Application of the Smoluchowski equation with a source term to the model of lipid pore formation during a phase transition

The Smoluchowski equation, which describes pore diffusion in the radius space, with a source term, is used in modeling the process of the formation of a hydrophilic pore in a lipid bilayer during phase transition. The introduction of a hydrophobic-pore source term into the equation reflects the emergence of additional defects in a bilayer caused by the decrease in the molecule area under the transition from the liquid crystalline to the gel phase. The distribution of the time probability density calculated within the model that is required for the formation of a hydrophilic pore is in good agreement with the previously published experimental data.     

Reversible electrical breakdown of lipid bilayers: formation and evolution of pores

The mechanism of reversible electric breakdown of lipid membranes is studied. The following stages of the process of pore development are substantiated. Hydrophobic pores are formed in the lipid bilayer by spontaneous fluctuations. If these water-filled defects extend to a radius of 0.3 to 0.5 nm, a hydrophilic pore is formed by reorientation of the lipid molecules. This process is favoured by a potential difference across the membrane. The conductivity of the pores depends on membrane voltage, and the type of this dependence changes with the radius of the pore. Hydrophilic pores of an effective radius of 0.6 up to more than 1 nm are formed, which account for the membrane conductivity increase observed. The characteristic times of changes in average radius and number of pores during the voltage pulse and after it are investigated.     

Reversible electrical breakdown of lipid bilayers: formation and evolution of pores

The mechanism of reversible electric breakdown of lipid membranes is studied. The following stages of the process of pore development are substantiated. Hydrophobic pores are formed in the lipid bilayer by spontaneous fluctuations. If these water-filled defects extend to a radius of 0.3 to 0.5 nm, a hydrophilic pore is formed by reorientation of the lipid molecules. This process is favoured by a potential difference across the membrane. The conductivity of the pores depends on membrane voltage, and the type of this dependence changes with the radius of the pore. Hydrophilic pores of an effective radius of 0.6 up to more than 1 nm are formed, which account for the membrane conductivity increase observed. The characteristic times of changes in average radius and number of pores during the voltage pulse and after it are investigated.     

Events leading to the opening and closing of the exocytotic fusion pore have markedly different temperature dependencies. Kinetic analysis of single fusion events in patch-clamped mouse mast cells.

The earliest event in exocytosis is the formation of a fusion pore, an aqueous channel that connects the lumen of a secretory granule with the extracellular space. We can observe the formation of individual fusion pores and their subsequent dilation or closure by measuring the changes in the admittance of patch-clamped mast cells during GTP gamma S-stimulated exocytotic fusion. To investigate the molecular structure of the fusion pore, we have studied the temperature dependency of the rate constants for fusion pore formation and closure. An Arrhenius plot of the rate of fusion pore formation shows a simple linear relationship with an apparent activation energy of 23 kcal/mol. In contrast, the Arrhenius plot of the rate of closure of the fusion pore is discontinuous, with the break at approximately 13 degrees C. Above the break point, the rate of closure has a weak temperature dependence (7 kcal/mol), whereas below 13 degrees C the rate of closure is temperature independent. This type of temperature dependency is characteristic of events that depend on diffusion in a lipid phase that undergoes a fluid-solid phase transition. We propose that the formation of the fusion pore is regulated by the conformational change of a molecular structure with a high activation energy, whereas the closure of the fusion pore is regulated by lipids that become phase separated at 13 degrees C.     

Kinetics of resealing of lipid pores

The resealing of lipid pores in BLM at the temperature of phase transition was studied. It is show that the size of a pore correlates with the time of its resealing. The correlated coefficient of pore diffusion is close to that of lipid molecules in the gel state.     

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.     

Effect of temperature on the formation and inactivation of syringomycin E pores in human red blood cells and bimolecular lipid membranes

The effects of temperature on the formation and inactivation of syringomycin E (SRE) pores were investigated with human red blood cells (RBCs) and lipid bilayer membranes (BLMs). SRE enhanced the RBC membrane permeability of 86Rb and monomeric hemoglobin in a temperature dependent manner. The kinetics of 86Rb and hemoglobin effluxes were measured at different temperatures and pore formation was found to be only slightly affected, while inactivation was strongly influenced by temperature. At 37 degrees C, SRE pore inactivation began 15 min after and at 20 degrees C, 40 min after SRE addition. At 6 degrees C, below the phase transition temperature of the major lipid components of the RBC membrane, no inactivation occurred for as long as 90 min. With BLMs, SRE induced a large current that remained stable at 14 degrees C, but at 23 degrees C it decreased over time while the single channel conductance and dwell time did not change. The results show that the temperature dependent inactivation of SRE pores is due to a decrease in the number of open pores.     

"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.     

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.     

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.     

