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Copyright © 2003, Biophysical Society Cascades of Transient Pores in Giant Vesicles: Line Tension and Transport Address reprint requests to Francoise Brochard-Wyart, E-mail: brochard/at/curie.fr. Received May 8, 2002; Accepted August 23, 2002. ![]() | |||||||||||||||||||||||||||||||
Abstract Under ordinary circumstances, the membrane tension of a giant unilamellar vesicle is essentially nil. Using visible light, we stretch the vesicles, increasing the membrane tension until the membrane responds by the sudden opening of a large pore (several micrometers in size). Only a single pore is observed at a time in a given vesicle. However, a cascade of transient pores appear, up to 30–40 in succession, in the same vesicle. These pores are transient: they reseal within a few seconds as the inner liquid leaks out. The membrane tension, which is the driving force for pore opening, is relaxed with the opening of a pore and the leakage of the inner liquid; the line tension of the pore's edge is then able to drive the closure of a pore. We use fluorescent membrane probes and real-time videomicroscopy to study the dynamics of the pores. These can be visualized only if the vesicles are prepared in a viscous solution to slow down the leakout of the internal liquid. From measurements of the closure velocity of the pores, we are able to infer the line tension, ![]() ![]() ![]() ![]() | |||||||||||||||||||||||||||||||
INTRODUCTION Transport of ions and molecules across membranes is central to many biological processes. Understanding transmembrane transport is also a key ingredient in the development of new technologies such as gene therapy (Verma and Somia, 1997), which requires transport of DNA fragments through cellular and nuclear membranes, and targeted drug delivery systems based on vesicular “baggies” where drug molecules initially contained in vesicles need to be released in a well-controlled fashion (Lawrence, 1994; Lasic and Needham, 1995; Moase et al., 2001; Cao and Suresh, 2000; Yu et al., 1999; Zasadzinski, 1997). Inasmuch as there exists a large body of empirical results on these subjects, there is little understanding of the fundamental mechanisms involved. An important step in this direction is the visualization of the dynamics of membrane reorganization. We have previously reported visualization of transient pores in tense vesicles (Sandre et al., 1999). These were unilamellar synthetic vesicles, 10–100 μm in radius, tensed either by adhesion to appropriately treated surfaces, or by intense optical illumination in the presence of fluorescent probes embedded in the membrane (Fig. 1). Pore opening is driven by the membrane tension, σ, and pore closure by the line tension,
In addition, we present our observations of transport across transient pores. The most convenient cargo to be transported is another vesicle: indeed, in a vesicle preparation it is not unusual to find a vesicle containing a smaller one inside. When the external vesicle makes a pore, the smaller one is dragged toward the hole by the liquid leaking through it. If the internal vesicle is very small compared to the pore size, it acts as a probe of the flow field. On the other hand, if the internal vesicle is larger than the pore size it can still be transported out due to its soft, deformable nature. Finally we present our observations concerning the regularity of intervals between successive pores: a given vesicle makes a series of pores (up to 30 or 40 in succession), separated by regular time intervals. Let us now summarize the essential features of the model quantitatively, following Brochard-Wyart et al. (2000). The overall geometry of the system is provided in Fig. 2. Just before the pore opening (Fig. 2 A) the vesicle has radius Ri, membrane tension σo, and projected area Ap = 4πRi2. It is more convenient to express the projected area in terms of the radius, Ro, that the vesicle would adopt were its membrane tension, σ, equal to zero. A finite membrane tension stretches the membrane area by a factor 1 + σ/E, whence
The dynamics of the pore radius, r, are somewhat reminiscent of bursting of soap films. However, in a soap film a hole grows at constant velocity, surrounded by a rim which collects the liquid. The growth kinetics are driven by inertia (Mysels et al., 1959; de Gennes, 1996). In contrast, we have never observed a rim collecting the lipid around a growing pore. In fact, pores in vesicles are more closely analogous to the opening of pores in viscous bare films which do not contain any surfactant. In these bare films pore opening is governed by the transfer of surface energy to viscous losses, and rims are absent (Debrégeas et al., 1995; Diederich et al., 1998). Pores in vesicles are more complex, however, inasmuch as i), the membrane tension relaxes as the pore grows (Eq. 2), and ii), the line tension
![]() The dynamics of the vesicle radius, R, on the other hand, are provided by considering the flux through the pore,
In summary, we have related the dynamics of the pore radius r (Eq. 3) to that of the vesicle radius R (Eq. 4), through the common constraint provided by the membrane tension (Eq. 2). Thus, we have three equations for three unknowns (r, R, and σ). In Fig. 4 we have plotted the numerical solutions of Eqs. 2, 3, and 4 for r(t) and R(t) along with experimental measurements. Details of numerical solutions are given in Brochard-Wyart et al. (2000).
