J. Phys. Chem. B 2008, 112, 13629–13634
13629
Dimpled Vesicles: The Interplay between Energetics and Transient Pores Susan D. Gillmor*,† and Paul S. Weiss*,‡ Department of Chemistry, George Washington UniVersity, 725 21st Street, N.W., Washington, D.C. 20052, and Departments of Chemistry and Physics, The PennsylVania State UniVersity, 104 DaVey Laboratory, UniVersity Park, PennsylVania 16802-6300 ReceiVed: April 1, 2008; ReVised Manuscript ReceiVed: August 8, 2008
The familiar biconcave shape of the red-blood cell (RBC) deforms as the cell travels through capillaries. Its dimpled configurations are unique cell shapes and display malleability to form echinocytes, discocytes and stomatocytes, in response to external perturbations. Sheetz and Singer introduced intercalating species to the exterior lipid leaflet of the membrane to promote cup-shaped stomatocytes, and observed that additives to the interior had the opposite effect. Shape transformations appear to be controlled via the RBC bilayer and the asymmetric surface areas of the two leaflets [Proc. Natl. Acad. Sci. U.S.A.1974, 71, 4457]. Our system promotes area-difference between the lipid bilayer leaflets from a fully symmetrical system and has mimicked the RBC discoid. In our analysis, we explore the system energetic and geometric confinements, which points to transient pores as enablers for the vesicles to deflate and thereby to assume lower profiles. Introduction Bilayer coupling has been the single dominant parameter used to explain the many shape transformations of the erythrocyte from a biconcave disk (discoid) to an echinocyte (spiny-featured cells or vesicles). As suggested by Sheetz and Singer,1 the asymmetry and the difference in area between the inner and outer leaflets promote formation of discoids and stomatocytes (cup-shaped cells or vesicles) or echinocytes in red blood cells (RBCs). Their experiments on drug intercalation into either the cytoplasmic leaflet or the exterior leaflet are classic examples of membrane-coupled response. The calculations from Lim et al. have pinpointed the role of leaflet area, which agrees with Sheetz and Singer’s earlier findings. If stretch and shear elasticities of the membranes are held constant, then the relaxedarea-difference (∆A) between the two leaflets is the dominant factor for erythrocyte shape transformations.2 For vesicles, Sventina and Zeˇksˇ have calculated the shape relationship between volume, bending energy of the lipid bilayer, and area-difference.3 Their work has contributed to the development of the area-difference elasticity (ADE) theory on vesicle shape parameters.3-5 These calculations predict vesicle transformation from ellipsoids to discoids and stomatocytes by varying the volume (Vmax/Vreal) of vesicles. Ka¨s and Sackmann have catalogued vesicle shape transformation in reduced volume conditions as a function of temperature.6 In their review, they built a detailed shape-phase diagram drawing from their own observations and from Sventina, Zˇeksˇ and Seifert et al.’s work.3,5-8 Berndl et al. added that the thermal expansivity differences between the two lipid layers create an asymmetry that promotes a variety of vesicle shapes and explains the variety.9,10 In their system, vesicles of a neutral lipid are placed in a temperature-isolated chamber and are heated from ∼20 to 44.1 °C. From their observations of vesicle shapes, they were * Corresponding authors. E-mail: (P.S.W.)
[email protected]. Telephone: (814) 865-3693. Fax: (814) 863-5516. † Department of Chemistry, George Washington University. ‡ Departments of Chemistry and Physics, The Pennsylvania State University.
Figure 1. Cross-sectional schematic illustration of vesicle confinement in a thin layer of sucrose solution. In thin regions of the aqueous medium, vesicles become sandwiched between the two interfaces (aqueous-glass and aqueous-air) and over time, change shape.
