Molecular dynamics simulation of a phosphatidylglycerol membrane

Although molecular dynamics simulations are an important tool for studying membrane systems, relatively few simulations have used anionic lipids. This paper reports the first simulation of a pure phosphatidylglycerol (PG) bilayer. The properties of this equilibrated palmitoyloleoylphosphatidylglycerol membrane agree with experimental observations of PG membranes and with previous simulations of monolayers and mixed bilayers containing PG lipids. These simulations also provide interesting insights into hydrogen bonding interactions in PG membranes. This equilibrated membrane will be a useful starting point for simulations of membrane proteins interacting with PG lipids.     

Life Cycle of an Electropore: Field-Dependent and Field-Independent Steps in Pore Creation and Annihilation

Electropermeabilization, an electric field-induced modification of the barrier functions of the cell membrane, is widely used in laboratories and increasingly in the clinic; but the mechanisms and physical structures associated with the electromanipulation of membrane permeability have not been definitively characterized. Indirect experimental observations of electrical conductance and small molecule transport as well as molecular dynamics simulations have led to models in which hydrophilic pores form in phospholipid bilayers with increased probability in the presence of an electric field. Presently available methods do not permit the direct, nanoscale examination of electroporated membranes that would confirm the existence of these structures. To facilitate the reconciliation of poration models with the observed properties of electropermeabilized lipid bilayers and cell membranes, we propose a scheme for characterizing the stages of electropore formation and resealing. This electropore life cycle, based on molecular dynamics simulations of phospholipid bilayers, defines a sequence of discrete steps in the electric field-driven restructuring of the membrane that leads to the formation of a head group-lined, aqueous pore and then, after the field is removed, to the dismantling of the pore and reassembly of the intact bilayer. Utilizing this scheme we can systematically analyze the interactions between the electric field and the bilayer components involved in pore initiation, construction and resealing. We find that the pore creation time depends strongly on the electric field gradient across the membrane interface and that the pore annihilation time is at least weakly dependent on the magnitude of the pore-initiating electric field and, in general, much longer than the pore creation time.     

Peridynamic Modeling of Ruptures in Biomembranes

We simulate the formation of spontaneous ruptures in supported phospholipid double bilayer membranes, using peridynamic modeling. Experiments performed on spreading double bilayers typically show two distinct kinds of ruptures, floral and fractal, which form spontaneously in the distal (upper) bilayer at late stages of double bilayer formation on high energy substrates. It is, however, currently unresolved which factors govern the occurrence of either rupture type. Variations in the distance between the two bilayers, and the occurrence of interconnections (“pinning sites”) are suspected of contributing to the process. Our new simulations indicate that the pinned regions which form, presumably due to Ca²⁺ ions serving as bridging agent between the distal and the proximal bilayer, act as nucleation sites for the ruptures. Moreover, assuming that the pinning sites cause a non-zero shear modulus, our simulations also show that they change the rupture mode from floral to fractal. At zero shear modulus the pores appear to be circular, subsequently evolving into floral pores. With increasing shear modulus the pore edges start to branch, favoring fractal morphologies. We conclude that the pinning sites may indirectly determine the rupture morphology by contributing to shear stress in the distal membrane.     

Atomistic Simulations of Pore Formation and Closure in Lipid Bilayers

Cellular membranes separate distinct aqueous compartments, but can be breached by transient hydrophilic pores. A large energetic cost prevents pore formation, which is largely dependent on the composition and structure of the lipid bilayer. The softness of bilayers and the disordered structure of pores make their characterization difficult. We use molecular-dynamics simulations with atomistic detail to study the thermodynamics, kinetics, and mechanism of pore formation and closure in DLPC, DMPC, and DPPC bilayers, with pore formation free energies of 17, 45, and 78 kJ/mol, respectively. By using atomistic computer simulations, we are able to determine not only the free energy for pore formation, but also the enthalpy and entropy, which yields what is believed to be significant new insights in the molecular driving forces behind membrane defects. The free energy cost for pore formation is due to a large unfavorable entropic contribution and a favorable change in enthalpy. Changes in hydrogen bonding patterns occur, with increased lipid-water interactions, and fewer water-water hydrogen bonds, but the total number of overall hydrogen bonds is constant. Equilibrium pore formation is directly observed in the thin DLPC lipid bilayer. Multiple long timescale simulations of pore closure are used to predict pore lifetimes. Our results are important for biological applications, including the activity of antimicrobial peptides and a better understanding of membrane protein folding, and improve our understanding of the fundamental physicochemical nature of membranes.     

