Determination of the Line Tension of Giant Vesicles from Pore-Closing Dynamics

Narayanan Srividya* and Subra Muralidharan*School of Molecular Biosciences, Washington State UniVersity, Pullman, Washington 99164

ReceiVed: December 20, 2007; ReVised Manuscript ReceiVed: April 8, 2008

Giant vesicles generated from synthetic and natural lipids such as phosphatidylcholines are useful models forunderstanding mechanical properties of cell membranes. Line tension is the one-dimensional force enablingthe closing of transient pores on cell membranes. Transient pores were repeatedly and reproducibly formedon the membrane edge of giant vesicles generated from synthetic and natural phosphatidylcholines employinga nitrogen-pumped coumarin dye laser (440 nm). Line tension was determined at room temperature fromclosing of these pores that occurred over several seconds when the radius of the vesicle could be consideredto be constant. The value of line tension depends on the nature of the lipid for single lipid systems, which,at room temperature, yielded a vesicle bilayer region in the gel, fluid, or mixed gel and fluid phases. The linetension for vesicles generated from phosphatidylcholines with saturated acyl chains of lengths of 12-18carbon atoms ranges from 1 to 12 pN, exhibiting an increase with chain length. Vesicles generated from thenatural Egg-PC, which is a mixture of lipids, are devoid of phase transition and exhibited the largest valueof line tension (32 pN). This value is much larger than that estimated from the line tensions of vesiclesobtained from lipids with homologous acyl chains. This study, to our knowledge, is the first to employ laserablation to generate transient pores and determine line tension from the rate of pore closure and demonstratea relationship between line tension and acyl chain length.

Introduction

Line tension is a fundamental mechanical property of cellmembranes that facilitates the closure of transient pores which,in turn, influence endocytosis, exocytosis, cell fusion, and celldivision. It is an important weak one-dimensional force on theorder of piconewtons (pN) that opposes surface tension to enablepore closing.1 A better understanding of pore-mediated cellularprocesses can be gained from a membrane structure-line tensionrelationship. Vesicles are excellent models for cell membranesand are useful for gaining an understanding of the influence ofcell membrane structure on cell mechanics and hence linetension.2–15 The major objectives of the studies reported herewere to demonstrate laser ablation as a useful approach forgenerating transient pores on vesicle membranes, to demonstratethat line tension can be determined from the rate of closing ofthese pores, and to determine if a correlation exists betweenline tension and number of methylene chains for vesiclesgenerated from lipids with homologous acyl chains. We haveemployed laser ablation to generate small transient pores in themembranes of vesicles derived from the saturated lipids DLPC,DMPC, DPPC, and DSPC with 12, 14, 16, and 18 carbon acylchains, the unsaturated lipid DOPC with a double bond in each18 carbon acyl chain, and the natural lipid Egg-PC, which is amixture of saturated and unsaturated lipids. The rate of poreclosing was determined from video microscopy, and the linetension was calculated from this rate under close to physiologicalconditions of pH and 11 mM MgCl2 without the inclusion offluorescent dyes in the membrane region. The radius of the

vesicle was constant during the experiments, indicating minimalleakage of the inner fluid. This, to our knowledge, is the firstreport of a systematic study of the line tension of syntheticvesicles by laser ablation.

The significance of transient pores and line tension has beenextensively discussed in the literature for model vesicles andcells. Several studies on the measurement of line tension haveappeared in the literature, many of which employ micropipetteaspiration for the generation of pores.3,11 Other approaches topore generation have included UV irradiation,1,9,10,12

electroporation,16–18mechanical forces,19–23 and pore-formingpeptides and proteins.24–28 Among the various studies reported,those of Brochard-Wyart1,10,12 and Rodriguez9 are of directrelevance to the studies that we have performed on thegeneration of transient pores and the determination of linetension from the rate of their closing.

Brochard-Wyart generated pores as large as 10 µm indiameter in giant unilamellar vesicles of 100 µm diameterprepared from the lipid DOPC and 1% fluorescent dye di6ASP-BS or C6-NBD-PC in a 66% glycerol medium.1 The pores weregenerated by UV irradiation, which increased the membranetension and eventually resulted in large pores. These poresclosed when the irradiation was stopped. The pores formed inseveral minutes and closed in several seconds. The glycerolmedium minimized the inner liquid leakage such that the radiusof the vesicle was constant during the process of pore formationand closing. The pore closing was recorded by video microscopyand the line tension determined from the analysis of the images.An average value of 6.9 pN was obtained for the line tension,which increased with varying amounts of cholesterol in thebilayer region.