able to equate the spontaneous curvature of bilayers with shape transformations. Red blood cells traverse small capillaries and deform to navigate these spaces. Our system uses geometric confinement to induce vesicle deformation. We form a thin (2-5 µm) aqueous film between a glass coverslip and an air bubble in a sealed compartment (Figure 1). We expect no net evaporation and no osmotic driving force to reduce the vesicle volume. Additionally, sucrose diffusion across lipid bilayers occurs more slowly than the shape and volume dynamics behavior in this system. At 25 °C, water permeability across the membrane is ∼3 × 10-3 cm/s.11 However, sucrose at 25 °C has a significantly lower permeability of ∼8 × 10-14 cm/s.12 Given these constraints, another mechanism must play a key role. We analyze the vesicle shape in terms of the system energetics and line tension of the lipid bilayer to account for the shape and volume changes. The resulting discoids and stomatocytes are induced by energy minimization. Our observed shapes match those predicted by ADE theory. Experimental Methods Materials. The following materials were used as purchased: phospholipid DOPC (1,2-dioleoyl-sn-glycero-3-phosphocholine) from Avanti (Alabaster, AL); the fluorescent probes TRITC
10.1021/jp802808x CCC: $40.75 2008 American Chemical Society Published on Web 10/07/2008
13630 J. Phys. Chem. B, Vol. 112, No. 43, 2008 (N-(6-tetramethylrhodaminethiocarbamoyl)-1,2-dihexadecanoylsn-glycero-3-phosphoethanolamine, triethylammonium salt) and DiI (1,1′-dioctadecyl-3,3,3′,3′-tetramethylindocarbocyanine perchlorate) from Molecular Probes (Eugene, OR); chloroform (VWR; West Chester, PA) and methanol (VWR). All water was filtered before use through a Barnstead Nanopure filter and had a resistivity greater than 18.0 MΩ-cm (Boston, MA). Vesicle Formation. Briefly, we form our giant unilamellar vesicles through an electroformation technique developed by Meleard et al.13 and modified by D’Onofrio et al.14 Our lipid solution consists of 450 µL chloroform, 20 µL 10 mg/mL DOPC and 2 µL of 100 µg/mL TRITC or DiI. Several drops of the lipid solution are applied along platinum (Pt) wires, anchored 3 mm apart. After vacuum drying for 1-2 h to form a lipid cake, the Pt wire electrodes are immersed in 50 mM sucrose at 60 °C15 and are then connected in parallel to a function generator (HP33120A, Hewlett-Packard, Palo Alto, CA) to expose the lipid cake to a varying AC field to produce vesicles.13 The vesicle solution and Pt electrodes are cooled to room temperature in an insulated box with a heated aluminum block. Sample Preparation. As schematically illustrated in Figure 1, ∼20 µL of the vesicle solution is placed inside a 20-mmwide, 0.5-mm-thick silicone ring on a microscope coverslip to form a thin film of vesicle solution. A microscope slide is placed on top of the ring and sealed. The total volume of the sample space is 150 µL. Microscopes. We have used an inverted Nikon Ellipse TE300 microscope (Melville, NY) and a LSM Pascal Zeiss confocal microscope (Thornwood, NY) for imaging. For confocal work, we use a 40× water immersion lens. All vesicles are imaged at ∼20 °C. Results and Analysis From the cross-sectional schematic in Figure 1, we show that vesicles are pinched between the two interfaces, which force them to deform. In Figure 2, one vesicle is tracked over a period of 30 min, and its shape transformation is documented. From the initial round form with a height greater than 8 µm in Figure 2a, the vesicle becomes increasingly flat, reaching a final height of ∼2.5 µm in Figure 2f. The decreasing height of the aqueous film on the glass substrate drives the shape transformation when the vesicle moves into a thinner region. From the individual XY slices in Figure 2d-f, dimple-like features first appear at the aqueous-air interface and are easily visualized due to lipid debris in the vesicle. In Figure 2e at t ) 21 min, the vesicle has become a discoid with shallow dimples at both the aqueousglass and the aqueous-air interfaces. The vesicle has a final height of ∼2.5 µm in Figure 2f before it ruptures. We have captured the transformation of several vesicles from spherical to dimpled and have observed many discoid and stomatocyte vesicles in their final deformed states. However, Figure 2 is the best example, showing the entire span from squat ellipsoid, to dimpled biconcave disk, to ruptured vesicle. In Figure 3, we observe a discoid and a stomatocyte under identical conditions as Figure 2. The deformed vesicles are oriented toward the aqueous-glass interface and the aqueous-air interface, respectively. These vesicles proved stable in their shapes and did not rupture after greater than 30 min. Through tracking the vesicle in Figure 2 from its rounded shape to the discoid, we have calculated the volume (V, eq 1) and have estimated the surface area (SA, eq 2) using Knud Thomsen’s formula. We approximate the surface area and volume to an ellipsoid and determine the axes from the largest XY slice at each time point:
