Direct Measurement of Polyethylene Glycol Induced Depletion

Buffalo, New York 14263, and Department of Chemical Engineering, SUNY at Buffalo, ..... (35) Marsh, D. CRC Handbook of Lipid Bilayers; CRC Press, Inc...
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Direct Measurement of Polyethylene Glycol Induced Depletion Attraction between Lipid Bilayers Tonya Kuhl,† Yuqing Guo,‡ James L. Alderfer,‡ Alan D. Berman,† Deborah Leckband,§ Jacob Israelachvili,† and Sek Wen Hui*,‡ Department of Chemical and Nuclear Engineering, University of California, Santa Barbara, Santa Barbara, California 93106, Department of Biophysics, Roswell Park Cancer Institute, Buffalo, New York 14263, and Department of Chemical Engineering, SUNY at Buffalo, Buffalo, New York 14260 Received September 27, 1995. In Final Form: February 20, 1996X Although polyethylene glycol (PEG) is widely used for aggregating or fusing cells, the forces responsible for these interactions have remained elusive. Through a variety of techniques including quasi-elastic light scattering, surface force measurements, and 31P-NMR, we have established that while PEG of molecular weight 8000-10000 is effective in causing the aggregation of vesicles, PEG of lower or higher molecular weight (1000 and 18 500, respectively) is ineffective. For the first time, direct force measurements between lipid bilayers in solutions of 8000-10000 molecular weight reveal the existence of an attractive osmotic force due to a polymer depleted layer near the bilayer surface. Lower molecular weight PEG does not have a large enough size (Flory radius, RF) to generate a significant depletion force, while higher molecular weight PEG adsorbs sufficiently on the bilayer surfaces to eliminate the depletion attraction and produces a repulsive steric barrier to aggregation. The measured forces can be quantitatively described in terms of current theories of colloidal and polymer interactions. These findings suggest that the differential osmotic pressure produced by the depletion layer is responsible for vesicle aggregation and that fusion is promoted when the depletion pressure is strong enough to locally destabilize two membranes by possibly thinning them at their point of closest approach. The results provide a physicochemical basis for using PEG of certain molecular weights as fusogens for cells, liposomes, and vesicles.

Introduction Among the many water soluble polymers, polyethylene glycol, H(OCH2CH2)nOH, is the most effective in inducing aggregation and fusion of vesicles and cells. Unlike other polyethers, PEG is water soluble at moderate temperatures in all proportions over a wide range of molecular weights (MWs). PEG’s unusual water solubility is believed to be the result of specific water structuring along the backbone,1 whereby the chains form helical coils which maximize hydrogen bonding while minimizing the number of exposed hydrophobic groups.2 Moreover, there are data suggesting that two water molecules are associated with each ethylene oxide monomer and that the diffusion coefficient of water near the chain is substantially lower than that in bulk water.3,4 Hence, PEG binds water with a high affinity, and PEG/water solutions are commonly used to regulate the amount of water between lipid lamellae and to osmotically stress cells and vesicles.5,6 However, less is known about the specific interaction of PEG with lipids and membranes. Owing to recent studies of PEG-induced fusion, the nature of the PEG-membrane interaction is gradually being understood in physicochemicalterms.14-20 There †

University of California, Santa Barbara. Roswell Park Cancer Institute. § SUNY at Buffalo. X Abstract published in Advance ACS Abstracts, May 15, 1996. ‡

(1) Bailey, F.; Koleske, J. In Nonionic Surfactants; Schick, M. J., Ed.; Marcel Dekker: New York, 1987; Vol. 23, p 927. (2) Kjellander, R.; Florin, E. J. Chem Soc. Faraday Trans. 1 1981, 77, 2053. (3) Liu, K.; Parsons, J. Macromolecules 1969, 2, 529. (4) Glowinkowski, S.; Jurga, K.; Pajak, Z. Polym. Bull. 1981, 5, 271. (5) Parsegian, V. A.; Fuller, N.; Rand, R. P. Proc. Natl. Acad. Sci. U.S.A. 1979, 76, 2750. (6) Evans, E.; Needham, D. In Molecular Mechanisms of Membrane Fusion; Ohki, S., Doyle, D., Flanagan, T. D., Hui, S. W., Mayhew, E., Eds.; Plenum Press: New York, 1988; p 83. Evans later refined the SCF theory. Evans, E. Macromolecules 1989, 22, 2277. (7) Napper, D. J. Colloid Interface Sci. 1977, 58, 390.

S0743-7463(95)00802-X CCC: $12.00

seem to be two vital steps in PEG-induced membrane fusion: aggregation followed by bilayer destabilization and subsequent fusion. Based on the results of a series of experiments on PEG-water-lipid systems utilizing ESR, 2H-NMR, osmotic pressure, polarity, and dielectric constant, Arnold et al. proposed that the effect of PEG 6000 (now known to be 8000 MW) on membranes can be explained by depletion attraction.21,22 Because the experimentally measured zeta potential was less in PEG 6000 solutions than expected, they suggested that PEG molecules were excluded from the bilayer surface. In contrast, when a PEG chain (EO8) was anchored to the vesicle surface by incorporation of octaethylene glycol (8) Napper, D. Polymeric Stabilization of Colloidal Dispersions; Academic Press: London, 1983. (9) de Gennes, P. G. In Physical Basis of Cell-Cell Adhesion; Bongrand, P., Ed.; CRC Press: Boca Raton, FL, 1988; p 39. (10) Fleer, G.; Scheutjens, J. In Polymer Adsorption and Dispersion Stability; Goddord, E., Vincent, B., Eds.; American Chemical Society: Washington, DC, 1984; p 245. (11) Joanny, J. F.; Leibler, L.; de Gennes, P. G. J. Polym. Sci.: Polym. Phys. Ed. 1979, 17, 1073. (12) Feigin, R.; Napper, D. J. Colloid Interface Sci. 1980, 74, 567. (13) Feigin, R.; Napper, D. J. Colloid Interface Sci. 1980, 75, 525. (14) Blow, A. M. J.; Botham, G. M.; Fisher, D.; Goodall, A. H.; Tilcock, C. P.; Lucy, J. A. FEBS Lett. 1978, 94, 305. (15) Tilcock, C. P. S.; Fisher, D. Biochim. Biophys. Acta 1982, 688, 645. (16) Boni, L. T.; Hah, J. S.; Hui, S. W.; Mukherjee, P.; Ho, J. T.; Jung, C. Y. Biochim. Biophys. Acta 1984, 775, 409. (17) Boni, L. T.; Hui, S. W. In Cell Fusion; Sowers, A., Ed.; Plenum Press: New York, 1987; p 301. (18) Arnold, K.; Hermann, A.; Pratsch, L.; Gawrisch, K. Biochim. Biophys. Acta 1985, 815, 515. (19) Hui, S. W.; Isac, T.; Boni, L. T.; Sen, A. J. Membr. Biol. 1985, 84, 137. (20) Lentz, B. R. Chem. Phys. Lipids 1994, 73, 91. (21) Arnold, K.; Pratsch, L.; Gawrisch, K. Biochim. Biophys. Acta 1983, 728, 121. (22) Arnold, K.; Hermann, A.; Gawrisch, K.; Pratsch, L. Stud. Biophys. 1985, 110, 135. (23) Arnold, K.; Lvov, Y. M.; Szogyi, M.; Gyorgyi, S. Stud. Biophys. 1986, 113, 7. (24) Arnold, K.; Zschoernig, O.; Barthel, D.; Herold, W. Biochim. Biophys. Acta 1990, 1022, 303.