* Towhomcorrespondenceshouldbeaddressed.E-mail:subra.murali@wsu.edu(S.M.); narayanan_srivid@wsu.edu (N. S.).

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2008, 112, 7147–7152

Rodriguez studied the formation and closing of pores onDOPC vesicles containing up to 10% C6-NBD-PC in theaqueous medium without glycerol.9 In these experiments, giantunilamellar vesicles of DOPC were generated by electroforma-tion, and a solution of C6-NBD-PC was added to them. Thedye molecules were incorporated in the outer leaflet of thevesicles within minutes by diffusion through nanopores that theauthor has shown to exist in the bilayer region.8 A 4 mMdithionite solution was added to the vesicles under illuminationwith a mercury lamp. The dark and photochemical reductionof C6-NBD-PC by dithionite resulted in transient pores that livedfor a few seconds to few minutes. Under these experimentalconditions, the vesicle liquid leaked, leading to a change in itsradius during illumination, and the pores still closed whenillumination was discontinued. The leaking velocity was usedto determine the line tension, which gave an average value of2 pN, much smaller than the one determined by Brochard-Wyart.1 The reduction in line tension was interpreted as due todithionite reduction of C6-NBD-PC and photosolubilization.These experiments indicate that line tension is influenced bymembrane solubilization leading to a change in the vesicleradius. Nevertheless, even a reduced value of the line tensionis sufficient to cause pores to close. Rodriguez demonstrated acascade of pore formation and closing in these studies.

These studies have addressed the line tension of the mem-brane edge that lies in the outer leaflet and at the interface ofthe vesicle and bulk aqueous medium in vesicles obtained fromsingle lipids. Lipid mixtures and biological membranes possessdomains, and theoretical modeling studies of Dan7 and Cohen15

have estimated line tension values between domains andbetween domains and the continuous phase. These estimatesrange from 0.1-10 pN. Baumgart and Longo have experimen-tally shown the line tension values between domains to besimilar to the theoretical calculations.29–31

Our studies reported here are complementary to those ofBrochard-Wyart and Rodriguez. We have determined the linetension at the membrane edge of vesicles in the aqueous phaseformed from lipids with homologous acyl chains and naturallyoccurring lipid mixtures in the absence of dye molecules bygenerating transient pores employing laser ablation such that theradius of the vesicle is constant. These studies are discussed here.

Materials and Methods

Egg-PC, DLPC, DMPC, DPPC, DSPC, and DOPC used inthis study were obtained from Avanti Polar Lipids, AL, andused as received. A modified rapid evaporation technique wasemployed for the generation of vesicles.32 This yielded vesiclesof various sizes with a large population of giant vesicles. Singlevesicles with diameters around 20 µm were chosen for poregeneration and line tension determination. An amount of 4 mg/mL of a given lipid in a 2:1 chloroform/methanol mixture wasadded to 1 mL of 11 mM MgCl2 and heated to 65 °C. Thevesicles formed rapidly, and the solution was maintained at thistemperature for 10 min and cooled to room temperature. A smallvolume of this solution was added to a well slide and coveredwith a flat microscope slide for the pore formation studies. Allpore formation and closing experiments were performed at theroom temperature of 24 ( 1 °C.

The home-built apparatus employed for the line tensionstudies is displayed in Figure 1 and described briefly here. ANikon TE 2000U inverted microscope was used to image thevesicles under bright field illumination. The microscope isequipped with a spatial light modulator, and light from a 1064nm CW Nd:YAG laser is allowed through the spatial light

modulator (SLM) to generate a holographic optical tweezer(Arryx Inc.). Up to 200 optical traps with the same light intensitycan be generated with this arrangement. The large vesicles(diameter ∼ 20 µm) could be studied without trapping, and afew vesicles of much smaller diameter were studied by trapping.One of the microscope ports was used for a nitrogen-pumpeddye laser for ablation and deformation of the vesicles. ACoumarin dye was used to obtain 440 nm laser emission, andRhodamine 610 dye was used to obtain 626 nm laser emission.The peak laser energy in each case was about 100 µJ. The 440nm laser was employed for ablation experiments, and the 626nm laser was used for the deformation experiments. The poreformation and closing, deformation, and return to original shapewere recorded with a Sentech STC630 CCD camera at 30frames/s. The images were analyzed with Videomach softwareto obtain line tension values.

