Strong Adhesion of Giant Vesicles on Surfaces: Dynamics and

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Strong Adhesion of Giant Vesicles on Surfaces: Dynamics and Permeability A.-L. Bernard,*,† M.-A. Guedeau-Boudeville,† L. Jullien,‡ and J.-M. di Meglio§ Laboratoire de Physique de la Matie` re Condense´ e CNRS URA 792, Colle` ge de France, 11 Place Marcelin Berthelot, 75231 Paris Cedex 05, France; De´ partement de Chimie CNRS UMR 8640, Ecole Normale Supe´ rieure, 24 Rue Lhomond, 75231 Paris Cedex 05, France, and Universite´ Louis Pasteur and Institut Universitaire de France, Institut Charles Sadron CNRS UPR 022, 6 Rue Boussingault, 67083 Strasbourg Cedex, France Received October 13, 1999. In Final Form: March 15, 2000 Evanescent wave induced fluorescence microscopy combined with phase contrast microscopy is applied to study the strong electrostatic adhesion of giant unilamellar vesicles (GUV) on flat surfaces. This technique gives the shape of the adsorbed vesicles and an insight into the dynamics of spreading. In addition, it is used to investigate the possible induction of membrane permeability by adhesion. We show that the vesicle shape on the surface is a spherical cap and that a three-regime process with characteristic times τ1, τ2, and τ3 rules the dynamics of spreading. τ1 is the time elapsed between the moment when the vesicle reaches the surface and the instant when the vesicle actually adheres. τ1 stands between 10 s and one minute and is determined by the drainage of the liquid film between vesicle and substrate. τ2 and τ3 are the characteristic times of the biexponential law that fits the curve of the radius of the contact area as a function of time. τ2 is about 0.05 s and corresponds to a regime of vesicle adhesion at constant volume. During τ2, the negatively charged lipids of the outer monolayer of the membrane bilayer flow toward the surface while the excess area of the membrane is resorbed; the vesicle bilayer is then under tension. The regime τ3 corresponds to a regime of water permeation through the membrane. We find that 0.5 s < τ3 < 5 s according to the experimental conditions. On average, vesicles lose 7% of their inner content through a process of pore formation along the contact line. The role of parameters such as vesicle size, medium viscosity, lipid composition, and surface charge on the adhesion phenomenon is investigated and analyzed.

Introduction The design of new strategies for inducing solute permeability through lipid bilayers is highly desirable for improving the efficiency of drug delivery. Among recent approaches, the application of transient external perturbations (temperature rise1 and electrical field pulses2) on the membrane have appeared promising for internalizing or externalizing even large solutes. Similarly, we have recently been concerned with the evaluation of mechanical shear for creating pores in bilayers.3,4 In the course of the corresponding studies, we have started to investigate the spreading behavior of giant vesicles on smooth surfaces. The static aspect of the interaction between a vesicle and a surface is well documented. From a theoretical point of view, the vesicle morphology on the surface depends on the competition between the adhesion energy and the curvature energy on one hand and on the constraints on its volume and surface on the other hand.5,6 When the adhesion energy is large compared to curvature energy * To whom correspondence should be addressed. Present address: L’Oreál, Service de Physico-Chimie, 66 Rue Henri Barbusse, 92117 Clichy Cedex, France. E-mail: albernard@recherche. loreal.com. † URA 792, Colle ` ge de France. ‡ UMR 8640, Ecole Normale Supe ´ rieure. § UPR 022, University Louis Pasteur and Institut Universitaire de France. (1) Lasic, D. D. Liposomes: From Physics to Applications. Elsevier Science Publishers: New York, 1993; p 318. (2) Zhelev, D.; Needham, D. Biochim. Biophys. Acta. 1993, 1147, 89. (3) Dvolaitzky, M.; de Gennes, P.-G.; Guedeau-Boudeville, M.-A.; Jullien, L.; di Meglio, J. M. C. R. Acad. Sci. Paris 1993, 316, II, 1687. (4) Guedeau-Boudeville, M.-A.; Jullien, L.; di Meglio, J.-M. Proc. Natl. Acad. Sci. 1995, 92, 9690. (5) Seifert, U.; Lipowsky, R. Phys. Rev. A. 1990, 42(8), 4768. (6) Lipowsky, R.; Seifert, U. Langmuir 1991, 7, 1867.

(larger than 10-3 mJ/m2), the vesicle shape is a spherical cap if both volume and surface are conserved whereas it is a flat pancake if there is only surface conservation.7 These shapes have already been observed using various techniques such as micropipet aspiration,8 electron microscopy,9 or reflection interference contrast microscopy (RICM).10 In the present paper, we study the dynamics of strong adhesion of giant vesicles on surfaces, using evanescent wave induced fluorescence microscopy (EWIF, also called total internal reflection fluorescence microscopy TIRFM), introduced by Gingell et al. for the study of cell adhesion.11 In a recent paper,12 we showed that this technique can be used to determine the shape of vesicles on a flat substrate. We here use this technique to analyze the membrane profile of an adhered vesicle and the dynamics of vesicle spreading or bilayer permeability from the contact area of vesicles on the surface or from the difference of optical density between the inner and the outer medium of the vesicle. We also present experiments using fluorescent lipids incorporated inside the vesicle membrane. The present paper is divided into three parts. We first describe our experimental setup. Then, we report on the spreading behavior of giant vesicles on surfaces under different conditions. Finally, we suggest a mechanism to account for the experimental results. (7) Lipowsky, R.; Seifert, U. Mol. Cryst. Liq. Cryst. 1991, 202, 17. (8) Evans, E.; Rawicz, W. Phys. Rev. Lett. 1990, 64(17), 2094. (9) Bailey, S.; Chiruvolu, S.; Israelachvili, J.; Zasadzinski, J. Langmuir 1990, 6, 1326. (10) Ra¨dler, J.; Sackmann E. J. Phys. II France 1993, 3, 727. (11) Gingell, D.; Todd, I.; Bailey, J. J. Cell Biol. 1985, 100, 1334. (12) Bernard A.-L.; Guedeau-Boudeville, M.-A.; Jullien, L.; Di Meglio, J.-M. Europhys. Lett. 1999, 46(1), 101.

10.1021/la991341x CCC: $19.00 © 2000 American Chemical Society Published on Web 07/22/2000