The organization of the article is as follows. In Materials and Methods, we provide experimental details. In Life of Transient Pores, we present analytical solutions to the pore dynamics in the limit of slow leakout which corresponds to our measurements. In the subsequent section, we present measurements of the line tension, | |||||||||||||||||||||||||||||||
MATERIALS AND METHODS We use the “electroformation” method (Angelova, 2000), which produces giant unilamellar vesicles (GUVs) with high efficiency and very few multilamellar aggregates. The lipid is 1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC, Sigma, structure 1 in Fig. 5) which is in the Lα fluid phase at room temperature and forms vesicles in arbitrary mixtures of water and glycerol (Öradd et al., 1994).
A solution of pure lipid (1 mg/ml in a 2:1 chloroform/methanol mixture) is cast onto both windows of a homemade preparation chamber composed of two transparent electrodes (formed by glass plates coated with indium tin oxide) separated by a 1-mm-thick Teflon spacer. The cast lipid film is dried overnight in a vacuum oven, then filled with ~1.5 ml of aqueous buffer, containing 0.1 M sucrose or glucose to control the osmolarity and 66% v/v glycerol to obtain a viscosity of ηo = 32.1 ± 0.4 cP, measured with an Ubbelohde viscometer. An AC voltage of ~1.1 V at 7 Hz is applied between the electrodes to allow the gentle swelling of the lipid film to form GUVs of 10–100 μm diameters at the end of ~6 h. The vesicles are let to “relax” overnight in the preparation chamber, then are drawn out carefully. This stock solution contains ~0.1 mg/ml lipid (≈130 μM). Unless noted otherwise, the vesicles are labeled using the lipophilic fluorescent dye n-(4-sulfopropyl)-4-(4-(dihexylamino)styryl)pyridinium (di6ASP-BS; kindly provided by Mireille Blanchard-Desce, UMR 6510 CNRS, U. de Rennes, France, Fig. 5), which is spontaneously inserted into the bilayer. 1% v/v of 560 μM of the dye (in ethanol) is incubated for a few hours with the vesicle solution before observation. The vesicles are either observed as such, or after sedimentation in an equiosmolar solution, in a closed microscope chamber (two glass slides spaced by parafilm of 200 μm thickness and sealed with hot paraffin), using a Reichert-Jung MET upright microscope equipped with an OLYMPUS 60× /0.90 LUMPlanFL water immersion objective. Epifluorescence excitation is provided by a 200-W mercury lamp and a 455–490 nm band-pass filter. The fluorescence peak at 580 nm is detected with a standard CCD camera. Images are digitized on an 8-bit frame grabber (LG-3, Scion, Frederick, MD) and analyzed using Scion Image software (Scion). In some experiments, the fluorescent marker n-(4-sulfobutyl)-4-(6-(4-(dibutylaminophenyl)hexatrienyl) pyridinium (RH237; Fig. 5), or 2-(6-(7-nitrobenz-2-oxa-1,3-diazol-4-yl) amino) hexanoyl-1-hexadecanoyl-sn-glycero-3-phosphocholine (NBD-C6-HPC, Fig. 5) is used instead of di6ASP-BS, as noted. For experiments in which surfactants are added to vesicles, a stock solution of the surfactant Tween 20 (Sigma; Fig. 9; also see section called Line Tension,
In experiments where cholesterol (Fig. 9; also see section called Line Tension, | |||||||||||||||||||||||||||||||
LIFE OF TRANSIENT PORES In this section we first summarize analytical solutions to the pore dynamics in different stages of the pore's lifetime, following Brochard-Wyart et al. (2000). In the following section we will use these results to infer the line tension from experimental data under various conditions. Consistent with the experimental observations in Figs. 2 and 4, we consider small variations in the vesicle radius R: R = Ro(1 + δ) and Ri = Ro(1 + δo), where Using the reduced units,
From Figs. 2 and 4 we see that the pore opening time is on the order of 100 ms, whereas the vesicle radius drops over the course of a few seconds. Thus, our experimental conditions correspond to the slow leakout regime We summarize below analytical solutions to Eqs. 5, 6, and 7 in the case of slow leakout Growth
Maximum pore radius When the pore reaches its maximum size, rm, we have
![]() Quasi-static leakout
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![]() ![]() Fast closure
These different stages are shown schematically in Fig. 6. In principle, experimental measurements of the pore (r(t)) and vesicle (R(t)) radii should allow the determination of all the relevant parameters: the membrane viscosity, ηs, the initial membrane tension, σo, and the line tension,
