Calculation of free energy barriers to the fusion of small vesicles

The fusion of small vesicles, either with a planar bilayer or with one another, is studied using a microscopic model in which the bilayers are composed of hexagonal- and lamellar-forming amphiphiles. The free energy of the system is obtained within the self-consistent field approximation. We find that the free energy barrier to form the initial stalk is hardly affected by the radius of the vesicle, but that the barrier to expand the hemifusion diaphragm and form a fusion pore decreases rapidly as the radius decreases. As a consequence, once the initial barrier to stalk formation is overcome, one which we estimate at 13 k_BT for biological membranes, fusion involving small vesicles should proceed with little or no further input of energy.     

Interplay between membrane dynamics, diffusion and swelling pressure governs individual vesicular exocytotic events during release of adrenaline by chromaffin cells

Release of adrenaline by chromaffin cells occurs through a process involving docking and then fusion of a secretory vesicle to the cytoplasmic membrane of the cell. Fusion proceeds in two main stages. The first one leads to the creation of a stable fusion pore passing through the two membranes and which gives a constant release flux of neurotransmitter (pore-release stage). After a few milliseconds, this initial stage which is not investigated here proceeds through a sudden enlargement of the initial pore (full-fusion stage) up to the complete incorporation of the vesicle membrane into that of the cell and total exposure of the initial matrix vesicle core to the extracellular fluid. The precise time-resolved dynamics of the release and of the vesicle membrane during the full-fusion phase can be extracted with a precision never achieved so far by de-convolution of experimental chronoamperometric currents monitored during individual exocytotic secretion events. The peculiar dynamics of the vesicle membrane proves that exocytotic events are powered by the swelling of the matrix polyelectrolyte core of the vesicle, although they are kinetically regulated by diffusion in the matrix and by the dynamics of the vesicle and cell membranes. Two simple theoretical models based on the dynamics of pores are developed to account for these dynamics and are shown to predict behaviors which are essentially identical to the experimental ones. This offers a new view of the kinetic grounds which control the full-fusion stage, and therefore provides a new interpretation of the sudden transition between the pore-release and the full-fusion stages. This transition occurs when the increasing membrane surface tension energy due to the refrained internal swelling pressure overcomes the edge energy of the pore, so that the initial fusion pore becomes unstable and is disrupted. This new view predicts that secretory vesicles which contain matrixes energetically similar to those of the adrenal cells investigated here can be separated into two classes according to their radius and catecholamine content. Small vesicles (less than ca. 25 nm radius, and containing less than ca. 20000 molecules) should always release through pores. Larger vesicles should always end into fusing except if another mechanism closes the pore before ca. 10000 molecules of catecholamines have been released.     

A theory of osmotic lysis of lipid vesicles

Osmotic lysis of vesicles is shown to begin when the membrane expansion due to osmotic pressure exceeds its critical value, delta S, at which a membrane ruptures to form a pore. The dependence of delta S on the vesicle radius and respective osmotic pressures are obtained. It is found that osmotic pressure necessary for small (100 A) vesicles to rupture should exceed 30 atm, for large (10 000 A) vesicles it being as small as 10(-3) atm. In the case of large (greater than or approximately 1000 A) vesicles the value of relative expansion of the membrane at which its rupture occurs in a reasonable time only depends slightly on the vesicle radius. For instance, for 10 000 A vesicles it amounts to 3%. The tension of membrane rupture is about 8 dyn/cm for large vesicles. Membrane tension, although it decreases considerably as a result of rupture and pore formation, does not vanish completely. It supports the residual intravesicular pressure causing the efflux of vesicle (cell) contents. Simultaneously, osmotic influx of water through the membrane occurs that results in either complete rupture of the membrane with the efflux of the whole of the contents, or its gradual washout in either of two, quasi-steady or pulse-wise regimes. In the first case a pore is steadily open, whereas in the second case it alternately opens and closes, ejecting about 5% of internal solution each time. Lysis kinetics is analyzed. Pulse-wise regime of lysis is shown to be the most likely one.     

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 ).     

Depletion of membrane skeleton in red blood cell vesicles.

A possible physical interpretation of the partial detachment of the membrane skeleton in the budding region of the cell membrane and consequent depletion of the membrane skeleton in red blood cell vesicles is given. The red blood cell membrane is considered to consist of the bilayer part and the membrane skeleton. The skeleton is, under normal conditions, bound to the bilayer over its whole area. It is shown that, when in such conditions it is in the expanded state, some cell shape changes can induce its partial detachment. The partial detachment of the skeleton from the bilayer is energetically favorable if the consequent decrease of the skeleton expansion energy is larger than the corresponding increase of the bilayer-skeleton binding energy. The effect of shape on the skeleton detachment is analyzed theoretically for a series of the pear class shapes, having decreasing neck diameter and ending with a parent-daughter pair of spheres. The partial detachment of the skeleton is promoted by narrowing of the cell neck, by increasing the lateral tension in the skeleton and its area expansivity modulus, and by diminishing the attraction forces between the skeleton and the bilayer. If the radius of the daughter vesicle is sufficiently small relative to the radius of the parent cell, the daughter vesicle can exist either completely underlaid with the skeleton or completely depleted of the skeleton.     