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Experimental Section Sample Preparation. Giant vesicles are prepared using the method of electric swelling.13 The lipid solution, 10 mg/mL EPC (egg phosphatidylcholine, Sigma-Aldrich in chloroform-methanol 9:1), is spread onto Indium-Tin-Oxide (ITO)-coated glass slides. After drying, the glass slides are assembled to form a cell which is filled with a 50 mM sucrose solution while applying an AC field across the cell (15 V/cm, 10 Hz) which is maintained overnight. A 10 µL aliquot of the resulting vesicle suspension is then directly diluted in the observation cell (composed of one treated surface facing one ordinary glass slide glued together with a spacer) in a 50 mM glucose solution containing calcein (Sigma-Aldrich) 100 µM, pH ) 7. The difference of density between the sucrose and the glucose solutions promotes the contact of the vesicles on the bottom surface. The hydrophilic fluorescent dye BODIPY 492/515 has also been tested instead of calcein at a concentration of 100 µM. The surfaces used for vesicle adhesion are ITO-coated slides covered by sputtering with a thin layer (10 nm) of gold. The gold deposition is carried out under a 5 Pa pressure of argon and a 250 V voltage. The surface roughness is evaluated to 0.5 nm by atomic force microscopy (AFM) working in contact mode. The gold surfaces are cleaned in a UV-ozone chamber for 1 h and rinsed afterward with ethanol. They are subsequently submitted at room temperature to the following stepwise treatment: (i) dipped into a 10 mM aqueous solution of sodium sulfonate 3-mercapto-propane (Sigma) for 4 to 6 h to become negatively charged; (ii) dipped into a 0.01% polylysine aqueous solution (Sigma) overnight to become positively charged. The high molecular weight of polylysine (Mw ) 150 000-200 000 Da) promotes membrane adhesion;14 (iii) thoroughly rinsed with Milli-Q (Millipore) water before use. The roughness of the prepared surfaces is about 0.3 nm, as measured by AFM in contact mode, which means that polylysine smoothes the surface. For membrane labeling, we used either a negatively charged fluorescent lipid, (β-BODIPY FL C5-HPA, Molecular Probes) or a neutral fluorescent lipid (see Supporting Information; Figure 1S).15 The fluorescent probes are incorporated in the vesicle membrane with a concentration of 1% mol/mol. Vesicle Observation. Our experimental setup allows a simultaneous observation in phase contrast and in EWIF microscopy (see Supporting Information; Figure 2S).12 A 10 mW Argon laser beam, (λ ) 488 nm) is shined on a silica prism in order to get total reflection on the observation cell surface. A system of two rotating mirrors allows us to change the incident angle θ of the laser beam on this surface. We used a Nikon 20/0.4 phase contrast objective, with a high numerical aperture and a large working distance, to observe the vesicles falling onto the surface. The high pass filter allows us to select only the fluorescent light in the video camera. When a labeled water-soluble species is added to the external pool of the vesicles, our setup provides the profile of spreading vesicles, the distance between the vesicles and the surface, and the bilayer permeability toward the dye. In addition, the same setup can be used to investigate the spatial distribution of lipids in the vesicle bilayer when labeled lipids are used. Determination of Vesicle Profiles. The intensity I(z) of the induced evanescent wave in the aqueous fluorescent solution reads I(z) ) kIocoe-z/Λ (see Figure 1), where co is the dye concentration, k is a constant related to the photophysical properties of the dye and the system geometry, Io is the incident light intensity and where the depth of penetration Λ is given by:

Λ)

λo 4π

1

xn21 sin2 θ1 - n22

(1)

θ1 is the angle of incidence of the laser beam with the surface, n1 and n2 are respectively the refractive indices of the prism and of the cell content, and λo is the wavelength of light in a vacuum. The continuity of the index of refraction between the prism and the cell is ensured by an interlayer of silicone oil. Assuming that (13) Angelova, M. I. Mol. Cryst. Liq. Cryst. 1987, 152, 89. (14) Huang, W. M. Histochemistry 1983, 77, 275. (15) Gosse, C.; Jullien, L. unpublished data.

Figure 1. Schematic representation of a vesicle adhering on a flat surface. the dye concentration is zero within the vesicle and uniform outside the vesicle, the intensity of fluorescence If(r) in the field of observation is:

∫ ce

If(r) ) kIo

∞

0

-z/Λ

o

dz

(2)

The origin is fixed as the contact point of the vesicle on the surface. We define an optical contrast C(r) along a radial line crossing the vesicle image by:

C(r) )

If(r) - If(0)

(3)

If(R) - If(0)

where R is the radius of the vesicle. For a spherical cap, the expected contrast is a function of the depth of penetration Λ, the vesicle radius R, and the radius of the contact area L (see Appendix A). R and L are respectively obtained from phase contrast and EWIF microscopy. Hence, for a spherical cap, Λ can be determined by adjusting the calculated contrast with the experimental data as explained in ref 12. Reciprocally, if Λ is known, it is possible to determine the vesicle profile near the surface from an observation at Λ e R. In addition, for an observation at a high depth of penetration (Λ g R), the whole vesicle profile can also be reconstructed upon assuming the vesicle to be symmetric with respect to the plane z ) (R2 - L2)1/2 (see Appendix A). Determination of the Distance between Vesicle and Substrate. EWIF microscopy can be used to evaluate the vesiclesurface distance h with a vertical resolution of a tenth of a nanometer.16 h(t) is estimated from the fluorescence intensity If(r ) 0,t) at the darkest point of the vesicle image with respect to the fluorescence intensity Ifmax outside of the vesicle. When R g Λ . h, one has:

(

h(t) ) -Λ ln 1 -

)

If(0,t) Imax f

(4)

In fact, h must be corrected from some residual light intensity Ifres , Ifmax:

(

h(t) ) -Λ ln 1 -

)

If(0,t) - Ires f Imax f

(5)

The incremental distance ∆h(t) ) h(t) - h(0) is given by:

(

∆h(t) ) -Λ ln

Imax + Ires f f - If(0,t)

)

Imax + Ires f f - If(0,0)

(6)

Qualitative Evaluation of the Bilayer Permeability. In the presence of a fluorescent dye added in the external vesicular pool, the difference of contrast between the inner (sucrose solution) and the outer (glucose solution) media of the vesicle is not simply related to the difference of dye concentration between the two sides of the membrane. Indeed, the depth of penetration (16) Olveczky, B. P.; Perriasamy, N.; Sverkmann, A. S. Biophys. J. 1997, 73, 2836.

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Figure 2. EPC vesicle spreading on a polylysine-coated surface as observed in phase contrast microscopy (before: (a) and (a′); and after: (e) and (e′) spreading) and in EWIF microscopy for two depths of penetration Λ at different times. Λ ≈ 800 nm: (b) 0.04 s; (c) 0.12 s; (d) 184 s; Λ ≈ 30 µm: (b′) 0 s; (c′) 0.24 s; (d′) 3 s. Bar ) 10 µm. strongly depends on the refractive index of the aqueous medium (see eq 1). In fact, we can distinguish two regimes since the inner and the outer vesicular compartments have different refractive indices. If the incident angle θ of the laser beam is such that sin-1(nglucose/nsucrose) e sin-1(nsucrose/nprism) (with nglucose (50 mM) ) 1.3355; nsucrose (50 mM) ) 1.3365), there is refraction inside the vesicle and evanescence outside. When θ g sin-1(nsucrose/nprism), evanescence appears everywhere, but the density of exciting energy is higher in the sucrose solution. This situation can become even more complex if the sucrose or the glucose can permeate through the bilayer. In such a case, the concentration and the refractive index of the vesicular content are not known, which does not allow an estimate of the contrast C(r) (see eq 1). Thus, EWIF microscopy remains qualitative to analyze the dye penetration inside the vesicle. Investigation of the Spatial Distribution of Lipids in the Vesicle Bilayer. We have performed experiments where the vesicle bilayer is labeled with a fluorescent lipid in the absence of any water-soluble fluorescent dye. The observations are made with a large depth of penetration Λ to avoid the difficulties associated with the presence of the gold layer. The latter could significantly affect the fluorescence signal of probes located at less than 500 nm from the surface.17 Adsorbed labeled vesicles are imaged as fluorescent rings (see Figure 7a-c). If I(t) designates the fluorescent intensity of the ring at time t and Io is the residual intensity of the outer vesicular pool, a contrast C(t) can be defined as:

C(t) )

I(t) - Io I(t)0) - Io

(7)

In principle, a calculation should be done for determining the vesicular contour as already was done when the external vesicle compartment was labeled. In the present case, the existence of some residual intensity limits the extent of data analysis.

