Bilayer permeability during phase transition as an Erlang flow of hydrophilic pores resulting from diffusion in the radius space

The formation of hydrophilic pores in a lipid bilayer during phase transition is described using the Smoluchowski equation with an additional term of the hydrophobic pore source. This term is added to account for defects in lipid packing during phase transition. We assume that the temporal sequence of the pores is a stochastic process, a non-stationary second-order Erlang flow. Flow characteristics depend on the equation solution and determine the formation times of the hydrophilic pores. The calculated distribution of the durations of intervals between hydrophilic pores is in a good agreement with experimental data published before. In the context of this model we describe the influence of poly(ethylene glycol) on the pore formation frequency.     

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.     

Diacylglycerols, lysolecithin, or hydrocarbons markedly alter the bilayer to hexagonal phase transition temperature of phosphatidylethanolamines

The bilayer to hexagonal phase transition temperatures of dielaidoylphosphatidylethanolamine and 1-palmitoyl-2-oleoylphosphatidylethanolamine are 65.6 and 71.4 degrees C, respectively. Using high-sensitivity differential scanning calorimetry, I have shown that these transition temperatures are extremely sensitive to the presence of small amounts of other lipid components. For example, at a mole fraction of only 0.01, dilinolenin lowers the bilayer to hexagonal phase transition temperature of 1-palmitoyl-2-oleoyl-phosphatidylethanolamine by 8.5 degrees C. Other diacylglycerols have similar effects on this transition temperature, although the degree of unsaturation of the acyl chains has some effect, with distearin being less potent. In comparison, the 20-carbon alkane eicosane lowers this transition temperature by 5 degrees C, while palmitoyl-lysolecithin raises it by 2.5 degrees C. Similar effects of these additives on the bilayer to to hexagonal phase transition temperature are observed with dielaidoylphosphatidylethanolamine. At these concentrations of additive, there is no effect on the gel-state to liquid-crystalline-state transition temperature. The observed shifts in the temperature of the bilayer to the hexagonal phase transition can be qualitatively interpreted in terms of the effects of these additives on the hydrophilic surface area and on the hydrophobic volume. Substances expanding the hydrophobic domain promote hexagonal phase formation and lower the bilayer to hexagonal phase transition temperature. The sensitivity of the bilayer to hexagonal phase transition temperature to the presence of additives is at least as great as that which has been observed for any other lipid phase transition.     

Stochastic model for electric field-induced membrane pores. Electroporation

Electric impulses (1-20 kV cm-1, 1-5 microseconds) cause transient structural changes in biological membranes and lipid bilayers, leading to apparently reversible pore formation ( electroporation ) with cross-membrane material flow and, if two membranes are in contact, to irreversible membrane fusion ( electrofusion ). The fundamental process operative in electroporation and electrofusion is treated in terms of a periodic lipid block model, a block being a nearest-neighbour pair of lipid molecules in either of two states: (i) the polar head group in the bilayer plane or (ii) facing the centre of a pore (or defect site). The number of blocks in the pore wall is the stochastic variable of the model describing pore size and stability. The Helmholtz free energy function characterizing the transition probabilities of the various pore states contains the surface energies of the pore wall and the planar bilayer and, if an electric field is present, also a dielectric polarization term (dominated by the polarization of the water layer adjacent to the pore wall). Assuming a Poisson process the average number of blocks in a pore wall is given by the solution of a non-linear differential equation. At subcritical electric fields the average pore size is stationary and very small. At supercritical field strengths the pore radius increases and, reaching a critical pore size, the membrane ruptures (dielectric breakdown). If, however, the electric field is switched off, before the critical pore radius is reached, the pore apparently completely reseals to the closed bilayer configuration (reversible electroporation ).     

