Langmuir 1999, 15, 8543-8546
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Notes Curvature of Zwitterionic Membranes in Transverse pH Gradients Josephine B. Lee,† Peter G. Petrov,‡ and Hans-Gu¨nther Do¨bereiner* Max-Planck-Institut fu¨ r Kolloid- und Grenzfla¨ chenforschung, Am Mu¨ hlenberg, 14476 Golm, Germany Received September 16, 1998. In Final Form: July 22, 1999
Introduction The curvature of a membrane depends on the elastic response of its bilayer to transverse solution asymmetry. We investigated the morphology of giant uni-lamellar phosphatidylcholine (PC) vesicles in solutions of varying pH-gradient across the membrane and found that raising the pH in the exterior of the vesicles induces budding. These shape changes are reversible upon lowering pH. Thus, the spontaneous curvature of a zwitterionic membrane can be controlled via the pH of the embedding solution. Controlling the curvature of amphiphilic interfaces is an important issue for both biological processes and technological applications. Vesicular transport of proteins in the cell1,2 proceeds via budding and fission3 of small satellite vesicles from their membranes of origin and final fusion with the target membranes. Mean curvature, which leads to budding, is induced by special protein coats.1,4,5 In the emulsification process of oil in water, the amphiphilic species and their molar ratio are responsible for the curvature of the newly created interface and, thereby, for the thermodynamic phase of the resulting microemulsion.6,7 Recently, there is also growing interest in amphiphilic membranes within the field of supramolecular chemistry.8 In this Note, we present first results on the curvature response of fluid zwitterionic membranes to pH asymmetry across the membrane. As a convenient model membrane system, we investigated giant unilamellar vesicles prepared from the single lipid 1-stearoyl2-oleoyl-sn-glycero-3-phosphocholine. The morphology of fluid lipid vesicles is governed by the bending elastic energy of their membrane.9-12 A † Present address: Department of Physics, University of Texas, Austin, TX. ‡ Permanent address: Bulgarian Academy of Sciences, Institute of Biophysics, 1113 Sofia, Bulgaria.
(1) Alberts, B.; Bray, D.; Lewis, J.; Raff, M.; Roberts, K.; Watson, J. D. Molecular Biology of the Cell, 2nd ed.; Garland: New York, 1989. (2) Rothman, J. E.; Wieland, F. T. Science 1996, 272, 227. (3) Do¨bereiner, H.-G.; Ka¨s, J.; Noppel, D.; Sprenger, I.; Sackmann, E. Biophys. J. 1993, 65, 1396. (4) Ju¨licher, F.; Lipowsky, R. Phys. Rev. E 1996, 53, 2670. (5) Mashl, R. J.; Bruinsma, R. Biophys. J. 1998, 74, 2862. (6) Gompper G.; Schick, M. Self-Assembling Amphiphilic Systems, Phase Transitions and Critical Phenomena, Vol 16; Domb, C., Lebowitz, J. L., Eds.; Academic Press: New York, 1994. (7) Safran, S. A. Adv. Phys. 1999, 48, 395. (8) Menger, F. M.; Gabrielson, K. D. Angew. Chem., Int. Ed. Engl. 1995, 34, 2091. (9) Helfrich, W. Z. Naturforsch. 1973, 28c, 693. (10) Evans, E. Biophys. J. 1974, 14, 923. (11) Lipowsky, R. Nature 1991, 349, 475. (12) Seifert, U. Adv. Phys. 1997, 46, 13.