The Mechanism of a Nuclear Pore Assembly: A Molecular Biophysics View

The basic problem of nuclear pore assembly is the big perinuclear space that must be overcome for nuclear membrane fusion and pore creation. Our investigations of ternary complexes: DNA–PC liposomes–Mg²⁺, and modern conceptions of nuclear pore structure allowed us to introduce a new mechanism of nuclear pore assembly. DNA-induced fusion of liposomes (membrane vesicles) with a single-lipid bilayer or two closely located nuclear membranes is considered. After such fusion on the lipid bilayer surface, traces of a complex of ssDNA with lipids were revealed. At fusion of two identical small liposomes (membrane vesicles) <100 nm in diameter, a “big” liposome (vesicle) with ssDNA on the vesicle equator is formed. ssDNA occurrence on liposome surface gives a biphasic character to the fusion kinetics. The “big” membrane vesicle surrounded by ssDNA is the base of nuclear pore assembly. Its contact with the nuclear envelope leads to fast fusion of half of the vesicles with one nuclear membrane; then ensues a fusion delay when ssDNA reaches the membrane. The next step is to turn inside out the second vesicle half and its fusion to other nuclear membrane. A hole is formed between the two membranes, and nucleoporins begin pore complex assembly around the ssDNA. The surface tension of vesicles and nuclear membranes along with the kinetic energy of a liquid inside a vesicle play the main roles in this process. Special cases of nuclear pore formation are considered: pore formation on both nuclear envelope sides, the difference of pores formed in various cell-cycle phases and linear nuclear pore clusters.     

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.     

The exocytotic fusion pore interface: a model of the site of neurotransmitter release

infrastructurel techniques have shown that an early event in the exocytotic fusion of a secretory vesicle is the formation of a narrow, water-filled pore spanning both the vesicle and plasma membranes and connecting the lumen of the secretory vesicle to the extracellular environment. Smaller precursors of the exocytotic fusion pore have been detected using electrophysio-logical techniques, which reveal a dynamic fusion pore that quickly expands to the size of the pores seen with electron microscopy. While it is clear that in the latter stages of expansion, when the size of the fusion pore is several orders of magnitude bigger than any known macromolecule, the fusion pore must be mainly made of lipids, the structure of the smaller precursors is unknown. Patch-clamp measurements of the activity of individual fusion pores in mast cells have shown that the fusion pore has some unusual and unexpected properties, namely that there is a large flux of lipid through the pore and the rate of pore closure has a discontinuous temperature dependency, suggesting a purely lipidic fusion pore. Moreover, comparisons of experimental data with theoretical fusion pores and with breakdown pores support the view that the fusion pore is initially a pore through a single bilayer, as would be expected for membrane fusion proceeding through a hemifusion mechanism. Based on these observations we present a model where the fusion pore is initially a pore through a single bilayer. Fusion pore formation is regulated by a macromolecular scaffold of proteins that is responsible for bringing the plasma membrane into a highly curved dimple very close to a tense secretory granule membrane, creating the architecture where the strongly attractive hydrophobic force causes the membranes to form a ‘hemifusion’ intermediate. Membrane fusion is completed by the formation of an aqueous pore after rupture of the shared bilayer. We also propose that the microenvironment of the interface when the pore first opens, dominated by the charged groups on the secretory vesicle matrix and phospholipids, will greatly influence the release of secretory products.     

Estimating the time course of pore expansion during the spike phase of exocytotic release in mast cells of the beige mouse

Our objective is to determine the time course of exocytotic fusion pore opening (P) in mast cells of the beige mouse from the measured efflux of the spike phase of exocytotic release (J). We show that a pore whose meridian or radius grows linearly with time cannot reproduce the efflux. We also show that a pore that opens very quickly [relative to the diffusivity of 5-hydroxytryptamine (5-HT)] and completely (P = π) also does not mimic the experimental efflux, and estimate maximum pore angles of 70(±20)°. We show that a larger class of opening functions reproduces the rising phase and part of the decay phase and calculate pore expansion rate, pore radius and pore angle, none of which can be readily measured. In the initial stages of the spike phase (50–200 ms) when the gel matrix has not expanded significantly, this model suggests that the pore radius increases exponentially with a time constant of 82(±62) ms with pore expansion reaching its maximum velocity of 20(±7) nm ms⁻¹. We conclude that the release process is dynamic and suggest that the velocity of pore opening (V) and the diffusivity of 5-HT (D), in addition to the size of the vesicle (R, radius), vary with time. We discuss assumptions and improvements to the model and propose that this methodology is applicable for determining P from measured J in other endocrine cells and neurons when D within the secretory vesicle is much less than D within the pore neck.     