Energetics of pore formation induced by membrane active peptides

Antimicrobial peptides are known to form pores in cell membranes. We study this process in model bilayers of various lipid compositions. We use two of the best-studied peptides, alamethicin and melittin, to represent peptides making two types of pores, that is, barrel-stave pores and toroidal pores. In both cases, the key control variable is the concentration of the bound peptides in the lipid bilayers (expressed in the peptide-lipid molar ratio, P/L). The method of oriented circular dichroism (OCD) was used to monitor the peptide orientation in bilayers as a function of P/L. The same samples were scanned by X-ray diffraction to measure the bilayer thickness. In all cases, the bilayer thickness decreases linearly with P/L and then levels off after P/L exceeds a lipid-dependent critical value, (P/L)*. OCD spectra showed that the helical peptides are oriented parallel to the bilayers as long as P/L < (P/L)*, but as P/L increases over (P/L)*, an increasing fraction of peptides changed orientation to become perpendicular to the bilayer. We analyzed the data by assuming an internal membrane tension associated with the membrane thinning. The free energy containing this tension term leads to a relation explaining the P/L-dependence observed in the OCD and X-ray diffraction measurements. We extracted the experimental parameters from this thermodynamic relation. We believe that they are the quantities that characterize the peptide-lipid interactions related to the mechanism of pore formation. We discuss the meaning of these parameters and compare their values for different lipids and for the two different types of pores. These experimental parameters are useful for further molecular analysis and are excellent targets for molecular dynamic simulation studies.     

Atomistic Simulations of Pore Formation and Closure in Lipid Bilayers

Cellular membranes separate distinct aqueous compartments, but can be breached by transient hydrophilic pores. A large energetic cost prevents pore formation, which is largely dependent on the composition and structure of the lipid bilayer. The softness of bilayers and the disordered structure of pores make their characterization difficult. We use molecular-dynamics simulations with atomistic detail to study the thermodynamics, kinetics, and mechanism of pore formation and closure in DLPC, DMPC, and DPPC bilayers, with pore formation free energies of 17, 45, and 78 kJ/mol, respectively. By using atomistic computer simulations, we are able to determine not only the free energy for pore formation, but also the enthalpy and entropy, which yields what is believed to be significant new insights in the molecular driving forces behind membrane defects. The free energy cost for pore formation is due to a large unfavorable entropic contribution and a favorable change in enthalpy. Changes in hydrogen bonding patterns occur, with increased lipid-water interactions, and fewer water-water hydrogen bonds, but the total number of overall hydrogen bonds is constant. Equilibrium pore formation is directly observed in the thin DLPC lipid bilayer. Multiple long timescale simulations of pore closure are used to predict pore lifetimes. Our results are important for biological applications, including the activity of antimicrobial peptides and a better understanding of membrane protein folding, and improve our understanding of the fundamental physicochemical nature of membranes.     

Paradoxical lipid dependence of pores formed by the Escherichia coli alpha-hemolysin in planar phospholipid bilayer membranes

alpha-Hemolysin (HlyA) is an extracellular protein toxin (117 kDa) secreted by Escherichia coli that targets the plasma membranes of eukaryotic cells. We studied the interaction of this toxin with membranes using planar phospholipid bilayers. For all lipid mixtures tested, addition of nanomolar concentrations of toxin resulted in an increase of membrane conductance and a decrease in membrane stability. HlyA decreased membrane lifetime up to three orders of magnitude in a voltage-dependent manner. Using a theory for lipidic pore formation, we analyzed these data to quantify how HlyA diminished the line tension of the membrane (i.e., the energy required to form the edge of a new pore). However, in contrast to the expectation that adding the positive curvature agent lysophosphatidylcholine would synergistically lower line tension, its addition significantly stabilized HlyA-treated membranes. HlyA also appeared to thicken bilayers to which it was added. We discuss these results in terms of models for proteolipidic pores.     