Results General Features of the Dynamics of Spreading of EPC Giant Vesicles on Positively Charged Surfaces. We are interested in the adhesion dynamics, that is, in all the processes between the time when the vesicle reaches the surface and the time when the vesicle adopts its final equilibrium shape. Three regimes are experimentally observed. The first one (regime I) will be examined from a qualitative point of view. It is determined by the time τ1 elapsed between the instant when the vesicle reaches the bottom of the cell (no more vertical translation toward the surface) and the instant when the vesicle starts to spread on the surface. τ1 varies from a tenth of a second to one minute depending on the experimental conditions (17) Hellen, E. H.; Axelrod, D. J. Opt. Soc. Am. 1987, B.4(3), 337.

Figure 3. Evolution of the normalized radius of the contact area L/Ro ([), the vesicle-surface relative distance ∆h (b) and the normalized vesicle volume V/Vo (Vo ) 4/3πR3o ) as a function of time for the vesicle of Figure 2a-e. The normalized volume is extracted either from the radius of the contact area assuming a spherical cap (2) or directly measured from the profile reconstruction by integration (0). The continuous line (s) is the best fit of the experimental data points using eq 8. The dotted lines are guidelines for eyes.

described in the next paragraph. The two subsequent regimes (regimes II and III) are evidenced by studying the contact area as a function of time in EWIF microscopy at a low depth of penetration (Figure 2a-e). The curve L(t) of the radius of the contact area is represented in Figure 3 for the vesicle of Figure 2a-e and can be fitted by a biexponential law:

L(t) ) Lf - L2e-t/τ2 - L3e-t/τ3

(8)

with L2 + L3 ) Lf. Lf is the equilibrium radius of the contact area and is measured experimentally. τ2 and τ3 are two characteristic times that correspond to two distinct regimes of the adhesion. Typically, τ2 ≈ 0.05 s and τ3 ≈ 0.5 to 5 s under the investigated conditions. The apparent radius Ro of the vesicle, obtained by phase contrast microscopy, is fairly constant during the whole adhesion process. Figure 3 also displays the relative distance ∆h(t) from the vesicle to the surface as a function of time. It can be observed that the vesicle approaches the surface by about 200 nm during the second regime of the spreading process. Then, the vesicle reaches an equilibrium distance heq, which shall be discussed later on. The experimental contrasts C(r) (as defined in eq 3) of the vesicle of Figure 2a-e are displayed in Figure 4a.

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Figure 4. Analysis of data obtained at low depth of penetration (Λ ≈ 800 nm): (a) Evolution of the image contrast of the vesicle of Figure 2a-e at different spreading times: 0.04 s ([); 0.08 s (9); 0.12 s (b); 184 s (2); (b) Reconstruction of the vesicle profile.

Figure 5. Analysis of data obtained at large depth of penetration (Λ ≈ 30 µm): (a) Evolution of the image contrast of the EPC vesicle displayed in Figure 2a′-e′ at different times: 0 s ([); 0.24 s (9); 3.0 s (b); (b) Reconstruction of the entire vesicle profile.

They are satisfactorily fitted as spherical caps (see Appendix A). All the fits give a unique value of Λ ) 800 nm. Thus, the vesicle remains spherical during the whole spreading process. The profile of the vesicle of Figure 2a-e is reconstructed in Figure 4b (see Appendix A) for z < 2-3 Λ. The same series of experiments is reproduced at a large depth of penetration (Λ ≈ R) (see Figure 2a′-e′ and 5a). Again, the fit of the experimental contrasts assuming a spherical cap allows the determination of Λ. Moreover, under the assumption that the vesicle is symmetric with respect to the equatorial plane, the vesicle profile can be entirely reconstructed (Appendix A), as displayed in Figure 5b. The fit is satisfactory not only in the equatorial plane but for the whole set of experimental points. This again reveals the spherical nature of the vesicle during the entire process of spreading. Eventually we notice that the contrast between the internal and external pool of the vesicles remains constant in phase contrast or in EWIF microscopy during the experiments on the polylysine-coated surface (see Supporting Information; Figure 3S); this indicates that no solute transport occurs through vesicle bilayers. Some Parameters Affecting the Dynamics of Vesicle Spreading. The different features of the spreading have been reviewed as a function of several physical parameters to determine possible mechanisms. The effects of vesicle size and medium viscosity have been investigated. Electric swelling leads to a large polydispersity of vesicle radii ranging between 10 and 100 µm. The viscosity η of the inner and outer medium of vesicles has been increased by a factor 4.2, using sucrose/ glycerol 1:1 and glucose/glycerol 1:1 (w/w) solutions. A study on a dozen vesicles shows that τ1 increases with η

and decreases with vesicle size. τ2 and τ3 are proportional to η and to the vesicle radius Ro before adhesion (Figure 6a).18 L2, L3, and Lf are proportional to Ro, and independent from η (Figure 6b). No clear effect of cholesterol is observed on τ1 (we use vesicles with a EPC/cholesterol 1:1 membrane composition). In contrast, it is clearly observed that the radii L2 and Lf are lowered as well as the two characteristic times τ2 and τ3 (Table 1). Vesicles swollen in a 50 mM sucrose solution have been submitted to an osmotic stress by dilution in a 80 mM glucose solution. The water loss needed to restore the osmotic balance increases their excess area during the sedimentation of the vesicles toward the surface. Under such conditions, τ1 is slightly shorter (tenth of seconds), in contrast to τ2 and τ3 which respectively increase by factors of 2.4 and 21. Contact areas at the end of the last two regimes also increase (Table 1). The significance of the interaction strength between the bilayer and the surface has been also investigated. In fact, the tiny amount of some negatively charged lipids arising from EPC hydrolysis is responsible for the bilayer adhesion. Increasing the charge density of the bilayer by adding negatively charged lipids such as sodium dicetyl phosphate leads to membrane rupture during the spreading process. On the other hand, replacing polylysine by the statistical copolymer poly(lysine/alanine) 1:1 decreases the adhesion energy. Whereas no significant difference is observed for τ1, τ2, and τ3 are increased by factors of 5 and (18) It must be pointed out that the characteristic time τ2 is very short with respect to the acquisition time of the camera. The resulting inaccuracy of τ2 also affects L2 and τ3.


Figure 6. Evolution of (a) τ2 ([) and τ3 (b) and of (b) L2 (9), L3 (2), and Lf ([) (see eq 8) as a function of the vesicle radius R0 before adhesion. Empty marks: η ) ηo ) 1.3344 cP; filled marks: η ) 4.2 ηo.

7 respectively (Table 1). The contact radii L2 and L3 are not modified. Evidence for a Lipid Flow during Membrane Adhesion. In view of the strong significance of the negatively charged lipids for altering the spreading behavior, we have been concerned with the spatial distribution of lipids during the adhesion process. EPC vesicles containing either a negatively charged or a neutral fluorescent lipid were swollen in the absence of any soluble fluorescent dye. Figure 7a-c represents the fluorescence of a vesicle labeled with a negative chromophore as a function of time. In both cases (charged or neutral), the contrast C(t) defined by eq 7 is measured as a function of time as shown in Figure 7d. The contrast of the vesicles labeled with the negatively charged fluorescent dye drops by 50% or 25% in a characteristic time τ comparable to τ2 ≈ 0.05 s. Conversely, the contrast related to the vesicles labeled with the neutral fluorescent dye decreases smoothly as a function of time. The experimental points can be fitted by a slowly decreasing exponential function (characteristic time ≈ 25 s) revealing the usual photobleaching. These results clearly show the existence of a massive flow of negatively charged lipids toward the positively charged surface, where they are instantly quenched either by a transfer of electronic excitation to surface plasmons or heat in the gold layer.17 The 1/2 and 1/4 factors suggest that only the negatively charged lipids of the outer leaflet of the membrane are affected at the experimental time scale. Then the 1/2 and 1/4 factors respectively should correspond to uni- and bilamellar vesicles.