Results and Discussion

The transient pores of radius rpore were generated on themembrane edge of vesicles of different lipids with a 440 nmlaser such that the radius R of the vesicle did not significantlychange during their formation and closing. This may be seenin the movie on the pore formation and closing on the membraneof Egg-PC vesicles included in the Supporting Information. Inall cases, the pores could be repeatedly and reproduciblygenerated rapidly and closed within a few seconds. As discussedby Brochard-Wyart1 and Rodriguez9 the rate of closing of thepore is driven by the competition between the line tension τand the surface tension σ and is given by eq 1

drpore

d t)

rpore(t)

2η [σ(t)- τrpore(t)] (1)

where η is the viscosity of the medium and is 1 cP for theaqueous medium employed in our studies. Since the radius Rof the vesicle is constant during the closing of the pore, thesurface tension σ(t) is constant, and eq 1 reduces to eq 2.

R2 ln rpore ≈ -2τ3πη

t (2)

Equation 2 indicates that by determining rpore as a function oftime at constant R, the line tension τ can be obtained from the

Figure 1. Home-built apparatus for line tension studies.

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slope of the plot of the quantity on the left-hand side as afunction of time t.

The formation and closing of a 1 µm pore on Egg-PC vesiclesis shown over selected time intervals in Figure 2, and the entireprocess is included as a movie in the Supporting Information.The plot of R2 ln rpore as a function of time is shown in Figure3, indicating a linear plot as predicted by eq 2. The linearity ofthis plot supports the assumption that the radius R of the vesicleis constant during the pore formation and closing, and very littleof the vesicle fluid leaks out during this process. The linetensions determined for Egg-PC and other vesicles are listed inTable 1. The line tension for DOPC determined in our studiesby laser ablation as seen from Table 1 is 11.4 ( 1.2 pN and ishigher than the value of 6.9 ( 0.42 pN obtained by Brochard-Wyart. This author noted that the DOPC lipid obtained fromSigma yielded a value of 6.9 ( 0.42 pN, while the one fromAvanti Polar Lipids, the one employed in our studies, yieldeda much higher value of 20.7 ( 3.5 pN. It is important to notethat the line tension values are sensitive to the source of thelipids and batches from the same source. It is likely that, whilewe used DOPC from Avanti Polar Lipids, the batch of oursamples and that of Brochard-Wyart were different, yieldingthe different values. All of the lipids in our studies were

purchased at the same time from Avanti Polar Lipids and likelyhad similar age and the same quality control. Despite thesensitivity of the line tension of vesicles to the source of thelipids, it is worthwhile to examine the trend of the line tensionvalues among lipids with homologous acyl chains.

The single lipid vesicles have distinct phases, namely, thegel phase and the fluid phase, and a phase transition temperaturewhich is also listed in Table 1. The membrane regions of theDOPC and DLPC vesicles exist in the fluid phase and those ofDPPC and DSPC in the gel phase at room temperature. Themembrane region of Egg-PC does not possess well-definedphases and a phase transition temperature. The lipid DOPC andDSPC differ only by the presence of a double bond in each ofthe 18 carbon acyl chains of DOPC. Evans has shown a linearcorrelation with a positive slope between (kc/KA)1/2 (kc is theelastic modulus for bending, and KA is the elastic modulus forarea stretch) and the thickness of the bilayer region for vesiclesgenerated from lipids with homologous acyl chains.33 In thesestudies, Evans has shown that the area stretch modulus KA isessentially constant for vesicles derived from lipids withhomologous acyl chains which are either completely saturatedor have a single double bond. The bending modulus in thesestudies bears an approximate linear correlation to the numberof methylene carbons in the acyl chain. We find a similar linearcorrelation between the line tension values of DLPC, DPPC,and DOPC within the standard deviations of the experimentalvalues. This result is in agreement with the predicted directproportionality of the line tension τ on the bending moduluskc.1,9 The line tension values for DLPC, DPPC, and DOPCindicate a (0.7 ( 0.2) pN contribution for each methylene groupin the acyl chain of the lipid, keeping in mind that there aretwo acyl chains in each lipid. It is interesting to find thiscorrelation despite the fact the phases of the membrane regionsof the different lipids are not the same at room temperature.