Disturb or Stabilize? A Molecular Dynamics Study of the Effects of Resorcinolic Lipids on Phospholipid Bilayers

Resorcinolic lipids, or resorcinols, are commonly found in plant membranes. They consist of a substituted benzene ring forming the hydrophilic lipid head, attached to an alkyl chain forming the hydrophobic tail. Experimental results show alternative effects of resorcinols on lipid membranes. Depending on whether they are added to lipid solutions before or after the formation of the liposomes, they either stabilize or destabilize these liposomes. Here we use atomistic molecular dynamics simulations to elucidate the molecular nature of this dual effect. Systems composed of either one of three resorcinol homologs, differing in the alkyl tail length, interacting with dimyristoylphosphatidylcholine lipid bilayers were studied. It is shown that resorcinols preincorporated into bilayers induce order within the lipid acyl chains, decrease the hydration of the lipid headgroups, and make the bilayers less permeable to water. In contrast, simulations in which the resorcinols are incorporated from the aqueous solution into a preformed phospholipid bilayer induce local disruption, leading to either transient pore formation or even complete rupture of the membrane. In line with the experimental data, our simulations thus demonstrate that resorcinols can either disturb or stabilize the membrane structure, and offer a detailed view of the underlying molecular mechanism.     

Ion transport across transmembrane pores

To study the pore-mediated transport of ionic species across a lipid membrane, a series of molecular dynamics simulations have been performed of a dipalmitoyl-phosphatidyl-choline bilayer containing a preformed water pore in the presence of sodium and chloride ions. It is found that the stability of the transient water pores is greatly reduced in the presence of the ions. Specifically, the binding of sodium cations at the lipid/water interface increases the pore line tension, resulting in a destabilization of the pore. However, the application of mechanical stress opposes this effect. The flux of ions through these mechanically stabilized pores has been analyzed. Simulations indicate that the transport of the ions through the pores depends strongly on the size of the water channel. In the presence of small pores (radius <1.5 nm) permeation is slow, with both sodium and chloride permeating at similar rates. In the case in which the pores are larger (radius >1.5 nm), a crossover is observed to a regime where the anion flux is greatly enhanced. Based on these observations, a mechanism for the basal membrane permeability of ions is discussed.     

Stalk mechanism of vesicle fusion

Å mechanism for rupture of a separating bilayer, resulting from vesicle monolayer fusion is investigated theoretically. The stalk mechanism of monolayer fusion, assuming the formation and expansion of a stalk between two interacting membranes is considered. The stalk evolution leads to formation of a separating bilayer and mechanical tension appearance in the system. This tension results in rupture of the separating bilayer and hydrophilic pore formation. Competition between the mechanical tension and hydrophilic pore energy defines the criteria of contacting bilayer rupture. The tension increases with an increase of the absolute value of the negative spontaneous curvature of the outer membrane monolayer, K _s ^o . The pore edge energy decreases with an increase of the positive spontaneous curvature of the inner membrane monolayer, K _s ⁱ . The relations of spontaneous curvatures of outer and inner monolayers, leading to separating bilayer rupture, is calculated. It is demonstrated that his process is possible, provided spontaneous curvatures of membrane monolayers have opposite signs: K _s ^o <0, K _s ⁱ <0. Experimental data concerning the fusion process are analysed.     

Influence of cholesterol on electroporation of bilayer lipid membranes: chronopotentiometric studies

This paper presents the results of constant-current (chronopotentiometric) measurements of the egg yolk phosphatidylcholine (PC) bilayer membrane without and with cholesterol. The experiments were performed on planar bilayer lipid membrane (BLM) formed by the Mueller-Rudin method. It is demonstrated that the constant-intensity current flow through bilayer membranes generated fluctuating pores in their structure. The presence of cholesterol in the membrane caused an increase in the value of the breakdown potential. It is postulated that greater stability of the bilayer with cholesterol can result from an increased critical pore radius (at which the bilayer would undergo irreversible rupture). This confirms that cholesterol has a stabilizing effect on BLM. Besides, our results suggest that addition of cholesterol causes shift in the distribution of pore conductance towards a smaller value. It is suggested that this can be connected with the phenomenon of domain formation in the membranes containing high concentration of cholesterol. Moreover, it is shown that chronopotentiometry with programmable current intensity is a promising method for observation of the membrane recovery process.     

