of fully atomic-resolution modeling of these biological systems, thus enabling unprecedented exploration of meso-scale phenomena (mechanisms, kinetics, energetics) with atomic detail at commodity hardware prices.     

耗散粒子动力学研究双层膜线张力与抗弯刚度的关系

利用耗散力粒子动力学模拟方法研究了拉伸状态下双层膜的抗弯刚度与膜孔线张力之间的关系.通过对双层膜在不同投影面积约束下的系统模拟,观察到3个区域:自由振动膜、伸展膜和穿孔膜.由前两个区域的应力张量计算得到的膜的面张力(σΣ)与拟合膜波动性质得到的面张力(σfluc)吻合的很好,除去在两区域的转变点附近σfluc略大于σΣ.当考虑在经典Helfrich弹性膜模型中被忽略的膜厚度时,线张力可以和抗弯刚度用一个简单的模型联系起来.通过对穿孔膜区域的数据进行分析,证明由本模型得到的抗弯刚度与拟合膜波动性质得到的抗弯刚度符合的很好.由此提出一种简便的测量方法,通过计算拉伸膜孔的面张力和统计膜厚度,拟合这个简单模型来测量膜的抗弯刚度.     

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.     

Laser induced adsorption site changes of CO adsorbed at nanoparticulate palladium aggregates on an alumina support driven by local adsorbate density fluctuations

UV-laser induced adsorption site changes of CO adsorbed at palladium aggregates will be reported using laser light of λ=355 nm. The aggregates with an average size of 100 atoms/island have been deposited on an epitaxial Al₂O₃/NiAl(1 1 0) film. As is apparent from IR and temperature programmed desorption spectroscopy (TPD) laser induced migration occurs. It necessitates the presence of adsorbate state density fluctuations. The observation is interpreted as being due to a collective process involving long range dynamical coupling of CO molecules which causes lateral displacements within areas of elevated local adsorbate densities.     

Simulations of lipid vesicle rupture induced by an adjacent supported lipid bilayer patch

Using a simple phenomenological model of a lipid bilayer and a surface, simulations were performed to study the bilayer-induced vesicle rupture probability as a vesicle adsorbs adjacently to a bilayer patch already adsorbed on the surface. The vesicle rupture probability was studied as a function of temperature, vesicle size, and surface-bilayer interaction strength. From the simulation data, estimates of the apparent activation energy for bilayer-induced vesicle rupture were calculated, both for different vesicle sizes and for different surface-bilayer interaction strengths.     

Application of combined Monte Carlo and molecular dynamics method to simulation of dipalmitoyl phosphatidylcholine lipid bilayer

We describe a new equilibration procedure for the atomic level simulation of a hydrated lipid bilayer. The procedure consists of alternating molecular dynamics trajectory calculations in a constant surface tension and temperature ensemble with configurational bias Monte Carlo moves to different regions of the configuration space of the bilayer, in a constant volume and temperature ensemble. The procedure is described in detail and is applied to a bilayer of 100 molecules of dipalmitoyl phosphatidylcholine (DPPC) and 3205 water molecules. We find that the hybrid simulation procedure enhances the equilibration of the bilayer as measured by the convergence of the area per molecule and the segmental order parameters, as compared with a simulation using only molecular dynamics (MD). Progress toward equilibration is almost three times as fast in CPU time, compared with a purely MD simulation. Equilibration is complete, as judged by the lack of energy drift in three separate 200-ps runs of continuous MD started from different initial states. Results of the simulation are presented and compared with experimental data and with other recent simulations of DPPC. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 1153–1164, 1999     

Emulsification in turbulent flow 1. Mean and maximum drop diameters in inertial and viscous regimes