LINE TENSION, The formation of a pore in a lipid bilayer implies the existence of a membrane edge. It is expected that the lipids near the edge reorient themselves to minimize the exposure of their hydrophobic chains to the aqueous environment. A plausible molecular arrangement is the formation of a cylindrical rim (Litster, 1975), as shown schematically in Fig. 3 (Introduction). The modified molecular packing of the lipids gives rise to an excess free energy with respect to the unperturbed bilayer. This energy, expressed per unit edge length, is the line tension, ![]() ![]() ![]() On the theoretical side, there exist two different approaches to describe the line tension. Molecular lipid models (Israelachvili et al., 1980) usually start with defining geometrical parameters to characterize the lipids which are then allowed to interact with one another through both attractive (hydrophobic) and repulsive forces (head group repulsion, hydration forces, etc.). In more elaborate molecular lipid models, the lipid chains may possess a conformational energy as well (May, 2000). The second approach is to use the membrane elasticity theory to calculate We are interested, in particular, on how the line tension,
Line tension of bare DOPC bilayers We first consider the case of “bare” DOPC bilayers, in which the membrane is devoid of any additives, except for the presence of the fluorescent probes (whose spontaneous curvatures are ≈0, due to their structural similarity with double chained lipid molecules).In the previous section, we have seen that a plot of R2 ln r versus t in the quasi-static leakout regime should be linear with a slope k = −2 Linear portions of plots of R2 ln r versus time are shown in Fig. 8 a for bare DOPC vesicles of various sizes. As an example let us consider the data for a vesicle of initial radius Ri = 13.8 μm (inverted triangles in the inset of Fig. 8 a). A least-squares fit to this set of data (0.28 s < t < 2.4 s) yields a slope k = −48.77 μm2/s, from which we infer
It should be mentioned that measurements of the line tension are quite sensitive to the presence of small impurities which may be inserted into the pore's edge. This is in line with the observations of Harbich and Helfrich (1979) who measured lower Cholesterol increases the line tension Cholesterol, shown in Fig. 9, is a central component in the regulation of the properties of eukaryotic cell membranes (Simons and Ikonen, 2000; Rukmini et al., 2001). It can be modeled as an inverted cone (Israelachvili et al., 1980; Carnie et al., 1979) (spontaneous curvature co < 0), and is thus expected to increase the line tension according to Eq. 14. Inferring the line tension from the slopes of R2 ln r versus t plots shown in Fig. 8 for a number of different vesicles and pores in the presence of varying amounts of cholesterol we have obtained the results shown in Fig. 10. For this set of experiments, we have used DOPC supplied by Sigma, and co-cast the cholesterol at given mole fractions with the lipid before the electroformation of the vesicles (see Materials and Methods). Thanks to this procedure, and due to the low solubility of cholesterol in the aqueous phase, we may assume that all the cholesterol that was co-cast with the lipid is incorporated into the bilayers. The cholesterol mole fraction in Fig. 10 refers to the nominal fraction (θm) of cholesterol co-cast with lipid before the formation of vesicles, which may differ from the actual fraction of cholesterol around the pore edge, θ. We see from Fig. 10 that the line tension increases linearly up to ~θm = 0.20, then appears to increase more rapidly for higher cholesterol content. The higher dispersity of data points for θm = 0.30 is explained in part by the increased uncertainty in the determination of the line tension due to shorter pore lifetimes at higher cholesterol content (see Fig. 8 d; the effect of the line tension on pore lifetimes will be discussed shortly). Another possibility for the higher dispersity of data points at 0.3 mol fraction cholesterol is that we may be close to the solubility limit of cholesterol in DOPC bilayers. In fact, when we tried to incorporate 50% cholesterol in the bilayers we obtained precipitates of cholesterol.