Influenza hemagglutinin-mediated fusion pores connecting cells to planar membranes: flickering to final expansion

We have studied the fusion between voltage-clamped planar lipid bilayers and influenza virus infected MDCK cells, adhered to one side of the bilayer, using measurements of electrical admittance and fluorescence. The changes in currents in-phase and 90 degrees out-of- phase with respect to the applied sinusoidal voltage were used to monitor the addition of the cell membrane capacitance to that of the lipid bilayer through a fusion pore connecting the two membranes. When ethidium bromide was included in the solution of the cell-free side of the bilayer, increases in cell fluorescence accompanied tee admittance changes, independently confirming that these changes were due to formation of a fusion pore. Fusion required acidic pH on the cell- containing side and depended on temperature. For fusion to occur, the influenza hemagglutinin (HA) had to be cleaved into HA1 and HA2 subunits. The incorporation of gangliosides into the planar bilayers greatly augmented fusion. Fusion pores developed in four distinct stages after acidification: (a) a pre-pore, electrically quiescent stage; (b) a flickering stage, with 1-2 nS pores opening and closing repetitively; (c) an irreversibly opened stage, in which pore conductances varied between 2 and 100 nS and exhibited diverse kinetics; (d) a fully opened stage, initiated by an instantaneous, time- resolution limited, increase in conductance leveling at approximately 500 nS. The expansion of pores by stages has also been shown to occur during exocytosis in mast cells and fusion of HA-expressing cells and erythrocytes. We conclude that essential features of fusion pores are produced with proteins in just one of the two fusing membranes.     

Simulations of skin barrier function: free energies of hydrophobic and hydrophilic transmembrane pores in ceramide bilayers

Transmembrane pore formation is central to many biological processes such as ion transport, cell fusion, and viral infection. Furthermore, pore formation in the ceramide bilayers of the stratum corneum may be an important mechanism by which penetration enhancers such as dimethylsulfoxide (DMSO) weaken the barrier function of the skin. We have used the potential of mean constraint force (PMCF) method to calculate the free energy of pore formation in ceramide bilayers in both the innate gel phase and in the DMSO-induced fluidized state. Our simulations show that the fluid phase bilayers form archetypal water-filled hydrophilic pores similar to those observed in phospholipid bilayers. In contrast, the rigid gel-phase bilayers develop hydrophobic pores. At the relatively small pore diameters studied here, the hydrophobic pores are empty rather than filled with bulk water, suggesting that they do not compromise the barrier function of ceramide membranes. A phenomenological analysis suggests that these vapor pores are stable, below a critical radius, because the penalty of creating water-vapor and tail-vapor interfaces is lower than that of directly exposing the strongly hydrophobic tails to water. The PMCF free energy profile of the vapor pore supports this analysis. The simulations indicate that high DMSO concentrations drastically impair the barrier function of the skin by strongly reducing the free energy required for pore opening.     

Influence of cholesterol on electroporation of bilayer lipid membranes: chronopotentiometric studies

This paper presents the results of constant-current (chronopotentiometric) measurements of the egg yolk phosphatidylcholine (PC) bilayer membrane without and with cholesterol. The experiments were performed on planar bilayer lipid membrane (BLM) formed by the Mueller-Rudin method. It is demonstrated that the constant-intensity current flow through bilayer membranes generated fluctuating pores in their structure. The presence of cholesterol in the membrane caused an increase in the value of the breakdown potential. It is postulated that greater stability of the bilayer with cholesterol can result from an increased critical pore radius (at which the bilayer would undergo irreversible rupture). This confirms that cholesterol has a stabilizing effect on BLM. Besides, our results suggest that addition of cholesterol causes shift in the distribution of pore conductance towards a smaller value. It is suggested that this can be connected with the phenomenon of domain formation in the membranes containing high concentration of cholesterol. Moreover, it is shown that chronopotentiometry with programmable current intensity is a promising method for observation of the membrane recovery process.     

Molecular dynamics simulations of pore formation dynamics during the rupture process of a phospholipid bilayer caused by high-speed equibiaxial stretching

Rupture of a phospholipid bilayer under mechanical stresses is triggered by pore formation in an intact bilayer. To understand the molecular details of the dynamics of pore formation we perform molecular dynamics simulations of a phospholipid bilayer under two different equibiaxial stretching conditions: first, unsteady stretching with various stretching speeds in the range of 0.1-1.0m/s, and second, quasistatic stretching. We analyze (i) patterns of pore formation, (ii) the critical area where a pore forms, (iii) the deformation of the bilayer, and (iv) the apparent breaking force. With stretching, the bilayer deforms anisotropically due to lipid chain packing and water penetrating into the hydrophilic region of the bilayer, and when the area exceeds a critical value, water filled pore structure penetrating the bilayer forms and develops into a large pore, resulting in rupture. For a high stretching speed, small pores (multipore) can temporarily form in a small area. It has been statistically determined that the probability of the multipore formation, the critical areal strain, and the apparent breaking force increase with the stretching speed in the range of 0-50%, 0.8-2.0, and 250-400 pN, respectively. The results qualitatively agree with the experimental and other simulation results, and rationalize the leakage of hemoglobin from erythrocytes in shock wave experiments.     