Gillmor and Weiss
[
SAEllipsoid ) 4π
VEllipsiod )
4π (L L L ) 3 1 2 3
(L1L2)1.61 + (L1L3)1.61 + (L2L3)1.61 3
(1)
]
(1/1.61)
(2) The above equation is an approximation to the general spheroid equation with an error of 1.06%.16 L1 and L2 are half of the major and minor ellipsoid axes, and L3 is half of the height. The height is determined from the total number of XY slices of the vesicle and the thickness (0.49 µm) of each slice. From this analysis, as shown in Figure 4, the surface area of the vesicle remains constant with an average value of 488 ( 19 µm2, fluctuating by 4%. In contrast, the volume decreases from 1010 to 380 fL over a period of 30 min. As the vesicle transforms its shape, the volume decrease does not occur in a linear fashion. While we have simplified the vesicle volume to that of an ellipsoid, fluctuating dimples at the interfaces decrease the volume, while the three axes of the ellipsoid remain constant. This approximation introduces some error into our estimate. Also, the volume decrease depends on the confines between the interfaces and does not necessarily follow a linear decline. Discussion The mechanism of vesicle deformation on the surface must accomplish two tasks simultaneously: (1) decrease the volume of the vesicle to allow for a high surface area/volume ratio for shape transformation, and (2) navigate the energetic barriers introduced through surface energies, which define the geometrically confined space. While the most likely actor in the decrease in vesicle volume would seem to be transmembrane diffusion or osmoticly driven dehydration of the vesicles, our analysis of the system does not support these mechanisms. If evaporation is occurring, then the media surrounding the vesicles would increase in sucrose osmolarity, dehydrate the vesicles and allow them to deform into the confined space. However, we seal our microscope slides. Initially, we have ∼20 µL of vesicle and sucrose solution in a 150 µL space, all at one bar pressure. The partial pressure of water (PH2O) at one bar is 2.34 kPa at 20 °C.17 In a worst case scenario, following the ideal gas law, if the slide experiences an increase in temperature (∆T) 15 °C, which we have not observed, then PH2O increases to 2.44 KPa, which corresponds to a loss of 0.0915 nL of water from the initial 20 µL. We expect that ∆T < 3 °C. Even in the worst case calculations, the decrease in water from the solution is less than 92 pL of the total 20 µL, which is insufficient for osmolarity to be the driving force behind the vesicle volume loss. At 25 °C, water permeability across the membrane is ∼3 × 10-3 cm/s.11 However, sucrose at 25 °C has a significantly lower permeability of ∼8 × 10-14 cm/s.12 Since the DOPC membrane does not undergo a phase transition, the sucrose permeability will rise slightly due to temperature, but will remain at the same order of magnitude (∼1 × 10-13 cm/s). Movement of sucrose across a 5-nm bilayer would take ∼1700 h, compared to 166 µs for water in a one-dimensional calculation. The inability of sucrose to diffuse across the lipid bilayer effectively maintains the volume of the vesicle. Without proteins to control the solute movement actively, the interior and exterior solutions must have identical concentrations (50 mM sucrose). Water molecules exchange across the bilayer,11,18 but any net loss of water would increase the concentration of sucrose inside the vesicle and create an osmotic gradient, which would then drive
Vesicle Shape Transformation
J. Phys. Chem. B, Vol. 112, No. 43, 2008 13631
Figure 2. Vesicle shape transformation. A single vesicle’s shape transformation is tracked over ∼30 min. The lipid debris in the vesicle interior highlight the depressions within the vesicle. (a-c) The images represent several viewpoints of the same vesicle. The stacked images adjacent to the equatorial slice are oriented such that the glass substrate edge corresponds to the equatorial image edge. The equatorial slice shows the vesicle in the XY plane at its maximum radius. The XZ and YZ views are reconstructions from the stack of XY slices. The three-dimensional renderings in parts a-c are composites of individual XY slices with a z-thickness of 0.49 µm. We observe the height begin to decrease from t ) 0 min in part a, to t ) 5 min in part b, to t ) 10 min in part c as the vesicle becomes confined in a thin region of the water film. In sequences d-f, the vesicle is increasingly squeezed from less than 5 µm at t ) 18 min in part d, to ∼3.5 µm at t ) 21 min in part e, to 2.5 µm in part f at t ) 26 min, as shown in the individual z-slices. In part d, we observe a depression in the middle of the vesicle as it faces the air interfaces, and similarly, in part f, there is a dimple at the glass surface. Only in part e do we observe dimples on both the glass-aqueous interface and the aqueous-air interface. We have cropped the images and have adjusted brightness and contrast; no other alterations have been made to the data.