comprehensive theory of vesicle shapes, the area-difference-elasticity (ADE) model, which includes the effects of bilayer elasticity, was recently developed.13,14 Briefly, the shape of a vesicle is determined by minimizing the bending energy of its bilayer with thickness D observing constraints on area A and volume V of the membrane capsule. The energy scale is set by the bending modulus κ. The relevant parameters are the reduced volume, v ) (V/(4π/3))/RA3, where RA ) (A/4π)1/2 defines the length scale, and a dimensionless combination of the preferred area difference between the monolayers, ∆a0 ) ∆A0/(8πDRA), and the spontaneous curvature of the membrane, c0 ) C0RA. It is given by
∆a0 ) ∆a0 +
1 c 2πR 0
(1)
where R denotes the ratio of elastic moduli for monolayer and bilayer bending. A careful comparison of experimental vesicle shapes with theoretical calculations allows a measurement of this quantity.15,16 The effect of pH on the morphology of fluid vesicles has been investigated before.17,18 In these studies, the membrane was composed of phosphatidylcholine phosphatidylglycerol (PC:PG) lipid mixtures. It was observed that vesicle curvature is very sensitive to pH gradients imposed across the lipid bilayer.18 It is the redistribution of PG (pH induced flip-flop) which is mainly responsible for the shape changes found in these systems. The redistribution leads to a change in the preferred area difference ∆a0 between the two monolayers. To the best of our knowledge, no systematic attempt has been made to investigate the curvature response of a single-component zwitterionic PC bilayer to transverse pH gradients. In this work, we concentrate on such a system. The important difference between the mixed PC:PG vesicles and single lipid PC vesicles is that the latter show negligible flip-flop.19,20 Nevertheless, we demonstrate experimentally that the curvature of a single-component zwitterionic membrane is sensitive to pH gradients across it. Obviously, this effect is due to reasons other than flip-flop. In the discussion, we suggest a simple theoretical picture for a possible mechanism involving association of negatively charged hydroxyl ions with the positive trimethylammonium group of the PC heads at high pH. The adsorption of ions induces an electrostatic spontaneous curvature c0 leading to a change in vesicle shape. Experimental Section 1-Stearoyl-2-oleoyl-sn-glycero-3-phosphocholine (SOPC) of purity greater than 99% was obtained from Avanti Polar Lipids, (13) Svetina, S.; Brumen, M.; Zˇ eksˇ, B. Stud. Biophys. 1985, 110, 177. (14) Miao, L.; Seifert, U.; Wortis, M.; Do¨bereiner, H.-G. Phys. Rev. E 1994, 49, 5389. (15) Do¨bereiner, H.-G.; Evans, E.; Kraus, M.; Seifert, U.; Wortis, M. Phys. Rev. E 1997, 55, 4458. (16) Do¨bereiner, H.-G.; Selchow, O.; Lipowsky, R. Eur. Biophys. J. 1999, 28, 174. (17) Farge, E.; Devaux, P. Biophys. J. 1992, 92, 347. (18) Mui, B. L.-S.; Do¨bereiner, H.-G.; Madden, T. D.; Cullis, P. R. Biophys. J. 1995, 69, 930. (19) Cornberg, R. D.; McConnell, H. M. Biochemistry 1971, 10, 1111. (20) Homan, R.; Pownall, H. J. Biochim. Biophys. Acta 1988, 938, 155.
10.1021/la981265i CCC: $18.00 © 1999 American Chemical Society Published on Web 09/03/1999
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Notes
Figure 1. Budding of a prolate vesicle induced by pH increase. A peanut-shaped vesicle (A) undergoes a shape transition to a budded shape (D) through transient pear shapes (B, C) as pH is raised to 10.1. USA. Sucrose and glucose (SigmaUltra grade, purity >99.5%) were from Sigma, Germany. Sodium hydroxide (SigmaUltra grade, purity >98%) and sodium chloride (5 M Sigma standard solution) also from Sigma, Germany, were used to adjust the pH and ionic strength of the external vesicle solution. All aqueous solutions were prepared using Millipore water. Giant vesicles were swollen from SOPC using a standard procedure. The essential steps of the preparation consisted of spreading a few drops (ca. 30 µL) of chloroform lipid solution (10 mg/mL) onto a roughened Teflon plate, evaporation of the solvent under vacuum, prehydration, and swelling in 219 mM sucrose solution. After successful swelling, vesicles were incubated in an iso-osmolal glucose solution of varying pH. At the range of pH values employed, the osmolarity is essentially fixed by the concentration of sugar molecules. To be able to observe and analyze vesicle morphology, we used a specially designed temperature-controlled microchamber,16 mounted on an inverted Zeiss Axiovert 135 TV microscope. In brief, our experimental protocol was as follows. First, the vesicles were transferred into the chamber by means of a microliter pump. Depending on their radius, the vesicles experienced a varying buoyancy force due to the different sugar solutions in the internal and external vesicle space. The larger vesicles quickly accumulated on the bottom of the chamber. At this stage, suitable prolate vesicles were selected for analysis. Phase contrast images were recorded at video-rate via a CCD camera, C 5985, Hamamatsu, Germany, and processed directly on a UNIX workstation, Indy R4400, 175 MHz, Silicon Graphics, Germany. A prominent advantage of our microchamber was that we could exchange the external solution during observation of a single vesicle, thus following and analyzing all vesicle shape changes. In this way, we managed to gradually increase pH of the external vesicle solution at iso-osmolal conditions and to determine the mean vesicle shape for several pH values. This was done by successful cycles of pumping of a solution with different pH and waiting for the system to equilibrate. This protocol created an increasing pH asymmetry across the vesicle membrane. The solution in the interior of the vesicles remained unchanged on experimentally relevant time scales.