If we assume that the fraction of cholesterol in the unperturbed membrane is the same as the fraction around the pore (θ = θm), we can attempt to analyze the results of Fig. 10 in light of Eq. 14. As predicted by this equation for an inclusion compound having a negative spontaneous curvature, at small θ the line tension For comparison, published values of the bending moduli κ range between (2–40) × 10−20 J for a number of phospholipid bilayers in their fluid state (Lipowsky, 1995). In particular, for DOPC monolayers, Chen and Rand (1997) have measured κ ≈ 4.0 × 10−20 J. The value of κ we have estimated thus seems to be somewhat lower than those previously reported. However, as noted above, when we use DOPC from Fluka or Avanti Polar Lipids, we find As for the spontaneous curvature of cholesterol, using x-ray diffraction and the osmotic stress method in DOPC/cholesterol inverted hexagonal phases, Chen and Rand (1997) have found co = 2/Rcurv It is known that in the presence of cholesterol, the rigidity of lipid bilayers is increased: hydrocarbon chains of the lipids are straightened, the bilayer is thickened, and its fluidity is reduced (Israelachvili et al., 1980). These effects are reflected in a corresponding increase in the bending modulus κ in Eq. 14 as cholesterol is added to the bilayer. Thus, the increase in the line tension that we observe as a function of increasing cholesterol content in Fig. 10 may be influenced by this increase in κ. However, Chen and Rand (1997) measured a bending modulus that is independent of cholesterol content for DOPC/cholesterol mixed monolayers containing up to θm ≈ 0.30 mol fraction cholesterol. Increasing θm further to 0.50 resulted in only a 30% increase in κ. Similarly, they obtained only a modest increase in the bending modulus of DOPE/cholesterol monolayers as cholesterol content was increased from 0 to 0.30 mol fraction. Chen and Rand (1997) noted that the increase they measured in the bending modulus by the incorporation of cholesterol in their hexagonal phase monolayers is much smaller than might be expected from cholesterol's increase of the area compressibility modulus in bilayers (Evans and Rawics, 1990; Needham and Nunn, 1990). Eliminating several possibilities for this discrepancy, they suggested that the difference may be due to the inadequacy of the treatment of the phospholipid monolayer as one of homogeneous mechanical properties through its thickness, with concomitant coupling of area and bending moduli. Detergents reduce the line tension Detergents are water-soluble amphiphiles which form micelles spontaneously when dissolved at a concentration above the critical micelle concentration. They can typically be modeled as cone-shaped molecules possessing positive spontaneous curvature; co > 0 (Fig. 7). The detergent micelles have an ability to dissolve insoluble or sparingly soluble materials in the aqueous solution by incorporating them into the micellar interior to form mixed micelles. Detergents can also solubilize phospholipids and other constituents of biomembranes. Due to this property, detergents are widely used in membranology, for example to disintegrate biomembranes to mixed micelles for isolation and purification of membrane proteins (Lichtenberg et al., 1983; Dennis, 1986; Silvius, 1992). The reverse course of action, the removal of detergent molecules from the solution of detergent/phospholipid mixed micelles by, e.g., gel filtration or dialysis, leads to the formation of phospholipid vesicles. Thus, detergents are also used in reconstituting functional membranes (Eytan, 1982; Rigaud et al., 1998) and in preparing phospholipid vesicles of controlled and homogeneous size (Ueno et al., 1984). Thanks to these important applications, the interaction of detergents with vesicles has received great attention (for recent reviews, see Inoue, 1996; Lasch, 1995; Heerklotz and Seelig, 2000).An emerging application with great potential is the use of vesicles as drug delivery vehicles (Lawrence, 1994; Lasic and Needham, 1995; Moase et al., 2001; Cao and Suresh, 2000; Yu et al., 1999; Zasadzinski, 1997), wherein the release of drugs entrapped in the vesicle's interior becomes an important problem. Vesicles are required to act as tight containers of a given drug, and to release their cargo under desired conditions. The membrane barrier efficiency for vesicles is affected by their interaction with amphiphilic molecules, when the vesicles are delivered into physiological fluids (Inoue, 1996). Thus, it is essential for the use of vesicles as a drug delivery system to know the manner in which the vesicular cargo is released in the presence of foreign molecules. The study of how detergents affect the permeability of vesicle membranes may provide useful information about this problem. We have studied the effect of the detergent Tween 20 (Fig. 9) on transient pores and the line tension in DOPC bilayers. Tween 20 is a common detergent used in the solubilization of membrane proteins (Kawasawa et al., 1999), having a hydrophilic-lipophilic balance of 16.7 which places it among good emulsifiers for oil-in-water emulsions (de Gennes et al., 2002). Thanks to its bulky polar head relative to its hydrophobic tail (Fig. 9 b), it can be modeled as a cone-shaped molecule with a positive spontaneous curvature, co > 0 (Fig. 7 a). Thus, we expect that it should insert itself into the highly curved edge of a pore, as shown schematically in Fig. 7 b. This should reduce the line tension, according to Eq. 14. In Fig. 11, a transient pore for a vesicle of size Ro ≈ 10 μm is shown in the presence of the detergent Tween 20. A striking feature is the very long duration, over 2 min, of the pore lifetime. This is consistent with a huge reduction in the line tension, estimated to be