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Demonstration of the Active Role of Calcein in the Vesicle-Surface Interaction. Reflection interference contrast microscopy (RICM)10 has also been used as a complementary tool to analyze vesicle spreading. Surprisingly, whereas vesicles exhibit a strong interaction when observed with EWIF microscopy, only a very weak adhesion is observed by RICM for the same experimental conditions except for the illumination (in the latter case, calcein is not excited since the laser wavelength is set on 630 nm where calcein does not absorb). To restore strong adhesion during RICM experiment, it is necessary to add hydrochloric acid to decrease the pH to 3-4. These puzzling observations lead us to consider that the phenolic calcein could be active for promoting the interaction between the bilayer and polylysine covered surfaces. In fact, it is wellknown that many phenols become more acidic under illumination.19 Since the charge density of the polylysine adsorbed layer increases when pH drops, RICM and EWIF observations should then be reconciled. To test our hypothesis, two series of experiments have been performed. We have first checked that the spreading only starts in EWIF microscopy when the vesicle is directly located in the trajectory of the laser beam where the excitation energy is the largest. This points to the direct involvement of illumination at the bilayer-surface interaction.20 In addition, the EWIF observations were repeated using a nonphenolic fluorescent label (BODIPY 492/515 disulfonate, Molecular Probes), which does not induce any pH jump under laser excitation. With these experimental conditions, EPC vesicles spread faster (in a fraction of a second) on the polylysine surface than when calcein is used. In addition, they either burst or become permeable to the fluorescent dye suggesting that adhesion is then stronger than with calcein. These features are explained by taking into account the competition between the fluorescent dye and the vesicle toward the interaction with the surface. Indeed, with 6 negative charges compared to 2 for the BODIPY derivative, calcein is expected to adsorb more strongly on the positively charged polylysine surface. As a conclusion, calcein does more than passively reveal the spreading in our system. The local acidity generated in the photoactivated state generates competition for adsorption; and this is required for observing the adhesion process reported in this paper. Discussion Our results point out that three distinct regimes can describe vesicle adhesion to a surface: (i) the first regime (characteristic time τ1 from a tenth of a second to one minute) corresponds to an approach regime of the vesicle. This regime ends when the membrane touches the surface; (ii) the second regime, occurring in a time τ2 of the order of 0.05 s, is characterized by a rapid increase of the contact area. In addition, the negatively charged lipids rush toward the positively charged surface. The vesicle goes on approaching the surface. At the end of this second step, the weaker amplitude of thermal fluctuations of the vesicle underlines that the bilayer is under tension; (iii) the third regime, of the order of one second, is characterized by a slow increase of the contact area taking place in a time τ3. The vesicle reaches an equilibrium state at the end of this third step. These three regimes are now successively reviewed and discussed. (19) Pines, E.; Huppert, D. J. Phys. Chem. 1983, 87, 4471. (20) It must be added that vesicle adhesion through the photoacidification process involving calcein is not reversible. Switching off the laser does not decrease the vesicle adhesion: vesicles do keep the same profile, since they lose water during the third regime of adhesion (vide infra).

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Table 1. Influence of Different Parameters Affecting the Spreading Behavior (Characteristic Times τ2 and τ3 and Prefactors L2 and Lf; See Eq 8) of Giant Vesicles on Surfaces conditions

L2/Ro ((0.1)

Lf/Ro ((0.1)

τ2/Ro ((0.1 ms/µm)

τ3/Ro ((1 ms/µm)

EPC/polylysine EPC:cholesterol 1:1/polylysine deflated EPC/polylysine EPC/poly(lysine:alanine 1:1)

0.7 0.55 0.85 0.7

0.9 0.7 1.2 0.8

1.6 1.1 3.9 7.8

11 5 230 54

Figure 8. Spreading/permeation mechanism of an EPC vesicle on a smooth surface exerting a strongly attractive interaction toward the lipid bilayer as a function of time (from left to right: Regime I: approach step limited by the drainage of the water film between vesicle and substrate; Regime II: spreading at constant lipid surface but increased projected area and constant volume, collective flow of charged lipids toward the surface, no permeation; Regime III: pore formation, spreading at constant lipid surface, the internal volume drops.

(kT)2

πL

2

3

2κcξ⊥

Figure 7. Vesicle labeled by a fluorescent negatively charged dye (1% mol/mol) during its spreading on a polylysine-coated surface at different times: (a) t ) 0-; (b) t ) 0+; (c) t ) 3 s; (d) Evolution of the contrast C(t) (eq 7) as a function of time for unilamellar vesicles labeled by a negatively charged fluorescent dye (2), for bilamellar vesicles labeled by a negatively charged fluorescent dye (9), for vesicles labeled by a neutral fluorescent dye (b). In the latter case, 1% mol/mol dicetyl phosphate-EPC vesicles were used to get a comparable surface charge density with the vesicles containing the negative fluorescent dye.

Regime I: The Vesicle Approaches the Surface. The vesicle sediments under the effect of gravity until the repulsive Helfrich force21 between its membrane and the surface becomes relevant. Thus, the time τ1 could correspond to the drainage of a water film under the vesicle, until the vesicle reaches a distance to the surface comparable to the amplitude ξ⊥ of the thermal fluctuations of the membrane (Figure 8). The radius L of the membrane disk sensitive to the water film drainage is determined by the equilibrium between the Helfrich repulsive force and the weight of the vesicle: (21) Helfrich, W. Z. Naturforsch., A 1978, 33, 305.

4 ) ∆Fg πRo3 3

(

)

(9)

where kT is the thermal energy, κc the rigidity constant,22 ∆F the difference of density between the inner and the outer medium of the vesicle, and g the gravitational constant. The electrostatic attractive force can be neglected since ξ⊥ ≈ 200 nm (experimental evaluation by optical microscopy) which is much larger than the Debye length κ-1 estimated at 10 nm (see ref 35). Taking κc (EPC) ) 10 kT,8 ξ⊥ ) 200 nm, Ro ) 20 µm, ∆F ) Fsucrose (50 mM) Fglucose (50 mM) ) 7 kg/m3, one obtains a reasonable order of magnitude for L: 5.4 µm i.e. L /Ro ≈ 0.25. The drainage of a liquid film between a disk of radius L and a rigid plane is ruled by Reynolds law:23

2 1 dh ) F h3 dt 3π T ηL

4

(10)

where FT is the resultant force of the Helfrich force and the weight. When h approaches ξ⊥, we can introduce a characteristic time τ1 from:

h ) ξ⊥ + (ho - ξ⊥)e-t/τ1 with

3 τ1 ) ηL 8

4

1 R3o ∆Fgξ2⊥

and (22) Helfrich, W. Z. Naturforsch., C 1973, 28, 693. (23) Reynolds, O. Philos. Trans. R. Soc. A 1886, 117, 157.