Results Numerous vesicles exposed to changing pH of the surrounding medium showed similar behavior. Increasing pH induced shape transitions toward more outward curved morphologies, such as budded vesicles, whereas lowering pH led to inward curved shapes, e.g., stomatocytes. A typical example is shown in Figure 1. Here, budding of a prolate vesicle with a reduced volume v ) 0.78 ( 0.03 induced by raising pH is shown. In this particular example, budding takes place from the peanut-shaped vesicle (Figure 1A) via transient pear shapes (panels B and C of Figure 1). The final equilibrium configuration at pH ) 10.1 is seen in Figure 1D. At this low reduced volume, the sequence exhibits no clear instability of the prolate shape.15,21,22 This is an indication of the nearby tricritical point of the budding transition, where the first-order transition becomes continuous. At higher reduced volumes, the instability of the prolate shape was clearly visible (21) Do¨bereiner, H.-G.; Evans, E.; Seifert, U.; Wortis, M. Phys. Rev. Lett. 1995, 75, 3360. (22) Ka¨s, J.; Sackmann, E. Biophys. J. 1991, 60, 825.
Figure 2. Shape transitions of a vesicle driven by pH change. The initial budded shape (A), stable at pH ) 10.1, undergoes a transition to a stomatocyte (B) when pH is lowered to 5.5. Increasing pH again to 10.1 reestablished the budded shape (C). The snapshots represent the same vesicle as in Figure 1.
with other vesicles as expected from the first-order character of the budding transition in this regime.14,15 The pH was then lowered to a value of 5.5. This caused a transition of the budded vesicle (Figures 1D and 2A) to a stable closed stomatocyte22 with an internal bud, see Figure 2B. The morphological change proceeded via intermediate steps involving prolate and oblate shapes which are not shown. Subsequent return to high pH ) 10.1 reestablished the budded shape shown in Figure 2C. Thus, this sequence demonstrates the reversibility of shape changes induced by pH. Within experimental resolution, area and volume of the vesicle stayed constant during the experiment. We note that all pictures in Figure 1 and Figure 2 show the same vesicle with a radius RA ) (A/4π)1/2 ) 3.2 µm. One may obtain the difference in the effective preferred differential area ∆a0 of the two extremal vesicle shapes (Figure 2A, Figure 2B) by comparison to the theoretical shape phase diagram.14 Both shapes are located near limiting lines in the phase diagram corresponding to two connected spheres which are known analytically as a function of the reduced volume. At v ) 0.78, one finds (∆a0(bud) - ∆a0(sto)) ) 1.36. Since vesicle shapes depend only on the combined quantity ∆a0, one cannot distinguish between the two separate contributions (see eq 1) to the effective preferred differential area. Nevertheless, from our analysis, we conclude that raising pH in the exterior vesicle solution clearly increases the curvature of a vesicle membrane. It is known that PC lipids have negligible flip-flop on the time scale of a few minutes;19,20 i.e., the difference in the number of molecules between the monolayers ∆N stays constant. Thus, assuming that the preferred headgroup area a0 does not change during variation of pH, we have ∆a0 ∼ ∆Na0 ) const, and the total change in ∆a0 ) ∆a0 + (1/2πR)c0 corresponds to a shift in the spontaneous curvature c0 of the vesicle. Using R ) 1.4,14 we find ∆c0 ) 12. The described shape sequence was obtained with only sodium hydroxide present as an electrolyte in external solution. Concentrations varied depending on pH but were generally less than 10-4 mol/L. We also performed control experiments with essentially fixed electrolyte concentration using sodium chloride at 7 mOsmol partial osmotic
Notes
Langmuir, Vol. 15, No. 24, 1999 8545
pressure for the external vesicle solution. In this case, we observed qualitatively the same kind of shape transitions.