Release of small transmitters through kiss-and-run fusion pores in rat pancreatic beta cells

Exocytosis of secretory vesicles begins with a fusion pore connecting the vesicle lumen to the extracellular space. This pore may then expand or it may close to recapture the vesicle intact. The contribution of the latter, termed kiss-and-run, to exocytosis of pancreatic beta cell large dense-core vesicles (LDCVs) is controversial. Examination of single vesicle fusion pores demonstrated that rat beta cell LDCVs can undergo exocytosis by rapid pore expansion, by the formation of stable pores, or via small transient kiss-and-run fusion pores. Elevation of cAMP shifted LDCV fusion pore openings to the transient mode. Under this condition, the small fusion pores were sufficient for release of ATP, stored within LDCVs together with insulin. Individual ATP release events occurred coincident with amperometric "stand alone feet" representing kiss-and-run. Therefore, the LDCV kiss-and-run fusion pores allow small transmitter release but likely retain the larger insulin peptide. This may represent a mechanism for selective intraislet signaling.     

The pore domain of the nicotinic acetylcholine receptor: molecular modeling, pore dimensions, and electrostatics.

The pore domain of the nicotinic acetylcholine receptor has been modeled as a bundle of five kinked M2 helices. Models were generated via molecular dynamics simulations incorporating restraints derived from 9-A resolution cryoelectron microscopy data (Unwin, 1993; 1995), and from mutagenesis data that identify channel-lining side chains. Thus, these models conform to current experimental data but will require revision as higher resolution data become available. Models of the open and closed states of a homopentameric alpha 7 pore are compared. The minimum radius of the closed-state model is less than 2 A; the minimum radius of the open-state models is approximately 6 A. It is suggested that the presence of "bound" water molecules within the pore may reduce the effective minimum radii below these values by up to approximately 3 A. Poisson-Boltzmann calculations are used to obtain a first approximation to the potential energy of a monovalent cation as it moves along the pore axis. The differences in electrostatic potential energy profiles between the open-state models of alpha 7 and of a mutant of alpha 7 are consistent with the experimentally observed change in ion selectivity from cationic to anionic. Models of the open state of the heteropentameric Torpedo nicotinic acetylcholine receptor pore domain are also described. Relatively small differences in pore radius and electrostatic potential energy profiles are seen when the Torpedo and alpha 7 models are compared.     

The resealing process of lipid bilayers after reversible electrical breakdown

The resealing process of lipid bilayer membranes after reversible electrical breakdown was investigated using two voltage pulses switched on together. Electrical breakdown of the membranes was induced with a voltage pulse of high intensity and short duration. The time course of the change in membrane conductance after the application of the high (short) voltage pulse was measured with a longer voltage pulse of low amplitude. The decrease in membrane conductance during the resealing process could be fitted to a single exponential curve with a time constant of 10-2 μs in the temperature range between 2 and 20°C. The activation energy for this exponential decay process was found to be about 50 kJ/mol, which might indicate a diffusion process. Above 25°C the resealing process is controlled by two exponential processes.The data obtained for the time course of the resealing process can be explained in terms of pore formation in the membranes in response to the high electrical field strength. A radius of about 4 nm is calculated for the initial pore size. From the assumed exponential change of the pore area with progressive resealing time a diffusion constant of 10^?8 cm²/s for lateral lipid diffusion can be estimated.     

Extrusion of electroformed giant unilamellar vesicles through track-etched membranes

Unilamellar vesicle populations having a narrow size distribution and mean radius below 100 nm are preferred for drug delivery applications. In the present work, 1,2-dipalmitoyl-sn-glycero-3-phosphocholine (DPPC) was used to prepare giant unilamellar vesicles (GUVs) by electroformation and multilamellar vesicles (MLVs) by thin film hydration. Our experiments show that in contrast to MLVs, a single-pass extrusion of GUVs through track-etched polycarbonate membranes at moderate pressure differences is sufficient to produce small liposomes having low polydispersity index. Moreover, we observe that the drug encapsulating potential of extruded liposomes obtained from GUVs is significantly higher compared to liposomes prepared by extrusion of MLVs. Furthermore, our experiments carried out for varying membrane pore diameters and extrusion pressures suggest that the size of extruded liposomes is a function of the velocity of GUV suspensions in the membrane pore.     