Modulation of the phase transition behavior of phosphatidylethanolamine by cholesterol and oxysterols

Cholesterol lowers the bilayer to hexagonal phase transition temperature of phosphatidylethanolamines up to a mole fraction of about 0.1. At cholesterol mole fractions above about 0.3, the effect of this sterol is to stabilize the bilayer phase. The relatively weak effects of cholesterol in altering the bilayer to hexagonal phase transition temperature can be explained on the basis of lateral phase separation. This is indicated by the horizontal liquidus line for the gel to liquid-crystalline transition in the phase diagram for mixtures of cholesterol with dielaidoylphosphatidylethanolamine (DEPE) as well as the fact that cholesterol does not greatly decrease the cooperativity of the bilayer to hexagonal phase transition. The enthalpy of this latter transition increased with increasing mole fractions of cholesterol. Two oxidation products of cholesterol are 5-cholesten-3 beta,7 alpha-diol and cholestan-3 beta,5 alpha,6 beta-triol. Compared with cholesterol, 5-cholesten-3 beta,7 alpha-diol had a greater effect in decreasing the bilayer to hexagonal phase transition temperature and broadening this transition. It is suggested that its effectiveness is due to its greater solubility in the DEPE. In contrast, cholestan-3 beta,5 alpha,6 beta-triol raises the bilayer to hexagonal phase transition temperature of DEPE. This is due to its larger and more hydrophilic head group. In addition, its length, being shorter than that of DEPE, would not allow it to pack efficiently in a hexagonal phase arrangement.We suggest that this same effect is responsible for cholesterol raising the bilayer to hexagonal phase transition temperature at higher mole fractions.     

Pore Formation in a Binary Giant Vesicle Induced by Cone-Shaped Lipids

We have investigated shape deformations of binary giant unilamellar vesicles (GUVs) composed of cone- and cylinder-shaped lipids. By coupling the spontaneous curvature of lipids with the phase separation, we demonstrated pore opening and closing in GUVs. When the temperature was set below the chain melting transition temperature of the cylinder-shaped lipid, the GUVs burst and then formed a single large pore, where the cone shape lipids form a cap at the edge of the bilayer to stabilize the pore. The pore closed when we increased the temperature above the transition temperature. The pore showed three types of shapes depending on the cone-shaped lipid concentration: simple circular, rolled-rim, and wrinkled-rim pores. These pore shape changes indicate that the distribution of the cone- and cylinder-shaped lipids is asymmetric between the inner and outer leaflets in the bilayer. We have proposed a theoretical model for a two-component membrane with an edge of bilayer where lipids can transfer between two leaflets. Using this model, we have reproduced numerically the observed shape deformations at the rim of pore.     

Stability of a melittin pore in a lipid bilayer: a molecular dynamics study

We have investigated the configuration and the stability of a single membrane pore bound by four melittin molecules and embedded in a fully hydrated bilayer lipid membrane. We used molecular dynamics simulations up to 5.8 ns. It is found that the initial tetrameric configuration decays with increasing time into a stable trimer and one monomer. This continuous transformation is accompanied by a lateral expansion of the aqueous pore exhibiting a final size comparable to experimental findings. The expansion-induced formation of an interface between the pore-lining acyl chains of the lipids and the pore water ("hydrophobic pore") is transformed into an energetically more favorable toroidal pore structure where some lipid heads are translocated from the rim to the central part of the interface ("hydrophilic pore"). The expansion of the pore is supported by the electrostatic repulsion among the alpha-helices. It is hypothesized that pore growth, and hence cell lysis, is induced by a melittin-mediated line tension of the pore.     

Contribution of the γ-secretase subunits to the formation of catalytic pore of presenilin 1 protein

γ-Secretase is an intramembrane-cleaving protease related to the etiology of Alzheimer disease. γ-Secretase is a membrane protein complex composed of presenilin (PS) and three indispensable subunits: nicastrin, Aph-1, and Pen-2. PS functions as a protease subunit forming a hydrophilic catalytic pore structure within the lipid bilayer. However, it remains unclear how other subunits are involved in the pore formation. Here, we show that the hydrophilic pore adopted with an open conformation has already been formed by PS within the immature γ-secretase complex. The binding of the subunits induces the close proximity between transmembrane domains facing the catalytic pore. We propose a model in which the γ-secretase subunits restrict the arrangement of the transmembrane domains of PS during the formation of the functional structure of the catalytic pore.     