water into the interior the vesicle. Therefore, transmembrane diffusion does not appear to be the determining factor for the vesicle deformation process. In order to deform into a stomatocyte, vesicles must first deflate, which diffusion does not allow on this time scale. If transmembrane diffusion and evaporation do not allow for net volume loss of the vesicle, another mechanism must be responsible. Transient pores or membrane defects have been used to model lipid flip/flop to redistribute lipid molecules between the inner and outer leaflets. Without defects in a lipid bilayer, the rearrangement of the lipid molecules between the bilayer leaflets is significantly hindered. The hydrophilic headgroup must dehydrate to pass through the hydrophobic core of the bilayer. Wimley and Thompson studied lipid flip/flop in
several different lipid environments and observed that the lipid flip/flop dynamics do not appear tied to the dehydration energy barrier.19-21 They observe dependence on a two-phase state, suggesting that flip/flop occurs at the boundaries of the domains, and at bilayer curvature. They have concluded that the universality of lipid flip/flop suggests a common bilayer response to lipid rearrangement pressures, such as defect sites.21 Raphael and Waugh have characterized the flip/flop rate in vesicles under mechanical stress and have concluded that higher than expected flip/flop rates point to lipid movement along defects to relax transmembrane stress.22 Similar behavior has been observed in phase transitions. de Gier’s discussion of membrane permeability points out that a maximum of permeability occurs during the transition between
13632 J. Phys. Chem. B, Vol. 112, No. 43, 2008
Gillmor and Weiss TABLE 1: Energy Contributionsa interaction energies water-water water-DOPC water-glass DPPC-glassb
value
references
23.3 kJ/mol 28 kJ/mol 72 mJ/m2 43-54 mJ/m2
Suresh and Naik34 Bhide and Berkowitz35 Vargaftik et al.36 Jurak and Chibowski37
a The table compares the interaction energies of the various components of the system. See text for further discussion. b The DPPC-glass value is used as an approximation for that of DOPC-glass.
Figure 3. Examples of vesicles in discoid and stomatocyte configurations. Similar to Figure 2, the images are reconstructions of XY slices, and XZ and YZ cut-aways are composed of a stack of XY slices. The XY images is a slice that shows the dimple of the vesicle, while the XZ and YZ cut-aways reveal the profile. Each of these vesicles has been observed under identical conditions as those seen in Figure 2. We have cropped the images and have adjusted brightness and contrast; no other alterations have been made to the data.
Figure 4. Decrease in vesicle volume. The volume of the vesicle in Figure 2 (9) decreases over the ∼30 min period of the vesicle shape transformation (1010 to 380 fL). In contrast, the surface area (b) remains stable with an average (line) value of 488 ( 19 µm2 or 4%.
gel and fluid phases.23 Structural defects from molecular packing mismatches create porous areas between mini-domains (below optical resolution) of ordered gel phase and disordered fluid phases during the phase transition. Vesicles leak cations, polar molecules and other small solutes through these pores estimated to be ∼8 Å.23-26 This phase transition leakage has been documented thoroughly for the 1,2-dimyristoyl-sn-glycero-3phosphocholine (DMPC) lipid vesicles, and has been shown to produce deformed vesicles on planar surfaces.27 While our DOPC vesicles do not undergo any phase transitions in our
temperature regime (20 °C), defects, induced through geometric confinement, would allow solutes to pass unhindered through the bilayer. Paula et al. investigated transient pores as a shortcut for ionic and neutral solutes to cross the lipid bilayer.28 They concluded that both saturated and unsaturated lipids play a role in the permeation mechanism due to the packing and defect formation differences in the lipids, which is supported in de Gier’s findings.23 However, they found that neutral-molecule crossings fit a solubility-diffusion mechanism, not a pore model. Unlike sucrose, their nonelectrolyte solutes (urea and glycerol) had moderate permeabilities (4.1 × 10-6 cm/s and 5.4 × 10-6 cm/s, respectively29). Due to the low permeability of sucrose, an exclusive diffusion-based model is unlikely. It is more probable that a pore-based mechanism dominates the process of low permeability solutes, ionic or nonionic. Following the defect transient pore model, Raphael et al. have modeled these defect pores as a means to alleviate transmembrane stress.22,30 They have found an experimental lipid flux of 6.3 × 109 molecules cm-2s-1.30 For a vesicle with a surface area of ∼1000 µm2, the corresponding movement of lipids molecules to the opposite leaflet is 6.3 × 104 molecules/s at 25 °C. Raphael22,30 and Evans31 have studied the transient pore phenomena under mechanical manipulation and have found a temperature dependence on pore population. The geometric confinement of our system drives the mechanical process and our temperature (20 °C) is sufficient for pore