(11)


ho ) h(t ) 0)

Langmuir, Vol. 16, No. 17, 2000 6815

(12)

This characteristic time τ1 is in good agreement with experiments: (i) it is proportional to the medium viscosity η; (ii) it decreases when the thermal fluctuations of the membrane or ξ⊥ increase; (ii) it decreases with Ro. The role of the cholesterol in the bilayer is not obvious since both L and ξ⊥ depend on κc. With L ) 5.4 µm, Ro ) 20 µm and ξ⊥ ) 200 nm, τ1 is of the order of 30 s, which agrees with the experimental results. Therefore, τ1 seems to be the signature of Reynolds film drainage under the vesicle.24 Regime II: The Vesicle Spreads at Constant Volume. Several phenomena occur during the second regime of characteristic time τ2: (i) the vesicle adopts a spherical cap shape; (ii) the charged lipids of the outer leaflet of the membrane migrate toward the surface; (iii) the vesicle continues its approach toward the surface until it reaches an equilibrium distance heq determined by electrostatic forces. The first observation suggests that the vesicle spreads at constant volume and total surface area until the initial excess of surface area and hence the surface undulations of the membrane are pulled out. At the end of the first step, the vesicle is characterized by its apparent radius Ro, and its surface So ) 4πRo2R, where (R - 1) represents the excess of surface area of the vesicle. Then, simple geometrical considerations determine L/Ro, R/Ro and the percentage of excess surface area ∆S/So ) R - 1 of the vesicle as a function of the contact angle θ2 at the end of the second regime (Figures 1S and 4S: see Supporting Information). In particular, the experimental determination L2 of the radius of the contact area at the end of the second regime allows for the determination of the contact angle τ2 and the excess of surface of the membrane ∆S/So. The obtained values of the excess surface area reported in Table 2 are similar to the values determined by the micropipet aspiration technique.8 It can be noted that: (i) the excess of surface area of the EPC vesicles is small; this can be explained by the fact that the vesicles are studied just a few hours after swelling. Vesicles obtained by electroformation are more stressed than vesicles obtained by spontaneous swelling;25 (ii) the vesicles deflated after dilution in a more concentrated medium only exhibit an excess of surface area of 3.7%; (iii) the addition of cholesterol to the bilayer decreases the excess of surface area. This decrease of the surfaceto-volume ratio of vesicles containing cholesterol has already been observed with the micropipet aspiration technique8 and is explained by the increased cohesion of the membrane.26 The above geometric considerations do not account for the dynamic phenomena that rule the adhesion process during the second regime. The characteristic time τ2 is proportional to the viscosity η and to the radius Ro of the vesicles. A dimensional analysis gives:

τ2 ≈

ηRo Σ2

(13)

(where ∑2 is the membrane surface tension) but does not (24) The vesicle surface submitted to the film drainage is not exactly a flat disk. In fact, the fluctuating membrane can be described as the sum of independent elements (see, e.g., de Gennes, P.-G.; Taupin, C. J. Phys. Chem. 1982, 86, 2294; Prost, J.; Manneville, J.-B.; Bruisma, R. Eur. Phys. J. B 1998, 1, 465) whose characteristic lengths ξ⊥ and ξ| are related by: ξ| ) (κch/kT)1/2. For ξ⊥ = h, this gives ξ| ≈ 600 nm when ξ⊥ ≈ 200 nm. (25) Angelova, M. I.; Soleáu, S.; Me´leárd, P.; Faucon, J.-F.; Bothorel, P. Prog. Colloid Polym. Sci. 1992, 89, 127. (26) Needham, D.; Nunn, R. S. Biophys. J. 1990, 58, 997.

Table 2. Influence of Different Parameters Affecting the Initial Excess of Surface Area and the Final Contact Angle θ3 conditions

θ3 ((5°)

∆S/S0 ((0.1%)

EPC/polylysine EPC:cholesterol 1:1/polylysine deflated EPC/polylysine

40 35 55

1.4 0.6 3.7

provide the value of Σ2. A first approach to determine the surface tension Σ2 at the end of the second regime consists of adapting the Tanner model27 of the spreading of a liquid droplet on a surface. Though this model (Appendix B) is an oversimplification in our case, it gives values for the adhesion energy W and the surface tension Σ2 that can be compared with the following estimates. An estimation for Σ2 can be independently obtained by evaluating the vesicle and the surface charge densities. It was experimentally observed that all the negatively charged lipids located in the outer leaflet of the membrane rush toward the surface during τ2. Under these conditions, we consider, ignoring the size of the lipids and screening effects, that the charge density σ2(t ) τ2) in the contact area is:

σ2(t)τ2) ) σo2(t)0)

4πR2o πL22

(14)

Since σ2 remains far smaller than the charge density σ1 of the polylysine surface,28 the adhesion energy W corresponding to the work of the electrostatic force to bring the membrane from h ) ∞ to the equilibrium distance heq, is equal to:

W)

[σ2(t)τ2)]2 orκc

(15)

with o the vacuum permittivity and r ) 80 the dielectric constant of water at room temperature. We obtain W ) 1.4 × 10-3 mJ/m2 and Σ2 ) 5.4 × 10-3 mN/m from the application of the Young-Dupre´ law:

W ) Σ2(1 - cos θ2)

(16)

Our experimental results support the hypothesis that the vesicle spreading during the second regime is limited by the hydrodynamic dissipation in the liquid edge of the contact line (Table 1). Thus (i) the larger the vesicle, the bigger the volume of water to evacuate and the longest τ2; (ii) as the solution flow is all the slower as the medium is viscous, it is expected that τ2 increases with the medium viscosity; (iii) by increasing the curvature modulus of the bilayer,25 cholesterol reduces the thermal fluctuations of the membrane. Hence the water flow below the vesicle occurs faster and τ2 is then reduced; (iv) on the contrary, deflating the vesicle increases the thermal fluctuations that slow the water flow and then increases τ2; (v) when the charge density of the positively charged surface is decreased, the electrostatic interaction is weaker and τ2 increases. With the present experimental setup, the absolute determination of the equilibrium distance heq between (27) de Gennes P.-G. C. R. Acad. Sc. (Paris) 1984, 298, 111. (28) EPC contains traces of negatively charged lipids. The amount was evaluated to about 0.1% or 2.3 10-4 C/m2 for an area per polar head equal to 70 Å2 (Pincet, F.; Cribier, S.; Perez, E., personal communication). In fact, such a value is expected to be strongly sample dependent. In contrast, considering that polylysine lies parallel to the surface in an extended conformation (see, e.g., Jordan, C. E.; Frey, B. L, Kornguth, S.; Corn, R. Langmuir 1994, 10, 3642) and neglecting screening effects, one obtains the overestimate 0.08 < σ1(C/m2) < 0.8.