© 1996 American Chemical Society

3004 Langmuir, Vol. 12, No. 12, 1996

mono(n-dodecyl) ether (C12EO8), a larger zeta potential was measured.23,24 Evans and Needham provided additional experimental proof of the depletion effect by micropipet aspiration measurements of PEG-enhanced adhesion of giant phospholipid vesicles and developed a depletion force theory to explain the stronger adhesion measured in the presence of nonadsorbing polymer.6 To study the nature of the bilayer-PEG interaction, we use a system consisting of supported phospholipid bilayers and vesicles (model cells) in aqueous PEG solutions. If the interfacial energy between the vesicle surface and PEG is less than that between the vesicle surface and water, PEG will adsorb to the vesicle surface and stabilize the vesicle suspension. Otherwise, if the vesicle-water interfacial energy is lower, PEG will be repelled from the vesicle surface. This will destabilize the suspensions via depletion attraction and induce vesicle aggregation.7-9 The osmotic depletion force occurs when nonadsorbing polymer is added to a colloidal or vesicle dispersion. A polymer chain in solution will maintain, on average, that configuration which is energetically most favorable, i.e., a random coil in a good solvent. The coil may approach a vesicle to a distance such that its outermost segments just meet the vesicle surface. To approach more closely, the coil would have to adopt a less favorable conformation with a resulting loss of conformational entropy. Thus, a gradient in the polymer segmental concentration exists in the vicinity of a surface. Depletion attraction arises when the depletion layers, ∆, associated with two surfaces overlap. Theoretically, at large separations, D > 2∆, the segment concentration increases from zero at the surface to that of the bulk solution in the middle of the gap between the surfaces. However, at smaller separations, D < 2∆, the concentration in the gap falls below that of the bulk. As a result, the pressure in the bulk solution is greater than that in the gap, and there is an attractive osmotic force between the surfaces.10-13 In this paper, we present systematic and quantitative studies of the depletion effect of PEG of MW ranging from 200 to 18 500 by direct force measurement between lipid membranes with the surface forces apparatus (SFA) and from rotational correlation times obtained with 31P-NMR. We then relate these findings to the extent of aggregation of egg phosphatidylcholine vesicles suspended in PEG solutions as determined by light scattering. From this study we conclude that PEG-induced vesicle or cell aggregation may be quantitatively described by a depletion attraction mechanism and that fusion of bilayers is facilitated by depletion attraction which appears to produce a local destabilization at the point of closest approach of two bilayers. Materials and Methods

Kuhl et al. the solvent was then evaporated in a rotavaporator. The dry lipid film was dispersed in His Tes buffer (2 mM L-Histidine, 2 mM Tes, and 0.02% NaNO3, pH 7.4, 30% D2O was added to samples for NMR) by vortexing for 5 min. The suspension was then sonicated in a water bath ultrasonicator under an atmosphere of nitrogen until a transparent suspension was obtained. Centrifugation at 11 000 rpm for 30 min was used to remove larger vesicles. The initial lipid concentration of the SUV suspension was usually 5 mM. Quasi-elastic Light Scattering. Quasi-elastic light scattering (QLS), or photon correlation spectroscopy (PCS), was performed with in a model 370 particle sizer (Nicomp Particle Sizing System, Santa Barbara, CA), with an argon ion laser source. The photon counts were at all times adjusted to about 300 kHz. A 0.25 W laser output was used for measurement of the hydrodynamic size of the PEG molecules. The apparatus was calibrated by measurement of monodisperse polystyrene latex spheres of known dimensions. In a typical vesicle aggregation experiment, 0.5 mL of SUV suspension was mixed with 2.0 mL of buffer or PEG solution to attain a 1 mM lipid concentration. After the sample was well-mixed, the steadystate volume-weighted mean vesicle diameter and polydispersity were determined for the initial SUV suspensions, as well as for those suspensions after PEG solutions were added. All the experiments were performed at 25 °C. The dispersivity was modeled with a Gaussian distribution for χ2 values below 5, otherwise, a polymodal dispersion model was used. Nuclear Magnetic Resonance. Symmetrical isotropic 31P NMR spectra were obtained in SUV suspensions of DLPA. These spectra reflect the isotropic reorientational motional averaging arising from two sources, namely, lateral diffusion of phospholipids within the SUV bilayers and rapid Brownian rotation (tumbling) of whole vesicles. The 31P-NMR line width, ∆ν1/2, of phospholipids in the vesicles can be expressed in terms of the effective correlation time for orientational exchange, τe, and the residual second moment, M2, by

π∆ν1/2 ) M2τe + C

(1)

where C is the intrinsic line width which is τe-independent.26 The effective reorientational rate, 1/τe, is related to the rates of vesicle tumbling, 1/τt, and phospholipid lateral diffusion, 1/τd, by

1 1 1 ) + τe τt τd

(2)

τt ) 4πηr3/3kT

(3)

τd ) r2/6DT

(4)

where

where η is the viscosity of the aqueous medium, r is the hydrodynamic radius of the vesicles, and DT is the lateral diffusion coefficient.27 Equations 1-4 can be combined to give

π∆ν1/2 )

{(

M2r2 kT + DT 6 8πηr

)

}

+C

(5)

Chemicals and Sample Preparation. Egg lecithin (EPC), dimyristoyl phosphatidylcholine (DMPC), dipalmitoyl phosphatidylethanolamine (DPPE), and dilauryl phosphatidic acid (DLPA) were purchased from Avanti Polar Lipids, Inc. (Alabaster, AL). PEG-200, -400, -600, -1000 (1k), and -10000 (10k) and potassium nitrate (purity >99.99%) were purchased from Sigma Chemical Co. (St. Louis, MO), PEG-8000 (8k) was from Fisher Scientific Co. (Fair Lawn, NJ), and PEG-18500 (20k) was from Polysciences, Inc. (Warrington, PA). All chemicals were used without further purification. Small unilamellar vesicles (SUV, 30 nm diameter) of DLPA or EPC were prepared using the method of Bangham (1974).25 Briefly, the stock solution of DLPA or EPC was sonicated, and

Equation 5 indicates that if the viscosity, η, of the medium is increased, the line width increases and reaches a constant value when lateral diffusion becomes the dominant averaging mechanism. Conversely, if the viscosity is always less than 8πrDT/ kT, the dominant averaging is provided by vesicle tumbling. With the above values, the latter condition is satisfied when η , 5.2 cP. Under these conditions, the line width measurement gives the local viscosity of the medium near the vesicle surface. During 31P-NMR experiments the volume of each sample was 0.5 mL and typically contained 5-6 mg of lipid. For the study of the effects of PEG and glycerol (as a comparison) on the line width of the SUV suspension, a given amount of glycerol, or PEG

(25) Bangham, A. D.; Hill, M. W.; Miller, N. G. In Methods in Membrane Biology; Korn, E., Ed.; Plenum Press: New York, 1974; p 1.

(26) McLaughlin, A. C.; Cullis, P. R.; Berden, J. A.; Richards, R. E. J. Magn. Reson. 1975, 20, 146. (27) Cullis, P. R. FEBS Lett. 1976, 70, 223.

PEG Induced Depletion Attraction

Figure 1. Schematic of the supported bilayer surfaces in concentrated PEG polymer solution including definition of the distance, D, where zero distance, D ) 0, refers to nominally dehydrated bilayers in contact.29 T is the thickness of the two outer DMPC monolayers and S ) D + T. Typical radii of the supporting mica sheets were R ≈ 1-2 cm, so that R . D.

Langmuir, Vol. 12, No. 12, 1996 3005 average volume of a saturated n-carbon chain in the frozen or gel state,32 Vhead ) 324.5 Å3 is the average headgroup volume of PC,33 and A is the deposited headgroup area. For example, the thickness of the two outer DMPC monolayers deposited at A ) 58 Å2 per molecule was calculated to be T ) 2[2(27.4 + (26.9 × 13)) + 324.4]/58 ) 37 Å. From the measured values of S and T, the bilayer separation, D, could then be determined in each experiment. The position of bilayer-bilayer contact, D ) 0, was of fundamental concern in the results to follow since the primary objective of these experiments was to distinguish between the van der Waals attraction between bilayers and the depletion attraction due to the free PEG chains in solution. It was also necessary to rule out the possibility that polymer bridging forces and enhanced hydrophobic interactions due to desorption of lipids from the bilayer surface contributed to the adhesion.34 The characteristics of these forces are listed in Table 1. The position of bilayer-bilayer “contact” and the adhesion strength were used in this work to distinguish between the different types of forces operating between the bilayers.