formation to alleviate both the transmembrane stress and to accommodate the energy barriers in the form of the aqueous-air interface and the aqueous-glass interface. To evaluate the decrease in volume and shape transformation in the geometrically confined space, we compare the system energies. As shown in Table 1, DOPC-water hydrogen affinity is slightly higher than the water-water intermolecular interactions, leading to fully hydrated polar headgroups. At the glass interface, while the water-glass energetics are known, the glassDOPC value is not. However, the glass-DPPC (1,2-dipalmitoylsn-glycero-3-phosphocholine) energies are known, and DOPC and DPPC have identical headgroups, which both interact with the water and glass. We thus assume that the glass-DPPC value is a reliable approximation for glass-DOPC. When the water-glass and glass-DPPC energies are compared, the water-glass interaction is favored over that of the glass-DPPC. Both the stronger water-DOPC values and the favored water-glass energetics reinforce the experimental finding of a water layer between supported lipid bilayers and glass supports.32,33 We do not have a DOPC-air interface energy value. In this evaluation of energetics, we find that the vesicle favors remaining fully in the aqueous medium, instead of attaching to either interface. To accommodate volume constraints due to geometric confinement, transient pores must play a key role to allow the vesicle to reshape and to avoid contact with the air and glass.
Vesicle Shape Transformation
J. Phys. Chem. B, Vol. 112, No. 43, 2008 13633
TABLE 2: Energetics of a Single Vesiclea
Summary
energetics on model vesicle (r ) 8.9 µm, SA ) 1000 µm2)b references water-water water-DOPC water-glass DPPC-glassc transient pores line tension nanopores (1-11 nm) micropores (2-10 µm)
6.3 pJ 7.6 pJ 72 pJ 43-54 pJ
Suresh and Naik34 Bhide and Berkowitz35 Vargaftik et al.36 Jurak and Chibowski37
10-30 pN 10-7 pJ, 24kBT 10-5 pJ, 2400kBT
Brochart-Wyart39 Raphael, Lenz30,38 Brochart-Wyart39,40
a The table scales the energies to a single vesicle and compares them to the energetic cost of a transient pore. b Using a DOPC head-head distance of 35 Å35,41 for each leaflet, the model vesicle represents 2.7 × 10-16 mole of DOPC. c The DPPC-glass value is used as an approximation for that of DOPC-glass. See text for further discussion.
At ∼20 °C, sucrose permeability through a bilayer is ∼8 × 10-14 cm/s, which is not sufficient to allow the sucrose to exit through diffusion over the 30 min time period.12 Berndl et al.’s vesicle system uses Millipore (high resistivity) water, which easily passes across the bilayer with a permeability of 3 × 10-3 cm/s.11 Also, transient pores have been proposed as a means to alleviate leaflet compression and tension under mechanical strain.30 Pores allow the exchange of lipid molecules from one leaflet to the other, allowing the hydrophilic headgroup to circumvent the hydrophobic bilayer core.20-22,30 Further, the exchange can induce or relieve asymmetry between the leaflets. In the case of the discoids and stomatocytes, the increase in asymmetry allows for flatter vesicles (or cells) and other unique shapes. Evans first proposed asymmetry as a means to explain crenation of RBCs in the presence of chemical perturbations.42 From ADE theory of Lipowsky, Ka¨s, Sackmann, Evans, Svetina, and others,3,4,6,9 asymmetry between the lipid leaflets is an accepted explanation for shape dynamics in vesicles. From Berndl et al.’s thermally induced stomatocyte example, the vesicle’s asymmetry occurred in the 43.8-44.1 °C temperature range.9 While we expect minor sample heating due to laser heat dissipation, we do not expect a ∼10-20 °C temperature increase during imaging. In our system, both the interface confinement and the transient pores lead to the asymmetric vesicle structures. The interfaces squeeze the vesicle and the transient pores allow for volume loss and lipid rearrangement between the leaflets. In Table 2, we compare the energies on the size scale of a model vesicle (radius ) 8.9 µm, SA ) 1000 µm2, V ) 2950 fL) and the energetic cost of a transient pore, which is the product of the pore diameter and the line tension. Transient pores have been postulated with 1-11 nm diameters to alleviate mechanical stress, allowing lipid flip-flop and solute exit.30,38 Large pores, induced via high intensity light radiation and detergents, have been observed on the micron size-scale (2-10 µm).39,40 Surface tension values range from 10-30 pN.39 When we analyze the energy required to form a pore compared to the energy associated with the aqueous-glass and aqueous-air interfaces, pore formation has a value many orders of magnitude lower (10-7-10-5 pJ/pore, 24-2400 kBT) than the interfacial energies (6-54 pJ) on the model vesicle. It therefore seems likely that, over the course of 30 min, the vesicle deflates through the transient pores to minimize interactions with air and glass surfaces. We have not observed transient pores optically, which would indicate that any pores that form are less than ∼500 nm in diameter and thus below our spatial resolution.