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Bernard et al.

the vesicle and the surface is difficult to establish due to the presence of residual light intensity. Consequently, another approach was used to derive a crude order of magnitude of heq. When no rearrangement of the lipids in the membrane takes place in the adhesion disk and when the charge density of the surface σ1 is larger than the one of the vesicle, σ2, heq has been theoretically evaluated,33 as:

||

heq ) κ-1 ln

σ1 σ2

(19)

The system becomes unstable when σ* < σ2 < σ1,34 and the lipid demixtion in the membrane leads to the formation of blisters (about a hundred nanometers thick) within strongly adhered patches. Estimating κ-1 ≈ 4-10 nm,35 we obtain σ* ) 0.7 × 10-5-1.75 × 10-5 C/m2. This suggests that our system is unstable. Indeed the presence of blisters has been observed on the adhesion disk with RICM but not with EWIF microscopy. It is possible that EWIF microscopy is not sensitive to the presence of blisters if any exist under our experimental conditions. Anyhow, the formation of blisters occurs in a time scale (about one minute according to ref 33) much longer than τ2. Using eq 19, we can estimate heq ≈ 20-80 nm.36 Nevertheless, this crude estimate gives a vesicle-substrate separation at the beginning of the second step equal to 220-280 nm, in good agreement with the ξ⊥ value. How can we account for the rapid migration of the negatively charged fluorescence probe of the outer membrane leaflet toward the surface if the electrostatic interaction range is at most 1 µm in pure water?29 We assume that this observation results from the succession (29) Israelachvili, J. Intermolecular and Surface Forces. Academic Press: London, 1985. (30) It is important to determine if dissipation occurs in the membrane (viscosity ηs) or in the liquid adjacent to the bilayer (viscosity η). If dissipation is more important in the aqueous medium, then the friction force is Ffriction/water ≈ ηVR where V is the tangential speed of the charged lipids and R is the vesicle radius. If dissipation is stronger in the bilayer, then the friction force is Ffriction/membrane ≈ ηsV. The interplay between these two forces introduces a characteristic length λ ) ηs/η. λ is of the order of 100 nm to 1 µm (taking η ) 10-3 Pa s and ηs ) 10-8-10-7 Pa m s as estimated by Bloom, M.; Evans, E.; Mouritsen, O. Q. Rev. Biophys. 1991, 24 (3), 293), that is far smaller than the radius R of the vesicle. Thus, the dissipation occurs in the bulk aqueous medium. (31) Vaz, W.; Clegg, R.; Hallmann. Biochem. 1985, 24, 781. (32) Farge, E.; Devaux, P. Biophys. J. 1992, 61, 347. (33) Nardi, J.; Bruinsma, R.; Sackmann, E. Phys. Rev. E. 1998, 58(5), 6340. (34) σ* is a critical charge density equal to σ* ) κkBT/e, with ) or, κ-1 the Debye length, and e the elementary charge (see ref 32). (35) The κ-1 value is difficult to establish: calcein is a multivalent salt. Moreover, many residual ions from the surface increase the ionic force to about 1 to 5 mM. In the present case, the monovalent salts determine the final value of κ-1 that was finally evaluated to 4 to 10 nm. (36) This crude estimate is larger than some given in the literature (see, e.g., Fromherz, P.; Kiessling, V.; Kottig, K.; Zeck, G. Appl. Phys. A 1999, 69, 571 who find an equilibrium distance of 1.1 nm between DOPC vesicles and a polylysine surface). Nevertheless, our working conditions are fairly different: (i) polylysine MW is 150 000-300 000 g/mol instead of 10 000 for Fromherz. In a good solvent, such long chains lead to radii of gyration Rg equal to 21 to 31 nm, which could increase the vesicle-substrate distance if polylysine does not lie flat on the surface; (ii) in our system, polylysine is adsorbed on a higher negatively charged surface (monolayer of sulfonate-terminated thiols instead of a silicon wafer for Fromherz). This is expected to strongly decrease the residual positive surface charge density of the polylysine layer; (iii) in the present system, the Debye length κ-1 is roughly equal to 10 nm contrary to 1.4 nm for Fromherz; (iv) eventually, an experimental observation supports that vesicle/polylysine interaction is much weaker in our case. Whereas good rinsing was crucial to avoid vesicles bursting on the surface in the Fromherz work, we never observed such a phenomenon in our system. In fact, in absence of calcein illumination, it was necessary to strongly decrease the pH to induce vesicle adhesion as during the RICM studies.

of two phenomena. First, negatively charged lipids located at a distance from the surface smaller than the Debye length are submitted to electrostatic attraction and therefore move toward the surface. This flow creates a gradient of charged lipids. The correspondingly induced gradient of interfacial tension of the membrane is directed toward the surface, to feed up this depletion in lipids (Marangoni effect) (Figure 8). In this steady-state regime, the constraint causing the collective flow of the charged lipids toward the surface is balanced by the viscous stress originating from the solvent shearing along the membrane. Thus, one has:

dV dΣ )η dz dy

(17)

with V ≈ R/τ2.30 This leads, after integration, to:

∆Σ =

ηR τ2

(18)

With R ) 20 µm, τ2 ) 5 × 10-2 s, and η ) 10-3 Pa s, we obtain ∆Σ ≈ 4 × 10-4 mN/m. The latter estimate is reasonable since it represents about 10% of the previously evaluated membrane tension at the end of the second regime. It must be pointed out that τ2 is very short compared to a characteristic time τo that would occur by a diffusive process: τo ≈ z2/4D where z is of the order of the vesicle radius and D is the lipid diffusion coefficient. We get τo ≈ 20-200 s, using D ≈ 10-8-10-7 cm2/s,31 and z ≈ R ≈ 20 µm. Finally, it is important to explain why only the negatively charged fluorescent lipids of the outer leaflet of the membrane are affected at the experimental time scale, as suggested by the 1/2 and 1/4 decrease factors of the fluorescence intensity. We propose two tentative explanations: (i) the vesicle can be considered as a conductor whose mobile charges are the charged lipids. Although any negatively charged species of the inner leaflet certainly migrate under the influence of interfacial tension, the surface concentration of the fluorescent probe located on the inner leaflet should remain homogeneous as there is no electrical field within the vesicle. Under these conditions, there should not be any concentration process of the charged lipids close to the substrate in the inner leaflet. In contrast, the negatively charged fluorescent lipids of the outer leaflet are attracted to the surface and quenched by transfer of electronic excitation into surface plasmons or heat in the gold layer; (ii) the presence of 1% mol/mol of negatively charged fluorescent lipid increases the charge density of the vesicle surface, in contrast to other experiences in the presence of calcein. This can lead to far smaller an equilibrium distance heq than that previously estimated (vide supra). If the quenching range is below 5-10 nm,17 it is then possible that selective quenching takes place only in the outer leaflet of the membrane. In addition, in the two cases, the shortness of τ2 forbids flip-flop processes from taking place at the relevant time scale for feeding the outer leaflet with fluorescent lipids from the inner one.32 Regime III: The Vesicle Leaks Out. At the end of the second regime, the vesicle membrane is under tension and keeps its spherical cap shape. The surface area can be considered as constant. Indeed it can only increase by 1 to 3% because of the stress, and only for tensions larger than 0.5 mN/m,8 i.e. for values much larger than our estimate. In fact, the vesicle volume must decrease during the third regime since vesicle spreading continues after completion of the second step. Under such conditions and using the same geometric approach as before, assuming


Langmuir, Vol. 16, No. 17, 2000 6817

surface conservation, the vesicle radius R, its volume V, and the contact angle θ are entirely determined as a function of the vesicle radius Ro before spreading, the radius of the contact area L, and the excess of surface area R.