Results of various MWs, was added to obtain the final desired suspension concentration. 31P-NMR spectra were acquired at 161.98 MHz at 45 °C with a π/2 pulse of 12.5 µs, and the broad band proton decoupling method. Usually 300-3000 free induction decays (FIDs) were acquired, depending on the signal to noise ratio (S/ N) of the spectrum. The S/N ratio was determined from the Fourier transformed FIDs during the acquisition. The acquired data were processed by NMR1 software (New Methods Research, Inc., E. Syracuse, NY) with 2 Hz line broadening. The viscosities of aqueous solutions of glycerol (0-100 wt %) in the temperature range 0-100 °C were determined from the data of Segur and Oberstar,28 while the bulk viscosities of the various aqueous solutions of PEG were directly measured at 45 °C with a Cannon-Ubbelohde viscometer. Surface Force Measurements. The apparatus used in the surface force measurements has been described extensively.29-31 Monolayers of DPPE or DMPC were spread from a 9:1 chloroform/ methanol solution at the air-water interface of a Teflon-coated Langmuir-Blodgett trough. The temperature of the subphase was maintained at 21 °C and the surface pressure was measured by the Wilhelmy balance method. The first layer of the supported bilayer used in these studies was DPPE deposited in the gel phase at a surface pressure of 37 mN/m, which corresponded to a packing area of 43 Å2 per headgroup. The solid support consisted of thin, molecularly smooth, back-silvered mica sheets which were glued onto cylindrical fused silica disks. DPPE binds physically but strongly to the bare mica surface. The second or outer layer was DMPC deposited at 30 mN/m, corresponding to 58 Å2 per headgroup. At 21 °C the onset of the transition between the liquid expanded and liquid condensed phases of DMPC is at 28 mN/m. DMPC was chosen because its force profile is known and PC vesicles are used predominately in PEG-induced aggregation and fusion experiments.29 After the second deposition, the disks were transferred under water to the measuring apparatus and mounted, as described elsewhere.29 Prior to the insertion of the bilayer coated disks, the apparatus was filled with a degassed PEG solution with 0.5 mM potassium nitrate saturated with free DMPC to prevent lipid desorption from the bilayers during experiments. A schematic of the bilayer-coated mica surfaces in PEG solution is shown in Figure 1. Throughout this work, D ) 0 was defined as contact between nominally dehydrated bilayers (cf. Figure 1). This position was determined as follows. First, the combined thickness of the two hydrated outer DMPC monolayers, S, was determined at the end of each experiment by measuring the thickness change following drainage of the solution from the apparatus and removal of the two outer monolayers (Figure 1). Second, the anhydrous bilayer thickness, T, was calculated from the physical volumes occupied by the hydrocarbon chains and PC headgroups as given by T ) 2[2Vhc + Vhead]/A, where Vhc ) (27.4 + 26.9n) Å3 is the (28) Segur, J.; Oberstar, H. Ind. Eng. Chem. 1951, 43, 2117. (29) Marra, J.; Israelachvili, J. Biochemistry 1985, 24, 4608. (30) Israelachvili, J. J. Colloid Interface Sci. 1973, 44, 259. (31) Israelachvili, J.; Adams, G. Nature (London) 1976, 262, 774.

Forces between DMPC Bilayers in Water (0% PEG). Surface force profiles between the lipid bilayers were measured in water as well as in aqueous solutions of both varying molecular weights and concentrations of PEG. The surface force profile between DMPC bilayers in lipid-saturated water is shown in Figure 2. The profile was similar to that measured previously,29 namely, van der Waals attraction and strong steric-hydration repulsion at small separations (D ≈ 20 Å). All surface force experiments were carried out at 25 °C where the outer DMPC monolayers were expected to be in the liquid expanded state since this temperature is slightly above the bulk chain melting temperature of 24.5 °C.35 Comparison with the work of Marra and Israelachvili29 indicates that the measured force profile and adhesion fall between those previously found for the purely liquid condensed and liquid expanded states. Moreover, it has been previously established36 that for bilayers on a solid support such as a frozen inner monolayer, the fluidity and lipid diffusion in the outer monolayer are less than expected. We will therefore assume that the DMPC monolayers deposited under our conditions (see Materials and Methods) are in the coexistence regime at 25 °C. The importance of this coexistence will become apparent when we discuss fusion. Forces in Aqueous Solutions of 8k PEG. The measured force profiles between bilayers in semidilute solutions of 5, 7, and 10 wt % 8k PEG (Figure 3) were significantly different from those measured in water. As can be seen, a repulsive barrier (possibly depletion stabilization) must be overcome before the surfaces jump into an enhanced attractive minimum. The magnitudes of both the repulsive and attractive extrema of the force profiles increased with increasing polymer concentration. The distance, D ≈ 75 Å, from which the surfaces jumped into adhesive contact was significantly larger than the jump-in distance expected from van der Waals attraction alone (cf. Figure 2). The difference between the distances from which the surfaces jumped-in on approach and jumped-out on separation should roughly equal the (32) Tanford, C. J. Phys. Chem. 1972, 93, 917. (33) Small, D. M. J. Lipid Res. 1967, 8, 551. (34) Helm, C.; Israelachvili, J.; McGuiggan, P. Science 1989, 246, 919. (35) Marsh, D. CRC Handbook of Lipid Bilayers; CRC Press, Inc.: Boca Raton, FL, 1990. (36) Helm, C.; Israelachvili, J.; McGuiggan, P. Biochemistry 1992, 31, 1794. (37) Asakura, S.; Oosawa, F. J. Chem. Phys. 1954, 22, 1255. (38) Derjaguin, B. Kolloid Z. 1934, 69, 155. (39) Michel, B. E. Plant Physiol. 1983, 72, 66.

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Kuhl et al. Table 1 type of attractive interaction between bilayers

features bilayer separation at “contact” range of force magnitude of force other features

van der Waalsa

depletion

bridging

hydrophobic

DVDW ≈ 4-20 Å

D ) DVDW

D > DVDW

D < DVDW

∼50 Å 1 weak force, but always present

RF gVDW maximum force given by maximum osmotic pressure, eqs 6, 7

RF >VDW attraction turns to repulsion at short range, can be slow to equilibrate

>VDW .VDW increased adhesion that can lead to fusion

a D VDW ) 0 is defined as the plane where the VDW attraction is balanced by the repulsive (steric/thermal fluctuation/hydration) forces. This occurs typically at D ≈ 20 Å out from the (dehydrated) contact separation of the bilayers which defines D ) 0.

Figure 2. Force profile, F/R vs D, between supported DPPE/ DMPC bilayers in water showing a van der Waals attraction and a strong steric-hydration repulsion at small separations, D < 20 Å. The distance D and D ) 0 are defined in the text (see also Figure 1). The right axis is the corresponding interaction energy per unit area E(D) between two planar surfaces where E(D) ) F(D)/2πR.38

polymer coil dimension. As can be seen in Figure 3, this difference was ≈45 Å, which is close to but somewhat more than the hydrodynamic coil diameter, RH ) 34 ( 5 Å, measured with dynamic light scattering (Table 2). In all cases, the magnitude of the attractive force at the minima exceeded that expected for van der Waals attraction alone (dotted curve). More significantly, the adhesive minima occurred at the same hard wall of bilayer-bilayer contact as measured in the absence of polymer (D ≈ 20 Å, cf. Figure 2). This indicated that the increased attraction was due to depletion rather than a bridging interaction (where a monolayer or two of adsorbed polymer would end up in a flattened configuration between the bilayers,40 and thereby push the contact position out by a small but measurable amount). Likewise, the fact that the final contact position was unchanged eliminated the possibility that the increased adhesion was due to depleted lipid layers exposing more hydrophobic groups. If that were the case, the final contact would be closer in, D < 20 Å, due to a less dense packing of the remaining lipids. The additional adhesive force that occurred at the same bilayer-bilayer separation and the locations of the jump distances indicated that the enhanced adhesion was due to a polymer-induced depletion attraction (Table 1). The magnitude of the adhesion depended on the polymer concentration, as expected for the osmotic pressuredependent depletion attraction. Simple calculations based on the osmotic pressure, Π, of the PEG solutions were used to estimate the expected increased adhesive force, Fa/R, between the bilayers due to a depletion interaction. (40) Scheutjens, J.; Fleer, G. Macromolecules 1985, 18, 1882.