as
Γ ) Γ0
Discussion The experimental results presented above clearly show that pH has a strong effect on the curvature of a zwitterionic PC bilayer. We put forward a simple model which demonstrates that the process of adsorption of hydroxyl ions on the trimethylammonium group of PC at high pH induces appreciable electrostatic spontaneous curvature. Electrostatic contributions to the elastic constants of membranes have been considered before.23-27 Calculations of the electrostatic spontaneous curvature have been done using Debye-Hu¨ckel23 and Poisson-Boltzmann theory.24 Electrostatic coupling of the two monolayers of a membrane25 and the important issue of neutral surfaces25,26 have been considered. Recently, a quite comprehensive treatment of the electrostatics of bilayer bending has been given including conservation of charge in the vesicle interior.27 However, ion adsorption has not been considered so far. Here, we make a first step in this direction. It is known that OH- binds to the trimethylammonium group of the PC molecule at high pH.28 Thus, the outer surface of the vesicles becomes charged, and this should lead to a change in the curvature of the vesicle membrane. It is important to note that the total number of adsorption centers N0 on the outer surface of the vesicle with area Aads is constant. This is due to the stoichiometry of the adsorption process (one OH- per trimethylammonium group). Therefore, during bending, the surface charge density changes due to the stretching of the outer membrane surface. This situation differs from the case of constant surface charge density considered earlier.23 We treat the problem in the framework of the Debye-Hu¨ckel approximation, which allows to obtain an analytical dependence of the electrostatic spontaneous curvature on pH. The affinity of the hydroxyl anions toward the PC headgroup is characterized by the corresponding intrinsic equilibrium constant of dissociation Kb
Kb )
[PC] [PCOH-]
COH- )
Γ0 - Γ Cb exp(eψs/kT) (2) Γ
where the surface concentrations ≡ Γ and [PC] + [PCOH-] ≡ Γ0 correspond to partial and full coverage, respectively. In eq 2, COH- is the bulk concentration of the hydroxyl ions in the immediate vicinity of the vesicle surface. It is related to the bulk OH- concentration away from the interface by COH- ) Cb exp(eψs/kT), where ψs is the electrostatic potential on the outer vesicle surface where the adsorption takes place. Cb is directly related to the solution pH via Cb ) NA10pH-14 mol/L, where NA is Avogadro’s constant. Equation 2 is the well-known Davies adsorption isotherm.29 Calculating the surface potential ψs for cylindrical symmetry within the Debye-Hu¨ckel approximation, the adsorption isotherm (2) can be written [PCOH-]
(23) Winterhalter, M.; Helfrich, H. J. Phys. Chem. 1988, 92, 6865. (24) Mitchell, D. J.; Ninham, B. W. Langmuir 1989, 5, 1121. (25) Winterhalter, M.; Helfrich, H. J. Phys. Chem. 1992, 96, 327. (26) May, S. J. Chem. Phys. 1996, 105, 8314. (27) Chou, T.; Jaric´, M. V.; Siggia, E. D. Biophys. J. 1998, 72, 2042. (28) Tatulian, S. A. In Phospholipids Handbook; Cevc, G., Ed.; Marcel Dekker: New York, Basel, Hong Kong, 1993; p 511. (29) Diamant, H.; Andelman, D. J. Phys. Chem. 1996, 100, 13732.