In these experiments, a concentration gradient was used (see Materials and Methods), inspired by the work of Nomura et al. (2001), who have recently visualized effects of some detergents on topological transformations of giant liposomes in low viscosity solutions using dark-field microscopy. For the example shown in Fig. 11, the concentration of the surfactant varied from zero to 0.6 mM (~10× the critical micelle concentration in water) across the gradient. Using another surfactant, sodium cholate (Fig. 9 b), we have observed similar increases in pore lifetimes. A difficulty with detergents is that they solubilize some of the dye and consequently increase the background fluorescence; this deteriorates the image quality. The propensity of amphiphiles with positive spontaneous curvature for facilitating transient pore formation was already noted (Israelachvili et al., 1980) in considering the increased permeability of lecithin vesicles to ions and small molecules in the presence of lysolecithin (which is similar to lecithin, but has only one rather than two hydrophobic tails and hence possesses positive spontaneous curvature). It was also observed that addition of cholesterol possessing negative spontaneous curvature into lecithin vesicles produced the opposite effect; it reduced permeabilities (Israelachvili et al., 1980). Our direct visualization of the effects of cholesterol and surfactants on transient pores are consistent with these previous observations. We are currently studying the effects of surfactant at much lower (sublytic) concentrations wherein the vesicles are not solubilized rapidly. The results of these studies will be reported elsewhere. | |||||||||||||||||||||||||||||||
PORES AND TRANSPORT ACROSS MEMBRANES Transient pores are intimately connected with transport across lipid bilayers. In this section we present two examples of transport through pores. The “cargo” to be transported in both cases is in fact a smaller vesicle initially residing in a larger one. This is the most convenient type of cargo, as a GUV preparation usually contains a small amount of such vesicle configurations. In Fig. 13 a small vesicle, of radius Rcargo ≈ 0.6 μm, marked by an arrow, is initially inside a larger one (R ≈ 16 μm, first frame in Fig. 13). When a pore appears in the container vesicle (second frame in Fig. 13, t = 0.76 s), the cargo is dragged toward the pore by the leaking fluid, eventually exiting the container vesicle just before the pore reseals (frames 3–6, Fig. 13). Inasmuch as the cargo vesicle is rather small, we may expect that it does not significantly perturb the flow field and it can be used as a rough probe of the fluid's leakout velocity. To this end, we plot the position, d, of the cargo vesicle's center with respect to the center of the pore, as a function of time, in Fig. 14. We set d = 0 when the cargo vesicle is in the middle of the pore, and d < 0 (d > 0) when it is inside (outside) the container vesicle. As can be seen in Fig. 14, d varies almost linearly with time, implying a constant velocity, Vcargo = dd/dt ≈ 2.1 μm/s. Also plotted in Fig. 14 is the radius, r, of the pore as a function of time.
The leakout velocity of the fluid through the pore, VL, is equal to VL = Q/(πr2), where Q = 2 σ r3/(3 ηo R) is the flux through the pore of radius r (Eq. 4, Introduction). During the quasi-static leakout regime (see Life of Transient Pores), we have σr ≈ What happens if the size of the vesicle to be transported through the pore is larger than the pore size? The internal vesicle can still exit thanks to its deformable nature, as shown in Fig. 15. In this example, soon after the opening of a pore, the internal vesicle, dragged toward the pore by the leaking fluid, plugs the pore (first frame in Fig. 15). The vesicles remain in this configuration for a few minutes. However, slow buildup of further membrane tension increases the pressure inside the container vesicle, pushing the cargo vesicle further through the pore (second and third frames). We remark that the contact line between the pore's edge and the exiting vesicle must be very tight. Otherwise, some leakout would occur, reducing the pressure pushing the cargo vesicle out. Once half the cargo vesicle has passed through the pore (which process takes ~400 s) things speed up considerably: now the force exerted by the line tension of the pore's edge works in the same direction as the pressure pushing the cargo vesicle out. Notice that the small displacement of the exiting vesicle between t = 389 s (third frame) and t = 504 s (fourth frame) removes enough volume from inside the container vesicle to relax its membrane tension considerably: large amplitude membrane fluctuations are apparent at t = 504 s (fourth frame), indicating a nearly nil membrane tension. Beyond this point the major driving force for the exit of the cargo vesicle is the line tension of the pore. An intriguing event occurs at the very end: the cargo vesicle is cut in two by the rapidly closing pore (see frames at t = 517 s and t = 520 s). The smaller cut portion remains inside the container vesicle after complete sealing of the pore. Thus, a closing pore in a phospholipid membrane may not only do work to displace a vesicle but also disrupt the integrity of another membrane!