Figure 3. Force profiles of DPPE/DMPC bilayers in different concentrations of 8k PEG. The dotted curve is the force profile in the absence of any polymer (Figure 2). Note that both the maxima and minima in the curves increase with increasing polymer concentration, but the distance at which they occur does not change (this also applies to Figure 4). In particular, in the presence of polymer, bilayer-bilayer contact is attained at the same separation as in pure water (dotted curve). The inset more clearly depicts the increased adhesive force, Fa/R, measured in the presence of 8k PEG over the always present van der Waals attraction, FVDW/R. In addition, a repulsive barrier, Fr/R, is measured before the surfaces jump into contact. Table 2 MW of PEG (k)

Flory radius, RF (Å)

hydrodynamic diameter, RH, from DLS (Å)

overlap concentration, C* (wt %)

1 8 10 18.5

23 80 90 130

34 ( 5 49 ( 5 75 ( 8

26.1 3.0 2.6 1.6

The expression for the (maximum) ideal osmotic pressure, Πi, between two flat surfaces in contact is

Πmax ) Πi(D)0) ) -F∞kT

(6)

where F∞ is the bulk polymer concentration (Table 3, column 2).37 If this pressure acts over a distance ∆ (the depletion layer thickness), the depletion energy at contact would be Π∆ per unit area which, using the Derjaguin approximation,38 gives for the normalized adhesion force, Fa/R, between two curved surfaces:

Fa/R ) 2π∆Π

(7)

The depletion layer thickness can be estimated from the

PEG Induced Depletion Attraction

Langmuir, Vol. 12, No. 12, 1996 3007

Table 3 PEG MW (k) 8 10

PEG wt %

ideal pressure value for Πi (based on eq 6) (mN/m2)

theoretical adhesion force -Fa/R (mN/m)

experimental adhesion force -Fa/R (mN/m)

5 7 10 3 5 7

1.5 × 107 2.2 × 107 3.1 × 107 0.7 × 107 1.2 × 107 1.7 × 107

0.63 0.75 0.97 0.28 0.47 0.69

0.5 ( 0.15 0.70 0.95 0.32 ( 0.15 0.72 2.8 (hemifusion)

difference in bilayer-bilayer contact and the onset of the attractive force in Figure 3 for each PEG concentration. Using eqs 6 and 7 the ideal depletion attraction is Fa/R ) -0.6, -0.8, and -1.0 mN/m in 8k PEG at concentrations of 5, 7, and 10 wt %, respectively (Table 3). Actual measured experimental values were Fa/R ) -0.6, -0.7, and -1.0 mN/m after the van der Waals contribution of 0.5 mN/m was subtracted from the total force measured (cf. Figure 2). More complex numerical calculations vary little from this simple approximation. The important point is that the results are well within the expected values for depletion attraction. At all polymer concentrations, a small but significant repulsive force barrier (possibly depletion stabilization regime) was measured at separations from 200 to 300 Å or ∼3RF before the shorter range attractive force dominated. The magnitude of this repulsive barrier, Fr/R, increased with increasing polymer concentration. One explanation for this repulsion stems from the possibility that as the two surfaces approached, polymer was initially compressed rather than excluded from the gap. Using a lattice model for nonadsorbing polymers at the solid/ solution interface, Scheutjens and Fleer40 found a concentration spike in the polymer concentration prior to the depletion regime. This increase in polymer concentration would result in a repulsive force barrier (eq 6). Conversely, the repulsive barrier could be due to a demixing free energy. At separations less than ∆, essentially no polymer remains between the surfaces, and a volume of pure water exists. The differential osmotic pressure between the pure water in the gap and that of the bulk polymer solution causes the surfaces to jump together into the measured adhesive minimum, Fa/R. However, the demixing required to create this volume of pure water is energetically unfavorable in a good solvent, and this demixing energy may result in a potential energy barrier.12,13 The source of this repulsive barrier will be clarified in the discussion section. Forces in Aqueous Solutions of 10k PEG. Similar profiles as measured in the 8k PEG solutions were obtained in 10k PEG at 3, 5, and 7 wt % (Figure 4). Again, both the initial repulsive barrier and final adhesion increased with increasing polymer concentration. The results at the lower concentrations of 3 and 5 wt % quantitatively followed those of the 8k PEG measurements. Namely, the adhesion varied linearly with the PEG volume fraction (Figure 5). The intercept at zero volume fraction, v ) 0, gave an attractive force of 0.5 ( 0.1 mN/m, which corresponded to the measured van der Waals force in the absence of polymer. Furthermore, the slope of the fitted line, ∆(F/R)/∆v ≈ 12 mN/m is comparable to the osmotic pressure gradient of PEG solutions at these volume fractions, 14 mN/m, assuming a depletion layer thickness of about 50 Å. Surprisingly, the adhesion measured at the highest concentration of 7 wt %, Fa/R ) -2.8 mN/m, was anomalously large compared to the expected adhesion, Table 3. This increased adhesion was associated with

Figure 4. Force profiles of DPPE/DMPC bilayers in different concentrations of 10k PEG. Again, the maxima of the curves increase with increasing polymer concentration. However, at a concentration of 7 wt %, the adhesion is much stronger than expected (see text) with hemifusion occurring at an applied force of only 3 mN/m (see also Figure 6).

Figure 5. The force, F/R, as a function of MW and volume fraction, v, of PEG. The extrapolated y-intercept corresponds to the always present van der Waals attraction between DMPC bilayers in pure water ∼0.5 mN/m as measured in Figure 1. The open and filled symbols represent data derived from PEG 8k and 10k, respectively. Note that the filled symbol at 0.042 volume fraction is for 10k PEG (5 wt %), indicating the strong dependence of MW on the interaction (see also Figure 11).

the onset of the observed hemifusion of the bilayers. When the lipid bilayers were pressed together under a compressive force of F/R ) +3 mN/m, corresponding to an applied pressure of about 0.3 atm, the bilayers hemifused (cf. top arrow in Figure 4). Real time video images of the FECO fringes during hemifusion are shown in Figure 6. An initial local “breakthrough” was observed at the center of the contact region where the lipids in the two outer DMPC monolayers moved radially outward from the fusion site and the two inner DPPE monolayers came into contact (Figure 6BfC). This process continued until only one DPPE bilayer remained in the contact zone (Figure 6CfD). The measured change in the distance of closest approach upon hemifusion was 55 Å and corresponded to the thickness of two hydrated DMPC monolayers (DVDW + T, cf. Figure 1 and Table 1). Such hemifused bilayers

3008 Langmuir, Vol. 12, No. 12, 1996

Kuhl et al.

Figure 6. Real time video images of the FECO fringes during hemifusion in 7 wt % 10k PEG. The white bars on the FECO images indicate the position of bilayer-bilayer contact, D ≈ 20 Å. Also shown are schematic representations of the corresponding surfaces showing the proposed PEG-induced membrane destabilization mechanism that leads to hemifusion. (A) The two DMPC bilayers are separated by ∼300 Å of bulk polymer solution. (B) The bilayers are in “contact” at a separation of 20 Å under a force of 3 mN/m (cf. Figure 4). No polymer is able to penetrate the gap and the solution is locally phase separated, which causes thinning of the DMPC monolayers in the contact zone. (C) The initial breakthrough of hemifusion is visible at the center of the fringe, where opposing hydrophobic DPPE monolayers come into contact. (D) The hemifused region has spread to cover a final contact area of ∼50 µm.