Initial structural and dynamic characterization of the M2 protein transmembrane and amphipathic helices in lipid bilayers

Amphipathic helices in membrane proteins that interact with the hydrophobic/hydrophilic interface of the lipid bilayer have been difficult to structurally characterize. Here, the backbone structure and orientation of an amphipathic helix in the full-length M2 protein from influenza A virus has been characterized. The protein has been studied in hydrated DMPC/DMPG lipid bilayers above the gel to liquid-crystalline phase transition temperature by solid-state NMR spectroscopy. Characteristic PISA (Polar Index Slant Angle) wheels reflecting helical wheels have been observed in uniformly aligned bilayer preparations of both uniformly 15N labeled and amino acid specific labeled M2 samples. Hydrogen/deuterium exchange studies have shown the very slow exchange of some residues in the amphipathic helix and more rapid exchange for the transmembrane helix. These latter results clearly suggest the presence of an aqueous pore. A variation in exchange rate about the transmembrane helical axis provides additional support for this claim and suggests that motions occur about the helical axes in this tetramer to expose the entire backbone to the pore.     

Molecular dynamics simulations of hydrophilic pores in lipid bilayers

Hydrophilic pores are formed in peptide free lipid bilayers under mechanical stress. It has been proposed that the transport of ionic species across such membranes is largely determined by the existence of such meta-stable hydrophilic pores. To study the properties of these structures and understand the mechanism by which pore expansion leads to membrane rupture, a series of molecular dynamics simulations of a dipalmitoylphosphatidylcholine (DPPC) bilayer have been conducted. The system was simulated in two different states; first, as a bilayer containing a meta-stable pore and second, as an equilibrated bilayer without a pore. Surface tension in both cases was applied to study the formation and stability of hydrophilic pores inside the bilayers. It is observed that below a critical threshold tension of approximately 38 mN/m the pores are stabilized. The minimum radius at which a pore can be stabilized is 0.7 nm. Based on the critical threshold tension the line tension of the bilayer was estimated to be approximately 3 x 10(-11) N, in good agreement with experimental measurements. The flux of water molecules through these stabilized pores was analyzed, and the structure and size of the pores characterized. When the lateral pressure exceeds the threshold tension, the pores become unstable and start to expand causing the rupture of the membrane. In the simulations the mechanical threshold tension necessary to cause rupture of the membrane on a nanosecond timescale is much higher in the case of the equilibrated bilayers, as compared with membranes containing preexisting pores.     

Coupling of Membrane Nanodomain Formation and Enhanced Electroporation near Phase Transition

Biological cells are enveloped by a heterogeneous lipid bilayer that prevents the uncontrolled exchange of substances between the cell interior and its environment. In particular, membranes act as a continuous barrier for salt and macromolecules to ensure proper physiological functions within the cell. However, it has been shown that membrane permeability strongly depends on temperature and, for phospholipid bilayers, displays a maximum at the transition between the gel and fluid phase. Here, extensive molecular dynamics simulations of dipalmitoylphosphatidylcholine bilayers were employed to characterize the membrane structure and dynamics close to phase transition, as well as its stability with respect to an external electric field. Atomistic simulations revealed the dynamic appearance and disappearance of spatially related nanometer-sized thick ordered and thin interdigitating domains in a fluid-like bilayer close to the phase transition temperature (T_m). These structures likely represent metastable precursors of the ripple phase that vanished at increased temperatures. Similarly, a two-phase bilayer with coexisting gel and fluid domains featured a thickness minimum at the interface because of splaying and interdigitating lipids. For all systems, application of an external electric field revealed a reduced bilayer stability with respect to pore formation for temperatures close to T_m. Pore formation occurred exclusively in thin interdigitating membrane nanodomains. These findings provide a link between the increased membrane permeability and the structural heterogeneity close to phase transition.     