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CASCADES OF PORES UNDER ILLUMINATION When a given vesicle is illuminated by the mercury arc lamp of our microscope (see Materials and Methods), a rather irreproducible induction period is required from the start of the illumination until the appearance of the first transient pore. The length of this induction period, which can vary from ~10 min to a few hours, is determined (for fixed illumination intensity) largely by the amount and nature of lipidic structures surrounding the observed vesicle. For example, thin lipid “wires”, or tubes, connecting the chosen, large vesicle to smaller vesicles and/or lipid aggregates are often observed to be incorporated into the large vesicle by being “sucked” into it, as tension is built up. It is also likely that there exist smaller lipidic structures, that cannot be resolved optically, which may undergo similar rearrangements. This slow incorporation of the smaller structures into larger ones results in the cleaning up of the environment of the chosen vesicle (for an example, see Fig. 5 of Sandre et al., 1999). When there are no more aggregates to be incorporated into the larger vesicle to relieve tension, the vesicle becomes completely spherical, and a transient pore appears. After the appearance of this first pore, subsequent ones appear at highly regular intervals. A typical observation is shown in Fig. 16 a, in which we have plotted the induction (or waiting) time between successive pores in a DOPC vesicle containing 20% cholesterol against the total time of illumination/observation. The first pore appeared 1165 s (or 19 min 25 s) after the start of the illumination. For the subsequent 10 pores, the waiting time was nearly constant and equal to ~3 min (175 ± 15 s). After the 10th pore, the waiting time started increasing almost linearly with the illumination time. In Fig. 16 b we have plotted the vesicle radius, R, as a function of the total illumination time for the same vesicle. A series of steps are apparent in this figure. Measurements of R taken just before the opening of a pore are marked by circles. When a transient pore opens, R drops abruptly, due to the leakout of the internal liquid, until the pore reseals a few seconds later. After the sealing of a pore, the vesicle radius remains constant or decreases very slightly (below optical resolution), until the next pore appears a few minutes later. This process is repeated many times, until the vesicle becomes very small, and the waiting time impractically long (up to 20 min for the last few pores). An interesting, but unexplained feature is the appearance of little bright fluorescent spots on the vesicle membrane beyond about the 22nd pore for the vesicle considered in Fig. 16. These spots are somewhat reminiscent of “particles” observed by Kummrow and Helfrich (1996) on collapsing giant phosphatidylcholine vesicles. The particles were interpreted by these workers to consist of the more stable cubic phases of phosphatidylcholine.
Just after the sealing of a pore, the membrane tension, σf, is lower than its value just before the pore opening, σo (numerical calculations indicate σf/σo ≈ 0.3–0.4; Brochard-Wyart et al., 2000). Thus, after the closure of a pore, the vesicle must recover its membrane tension to σo before the subsequent pore can appear. Inasmuch as R does not vary significantly between two successive pores, we conclude that the tension buildup is due to a loss of membrane surface, presumably in the form of small-sized lipidic aggregates not resolvable optically. We remark that the radius R measured by optical microscopy is a rather poor estimate of the true lipid surface area because of the unresolved excess area contained in thermal fluctuations. Thus, the true lipid area may change, whereas the measured, projected area remains constant within experimental error. Currently, the mechanism leading to the loss of phospholipid from vesicle membranes is unexplained. To check whether the lipid loss could be due to local heating of the sample, we measured the temperature change at the illuminated region of the sample by a small thermocouple. We recorded temperature increases of 3–4°C which level off after ~10 min, under conditions similar to those employed in the observation of transient pores in GUVs. It is unlikely that such a temperature change be relevant, except in the vicinity of a phase transition (DOPC bilayers remain fluid down to −22°C; Ladbrooke and Chapman, 1969). We have also qualitatively tested the effect of reducing the incident light intensity by