PEG Induced Depletion Attraction

have previously been observed as stable or metastable states during the fusion of large unilamellar vesicles in solution.34,41-44 As depicted schematically in Figure 6, the asymmetry of the local environment of the bilayers at contact appears to provide the destabilization necessary to induce the hemifusion events described above. At large separations, D > RF, the lipid bilayers are exposed to a continuous bulk polymer solution (Figure 6A). However, as the separation between the surfaces decreases, the concentration of polymer in the intervening gap falls below that of the bulk phase, until at D ≈ 20 Å (Figure 6B), the lipids in the contact zone are in contact and no PEG is present in the gap between the bilayers. However, just outside of this contacting region, the lipids facing the solution are still surrounded by PEG chains. It has been well established that PEG causes a “condensation” of lipids, i.e., a reduction in their surface area.45-49 This condensation is most likely to be due to the same attractive depletion force operating laterally between adjacent headgroups, as the transverse depletion force between two approaching surfaces. For example, in experiments conducted with PC lipids at the air-water interface, 6k PEG caused the condensation of the film, and elimination of the liquid-expanded-liquid-condensed phase transition.46 Moreover, films at or near the liquid expanded-liquid-condensed phase transition, as studied in the experiments here, have been shown to be particularly sensitive to the presence of PEG in the medium.45 Likewise, an extensive body of work which utilized X-ray diffraction from lipid lamellae demonstrated that increasing the applied osmotic stress (usually with aqueous dextran or PEG solutions) caused the lateral spacing between the lipid headgroups to decrease. For example, a solution of 7 wt % PEG 10k results in an applied pressure of up to 8.2 × 104 N/m2 (Table 3). Under similar conditions of applied osmotic stress, Parsegian et al.5 found that the area per headgroup of EPC lamellae decreased by 3%. These observations lead us to propose the following mechanism for PEG induced fusion of vesicles.50 The key is the asymmetry of the local polymer concentration formed once the bilayers are adhering in the depletion attraction enhanced minimum. This asymmetry in polymer concentration inside and outside the contact zone (Figure 6B) should cause a condensation of the headgroups and effectively thicken the DMPC monolayer, but only outside the contact zone. This would lead to a corresponding thinning of the monolayer inside the contact zone (Figure 6B). The PEG condensation effect, together with the additional effective compressive depletion pressure acting on the surfaces in the contact region would result in an increased area per lipid headgroup in the contacting region. An increase in area is known to enhance the adhesion of bilayers (stress-induced adhesion), and to lower the activation barrier to fusion.44 Moreover, in this work, the hemifusion was observed at the center of the (41) Shotton, D. Nature 1978, 272, 16. (42) Neher, E. Biochim. Biophys. Acta 1974, 73, 327. (43) Ficher, L.; Parker, N. Biophys. J. 1984, 46, 253. (44) Horn, R. G. Biochim. Biophys. Acta 1984, 788, 224. (45) Cadenhead, D.; Bean, K. Biochim. Biophys. Acta 1972, 290, 43. (46) Maggio, B.; Lucy, J. A. FEBS Lett. 1978, 94, 301. (47) Tilcock, C. P. S.; Fisher, D. Biochim. Biophys. Acta 1979, 577, 53. (48) Yamazaki, M.; Ohshika, M.; Kashiwagi, N.; Asano, T. Biophys. Chem. 1992, 43, 29. (49) Lehtonen, J. Y. A.; Kinnunen, P. K. J. Biophys. J. 1994, 66, 1981. (50) We are presenting a possible mechanism for PEG-induced fusion based on the observed hemifusion of substrate-supported bilayers. Our purpose in extending this hypothesis is to stimulate further discussion and experimentation.

Langmuir, Vol. 12, No. 12, 1996 3009

Figure 7. Force profiles of DPPE/DMPC bilayers in 10 wt % 1k PEG. The dotted curve is the force profile in the absence of polymer (Figure 2). The increased attraction is much less than that measured in solutions of 8k and 10k PEG.

thinned region which corresponds to the location of the highest stress on the DMPC monolayer (Figure 6C). On breakthrough and hemifusion, the change in distance (54 ( 1 Å) equaled the thickness of a slightly thinned DMPC bilayer. The thickness of two unstressed DMPC monolayers was 57 ( 1 Å, as measured in these experiments in the absence of PEG. On the basis of this difference, the area change per lipid was ∼5%, consistent with a locally stressed bilayer. A more quantitative description of this process is given in the Discussion. Forces in Aqueous Solutions of 1k PEG. In solutions of 10 wt % 1k PEG, the force profile between the DMPC monolayers was not significantly different from that in water alone. As seen in Figure 7, there was a small repulsive barrier prior to the jump into a weakly enhanced adhesive contact from separations of ∼55 Å, comparable to the expected van der Waals jump distance of 50 Å. For comparison, 8k PEG at 10 wt % had a measured adhesion of Fa/R = -1.0 versus -0.3 mN/m for 1k PEG at 10 wt %. The measured forces with 1k PEG are as anticipated, since 1k PEG is too small (RF) to generate a significant depletion layer, and they also explain why this lower MW polymer is less effective in inducing vesicle aggregation and fusion compared to 8k and 10k PEG.15 Forces in Aqueous Solutions of 20k PEG. The force profiles measured in 5 and 10 wt % 20k PEG were entirely repulsive and showed no measurable attractive force (Figure 8). Thus, the larger molecular weight PEG either adsorbed to or was kinetically trapped between the bilayer surfaces, resulting in steric repulsion due to confinement and elastic compression of the chains. The measured repulsive force extended 700 Å or 5RF, and the bilayers could not be forced closer together than 50 Å. It is generally accepted that polymers can adsorb on surfaces even in good solvents40 and that under restricted equilibrium conditions this gives rise to a monotonically repulsive force that can extend many times the Flory radius.51,52 Klein and Luckham found that 40k PEG (RF ) 200 Å) adsorbed very strongly on bare mica surfaces from water.51 Even at very low concentrations, C , C*, where C* is the critical overlap concentration, this resulted in a compressible polymer layer extending approximately 800 Å. The incompressible “hard wall” was at about 100 (51) Klein, J.; Luckham, P. Macromolecules 1984, 17, 1041. (52) Luckham, P.; Klein, J. Macromolecules 1985, 18, 721.

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Figure 8. Force profiles of DPPE/DMPC bilayers in 10 wt % 20k PEG. A strong steric repulsion is measured due to adsorbed PEG on the bilayer surface. The hysteresis upon approach and separation of the surfaces is characteristic of adsorbed PEG layers in water.51,52