The asymmetry of inner and outer leaflet surface areas has been inferred from the shape transformation of the vesicle, when it is squeezed into a thin aqueous film. From Sheetz and Singer’s findings, asymmetry can be induced in red blood cells (RBCs) through the intercalation of drugs to the cystolic or extracellular leaflets.1 Vesicle asymmetry and shape transformation is similarly imposed through intercalation of additives in the extracellular leaflet. Indeed, Yamashita et al. have captured liposome shape transformation when a short-chain peptide intercalates into the outer leaflet.43 Additionally, vesicle manipulation through this strategy creates an advantageous means to perform complex experiments within confined volumes. The interface sandwich induces vesicle deformation, and the asymmetric response of the leaflets results in discoids and stomatocytes. Red blood cells respond to the narrowing of capillaries and deform to perfuse and to deliver oxygen throughout the body. While vesicles lack the interior Actin structure, inducing vesicle shape transformation via external forces gives us a model to test the RBC unique shape and response to confined geometries. Exposing vesicles to a thin water film induces deformation when the vesicle is confined between interfaces. Transient pores offer the lowest energy pathway to reduce the vesicle volume and allow it to flatten in the presence of sucrose. The pores also allow lipid molecules to flip leaflets. The discoid and stomatocyte shapes are indicative of asymmetry between the leaflets. We expect the largest contributions to the asymmetric response from the interfaces and transient pores and minor contributions from sample heating and thermal expansivity. The energetic analysis of the shape transformation from sphere to biconcave ellipsoid elucidates the roles of interfaces and confined geometries in vesicle shape. Acknowledgment. The authors thank Professor Q. Du for many useful discussions and the Center for Quantitative Cell Analysis in the Huck Institutes of Life Sciences. We also thank the Penn State Center for Nanoscale Science (a National Science Foundation MRSEC) for financial support. The authors declare no financial conflict of interest. References and Notes (1) Sheetz, M. P.; Singer, S. J. Proc. Natl. Acad. Sci. U.S.A. 1974, 71, 4457. (2) Lim, H. W. G.; Wortis, M.; Mukhopadhyay, R. Proc. Natl. Acad. Sci. U.S.A. 2002, 99, 16766. (3) Svetina, S.; Zˇeksˇ, B. Eur. Biophys. J. 1989, 17, 101. (4) Miao, L.; Seifert, U.; Wortis, M.; Dobereiner, H. G. Phys. ReV. E 1994, 49, 5389. (5) Svetina, S.; Zˇeksˇ, B. Anat. Rec. 2002, 268, 215. (6) Ka¨s, J.; Sackmann, E. Biophys. J. 1991, 60, 825. (7) Svetina, S.; Zˇeksˇ, B.; Waugh, R. E.; Raphael, R. M. Eur. Biophys. J. 1998, 27, 197. (8) Seifert, U.; Berndl, K.; Lipowsky, R. Phys. ReV. A 1991, 44, 1182. (9) Berndl, K.; Ka¨s, J.; Lipowsky, R.; Sackmann, E.; Seifert, U. Europhys. Lett. 1990, 13, 659. (10) Lipowsky, R. Nature 1991, 349, 475. (11) Finkelstein, A. J. Gen. Physiol. 1976, 68, 127. (12) Brunner, J.; Graham, D. E.; Hauser, H.; Semenza, G. J. Membr. Biol. 1980, 2, 133. (13) Meleard, P.; Gerbeaud, C.; Pott, T.; Fernandez-Puente, L.; Bivas, I.; Mitov, M. D.; Dufourcq, J.; Bothorel, P. Biophys. J. 1997, 72, 2619. (14) D’Onofrio, T. G.; Binns, C. W.; Muth, E. H.; Keating, C. D.; Weiss, P. S. J. Biol. Phys. 2002, 28, 605. (15) Akashi, K.; Miyata, H.; Itoh, H.; Kinosita, K., Jr. Biophys. J. 1998, 74, 2973. (16) McGahon, M. K.; Dawicki, J. M.; Arora, A.; Simpson, D. A.; Gardiner, T. A.; Stitt, A. W.; Scholfield, C. N.; McGeown, J. G.; Curtis, T. M. Am. J. Physiol. Heart Circ. Physiol. 2007, 292, H1001.