A novel mechanism of pore formation: membrane penetration by the N-terminal amphipathic region of equinatoxin

Equinatoxin II is a representative of actinoporins, eukaryotic pore-forming toxins from sea anemones. It creates pores in natural and artificial lipid membranes by an association of three or four monomers. Cysteine-scanning mutagenesis was used to study the structure of the N terminus, which is proposed to be crucial in transmembrane pore formation. We provide data for two steps of pore formation: a lipid-bound monomeric intermediate state and a final oligomeric pore. Results show that residues 10-28 are organized as an alpha-helix in both steps. In the first step, the whole region is transferred to a lipid-water interface, laying flat on the membrane. In the pore-forming state, the hydrophilic side of the amphipathic helix lines the pore lumen. The pore has a restriction around Asp-10, according to the permeabilization ratio of ions flowing through pores formed by chemically modified mutants. A general model was introduced to derive the tilt angle of the helix from the ion current data. This study reveals that actinoporins use a unique single helix insertion mechanism for pore formation.     

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.     

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.     

Hemifusion between cells expressing hemagglutinin of influenza virus and planar membranes can precede the formation of fusion pores that subsequently fully enlarge

The chronological relation between the establishment of lipid continuity and fusion pore formation has been investigated for fusion of cells expressing hemagglutinin (HA) of influenza virus to planar bilayer membranes. Self-quenching concentrations of lipid dye were placed in the planar membrane to monitor lipid mixing, and time-resolved admittance measurements were used to measure fusion pores. For rhodamine-PE, fusion pores always occurred before a detectable amount of dye moved into an HA-expressing cell. However, with DiI in the planar membrane, the relationship was reversed: the spread of dye preceded formation of small pores. In other words, by using DiI as probe, hemifusion was clearly observed to occur before pore formation. For hemifused cells, a small pore could form and subsequently fully enlarge. In contrast, for cells that express a glycosylphosphatidylinositol-anchored ectodomain of HA, hemifusion occurred, but no fully enlarged pores were observed. Therefore, the transmembrane domain of HA is required for the formation of fully enlarging pores. Thus, with the planar bilayer membranes as target, hemifusion can precede pore formation, and the occurrence of lipid dye spread does not preclude formation of pores that can enlarge fully.     

Membrane Lipids Determine the Antibiotic Activity of the Lantibiotic Gallidermin

Lantibiotics, a group of lanthionine-containing peptides, display their antibiotic activity by combining different killing mechanisms within one molecule. The prototype lantibiotic nisin was shown to possess both inhibition of peptidoglycan synthesis and pore formation in bacterial membranes by interacting with lipid II. Gallidermin, which shares the lipid II binding motif with nisin but has a shorter molecular length, differed from nisin in pore formation in several strains of bacteria. To simulate the mode of action, we applied cyclic voltammetry and quartz crystal microbalance to correlate pore formation with lipid II binding kinetics of gallidermin in model membranes. The inability of gallidermin to form pores in DOPC (1,2-dioleoyl-sn-glycero-3-phosphocholine) (C18/1) and DPoPC (1,2-dipalmitoleoyl-sn-glycero-3-phosphocholine) (C16/1) membranes was related to the membrane thickness. For a better simulation of bacterial membrane characteristics, two different phospholipids with branched fatty acids were incorporated into the DPoPC matrix. Phospholipids with methyl branches in the middle of the fatty acid chains favored a lipid II–independent DPoPC permeabilization by gallidermin, while long-branched phospholipids in which the branch is placed near the hydrophilic region induced an identical lipid II–dependent pore formation of gallidermin and nisin. Obviously, the branched lipids altered lipid packing and reduced the membrane thickness. Therefore, the duality of gallidermin activity (pore formation and inhibition of the cell wall synthesis) seems to be balanced by the bacterial membrane composition.     

Soft perforation of planar bilayer lipid membranes of dipalmitoylphosphatidylcholine at the temperature of the phase transition from the liquid crystalline to the gel state

In contrast to the widely used method of electroporation, the method of soft perforation of lipid bilayers is proposed. It is based on the structural rearrangement of the lipid bilayer formed from disaturated phospholipids at the temperature of the phase transition from the liquid crystalline state to the gel state. This allows us to obtain a lipid pore population without the use of a strong electric field. It is shown that the planar lipid bilayer membrane (pBLM) formed from dipalmitoylphosphatidylcholine in 1 M LiCl aqueous solution exhibits the appearance of up to 50 lipid pores per 1 mm² of membrane surface, with an average single pore conductivity of 31±13 nS. The estimation of a single pore radius carried out with water-soluble poly(ethylene glycol)s (PEGs) showed that the average pore radius ranged between 1.0–1.7 nm. It was found experimentally that PEG-1450, PEG-2000, and PEG-3350 should be in a position to block the single pore conductivity completely, while PEG-6000 fully restored the ionic conductivity. The similarity of these PEG effects to ionic conductivity in protein pores makes it possible to suggest that the partition of the PEG molecules between the pore and the bulk solution does not depend on the nature of the chemical groups located in the pore wall.     

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.     

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.     

Imaging the Lipid-Phase-Dependent Pore Formation of Equinatoxin II in Droplet Interface Bilayers

Using phase-separated droplet interface bilayers, we observe membrane binding and pore formation of a eukaryotic cytolysin, Equinatoxin II (EqtII). EqtII activity is known to depend on the presence of sphingomyelin in the target membrane and is enhanced by lipid phase separation. By imaging the ionic flux through individual pores in vitro, we observe that EqtII pores form predominantly within the liquid-disordered phase. We observe preferential binding of labeled EqtII at liquid-ordered/liquid-disordered domain boundaries before it accumulates in the liquid-disordered phase.