use of neutral density filters. Cutting the incident light intensity by a factor of 100 resulted in longer waiting times to tense the vesicles (a few hours), but at the end, series of transient pores appeared in DOPC vesicles. Similarly, illuminating only part of a vesicle by closing down the diaphragm of the microscope resulted in a longer wait for tension buildup, but eventually a series of pores appeared, with rather long waiting times between successive pores (several minutes). A possible explanation for the loss of surface is the oxidation of the lipid. Most phospholipid oxidation products are lower molecular weight compounds with increased solubility in the aqueous phase (Gunstone, 1994). Oxidation can be accelerated considerably by photooxygenation, which involves interaction between a double bond and singlet oxygen produced from ordinary triplet oxygen by light in the presence of a sensitizer. Thus, photooxidized products may leave the membrane, perhaps in the form of small aggregates also containing intact phospholipid. Unfortunately, standard methods of removing oxygen are difficult to apply to our suspensions of GUVs. For example, bubbling argon gas through the solution not only damages vesicles but causes foaming due to the presence of glycerol, as well. To test whether the dye could act as a sensitizer for generating singlet oxygen we varied the lipid-to-dye ratio between 13:1 and 13:3 DOPC:RH237, hoping to see different rates of surface loss. Presumably, different rates of surface loss would result in different waiting periods between successive pores (in the early, constant period regime, see Fig. 16 a). For similarly sized vesicles, we were not able to observe any systematic variation in the waiting time as a function of the dye-to-lipid ratio. The difficulty here is that pores are formed through inhomogeneous nucleation (see Life of Transient Pores). Thus, the interval between pores is hard to reproduce: this interval is determined not only by the rate of lipid loss, but also by the nature of the nucleation defect. It would be quite useful to have a well-characterized nucleation defect to study systematically the rate of photoinduced surface loss. We have observed cascades of transient pores using any one of the dyes di6ASP-BS, RH237, or NBD-C6-HPC (Fig. 5, Materials and Methods), with periods which are hard to relate to the nature of the dye. A good test to determine the role of dye would be to illuminate the vesicles in the absence of dye. However, in the glycerol-water mixtures we employ, vesicles are hardly visible using bright-field microscopy techniques such as phase contrast, due to the small difference between the refractive indices of the lipid bilayers and the solvent (n = 1.43 for 66% glycerol). In solutions not containing glycerol, we have rarely observed vesicles becoming tense. However, we have never observed measurable changes in vesicle sizes in such low viscosity solutions, even after several hours of intense illumination. Finally, focusing the 488-nm beam of an Ar laser (Beamlock, Spectra Physics) at the equator of a marked DOPC vesicle, we were able to tense it in glycerol-water solutions, in a way similar to Bar-Ziv et al. (1998). Further application of the laser spot on the vesicle resulted in the appearance of a series of transient pores, away from the laser spot. We were unable to correlate the period between pores with the laser intensity which was varied. | |||||||||||||||||||||||||||||||
FINAL REMARKS Opening of pores in lipid bilayers is an ubiquitous process in cellular biology, implicated in the transport of small molecules and ions across membranes and in membrane fusion. In liposome-based drug delivery applications, pores are implied in the release of the encapsulated cargo molecules. In this article, we have concentrated on the closure dynamics of transient pores in giant unilamellar vesicles, prepared in viscous solutions (containing 66% by volume glycerol). Here, we have used optical illumination to put the vesicles under tension. Other methods, such as adhesion to a surface (Bernard et al., 2000), shearing (Guedeau-Boudeville, 2002), or the spreading of the excess vesicle membrane onto an adhesive bead (Dietrich et al., 1997) could also be used to increase the membrane tension for practical applications. Examples of the latter method are shown in Fig. 17, wherein beads covered by the polycation poly(allylamine hydrochloride) are brought into contact with DOPC vesicles, using laser tweezers (A. Fery, Max Planck Institute, Potsdam, Germany; private communication, 2001).