Lipid-protein interactions of the human erythrocyte concanavalin a receptor in phospholipid bilayers

The interaction of the human erythrocyte concanavalin A receptor (a subpopulation of Band 3) with phospholipids has been investigated using differential scanning microcalorimetry of reconstituted vesicles prepared by detergent dialysis. The mean diameter of dialyzed phospholipid vesicles jumps dramatically on inclusion of the concanavalin A receptor and then increases linearly with the fraction of protein in the bilayer. The glycoprotein has a dramatic effect on the phospholipid gel to liquid-crystalline phase transition, and ΔH decreases linearly with increasing mole fraction of protein up to a protein/lipid mole ratio of around 1:1160. Extrapolation of this data indicates that each concanavalin A receptor is able to perturb about 685 molecules of dimyristoylphosphatidylcholine, withdrawing them from the main phase transition. The cooperativity of phospholipid melting is profoundly disrupted by small amounts of glycoprotein, with the cooperative unit dropping to less than half its initial values at a protein/lipid mole ratio of 1:3800. A break occurs in the ΔH curve as the protein/lipid mole ratio is increased above 1:1160, and ΔH then increases linearly with increasing amounts of concanavalin A receptor in the bilayer. This phenomenon may be interpreted in terms of protein-protein aggregation which occurs in the phospholipid bilayer above a certain critical mole fraction of concanavalin A receptor, resulting in perturbed phospholipids being returned to the phase transition. In addition, the hydrophilic domains of the glycoprotein may exist in two different conformations depending on the protein concentration in the bilayer, and these may differ in their ability to interact with phospholipid headgroups at the membrane surface.     

PEG blocking of single pores arising on phase transitions in unmodified lipid bilayers

Changes in ionic permeability of bilayer lipid membranes (BLM) from dipalmitoyl phosphatidylcholine at temperature of phase transition in 1 M LiCl solution in the presence of polyethyleneglycols (PEG) of various molecular masses are studied. The transition of ionic membrane channels from conducting to blocked nonconducting state using polymers makes it possible to calibrate lipid pores. It is shown that low-molecular weight glycerol and PEG with molecular weights of 300 and 600 decrease the amplitude of current fluctuations through the membrane, the decrease being proportional to the size of the polymer molecule incorporated. The addition of PEG with molecular masses of 1450, 2000, and 3350 decrease the current fluctuations to the basal noise level. The result is considered as a complete blockade of ion channel conductivity. In the presence of rather large polymers, such as PEG with molecular masses of 6000 and 20000, which are hardly incorporated in the pore, single current fluctuations occur again; however, their amplitudes are somewhat smaller than in the absence of PEG. It is assumed that a complete blockade of the conductivity of lipid ionic channels by PEG with molecular masses of 1450, 2000, and 3350 is due to dehydration of the pore gap and the conversion of the hydrophilic pore to a hydrophobic one.     

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.     

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.     

"Blocking" by polyethyleneglycol of single lipid pores arising in unmodified bilayer lipid membranes during phase transitions

Changes in the ionic permeability of bilayer lipid membranes from dipalmitoyl phosphatidylcholine at temperatures of phase transition in LiCl (1 M) solution after the addition of polyethyleneglycols of different molecular masses have been studied. The transition of ionic membrane channels from the conducting state to a blocking nonconducting state using polymers makes it possible to calibrate lipid pores. It was shown that low-molecular-weight glycerol, polyethyleneglycols with molecular masses of 300 and 600 decrease the amplitude of fluctuations of the current through the membrane, the decrease being proportional to the size of the polymer molecule being incorporated. The addition of polyethyleneglycols with molecular masses of 1450, 2000, and 3350 decrease the current fluctuations to the basal noise level. This result is considered as a complete blockade of ion channel conductivity. In the presence of rather large polymers, such as polyethyleneglycols with molecular masses of 6000 and 20000, which are practically not incorporated into the pore, single current fluctuations occur again; however, their amplitudes are somewhat smaller than in the absence of polyethyleneglycol. It is assumed that the complete blockade of the conductivity of lipid ionic channels by polyethyleneglycols with molecular masses of 1450, 2000, and 3350 is due to the dehydration of the pore gap and the conversion of the hydrophilic pore to a hydrophobic pore.     

The shape of lipid molecules and monolayer membrane fusion

The contact between two bilayer membranes results in their monolayer fusion comprising the formation of a trilaminar structure (a single bilayer connected to two bilayers over the whole perimeter) in the contact region. The time required for monolayer fusion was measured and irreversible electrical breakdown was studied for membranes of different compositions. A theoretical model of the monolayer fusion is suggested to explain the results. It assumes that the structural reorganization underlying the process involves the formation of a stalk between bilayers as a result of local bending of the interacting monolayers. This structural reorganization is similar to the hydrophilic pore formation in a bilayer under irreversible breakdown. However, the directions of the monolayer bending are different in the two processes and, therefore, the bending energies depend oppositely on the effective shape of lipid molecules. Theoretical predictions agree well with experimental data. The applicability of the suggested mechanism to biomembrane fusion is discussed.     