Å from bare mica-mica contact. In contrast, in our study with much higher polymer concentrations, C > C*, the hard wall between DMPC bilayers in 20k PEG was at D ≈ 50 Å. Thus, it would appear that 20k PEG adsorbed more weakly to a lipid bilayer surface or was simply trapped in the gap between the surfaces. Also noteworthy was the significant hysteresis between the approach and separation of the surfaces observed in the force profile (Figure 8). The repulsive force measured on separation was much less than that measured during the approach. There are two possible mechanisms for hysteresis: namely, chain rearrangement and/or chain expulsion from the contact zone. Either of these mechanisms could account for the observed hysteresis in the measured force profile; however, this was not investigated. Regardless, the significant repulsion observed in the presence of 20k PEG provides an explanation for the steric barrier to vesicle aggregation and fusion observed in previous vesicle experiments.53 Vesicle Tumbling Experiments. The line width of 31 P-NMR spectra of DLPA vesicle suspensions provides a measurement of the local viscosity of the medium near the vesicle surface, where the line width normally increases as a function of the solution viscosity. In a control sample, DLPA vesicles in buffer gave a single isotropic peak with a relatively narrow line width of 15 Hz. In contrast, DLPA vesicles in 8 vol % PEG-600 solution had a broadened peak with a line width of 17 Hz. Charged DLPA instead of zwitterionic DMPC vesicles were chosen to avoid spontaneous aggregation/fusion, ensuring that this line width broadening in the presence of PEG was the result of increasing solution viscosity, not an increase in particle size. Moreover, vesicle sizes were checked by electron microscopy and QLS and found to be unchanged in PEG concentrations up to the maximum used in the NMR experiments. Hence, the measured line width should only be sensitive to the viscosity of the medium. Figure 9 shows the line widths measured as a function of solution viscosity. The line width in the presence of glycerol (up to 40% (v/v)) is shown for comparison (dashed line), since glycerol should neither adsorb nor deplete against the vesicle surface. As the glycerol solution viscosity increased from 0.6 to 2.5 cP, the measured line (53) Rupert, L. A. M.; Engberts, J. B. F. N.; Hoekstra, D. Biochemistry 1988, 27, 8232.

Kuhl et al.

Figure 9. 31P-NMR line widths of DLPA vesicles in solutions of various bulk viscosities: glycerol (b) PEG 200 (0), PEG 600 ([), PEG 8k (]), PEG 10k (9), and PEG 20k (O). Normally, the line width increases linearly with increasing solution viscosity as shown in the presence of the glycerol control (dashed curve). However, in solutions of PEG 8k and 10k, no change is seen relative to the polymer-free solution, indicative of a depletion layer surrounding the vesicles.

width increased linearly as expected. Similar behavior is seen when PEG-200 (up to 16% (v/v)) or PEG-600 (up to 16% (v/v)) were added to the DLPA suspensions. In contrast, when 8k or 10k PEG were added (up to 9 wt %), although the bulk viscosity increased from 0.6 to 2.5 cP, the line widths remained unchanged. This pointed to the existence of a lower local solution viscosity surrounding the DLPA vesicles and, consequently, to the existence of a polymer depletion layer near the vesicle surface. Conversely, when a small amount of 20k PEG was added (up to 4 wt %), the line width increased more rapidly with viscosity. This indicated that the local solution viscosity surrounding the vesicles was slightly higher than that of the bulk (due to, for example, a nonslip condition at the vesicle-solution interface consistent with PEG adsorption). Vesicle Aggregation Experiments. In the light scattering (QLS) experiments, aggregation or fusion of vesicles correlates with an increase in the measured particle size. Fluid phase Egg PC vesicles were used (rather than DMPC vesicles) to avoid spontaneous aggregation/fusion associated with gel-phase vesicles.16 Therefore, the final average size measurement by QLS can be interpreted as a measurement of the PEG-induced vesicle aggregation or fusion. Three minutes after adding PEG to a vesicle suspension, aggregate sizes were measured. (The distributions were stable within 3 min of PEG-vesicle mixing.) Initially, all SUV preparations had Gaussian distributions with mean diameters of 27 ( 3 nm. After PEG-induced aggregation, usually only two vesicle sizes were present: a dominating population of large aggregates with a broad but still Gaussian distribution, and a small population (a few percent by volume) of unaggregated vesicles of the initial size. When the final average vesicle size was plotted as a function of PEG MW at different concentrations (Figure 10), one immediately sees that only 8k and 10k PEG, regardless of the PEG concentration, induce extensive aggregation of the vesicles. As expected, 1k PEG exhibits only a weak aggregation potency, while in solutions of 20k PEG there was no detectable size change at concentrations up to 10 wt %. These results are consistent with the direct force measurements and with the results reported by Rupert et al.,53 where they proposed that 20k

PEG Induced Depletion Attraction

Figure 10. MW dependence of PEG-induced aggregation of EPC vesicles at the indicated PEG concentrations (wt %). Significant aggregation is measured only in solutions of 8k or 10k PEG. Half values of standard deviations of Gaussian distributions were used as error bars.

PEG stabilized dispersions of didodecyl phosphate (DDP) and didodecyldimethylammonium bromide (DDAB) vesicles by adsorbing to the bilayer surface. Discussion The use of PEG as a fusogen for cells is based mostly on empirical findings. The common protocol calls for adding 35-45% of PEG 8k or 10k to cell suspensions or pellets, which induces aggregation.16,17,54 Fusion is achieved after the cell/PEG mixture is diluted. If aggregation is inhibited, so is fusion.53 Lower or higher MW PEG do not work as well, if at all.53,55 In spite of much recent effort to determine the molecular mechanism for PEG-induced aggregation and fusion, there has not yet been a satisfactory explanation.20 Our studies present a coordinated effort to elucidate the PEG-induced aggregation of cells and vesicles, within the context of polymer and colloid science. We have established that vesicle aggregation is driven by a differential osmotic pressure effect due to a PEG-depletion layer at the vesicle surface. The latter effect is maximally effective for PEG of MW ∼10 000. The reason for this maximum is given below. Depletion Attraction and Molecular Weight Dependence. Our direct force measurements provide the first precise evidence at the molecular level that the enhanced attractive force between membrane vesicles in PEG solutions is due to polymer depletion rather than to a dehydration, electrostatic, polymer bridging, or hydrophobic force. The depletion force acts between the outer DMPC monolayers and starts to come in at bilayer separations of 60-75 Å. This enhanced attractive force relative to the expected van der Waals interaction occurs in solutions of PEG having MW up to about 10k, and in both magnitude and range it is close to what is expected from the osmotic pressure of the bulk PEG solutions. In marked contrast to this, no attraction was detected between bilayers in solutions of 20k PEG. Instead, a soft repulsion from about 700 Å was observed, which corresponded to 5 times the Flory radius. This suggested a steric effect of adsorbed or trapped PEG 20k on the bilayer surfacessthe converse of a depletion layer. There are two possible explanations for the elimination of the attractive interaction in the presence of high MW polymer (20k PEG). First, at any given bulk polymer concentration, depletion attraction is proportional to ∆ (54) Massenburg, D.; Lentz, B. R. Biochemistry 1993, 32, 9172. (55) Boni, L. T.; Stewart, T. P.; Hui, S. W. J. Membr. Biol. 1984, 80, 91.