When σ reaches a sufficiently high value, a pore suddenly appears in a vesicle. During the fast opening of a pore, the inner liquid does not have time to leak out due to its high viscosity: in this regime the membrane tension is relaxed by the redistribution of the lipid over a smaller projected area. When the pore reaches its maximum radius, nearly all the membrane tension has relaxed. The remaining membrane tension is balanced by the weak restoring force, the line tension Using this method, we have first measured the line tension for bare DOPC vesicles. We have found that using phospholipids from different suppliers results in different measured values: We have demonstrated that the detergent Tween 20, with a large polar head group, relatively small hydrophobic tail, and thus possessing positive spontaneous curvature, has the opposite effect on the line tension: Quantitative analysis of our data in the presence of detergent is complicated by several factors. First, unlike cholesterol, the detergent has significant solubility in the aqueous phase. Thus, it is not trivial to estimate its fraction in the vesicle membranes. Secondly, at the concentrations of detergent employed, the vesicles become fragile, and are solubilized in the course of several hours. Thus, to see the immediate effect of the detergent on the vesicles we used a concentration gradient. This makes it difficult to quantify the total concentration of detergent in the vicinity of a given vesicle. Some of these difficulties can be overcome by using lower concentrations of detergent (the amount of lipid is fixed). When sublytic concentrations of detergent are used, vesicles are not solubilized. Thus, homogeneous mixtures of detergent and vesicles, at known total detergent concentration, can be prepared before observation. The phase behavior of detergent/vesicle mixtures is also simpler, and analogous to Langmuir adsorption, at low detergent content. We have recently started investigating the variation of the line tension at sublytic detergent concentrations. The results of this study will be reported in a future article. In our discussion of the effect of inclusion molecules on the line tension, we mentioned the possibility that the pore edge may be enriched or depleted in inclusion molecules compared to their fraction in the unperturbed regions of the bilayer. In fact, we expect that the energy of a molecule with co < 0 (co > 0) should be higher (lower) at the bilayer edge. Thus, cholesterol, having co < 0, should be depleted at the edges of the pore compared to its number density in the unperturbed bilayer. Conversely, the pore edge should be enriched in molecules with co > 0, such as Tween 20. This problem will be treated quantitatively in a forthcoming article. We presented examples of how cargo can be transported through transient pores. The cargo in the first example given was a small vesicle whose exit velocity allowed us to have an independent estimate of the line tension, Finally, we presented a peculiarity of the transient pores: these appear in series in a given vesicle, with regular time intervals between two successive pores. Two regimes are observed: first, the waiting time between pores is constant for about a dozen pores, then it increases almost linearly as a function of the observation time. We have argued that the increase of the membrane tension is due to a loss of lipid from the vesicle membrane. However, the mechanism of this loss is unexplained for the moment. In their studies of lipid bilayers (not containing any dye) excited by laser tweezers, Bar-Ziv and colleagues also observed loss of vesicle surface area (Bar-Ziv et al., 1995, 1998; Moroz et al., 1997). Their interpretation is that lipid is pulled into the optical trap by the familiar dielectric effect, is disrupted, and finally is repackaged into an optically unresolvable suspension of colloidal particles. In our studies using a microscope lamp with a much lower photon flux, the loss of surface is quite unlikely to be due to the same mechanism. We have been able to visualize transient pores only in sufficiently viscous solutions. If the inner liquid is a low viscosity liquid, such as water, leakout through a pore becomes fast and limits the size and lifetime of pores, making it difficult to visualize them (Brochard-Wyart et al., 2000; Sandre et al., 1999). However, the presence of pores in such systems have been suggested by indirect measurements: anomalously high permeation rates, explained by the presence of small, transient pores, have been observed for vesicles tensed by adsorption in water (Sandre et al., 1999; Guedeau-Boudeville et al., 1995; Bernard et al., 2000). Other researchers have been able to visualize long-lived, large pores in low viscosity solutions by creating the pores by electroporation, and maintaining large membrane tensions using micropipette aspiration (Zhelev and Needham, 1993; Moroz and Nelson, 1997). If the driving force for pore opening, the membrane tension, is allowed to relax, as is the case with freely floating vesicles, then pores would be aborted before reaching observable sizes in water. Lipid membranes do not like having edges. They possess a self-healing capacity: if punctured, a membrane reseals itself. This is essential for maintaining the integrity of all membranous cellular compartments and hence for maintaining life itself. This amazing capacity of lipid membranes is due to the line tension. Despite its foremost importance, the line tension has received little attention in the past, partly due to a lack of a convenient, simple, and robust method for its measurement. We hope that the method described here will help in filling this void. | |||||||||||||||||||||||||||||||
Acknowledgments We thank A. Fery and A. Buguin for stimulating discussions, M. Sickert for help with tensing vesicles using a laser, and A. Fery for kindly authorizing us to use Fig. 17. E. K. thanks J. L. Viovy for his infinite patience. We gratefully acknowledge funding by Institut Curie, ARC (Association pour la Recherche contre le Cancer), and FRM (Fondation pour la Recherche Médicale). | |||||||||||||||||||||||||||||||
References
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