R)

2 2 1 4Ro R - L 2 x4R2oR - 2L2

[

θ ) cos-1 V)

π 3x

4R2o R

(20)

]

4R2o R - 3L2 4R2o R

2

-L

(21)

(4R2o R + L2)(2R2o R - L2) (22)

2

- 2L

Figure 3 displays the variation of the volume of the vesicle as determined either from the reconstruction of the 3D profile (eq A-5 and eq A-6) or from the experimental L(t) using eq 22. The volume of the vesicle is nearly constant in the second regime and decreases by 7% during τ3. Two mechanisms have been considered to explain the decrease of vesicle volume. The leakage may occur either through the bilayer under tension or thanks to the formation of defects or pores. Both viewpoints are analyzed below. If water permeation occurs through the spherical cap, it is induced by the Laplace pressure. Assuming that the pressure is homogeneous and establishes instantaneously, the Laplace pressure is given by:

∆Π ) 2

x4Ro2R - 2L2W 2

L

(23)

where the adhesion energy W is given by the YoungDupre´ relation:

W ) Σ(1 - cos θ)

(24)

We assume that W remains constant, i.e., that an eventual demixtion of the charged lipids in the membrane is not considered. The flow of water Φ crossing the membrane is defined as:

1 dV Φ)Ac dt

(25)

where the volume V and the surface through which water leaks Ac, are a function of Ro, R, and L. Φ is related to the Laplace pressure ∆Π by:

Φ ) p∆Π

(26)

if we introduce the coefficient of hydraulic permeability p. Expressing θ and Σ as a function of W, Ro, and R, the expression of p(t) becomes:

p(t) )

1 dL L5 2 2 2 2 W dt 2(4Ro R - L )(4Ro R - 2L )

(27)

Both terms of eq 27 can be multiplied by RT/vwater, vwater being the molar volume of water, to obtain a value of p in ms-1. Equation 27 demonstrates that the permeability coefficient decreases with time. In contrast it reaches

values of the order of 104 cm/s whereas typical permeability coefficients measured for an EPC bilayer are around 10-4 cm/s!37 We can also suppose that the leak occurs along the contact line. In the latter case, the tension is induced by curvature and can be estimated by:

Σ∼

κc

(28)

Rc2

where 1/Rc ) (2W/κc)1/2 is the curvature at the contact point.5 Taking W ) 1.4 × 10-3 mJ/m2 to estimate an order of magnitude, one obtains values smaller or equal to 120 nm for Rc and local tensions larger or equal to 3 × 10-3 mN/m. The value for W is similar to the estimation given by eq 15. The induced dilation can be written as:

A - Ao Σ2 ) Ao µ

(29)

It is equal to 0.005% by taking 140 mJ/m2 for the elastic compressibility modulus µ of EPC.38 Such a value of the bilayer dilation is by far too low to induce the observed permeation. Hence, wherever the leak takes place through the vesicle, it is not possible to account for the experimental results by assuming the bilayer to be homogeneous. The pore formation in the bilayer has been then considered. We use the model of Taupin et al. that describes a circular hole of radius r in the bilayer.39 The pore energy Ep(r) can be written as:

Ep(r) ) γ2πr - Σπr2

(30)

where Σπr2 is the interfacial energy and γ2πr is the line energy. In the case of stable pores, the corresponding increase of permeability is given by:39

( )

p - po 3 kTΣ ∼ po π γ2

2

(31)

The relative increase of permeability requires the evaluation of γ. A typical value for EPC is 10-11 N.39 In fact, the migration of the negatively charged species originating from EPC degradation is expected to lead to their clusterization on the vesicle surface contact line. Indeed it is known that polyelectrolyte adsorption on membrane surfaces is responsible for a lipid demixtion in the membrane.40 In view of their possible detergent action or the local heterogeneity leading to some mechanical fragility, the line energy should be lower in the present case than for EPC. In fact, a series of complementary experiments (not published) have shown that the adhesion of charged dextrans on oppositely charged giant vesicles creates membrane permeability. Since W is an increasing function of the concentration of the negatively charged lipids, eq 30 shows that the pore energy Ep is a decreasing function of the concentration of anionic lipids. Thus, the mechanism responsible for the spreading of the vesicle during the third regime could be the following. After the second regime of the spreading, the anionic lipids reached (37) Boroske, E.; Elwenspoek, M.; Helfrich, W. Biophys. J. 1981, 34, 95. (38) Faucon, J.-F.; Mitov, M.; Me´leárd, P.; Bivas, I.; Bothorel, P. J. Phys. France. 1989, 50, 2389. (39) Taupin, C.; Dvolaitzky, M.; Sauterey, C. Biochemistry. 1975, 14(21), 4768. (40) Crowell, K. J.; MacDonald, P. M. J. Phys. Chem. B 1997, 101, 1105.

6818


Bernard et al.

the substrate surface41 and the membrane tension is large. Pore formation does not require much energy and water starts to leak out of the vesicle. A priori, in the absence of volume constraint and when adhesion energy dominates over curvature energy (that is W . κc/Ro2, which is the case here), the final equilibrium shape of the vesicle on the surface is a pancake profile.7 This shape was never observed during the present series of experiments. In fact, as long as the vesicle is spreading, the activation energy for pore formation increases due to the dilution of charged lipids either on the contact line or area. Consequently, γ and W are expected to respectively increase and decrease as a function of time. Eventually when Ep . kT, the permeation process stops and equilibrium is reached. A similar approach accounts for the permeation as the consequence of defects in the membrane. As the vesicle spreads and leaks out, the membrane tension and the consequent density of defects decrease, which eventually ends the leakage process. The formation of pores is supported by the experimental results. Pores can be considered as pipes with a length equal to the membrane thickness l and a radius r. A Poiseuille flow through such a pore leads to a characteristic time τ per mass unit:42

membranesare kinetically controlled by the density and the mobility of the charged lipids inside the membrane. Although using a very simple membrane model, the present investigation should increase the understanding of adhesion processes of biological membranes that always involve electrostatic interactions. Acknowledgment. This research has been supported by L’Oreál. We thank Dr. H. Hervet for his help in setting the EWIF microscope, Dr. V. Ponsinet for her help in AFM measurements, S. Palacin (CEA) who allowed the preparation of gold surfaces, and J.-M. Frigerio for discussions about surface states of gold layers. Finally, we thank Pr. P.-G. de Gennes for fruitful discussions. Appendices Appendix A. In the general case, the intensity If(r), r being the radial distance from the projection of the center of the vesicle of Figure 1, reads: ∞ -z/Λ e dz for r e L, ∫z′(r)

If(r) ) kIoco I(r) ) kIoco[

(A-1)

∞ e-z/Λdz] for L e r e R ∫0z′(r)e-z/Λdz + ∫z′′(r)

(A-2)

ηlR τ≈ FΣr4

(32)

where η and F are the viscosity and the density of the sucrose solution, and Σ is the membrane tension. Our experimental results agree with this expression (Table 1). τ3 is proportional to the initial radius Ro of the vesicle and to the viscosity η. The characteristic time τ3 is at least 10 times longer for a deflated vesicle. Since the contact area is larger at the end than at the beginning of the second regime, the local concentration in charged lipids is expected to be smaller. Thus, the pore formation should be less favorable leading to an increase of the permeation time τ3. The presence of cholesterol increases the cohesion of the bilayer and decreases the density of anionic lipids in the membrane. One thus expects both an increase of the line tension and a decrease of the membrane tension, therefore a decrease of the permeation time. This is consistent with our experiments. τ3 is smaller and the vesicle volume variation is only 2.5% in the presence of cholesterol. The third regime depends on the interaction force. When the charge density of the surface σ1 decreases, the equilibrium distance heq ) κ-1 ln(σ1/σ2) increases. Therefore, the adhesion energy and the membrane tension should be lower at the end of the second regime and should lead to a slower water permeation, which explains the higher value of τ3. Conclusion This study shows that EWIF microscopy is a useful tool for analyzing and understanding the dynamics of vesicle adhesion on surfaces. It demonstrates that vesicles adopt a spherical shape when they spread on attractive substrates and that the dynamics of spreading can be described reasonably in a three-regime process. The first one is limited by the water flow below the vesicle when it approaches the surface. The otherssresorption of the excess surface area and water permeation through the (41) They might remain along the contact line during τ3, either because of the high local curvature or because of the slow diffusion of the anionic lipids towards the core of the contact zone. (42) Landau, L.; Lifchitz, E. Physique the´ orique. Me´ canique des fluides, 2nd ed.; Librairie du Globe: Moscow, 1989.