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and therefore to (MW)1/2. In contrast, the adsorption of polymer to surfaces generally increases much faster with the MW. In fact, theoretically, it is expected that the transition from zero adsorption to finite adsorption with increasing MW or segment number should occur abruptly, similar to a first-order phase transition, above some critical MW, and to depend only weakly on the bulk polymer concentration.56 Thus, as the MW increases, a crossover from depletion to adsorption may occur.57 It may not even be necessary to have a repulsive interaction between the polymer segments and the bilayer surface in order for a depletion layer to exist. Unless the binding is strong, a depletion zone extending a few segment lengths from a surface will always be present.56,58 However, as the number of segments in a chain increases, so does the population of bound segments. This in turn modifies the relative contributions of attractive depletion and repulsive steric forces between the two surfaces, and the overall measured interaction is altered accordingly. At a certain “critical” chain length, a sufficient number of segments can form physical bonds with the surface, binding the whole chain to the surface. On the basis of these results, the crossover point for PEG-mediated interactions between PC bilayers appears to occur at polymer MWs between 10k and 20k. Alternatively, the steric repulsion observed in the 20k PEG case may be due to the polymer chain kinetics instead of physical adsorption. Slow migration of the high MW chains may cause them to be trapped between the surfaces during the time of the force measurements. This would suggest a nonequilibrium origin for the repulsion. The entanglement molecular weight for PEG is 17 600.59 Hence, for 20k PEG at concentrations of 5 to 10 wt % (C* ) 1.6%), molecular entanglements with an appreciable lifetime may exist, and single polymer molecules no longer diffuse separately, but must drag along neighbors. As a result, the polymer chains may remain kinetically trapped in the gap between the approaching surfaces. The measured repulsive force would then be due to the entropic confinement and elastic compression of the trapped chains. However, this explanation seems less likely than the critical adsorption model: Rupert et al.53 found that concentrations as low as 0.5 wt % of 20k PEG inhibited the aggregation and fusion of DDP vesicles, suggesting that 20k PEG binds to both PC and DDP bilayers, and that this binding may be a general phenomena. Finally, the vesicle tumbling experiments in solutions of 8k and 10k MW PEG (Figure 9) strongly support the notion of polymer depletion layers at bilayer surfaces: the near independence of vesicle tumbling rates on the bulk viscosity of solutions of PEGs of moderately high MW (8k and 10k) indicates that these molecules are repelled from the vesicle surface. On the other hand, in solutions of both lower and higher MW PEG, significant 31P-NMR line broadening was observed (cf. Figure 9). This implies that low MW PEG does not form an effective depletion layer around the vesicle surface, whereas PEG 20k binds sufficiently to eliminate the depletion layer. (56) Klein, J.; Pincus, P. Macromolecules 1982, 15, 1129-1135. Equations III.9-III.13 define the critical condition at which polymer adsorbs to a surface. The critical condition is determined by the parameter β which is proportional to 1/Rg or 1/(MW)1/2, and on ln(1/φb) where φb is the bulk polymer concentration. For the same binding energy per segment, the critical condition is therefore sensitive mainly to the segment number and less so (through the log-dependence) on the concentration. Thus, below some critical polymer concentration there is ZERO adsorption, above it there is finite (even quite high) adsorption. While this paper applies to poor solvent conditions, the general ideas are believed to also apply to theta and good solvent conditions. (57) Sato, T.; Ruch, R. Stabilization of Colloidal Dispersions by Polymer Adsorption; Marcel Dekker: New York, 1980; p 7. (58) de Gennes, P. G. Macromolecules 1981, 14, 1637. (59) Berry, G.; Fox, T. Adv. Polym. Sci. 1968, 5, 261.

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Our findings of the peculiar dependence of vesicle aggregation on polymer MW are as expected from basic theories of colloidal interactions. PEG MW’s less than 1k are ineffective aggregants since their size is insufficient for generating a significant depletion layer. Conversely, high MW chains (i.e., 20k MW PEG) sufficiently adsorb to act as steric stabilizers of the vesicle suspensions, whereas 8k and especially 10k MW PEG are potent aggregants as the result of their exclusion from the interface and the consequent induction of a depletion interbilayer attraction. Depletion Stabilization. One of the principal findings of this study is that a small but significant repulsive force barrier is measured prior to the depletion attraction regime. Both the magnitude and range of this repulsive barrier increase with polymer concentration and molecular weight (see Figures 3 and 4). There are two competing views regarding the origin of the depletion stabilization repulsive barrier. A simple yet elegant explanation for this repulsion revolves around the exact nature of the depletion interaction. Namely, that it is the last oscillation of an oscillatory force.60,61 Hence, as with any excluded volume oscillatory interaction, there are both attractive and repulsive maxima, the periodicity of which coincide with the length scale of the excluded molecule as the separation between the two confining surfaces decreases below 5-10 excluded molecule diameters. These shortrange oscillatory forces arise from the molecular geometry and local structure of the aqueous polymer medium, and they reflect the ordering of the polymer molecules into discrete but diffuse layers when constrained between two surfaces. The fact that we have (1) a “rough” bilayer surface and (2) flexible polymer chains is enough to smear out the oscillations so that we measure only the last oscillation, viz., a depletion stabilization hump and depletion attraction only after the last polymer molecules have been excluded from the intervening gap between the bilayer surfaces.62,63 However, the large distance at which we measure this repulsive hump (three to four polymer diameters) makes the above explanation less satisfactory. Another possible explanation for the repulsive barrier further clarifies the difference between a constant depletion layer and the depletion attraction phenomena observed when two surfaces approach. Utilizing 31P-NMR, the vesicle tumbling experiments provide direct evidence of a lower local solution viscosity or depletion layer surrounding vesicles in solutions of 8k and 10k PEG. Depletion attraction phenomena arise when the depletion layers associated with two vesicles overlap, or, as in the case with the direct force measurements, when the two depletion layers associated with the bilayer-coated surfaces interact. The geometric confinement provided by two approaching vesicles or surfaces results in a lower concentration of polymer in the gap than in the bulk, resulting in a differential osmotic pressure. At closer separations, essentially no polymer remains between the surfaces, and thus a volume of pure water exists in the gap. This large osmotic difference now drives the two surfaces together into a depletion attraction enhanced attractive minima. However, the demixing required to create this volume of pure solvent is energetically unfavorable in a good solvent, resulting in a potential energy barrier.12,13 This could explain the monotonically increasing energy barrier measured with the SFA at separations of 3-4 RF. As the surfaces continue to approach, a larger (60) Richetti, P.; Kekicheff, P. Phys. Rev. Lett. 1992, 68, 1951. (61) de Gennes, P. G. Scaling Concepts in Polymer Physics; Cornell University Press: Ithaca, NY, 1979. (62) Israelachvili, J. Acc. Chem. Res. 1987, 20, 415. (63) Woodward, C. J. Chem. Phys. 1992, 97, 695.

Kuhl et al.

and larger demixing is required, increasing the energy barrier, until essentially no polymer remains in the gap at separations of 1RH and the surfaces jump together. Hence, the magnitude and the distance that the repulsive barrier is measured increases with polymer concentration and molecular weight. However, the demixing energy is not large enough to be the source of the repulsive barrier as shown in the following section.63 Lastly, and most likely, the repulsive barrier measured during the SFA experiments could be due to weak polymer adsorption to the supported bilayer surface with a transition from adsorption to depletion behavior as a function of separation. At large separations the polymer chains would not experience a significant confinement energy loss and could weakly adsorb to the bilayer surface. As the surfaces approach, these adsorbed polymer chains would be compressed leading to a repulsive force due to their confinement in the gap. At still smaller separations, this confinement would become more unfavorable, essentially driving the chains from the gap resulting in the established depletion interaction. The fact that the 31PNMR experiments show that 8k and 10k PEG do not adsorb on a vesicle surface is strong evidence against this supposition but does not preclude weak adsorption on supported bilayers as studied in the SFA. Entropic fluctuations and lipid mobility are greatly reduced when bilayers are deposited on a solid substrate.36 Moreover, we have already established that in the case of 20k PEG, the polymer does adsorb on both a supported bilayer and vesicle surface extending many times the coil size. Hence, it is quite possible that the repulsive barrier may be due to weak polymer adsorption at larger surface separations. Vesicle Interactions. The SFA experiments were conducted to model actual vesicle interactions. The measured repulsive barrier can be clarified by converting the measured force profiles (crossed cylinder geometry, also equivalent to a sphere on a flat) to the interaction energy of two vesicles. In the simplest approximation, we can model the vesicles as hard spheres in a solution of smaller polymer spheres. As shown in Figure 11A, the force profile (F/R vs D) measured with the SFA can be converted to the interaction energy, E, between two spherical vesicles of radii r1 and r2 using64

E(D) )

(

)∫

r1r2 r1 + r2

F dD R

(8)

where r1 ) r2 ) 150 Å for the EPC vesicles used in the light scattering measurements. Thus, as shown in Figure 11A, the corresponding energy barrier prior to the depletion enhanced attraction between two vesicles in 8k PEG increases from about 1kT at 5 wt % to almost 7kT at 10 wt %. Energy barriers of this magnitude are consistent with the kinetics of aggregation in the light scattering measurements, where aggregation occurred within 2 min of addition of PEG to the vesicle suspension. These calculations also explain why vesicles aggregate at a much reduced or insignificant rate once their diameter increases above 1000 Å, since the energy barrier for vesicles of this size under similar solution conditions would be in excess of 20kT.65 (We are currently conducting experiments to study the kinetics of vesicle aggregation as a function of vesicle radius and PEG concentration.) The demixing energy as two vesicles approach each other can be approximated by considering the restriction of the (64) Gee, M. L.; Tong, P.; Israelachvili, J. N.; Witten, T. A. J. Chem. Phys. 1990, 93, 6057. (65) Lentz, B. R.; McIntyre, G. R.; Parks, D. J.; Yates, J. C.; Massenburg, D. Biochemistry 1992, 31, 2643.