Systematic experimental study of the effects of several factors on the mean and maximum drop sizes during emulsification in turbulent flow is performed. These factors include: (1) rate of energy dissipation, epsilon; (2) interfacial tension, sigma; (3) viscosity of the oil phase, eta(D); (4) viscosity of the aqueous phase, eta(C); and (5) oil volume fraction, Phi. The emulsions are prepared by using the so-called "narrow-gap homogenizer" working in turbulent regime of emulsification. The experiments are performed at high surfactant concentration to avoid the effect of drop-drop coalescence. For emulsions prepared in the inertial turbulent regime, the mean and the maximum drop sizes increase with the increase of eta(D) and sigma, and with the decrease of epsilon. In contrast, Phi and eta(C) affect only slightly the mean and the maximum drop sizes in this regime of emulsification. These results are described very well by a theoretical expression proposed by Davies [Chem. Eng. Sci. 40 (1985) 839], which accounts for the effects of the drop capillary pressure and the viscous dissipation inside the breaking drops. The polydispersity of the emulsions prepared in the inertial regime of emulsification does not depend significantly on sigma and epsilon. However, the emulsion polydispersity increases significantly with the increase of oil viscosity, eta(D). The experiments showed also that the inertial turbulent regime is inappropriate for emulsification of oils with viscosity above ca. 500 mPa s, if drops of micrometer size are to be obtained. The transition from inertial to viscous turbulent regime of emulsification was accomplished by a moderate increase of the viscosity of the aqueous phase (above 5 mPa s in the studied systems) and/or by increase of the oil volume fraction, Phi>0.6. Remarkably, emulsions with drops of micrometer size are easily formed in the viscous turbulent regime of emulsification, even for oils with viscosity as high as 10,000 mPa s. In this regime, the mean drop size rapidly decreases with the increase of eta(C) and Phi (along with the effects of epsilon, sigma, and eta(D), which are qualitatively similar in the inertial and viscous regimes of emulsification). The experimental results are theoretically described and discussed by using expressions from the literature and their modifications (proposed in the current study).     

Collective membrane motions of high and low amplitude, studied by dynamic light scattering and micro-interferometry

Undulations of lipid bilayers were experimentally studied for the two limiting cases of high and weak lateral tension using two well established model systems: freely suspended planar lipid bilayers, so-called black lipid membranes (BLM) for high-tension studies and large unilamellar vesicles (LUV) for measurements at weak tension. This variation in tension results in changes of undulation amplitudes from several hundred nm (LUV) down to 1 nm (BLM), thus requiring different physical methods for their detection. We have employed microinterferometric techniques (RICM) for studying the regime of weak tension and dynamic light scattering (DLS) for that of high tension. The dedicated DLS set-up allowed the measurements of undulations over a wide wave vector range of 250 < q/cm-1 < 35,000 cm-1. This enabled the observation of collective membrane modes in two regimes, the oscillating one at low q and the overdamped regime at high q. The transition between both regimes at the bifurcation point is rather abrupt and depends on the lateral tension of the bilayer, as is demonstrated by comparing the dispersion curves of pure lipid and of lipid-cholestrol BLMs over the same q-range. The DLS measurements allowed a critical test of a hydrodynamic theory of the dispersion behaviour of membrane collective modes under tension. The DLS measurements are compared with RICM results of undulatory excitations of giant vesicles weakly adhering to substrates in the 10(-6)-2.5 x 10(-7) m wavelength regime and at low frequencies (0.1-25 Hz). Experimental evidence for the strong decrease in the relaxation rate by the hydrodynamic coupling of the membrane with the wall is established.     

Influence of nanotopography on phospholipid bilayer formation on silicon dioxide

We have investigated the effect of well-defined nanoscale topography on the 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC) lipid vesicle adsorption and supported phospholipid bilayer (SPB) formation on SiO2 surfaces using a quartz crystal microbalance with dissipation monitoring (QCM-D) and atomic force microscopy (AFM). Unilamellar lipid vesicles with two different sizes, 30 and 100 nm, were adsorbed on pitted surfaces with two different pit diameters, 110 and 190 nm, as produced by colloidal lithography, and the behavior was compared to results obtained on flat surfaces. In all cases, complete bilayer formation was observed after a critical coverage of adsorbed vesicles had been reached. However, the kinetics of the vesicle-to-bilayer transformation, including the critical coverage, was significantly altered by surface topography for both vesicle sizes. Surface topography hampered the overall bilayer formation kinetics for the smaller vesicles, but promoted SPB formation for the larger vesicles. Depending on vesicle size, we propose two modifications of the precursor-mediated vesicle-to-bilayer transformation mechanism used to describe supported lipid bilayer formation on the corresponding flat surface. Our results may have important implications for various lipid-membrane-based applications using rough or topographically structured surfaces.