Dynamically stabilized pores in bilayer membranes.

Zhelev and Needham have recently created large, quasistable pores in artificial lipid bilayer vesicles. Initially created by electroporation, the pores remain open for up to several seconds before quickly snapping shut. This result is surprising, in light of the large line tension for holes in bilayer membranes and the rapid time scale for closure of large pores. We show how pores can be dynamically stabilized via a new feedback mechanism. We also explain quantitatively the observed sudden pore closure as a tangent bifurcation. Finally, we show how Zhelev and Needham's experiment can be used to measure accurately the pore line tension, an important material parameter. For their stearoyloleoylphosphatidylcholine/cholesterol mixture we obtain a line tension of 2.6 x 10(-6) dyn.     

Pore formation by a Bax-derived peptide: effect on the line tension of the membrane probed by AFM

Bax is a critical regulator of physiological cell death that increases the permeability of the outer mitochondrial membrane and facilitates the release of the so-called apoptotic factors during apoptosis. The molecular mechanism of action is unknown, but it probably involves the formation of partially lipidic pores induced by Bax. To investigate the interaction of Bax with lipid membranes and the physical changes underlying the formation of Bax pores, we used an active peptide derived from helix 5 of this protein (Bax-alpha5) that is able to induce Bax-like pores in lipid bilayers. We report the decrease of line tension due to peptide binding both at the domain interface in phase-separated lipid bilayers and at the pore edge in atomic force microscopy film-rupture experiments. Such a decrease in line tension may be a general strategy of pore-forming peptides and proteins, as it affects the energetics of the pore and stabilizes the open state.     

Mechanical stresses in erythrocyte membranes (theoretical models)

The type of mechanical stresses that arise in erythrocyte membranes on exposure to catecholamines and steroid hormones is considered. Tensors of mechanical stresses and displacements were obtained for a membrane interacting with hormones. A possible mechanism of membrane rupture under mechanical stresses is discussed. Catecholamines and androgens increase the microviscosity of membranes, and alternating kink and stretching sites occur in the lipid membrane bilayer to produce a checker-wise pattern. The membrane becomes thinner in a stretching site (smectic A → smectic C transition). When tensile stresses increase further and exceed a certain critical value the membrane may rupture. It is possible that a gel phase L_β? → liquid crystalline phase L_α transition takes place in the stretching site of the lipid bilayer prior to disruption. The density of the lipid bilayer decreases in the process, pores form, and then cracks occur.     

Crystallization of antimicrobial pores in membranes: magainin and protegrin

Membrane pores spontaneously formed by antimicrobial peptides in membranes were crystallized for the first time by manipulating the sample hydration and temperature. Neutron diffraction shows that magainins and protegrins form stable pores in fully hydrated fluid membranes. At lower hydration levels or low temperature, the membrane multilayers crystallize. In one crystalline phase, the pores in each bilayer arrange in a regular hexagonal array and the bilayers are stacked into a hexagonal ABC lattice, corresponding to the cubic close-packed structure of spheres. In another crystalline phase, the bilayers are modulated into the rippled multilamellae, corresponding to a 2D monoclinic lattice. The phase diagrams are described. Crystallization of the membrane pores provides possibilities for diffraction studies that might provide useful information on the pore structures.     

Kinetics of pore size during irreversible electrical breakdown of lipid bilayer membranes.

The kinetics of pore formation followed by mechanical rupture of lipid bilayer membranes were investigated in detail by using the charge-pulse method. Membranes of various compositions were charged to a sufficiently high voltage to induce mechanical breakdown. The subsequent decrease of membrane voltage was used to calculate the conductance. During mechanical breakdown, which was probably caused by the widening of one single pore, the membrane conductance was a linear and not exponential function of time after the initial starting process. In a large number of experiments using various lipids and electrolytes, the characteristic opening process of the pore turned out to be independent of the actual membrane potential and electrolyte concentration. Our theoretical analysis of the pore formation suggested that the voltage-induced irreversible breakdown is due to a decrease in edge energy when the pore had formed. After initiation of the pore, the electrical contribution to surface tension is negligible. The time course of the increase of pore size shows that our model of the irreversible breakdown is in good agreement with mechanical properties of membranes reported elsewhere.