The line tension τ is related to the bending rigidity κ and thebilayer thickness e as given in eq 3.1

τ) πκ

e(3)

Evans has determined the κ and e values for DOPC to be 0.85× 10-19 J and 3.69 nm, respectively.33 These values yield a τvalue of 7.7 pN, which is smaller than the value of 11.4 pNthat we have determined but closer to the value of 6.9 pNreported by Brochard-Wyart1 This agreement is fortuitousconsidering the fact that lipids from different sources yieldeddifferent line tension values. Evans has not reported the κ ande values for all of the lipids in the homologous series of 12-18carbon atoms in the hydrocarbon chain. We have estimated theκ values for DLPC and DPPC from the reported values to be0.56 × 10-19 and 0.75 × 10-19 J, respectively. Using eq 3 andthe τ values determined in our study and the κ values fromEvans’s work, the thickness of the bilayer (e) for DLPC andDPPC is found to be 7 and 2.4 nm, respectively. Both of thesevalues are unrealistic, with the thickness being overestimatedin the case of DLPC and underestimated in the case of DPPC,with a more realistic number being 3-4 nm. Several possiblefactors could contribute to the disagreement between the linetension and bilayer thickness values calculated from eq 3 andthe experimental results, namely, (i) eq 3 is obtained for smallelastic deformations of the lipid membrane; laser ablation yieldspores of 1 µm and larger diameters, which are not smallperturbations, (ii) the different lipids result in bilayers in thegel, fluid, or mixed gel and fluid phases at room temperature(Table 1) characteristic of the lipid carbon chain length;

Figure 2. Formation of a 1 µm pore on the membrane edge of the 20µm Egg-PC vesicle in 11 mM MgCl2 at room temperature. The numbersunder the figure denote the elapsed time in seconds after ablation witha 440 nm laser (zero time).

Figure 3. The plot of the quantity R2 ln rpore as a function of time t(eq 2) for the Egg-PC vesicle in Figure 1.

TABLE 1: Line Tension Calculated for Different GiantVesicles in 11 mM MgCl2 at Room Temperature

lipidcarbon

chain lengthaphase transition

temp °Cline tension, pN

DLPC 12:0 -1 2.5 ( 0.3DPPC 16:0 41 9.5 ( 1.0DSPC 18:0 55 0.8-1.2 ( 0.5DOPC 18:1 -20 11.4 ( 1.2Egg-PC variable no specific phase 32.3 ( 2.0

a The first number represents the number of carbon atoms in asingle acyl chain. The second number denotes saturation (0, nodouble bonds) and unsaturation (1, one double bond).

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theoretical models have not considered the influence of differentphases on elastic deformation, and (iii) the curvature of vesiclesvaries with size, influencing the membrane mechanical proper-ties like line tension, bending rigidity, and area stretch modulus,which is manifested in the experimental determinations; theo-retical models are based on small vesicles, and the disagreementsbetween values predicted by models and experimental resultscould result from size effects.

A relevant molecular model for understanding variation inthe line tension of vesicles generated from a homologous seriesof lipids is the one proposed by May.34 This model considersthe free energy of the lipid molecule at the membrane edge andrelates the line tension to the repulsive interactions of the lipidhead groups and specifically relates the line tension to the headgroup interaction parameter B. Line tension is the one-dimensional force that overcomes surface tension to facilitatepore closing on the membrane edge. The pore formation perturbsthe position of the head groups from their self-assembledequilibrium structure, and pore closing is driven by the returnof the head groups from the perturbed to the equilibriumstructure. Line tension, which is a manifestation of the returnto the equilibrium, can be expected to depend on the head groupinteraction parameter B. May has generated theoretical curvesfor the dependence of line tension on B for the vesicles formedfrom DLPC, DMPC, and DPPC lipids. The B parameter forDLPC corresponding to the line tension that we have measuredyields a head group radius of 0.8 Å, which is a reasonable value.However the B value for DPPC yields an unrealistic head groupradius of 13.9 Å. It is reasonable to expect the head group radiiof DLPC and DPPC to be similar. The line tension for DPPCcan be calculated using a head group radius of 0.8 Å from theline tension versus B plots in May’s model. This value is 3.2pN, almost a third of the value determined by laser ablation(Table 1).