13634 J. Phys. Chem. B, Vol. 112, No. 43, 2008 (17) CRC Handbook of Chemistry and Physics; Lide, D. R., Ed.; Taylor & Francis Group, 2007; Vol. 89. (18) Huster, D.; Jin, A. J.; Arnold, K.; Gawrisch, K. Biophys. J. 1997, 73, 855. (19) Wimley, W. C.; Thompson, T. E. Biophys. J. 1990, 57, A268. (20) Wimley, W. C.; Thompson, T. E. Biochemistry 1990, 29, 1296. (21) Wimley, W. C.; Thompson, T. E. Biochemistry 1991, 30, 1702. (22) Raphael, R. M.; Waugh, R. E. Biophys. J. 1996, 71, 1374. (23) de Gier, J. Chem. Phys. Lipids 1993, 64, 187. (24) Blok, M. C.; van der Neut-Kok, E. C. M.; van deenen, L. L. M.; de Gier, J. Biochim. Biophys. Acta 1975, 406, 187. (25) Haest, C. W. M.; de Gier, J.; van deenen, L. L. M.; Verkleij, A. J.; van Es, G. A. Biochim. Biophys. Acta 1972, 288, 43. (26) Phillips, M. C.; Graham, D. E.; Hauser, H. Nature 1975, 254, 154. (27) Lai, A. C.; Wan, K.; Chean, V. Biophys. Chem. 2002, 99, 245. (28) Paula, S.; Volkov, A. G.; van Hoek, A. N.; Haines, T. H.; Deamer, D. W. Biophys. J. 1996, 70, 339. (29) Mitragotri, S.; Johnson, M. E.; Blankschtein, D.; Langer, R. Biophys. J. 1999, 77, 1268. (30) Raphael, R. M.; Waugh, R. E.; Svetina, S.; Zˇeksˇ, B. Phys. ReV. E 2001, 64, 051913. (31) Evans, E.; Heinrich, V.; Ludwig, F.; Rawicz, W. Biophys. J. 2003, 85, 2342.
Gillmor and Weiss (32) Kiessling, V.; Tamm, L. K. Biophys. J. 2003, 84, 408. (33) Johnson, S. J.; Bayerl, T. M.; McDermott, D. C.; Adam, G. W.; Rennie, A. R.; Thomas, R. K.; Sackmann, E. Biophys. J. 1991, 59, 289. (34) Suresh, S. J.; Naik, V. M. J. Chem. Phys. 2000, 113, 9727. (35) Bhide, S. Y.; Merkowitz, M. L. J. Chem. Phys. 2005, 123, 224702. (36) Vargaftik, N. B.; Volkov, B. N.; Voljak, L. D. J. Phys. Chem. Ref. Data 1983, 12, 817. (37) Jurak, M.; Chibowski, E. Langmuir 2006, 22, 7226. (38) Lenz, P.; Johnson, J. M.; Chan, Y.-H. M.; Boxer, S. G. Europhys. Lett. 2006, 75, 659. (39) Karatekin, E.; Sandre, O.; Guitouni, H.; Borghi, N.; Puech, P. H.; Brochard-Wyart, F. Biophys. J. 2003, 84, 1734. (40) Sandre, O.; Moreaux, L.; Brochard-Wyart, F. Proc. Natl. Acad. Sci. U.S.A. 1999, 96, 10591. (41) Tristram-Nagle, S.; Petrache, H. I.; Nagle, J. F. Biophys. J. 1998, 75, 917. (42) Evans, E. A. Biophys. J. 1974, 14, 923. (43) Yamashita, Y.; Masum, S. M.; Tanaka, T.; Yamazaki, M. Langmuir 2002, 18, 9638.
JP802808X