L is the radius of the contact area, co is the dye concentration, k is a constant, and Io is the intensity of excitation. For a spherical cap of radius R, the contrast C(r) defined in eq 3 reads:

C(r) )

e

(

)-e

xR2-x2

-b-

Λ

1 - e-a

xR2 - x2

1 - 2e-b sinh

1 - e-a 1 - e-a

C(r) )

-a

,reL

(A-3)

- e-a , L e r e R (A-4)

with

a)

xR2 - L2 Λ

+

xR2 - L2 R b) Λ Λ

For Λ , R, the signal contribution for z g

xR -r 2

2

xR2-L2 +

is negligible. Then:

If(r) ≈ 0 for r e L

∫0z′(r)e-z/Λdz for L e r e R

If(r) = kIoco

(A-5) (A-6)

which leads to:

C(r) ≈ 0 for r e L C(r) ≈

∫0v′e-z/Λdz for L e r e R

1 Λ

(A-7) (A-8)

We have made no assumptions on the vesicle profile z(r) in these expressions. Using the experimental contrast C(r) and the penetration length Λ, we can build z(r):

z ≈ 0 for r e L

(A-9)

y ≈ -Λ ln(1 - C(r)) for L e r e R

(A-10)

For Λ g R, one has:


Langmuir, Vol. 16, No. 17, 2000 6819

∞ e-z/Λdz for r e L ∫z′′(r)

If(r) ) kIoco Iexp(r) ) kIoco[

(A-11)

∫0z′e-z/Λdz + ∫z′′∞e-z/Λdz] for L e r e R

(A-12)

If we consider that the equatorial plane y ) (R2 - L2)1/2 is a symmetry plane for L e r e R, one can obtain the profile z(r) of the adsorbed vesicle from: -a -a y (x) ) -Λ ln e + C (x)(1 - e ) xeL xeL

[

]

(A-13)

[

1 ) xR2 - L2 - Λ arcsin h eb 1 2 xgL,y e xR2-L2 e-a - C (x)(1 - e-a) (A-14) xgL y(x)

(

] 1 y(x) ) xR - L + Λ arcsin h e 1 [ 2 ( xgL,ygxR -L e - C (x)(1 - e ) (A-15) ] xgL 2

2

2

b

2

-a

-a

Appendix B. We have adapted the de Gennes model27 of wetting of a liquid droplet on a surface to the spreading of the vesicle. The vesicle is supposed to spread at constant volume and to keep a spherical cap shape during the adhesion process. Assuming that dissipation takes place in the wedge of liquid of contact angle θ and neglecting the curvature along the contact line, it is possible to write (in a steady-state regime) that the driving force for the vesicle spreading on the contact line is equal to the viscous force in the corner:

Σ(cos θ - cos θ2) )

dx ∫abη∂V ∂z

(B-1)

where θ2 is the external contact angle at the end of regime II, V is the velocity of the contact line along the r-direction, a is a lower cutoff length equal to a molecular length and b is an upper cutoff length that we will choose as the radius R of the vesicle. For small ∂V/∂z = V/z = V/x tanθ and eq B-1 transforms into:

tan θ(cos θ - cos θ2) ) l

V V*

(

)

R(θ2) )

(B-3)

Thus, for R ≈ Ro, d/dt (L/Ro) can be written as a function of L/Ro, L2/Ro and t/τ, with L ) Ro sinθ, L2 ) Ro sinθ2 and τ ) ηRo/Σ ) Ro/V*. L/Ro is plotted versus t/τ, in Figure 9a together with the experimental points obtained for the EPC vesicle of Figure 2a-e. When t is not too small,43 it is possible to determine a slope R depending on the contact angle at the end of the second step θ2, as: (43) L/Ro varies very slowly at short times since the viscous friction is very important when the contact angle θ is small. Experimentally, this phenomenon is scarcely observed since the radius of the contact area is badly defined and the angle θ at t ) 0 is not equal to zero because the vesicle is not stretched.

L2(θ2)/Ro τ2/τ

(B-5)

The characteristic time τ2 is then related to the membrane tension Σ2 by:

τ-1 2 )

(

R(θ2)

)

Σ2 L2(θ2)/Ro ηRo

(B-6)

Our numerical results suggest that the fit of χ(θ2) ) (R(θ2)/L2(θ2)/Ro) ) τ/τ2 leads to (Figure 9b):

(B-2)

with V* ) Σ/η and l ) ln(b/a) (l is a constant of the order of ln((50 × 10-6)/(50 × 10-9)) = 10. Using V ) d(R sinθ)/dt and the conservation of vesicle volume: Vo ) πR3(2/3 + cosθ - (cos3θ)/3), we get:

dR tan θ(cos θ - cos θ2) V* ) 3Vo cos θ l dt sin θ + πR3 sin3 θ

Figure 9. (a) Fit of L/Ro during the second regime of the adhesion process: (b) χ as a function of θ2 deduced from the fit of the experimental data of (a) (See Appendix B).

χ(θ2)

(

R(θ2)

)

L2(θ2)/Ro

V*(θ2)3.5 lRo

τ2-1 ) 30

(B-7)

This expression is to be compared with de Gennes formula in the case of a liquid droplet on a surface:27

τ2-1 )

V*(π - θ2)3 3lRe

with Re ) Ro sin(π - θ2) and (π - θ2) , 1. In the case of the liquid droplet, the dissipation stages occur inside the drop contrary to the case of the vesicle for which dissipation is stronger in the outside medium, when the contact angle is small. Our model has several limitations: (i) it does not take into account the viscous dissipation in the water film underneath the vesicle that is getting thinner during the second regime of the adhesion process; (ii) the vesicle curvature is neglected; (iii) membrane tension is considered as a constant whereas it is expected to increase with time; (iv) the thermal fluctuations of the membrane are

6820


not taken into account but an excess of membrane surface is allowed since only a condition on the vesicle volume is fixed. The experimental results may not be in agreement with eq B-7 because of point (iv). Indeed, τ2 and θ2 experimentally vary in the same direction. This emphasizes that membrane fluctuations that increase with the excess of surface area slow the vesicle spreading. Nevertheless despite the simplicity, this model leads to a better fit of the experimental data. In addition, it gives a value of the membrane tension Σ2 at the end of the second step.

Bernard et al.

Using:

Σ2 )

1 ηRo χ(θ2) τ2

(B-8)

we find that Σ2 is equal to 5.5 × 10-3 mN/m, which corresponds to a stretched membrane. This also gives an estimate of the adhesion energy using the Young-Dupre´ law (eq 16). Thus W = 1.4 × 10-3 mJ/m2, which is a characteristic value of a strong adhesion. LA991341X

Strong Adhesion of Giant Vesicles on Surfaces: Dynamics and

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