Electroporative deformation of salt filled lipid vesicles

Membrane electroporation, vesicle shape deformation and aggregation of small, NaCl-filled lipid vesicles (of radius a = 50 nm) in DC electric fields was characterized using conductometric and turbidimetrical data. At pulse durations t_E≤ 55 ± 5 ms the increase in the conductivity of the vesicle suspension is due to the field-induced efflux of electrolyte through membrane electropores. Membrane electroporation and Maxwell stress on the vesicle membrane lead to vesicle elongation concomitant with small volume reduction (up to 0.6% in an electric field of E = 1 MV m^–1). At t_E > 55 ± 5 ms, further increases in the conductivity and the optical density suggest electroaggregation and electrofusion of vesicles. The conductivity changes after the electric pulse termination reflect salt ion efflux through slowly resealing electropores. The analysis of the volume reduction kinetics yields the bending rigidity κ = (4.1 ± 0.3) ⋅ 10^–20 J of the vesicle membrane. If the flow of Na⁺ and Cl^– ions from the vesicle interior is treated in terms of Hagen-Poiseuille's equation, the number of permeable electropores is N = 39 per vesicle with mean pore radius r_p = 0.85 ± 0.05 nm at E = 1 MVm^–1 and t_E≤ 55 ± 5 ms. The turbidimetric and conductometric data suggest that small lipid vesicles (a ≤ 50 nm) are not associated with extensive membrane thermal undulations or superstructures. In particular with respect to membrane curvature, the vesicle results are suggestive for the design and optimization of electroporative delivery of drugs and genes to cell tissue at small field strengths (≤1 MVm^–1) and large pulse durations (≤100 ms). Received: 8 July 1997 / Accepted: 15 September 1997     

Exocytotic fusion pore stability and topological defects in the membrane with orientational degree of ordering

Regulated exocytosis is a process that strongly depends on the formation and stability of the fusion pore. It was indicated experimentally and theoretically that narrow and highly curved fusion pore may be stabilized by accumulation of anisotropic membrane components possessing orientational ordering. On the other hand, narrow fusion pore may also undergo repetitive opening and closing, disruption in the so called kiss and run process or become completely opened in the process of full fusion of the vesicle with the membrane. In this paper we attempt to elucidate the subtle interplay between the stabilizing and destabilizing processes in the fusion neck. A possible physical mechanism which may lead to disruption of the stable fusion pore or complete fusion of the vesicle with the membrane is discussed. It is indicated that topologically driven defects of the in-plane orientational membrane ordering in the region of the fusion pore may disrupt the fusion. Alternatively, it may facilitate repetitive opening and closing of the fusion pore or induce full fusion of the vesicle with the target membrane.     

Visualization of Membrane Loss during the Shrinkage of Giant Vesicles under Electropulsation

We study the effect of permeabilizing electric fields applied to two different types of giant unilamellar vesicles, the first formed from EggPC lipids and the second formed from DOPC lipids. Experiments on vesicles of both lipid types show a decrease in vesicle radius, which is interpreted as being due to lipid loss during the permeabilization process. We show that the decrease in size can be qualitatively explained as a loss of lipid area, which is proportional to the area of the vesicle that is permeabilized. Three possible modes of membrane loss were directly observed: pore formation, vesicle formation, and tubule formation.     

The working of a pulsatory liposome

Under positive osmotic stress, a greater lipid vesicle swells to a critical diameter, when suddenly a transbilayer pore appears and grows to a maximum radius, then decreases and finally disappears. An amount of liquid was leaked out through the pore and the vesicle returns to the initial state and can start another cycle. This is a pulsatory lipid liposome. In this paper, we have considered the problem of such liposomes. We have obtained the condition that a pulsatory liposome to run an a priori settled number of cycles. The length time of each cycle and its activity life was calculated. Also, we have calculated the quantities of solute leaked out through a pore in each cycle. The pulsatory liposome may be regarded as a biotechnological device to dose drugs at fixed intervals time.     

Tubular Membrane Formation of Binary Giant Unilamellar Vesicles Composed of Cylinder and Inverse-Cone-Shaped Lipids

We have succeeded in controlling tubular membrane formations in binary giant unilamellar vesicles (GUVs) using a simple temperature changing between the homogeneous one-phase region and the two-phase coexistence region. The binary GUV is composed of inverse-cone (bulky hydrocarbon chains and a small headgroup) and cylinder-shaped lipids. When the temperature was set in the two-phase coexistence region, the binary GUV had a spherical shape with solidlike domains. By increasing the temperature to the homogeneous one-phase region, the excess area created by the chain melting of the lipid produced tubes inside the GUV. The tubes had a radius on the micrometer scale and were stable in the one-phase region. When we again decreased the temperature to the two-phase coexisting region, the tubes regressed and the GUVs recovered their phase-separated spherical shape. We infer that the tubular formation was based on the mechanical balance of the vesicle membrane (spontaneous tension) coupled with the asymmetric distribution of the inverse-cone-shaped lipids between the inner and outer leaflets of the vesicle (lipid sorting).