A tetrameric porin limits the cell wall permeability of Mycobacterium smegmatis

Mycobacteria protect themselves with an outer lipid bilayer, which is the thickest biological membrane hitherto known and has an exceptionally low permeability rendering mycobacteria intrinsically resistant against many antibiotics. Pore proteins mediate the diffusion of hydrophilic nutrients across this membrane. Electron microscopy revealed that the outer membrane of Mycobacterium smegmatis contained about 1000 protein pores per microm(2), which are about 50-fold fewer pores per microm(2) than in Gram-negative bacteria. The projection structure of the major porin MspA of M. smegmatis was determined at 17 A resolution. MspA forms a cone-like tetrameric complex of 10 nm in length with a single central pore. Thus, MspA is drastically different from the trimeric porins of Gram-negative bacteria and represents a new class of channel proteins. The formation of MspA micelles indicated that the ends of MspA have different hydrophobicities. Oriented insertion of MspA into membranes was demonstrated in lipid bilayer experiments, which revealed a strongly asymmetrical voltage gating of MspA channels at -30 mV. The length of MspA is sufficient to span the outer membrane and contributes in combination with the tapering end of the pore and the low number of pores to the low permeability of the cell wall of M. smegmatis for hydrophilic compounds.     

Modulation of the bilayer to hexagonal phase transition and solvation of phosphatidylethanolamines in aqueous salt solutions

Several salts affect the temperature of the bilayer to hexagonal phase transition of phosphatidylethanolamines. Their effects are dependent on the anion as well as the cation of the salt. Salt effects on this transition can be explained by preferential hydration and ion binding. Those salts which are excluded from the solvation sphere of the membrane promote hexagonal phase formation. For example, Na2SO4 promotes preferential hydration and is a hexagonal phase promoter while NaSCN does not do this and is a bilayer stabilizer. Unlike amphiphiles and hydrocarbons, salts can shift the bilayer to hexagonal phase transition temperature without altering the cooperativity of the transition. The effect of these salts on the gel to liquid-crystal transition is opposite to their effect on the bilayer to hexagonal phase transition. We also find that MnCl2 markedly raises the gel to liquid-crystal transition temperature. This effect is due to binding of the cation to the membrane surface. The effect is reduced with MnSO4 because of preferential hydration. Our results demonstrate that the nature of the anion as well as the cation can alter the effect of salts on lipid phase transition properties. The observed effects can be explained as resulting from preferential hydration and ion binding.     

The effects of ethylene oxide containing lipopolymers and tri-block copolymers on lipid bilayers of dipalmitoylphosphatidylcholine.

A comparative study is conducted on the influence of two types of polymeric compounds on the phase behavior of 1,2-dihexadecanoyl-s,n-glycero-3-phosphotidylcholine (DC16PC) lipid bilayers. The first polymeric compound is a lipopolymer, with two different lengths of a hydrophilic polyethylene oxide moity, anchored to the bilayer by a 1,2-dioctadecanoyl-s,n-glycero-3-phosphoethanolamine (DC18PE) lipid. The second type, which is a novel type of membrane-spanning object, is an amphiphilic tri-block copolymer composed of two hydrophilic stretches of polyethylene oxide separated by a hydrophobic stretch of polystyrene. Hence the tri-block copolymer may act as a membrane-spanning macromolecule mimicking an amphiphilic protein or polypeptide. Differential scanning calorimetry is used to determine a partial phase diagram for the lipopolymer systems and to assess the amount of lipopolymer that can be loaded into DC16PC lipid bilayers before micellization takes place. Unilamellar and micellar phase structures are investigated by fluorescence quenching using bilayer permeating dithionite. The chain length-dependent critical lipopolymer concentration, denoting the lamellar-to-micellar phase transition, compares favorably with a theoretical prediction based on free-energy considerations involving bilayer cohesion and lateral pressure exerted by the polymer chains.