The difference between the line tensions of DLPC and DPPCmay be rationalized based on the expected differences in theelastic area compressibility modulus of the bilayers of vesiclesformed from these lipids. Evans has determined the elastic areacompressibility factor for DMPC in the fluid (LR phase) andgel (L� phase) to be 144 and 855 dyne/cm, respectively.35

Differences in the values are attributable to the differences inthe phases. The bilayers of DLPC and DPPC are in the fluidand gel phases, respectively, at room temperature. As a result,the elastic area compressibility modulus of DPPC vesicles canbe expected to be larger than that for DLPC vesicles, analogousto the fluid and gel phases of DMPC. This difference may alsoexplain the much smaller value for the line tension of DPPCvesicles from May’s model compared to the experimental value.The head group interaction parameter B like the elastic areacompressibility modulus can be expected to have a strongdependence on the phase of the bilayer region, where thepacking of the lipid hydrocarbon chains is a function of theirlength and temperature.

As seen from Table 1, the line tensions of DSPC and Egg-PC do not fit the approximate linear correlation observed forDLPC, DPPC, and DOPC. The vesicles of DSPC presented anexperimental difficulty in terms of following pore formationdynamics, as reproducible results could not be obtained. Thevalue shown in Table 1 is the best value that could be obtainedfrom a limited set of data. One of the difficulties encounteredwas the irregular behavior of pore closing. In all cases studiedexcept DSPC, the pores closed uniformly over several secondsto yield linear R2 ln rpore versus t plots. The pores on DSPCpartially closed over a few seconds and took much longer to

close completely. These images individually yielded linear R2

ln rpore versus t plots with a break, indicating two different ratesof pore closing as displayed in Figure 4. The entire pore closingvideo is included as Supporting Information. Clearly, the valuesare much lower than the average value of 11 pN expected basedon the contributions from the methylene groups for homologousacyl chains in the lipids.

A explanation for the behavior of DSPC may lie in the surfaceshear viscosity of the vesicle bilayer defined as the ratio oftangential force per unit length of the surface to the rate of strainof the surface as a result of stress. Needham has determinedthe surface shear viscosities of fully compressed monolayersformed from lipids with 16-24 carbon atoms in their alkylchains.36 The shear viscosity was almost zero for DPPC, showeda dramatic increase between the monolayers of DPPC andDSPC, and exhibited an almost linear dependence on thereduced temperature Tr (Tr ) Tm - T/Tm, T ) experimentaltemperature (24 °C) and Tm ) phase transition temperature in°C) for lipids with 18-24 carbon atoms in their alkyl chains.This increase in shear viscosity, which is a measure of theresponse of the vesicle membrane edge to stress, could have atime-dependent behavior for DSPC. As the pore closes, the rateof strain on the surface changes, leading to approximately twodifferent average time-dependent behaviors. The pores closeinitially at a slower rate, yielding a line tension of 0.8 pN, andmore rapidly after 30% of the pores have closed to yield a linetension of 1.2 pN. This indicates that the membrane around thepore when it is formed is less elastic, with a significant influenceof shear viscosity, and becomes more elastic as the pore closes,with a reduced dependence on the shear viscosity. The twovalues determined from the break in the linear plot of R2 lnrpore versus time can be considered as average values represent-ing nonelastic and elastic behavior of the membrane around thepore. This anomaly vanishes when a double bond is introducedin the alkyl chains, as in DOPC, which seems to have a uniformpore closing behavior as in DLPC and DPPC. The DOPC vesiclebilayer is in the fluid phase at room temperature, and themembrane edge is elastic.

The line tension values at the membrane edge for all vesiclesformed from single lipids in Table 1, except for Egg-PC, lie inthe range of line tension values between domains in the bilayerregion of vesicles generated from a mixture of lipids. The linetension between domains is the one-dimensional force thatrestores the organization of the lipids to maintain the domainstructure upon distortion of the vesicle with an external force.It is analogous to the line tension at the membrane edge thatfacilitates pore closing by restoring the organization of the lipid

Figure 4. The plot of the quantity R2 ln rpore as a function of time tfor the DSPC vesicle.