1 + 8π Kb
lB χ2
1
[
lB K0(χRads) 1 + 4π Γ χ K1(χRads)
]
(3)
where lB ) e2/kT denotes the Bjerrum length and χ-1(pH) ) [8πCb(pH)lB]-1/2 is the Debye screening length. Note that in the present case, where no inert electrolyte is added, the Debye length χ-1 is set by the solution pH via Cb. The surface coverage Γ controls the surface charge density on the outer vesicle surface, which has area Aads and radius of curvature Rads. K0 and K1 are the modified Bessel functions of zeroth and first order, respectively. Within the Debye-Hu¨ckel approximation, the electrostatic free energy per unit area, gel, can be calculated as gel ) -ψsΓe/2. In this way, the dependence of gel on pH, the surface coverage Γ, and the radius Rads is obtained
lB K0(χRads) gel ) 2π Γ2 kT χ K1(χRads)
(4)
The essential step in our derivation is to find the preferred mean curvature (in cylindrical symmetry), C ) 1/2R, of the elastic lipid bilayer, which minimizes the sum of the electrostatic and bending elastic energies. We make use of a minimization procedure described earlier.30 The important point is that the area, Aads ) (1 + DC)A, and the radius, Rads ) R + D/2, of the outer interface, where the adsorption takes place, are slightly larger than the area A and the radius R of the central surface, respectively. The relevant length is the thickness D of the membrane. During bending of the membrane, both Rads and Aads change their respective magnitudes. The preferred differential area ∆a0 may stay constant, nevertheless. We expand the total electrostatic energy, gelAads, in powers of (χR)-1 up to second order taking into account all implicit dependences on the curvature radius. Then, the electrostatic energy is balanced against the bending elastic energy of the membrane 2κC2A, where κ is the bending modulus. This leads to the following expression for the dimensionless spontaneous curvature
c0 )
1 kT R (1 + 64πlB κ A
(
χ(pH)D) 1 +
)
(
˜0 χ2(pH) 2 2Γ G 8πlBKb Kb
[
χ(pH)
])
χ2(pH) 1+ 8πlBKb
2
(5)
where Γ ˜ 0 ) N0/A denotes the fixed number density of adsorption sites with respect to the central surface. The function G is defined by G(u) ) ((u + 1)1/2 - 1)2/(u + 1)1/2. Equation 5 gives the spontaneous curvature as a function of pH provided the dissociation constant Kb is known. Let us compare our theoretical prediction with the experimentally derived value (∆c0)exp ) 12 (see Results). The equilibrium constant Kb can be found from the corresponding pK value of association, Kb ) NA10(pK-14) mol/L; we take pK ) 11.28 Inserting the vesicle radius (RA ) 3.2 µm) and known values for the other constants14 into eq 5, (kT/κ ) 0.04, D ) 5 nm, Γ ˜ 0 ) 1/(0.7 nm2), we find (∆c0)theo ) c0(pH ) 10.1) - c0(pH)5.5) ≈ 13 for the change in the spontaneous curvature. Thus, it seems that a reasonable agreement between theory and experiment for ∆c0 is obtained. However, we note that the Debye(30) Lipowsky, R.; Do¨bereiner, H.-G. Europhys. Lett. 1998, 42, 219.
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Hu¨ckel approximation used is not strictly valid under the conditions of our experiment. Further, we have neglected any dependence of the preferred headgroup area a0 on charge density. Although the membrane is charged only weakly by 2% as pH is raised from 5.5 to 10.1, such an effect could also contribute appreciably to the observed increase in ∆a0. In general, a full analysis should take into account all changes in the intrinsic elastic constants which may be caused by adsorption. Experimentally, there is clear evidence that pH variations strongly affect the curvature of zwitterionic membranes. Our theoretical result, eq 5, which gives the right order of magnitude,
Notes
quantifies one of several possible (electrostatic) mechanisms. Further measurements of the spontaneous curvature of charged vesicles in asymmetric electrolyte solutions of controlled concentration and pH are underway in our laboratory. Acknowledgment. J.B.L. and P.G.P. gratefully acknowledge financial support from the Max Planck Gesellschaft. We enjoyed useful discussions with G. Gompper, J. Ka¨s, R. Lipowsky, R. Netz, and U. Seifert. LA981265I