PEG Induced Depletion Attraction

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deform at constant internal volume, the minimum interaction energy, E0, is a combination of a negative adhesion energy term, Fa, and positive elastic bilayer stretching term, kc, which can be approximated by67

E0 )

Figure 11. Conversion of the measured force between two substrate-supported lipid bilayers in a solution of 8k PEG at 5 and 10 wt %, as measured using the surface force apparatus, to the interaction energy between two vesicles of 150 Å radii as a function of their separation. (A) The vesicles are modeled as hard sphere using eq 8. (B) The elastic deformation of the vesicles is included in the computation via eq 10.

polymer chains from the region between them. Using self-consistent mean field theory and assuming an ideal gas of hard polymer spheres, the magnitude of the demixing energy barrier at separation D ) ∆ can be approximated by

S ν ν ) Vexcluded log kT N N

(9)

since there are no enthalpic contributions,61 where ν is the polymer volume fraction, N is the number of monomers in a chain, and the maximum excluded volume, Vexcluded, occurs when the spheres are separated by the depletion layer, D ) ∆.66 Using eq 9, the demixing energy barrier is less than kT to kT for 5 and 10 wt %, respectively, and is not sufficient to account for the experimentally observed energy barriers. Thus, the repulsion seen prior to the attractive regime is most likely due to weak polymer adsorption with a transition from adsorption to depletion for MW less than 20k as the separation between the bilayer surfaces decreases. The hard sphere vesicle approximation breaks down once the energy barrier is overcome, since the attractive adhesion force (van der Waals and depletion attraction) will pull the two membranes together causing them to deform elastically and flatten.67 If the vesicles initially (66) Russel, W. B.; Saville, D. A.; Schowalter, W. R. Colloidal Dispersions; Cambridge University Press: Cambridge, 1989. Vexcluded between two spheres of equal radii, r, as a function of distance is given by

Vexcluded )

[

D3 4π 3D + (r + ∆)3 1 3 4(r + ∆) 16(r + ∆)3

]

(12)

πr2Fa4/3 41/3kc

(10)

As shown in Figure 11B, accounting for the deformation of the vesicles due to the attractive interaction modifies the interaction energy significantly at small separations. Moreover, this adhesion-induced deformation leads to the stretching of the bilayer, which will facilitate fusion as discussed in the next section. Fusion. Although both 8k and 10k PEG are commonly used to induce fusion, the exact nature of the mechanism by which this occurs has remained elusive.68 Through these studies it has been demonstrated that these molecular weights induce aggregation through a depletion mechanism. In regards to fusion,50 we propose that the exclusion of PEG, which induces the strong depletion attraction interaction, is essential in the aggregation/ fusion process.68,69 This depletion attraction, which was directly measured between two approaching bilayer surfaces in these studies, should also act laterally between adjacent headgroups.70 The condensation of headgroups by PEG is analogous to the effect of multivalent cations (Ca2+, Mg2+, etc.) on lipid bilayers.68 Both cause the exposure of more hydrophobic groups (inducing the very strong hydrophobic interaction), which then promotes fusion.44 Hence, in the case of PEG-mediated aggregation and fusion, the indirect action of PEG on the lipid membrane induces destabilization via the asymmetry of the local membrane environment at the contact region. Lipid molecules in the contact zone are exposed to pure water, while the lipids outside the contact region are exposed to bulk polymer solution (Figure 6). Since it has been well established that PEG causes condensation of lipids,45-49 this resulting asymmetry of the local polymer concentration leads to a thinning of the outer monolayers in the contact zone. Moreover, the deformation of the bilayers due to the depletion attraction enhanced adhesion will also lead to the stretching and thinning of lipids in the contacting region.66 Both of these effects render the bilayers in the contacting region more hydrophobic, which enhances their adhesion (stress-induced adhesion) and lowerssvia a long-range hydrophobic forcesthe activation barrier to fusion dramatically.44 The effect of the lateral depletion pressure on increasing the surface area of the lipids in the PEG-free interaction zone from a0, the equilibrium value, to a can be quantified, to first order, by considering the interfacial energy, µN, to be given by

(a - a0)2 + δaΠ a

µN ) 2γa0 + γ

(11)

where δ is the thickness of the outer monolayer and γ is (67) Chiruvolu, S.; Walker, S.; Israelachvili, I.; Schmitt, F.-J.; Leckband, D.; Zasadzinski, J. A. Science 1994, 264, 1753. (68) Ohki, S.; Doyle, D.; Flanagan, T. D.; Hui, S. W.; Mayhew, E. Molecular Mechanisms of Membrane Fusion; Plenum Press: New York, 1988. (69) Burgess, S. W.; McIntosh, T. J.; Lentz, B. R. Biochemistry 1992, 31, 2653. (70) Thus, PEG not only condenses lipid headgroups but also causes membrane proteins to aggregate outside of the contacting region, further aiding fusion. Atha, D. H.; Ingham, K. C. J. Biol. Chem. 1981, 256, 12108. (71) Yamazaki, M.; Ito, T. Biochemistry 1990, 29, 1309.

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the interfacial tension of the hydrocarbon-water interface. Minimizing eq 11 and in the limit of small ∆a/a we find

γ

a2 - a02 a2

)

2 2 a - a0 1 a - a0 ≈ kc kc ) 2 2 a a ∆a kc ) δΠ ) RkT (12) a

Using the following values for EPC vesicles at 25 °C, δ ) 20 Å, Π ) 105 N/m (Table 3, column 4), and kc ) 20 mN/m (this low value is presumably why fusion is more likely in the coexistence regime), we obtain ∆a/a ) 0.01 ) 1.0%. Since most bilayers cannot be stretched much beyond a few percent before they rupture, a similar but higher critical value should also apply to fusion (i.e., a value for ∆a/a of about 1-3%). Equation 12 shows that, all other things being equal, the factors favoring fusion would be an increasing (negative) osmotic pressure, increasing (negative) nonideal activity coefficient, increasing temperature, increasing monolayer thickness, and decreasing membrane elastic modulus. With these ideas in mind, we can now postulate the role of PEG in inducing vesicle fusion. As previously stated, the common protocol calls for adding 35-45% of PEG 8k

Kuhl et al.

or 10k to vesicle suspensions, which induces aggregation through depletion attraction.16,17,53 The large and highly nonideal osmotic gradient of PEG causes the outward flow of water, effectively deflating the vesicle.69 As a result, the floppy vesicles adhere strongly but without rupturing because the large stresses on the bilayer are released by the deflated membranes. Fusion is usually achieved after the mixture is diluted at which point the vesicles swell while still adhering to each othersa situation that results in stresses that can lead directly to fusion as discussed above.68 Conclusions. From this study, we have provided a physical basis for PEG-induced vesicle aggregation based on the polymer depletion forcesa well-known destabilizing interaction in colloid science. Thus, the first step in PEGinduced adhesion and fusion may now be understood in physicochemical terms. Acknowledgment. The work was supported by Grants GM30969 (S.W.H.) and PHS GM47334 (D.L.) from the National Institutes of Health and CTS-93 05868 (T.K.) and CTS-93-05868 (A.B.) from the National Science Foundation. Part of the work was carried out when S.W.H. was on sabbatical leave at UCSB. LA950802L