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molecules. In other words, the line tension between domainsand on the membrane edge are forces that act to restore theself-assembled equilibrium structures of the membrane bilayer.The similarities in the values of line tension at the membraneedge and between domains can be understood on this basis. Itwas also difficult to generate pores on the vesicles of DMPCas the vesicle either deformed or disintegrated, depending onthe energy of the laser beam. A possible reason could be thepresence of the DMPC vesicle membrane in both the gel andfluid phases as its phase transition temperature of 23 °C is closeto the room temperature. The formation of defects at phaseboundaries possibly results in the deformation or disintegrationof the vesicle upon pore formation.

Egg-PC is a mixture of lipids with saturated and unsaturatedacyl chains (34% 16:0, 2% 16:1, 12% 18:0, 32% 18:1, 20%18:2, and 4% 20:4) and does not possess a phase transitiontemperature. A weighted average of the line tensions of thedifferent lipids based on the line tensions determined by laserablation yields a value of 13.2 pN, while an additive value ofthe line tensions of the vesicles of the main lipid componentsis 24.8 pN. It is evident from Table 1 that the experimentalvalue of 32.3 pN is much higher than both of these values. Themixture of lipids appears to make the membrane robust andresistant to pore formation by laser ablation. Brochard-Wyartshowed that the inclusion of cholesterol in DOPC vesiclesincreased the value of the line tension, for example, to 14 pNwhen 30 mol % cholesterol was included in the DOPCmembrane.1 They attribute the increase to the increase in thebending modulus and the rigidity of the membrane. The Egg-PC vesicles only deformed without any pore generation evenat the highest energy when a 620 nm laser from Rhodamine610 was employed. This is included as a movie in the SupportingInformation.

One of the reviewers has pointed out during the initial reviewthat the lysis tension of Egg-PC is about 3 dyne/cm, while amuch larger value may be expected based on the line tensionmeasured by laser ablation. Lysis tension is the force requiredto lyse the vesicle, while line tension is the force acted to restoreself-assembly of the lipid molecules following pore formation.Both of these forces are a function of the bending rigidity,surface shear viscosity, and elastic area compressibility of thelipid bilayer.37–39 The Egg-PC lipid bilayer region is uniformwithout the presence of domains, despite the fact that it is amixture of various lipids. Lipid mixtures often result in domainsin the membrane region of the vesicles formed from them. Boththe lysis tension and line tension are experimentally determinedby perturbing the vesicle bilayer by the application of an externalforce employing micropipette aspiration and laser ablation. Theresponse of the Egg-PC membrane region to such external forcescan be complex given its composition of mixed lipids that donot result in domain formation. A better understanding of thelysis and line tensions of Egg-PC could be gained by determin-ing its bending rigidity, surface shear viscosity, and elastic areacompressibility. Additionally, the determination of the lysistension by lysing the vesicle with high laser energy may alsoprovide insight into the lysis and line tensions of the Egg-PCmembrane bilayer.

Our preliminary studies have clearly shown that laser ablationis a useful method for determining the line tensions ofmembranes of lipid vesicles in their native form without theneed to include fluorescent dyes. We have also shown that linetension is a function of the lipid employed for the generationof vesicles. A correlation between line tension and the numberof carbon atoms in the acyl chain has been shown for lipids of

homologous chains. The line tension values have been rational-ized based on the existing molecular models of the vesiclebialyer region. The behavior of vesicles of mixed lipids suchas Egg-PC is more complex. Further studies to understand theline tensions of vesicles of single and mixed lipid systemsdetermined by pore generation by laser ablation are underway.

Acknowledgment. This research was supported by the W. M.Keck Foundation when the authors were at Western MichiganUniversity, Kalamazoo, MI. We would like to thank thereviewers of the manuscript for bringing to our attentionimportant experimental and theoretical investigations in theliterature that enabled us to provide better rationale for ourresults.

Supporting Information Available: Movies of the poreclosing at the membrane edge of Egg-PC and DSPC vesiclesfollowing laser ablation. This information is available free ofcharge via the Internet at http://pubs.acs.org.

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