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

27 May 2008 - line tension and number of methylene chains for vesicles generated from lipids with homologous acyl chains. We have employed laser ablat...
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2008, 112, 7147–7152 Published on Web 05/27/2008

Determination of the Line Tension of Giant Vesicles from Pore-Closing Dynamics Narayanan Srividya* and Subra Muralidharan* School of Molecular Biosciences, Washington State UniVersity, Pullman, Washington 99164 ReceiVed: December 20, 2007; ReVised Manuscript ReceiVed: April 8, 2008

Giant vesicles generated from synthetic and natural lipids such as phosphatidylcholines are useful models for understanding mechanical properties of cell membranes. Line tension is the one-dimensional force enabling the closing of transient pores on cell membranes. Transient pores were repeatedly and reproducibly formed on the membrane edge of giant vesicles generated from synthetic and natural phosphatidylcholines employing a nitrogen-pumped coumarin dye laser (440 nm). Line tension was determined at room temperature from closing of these pores that occurred over several seconds when the radius of the vesicle could be considered to be constant. The value of line tension depends on the nature of the lipid for single lipid systems, which, at room temperature, yielded a vesicle bilayer region in the gel, fluid, or mixed gel and fluid phases. The line tension for vesicles generated from phosphatidylcholines with saturated acyl chains of lengths of 12-18 carbon atoms ranges from 1 to 12 pN, exhibiting an increase with chain length. Vesicles generated from the natural Egg-PC, which is a mixture of lipids, are devoid of phase transition and exhibited the largest value of line tension (32 pN). This value is much larger than that estimated from the line tensions of vesicles obtained from lipids with homologous acyl chains. This study, to our knowledge, is the first to employ laser ablation to generate transient pores and determine line tension from the rate of pore closure and demonstrate a relationship between line tension and acyl chain length. Introduction Line tension is a fundamental mechanical property of cell membranes that facilitates the closure of transient pores which, in turn, influence endocytosis, exocytosis, cell fusion, and cell division. It is an important weak one-dimensional force on the order of piconewtons (pN) that opposes surface tension to enable pore closing.1 A better understanding of pore-mediated cellular processes can be gained from a membrane structure-line tension relationship. Vesicles are excellent models for cell membranes and are useful for gaining an understanding of the influence of cell membrane structure on cell mechanics and hence line tension.2–15 The major objectives of the studies reported here were to demonstrate laser ablation as a useful approach for generating transient pores on vesicle membranes, to demonstrate that line tension can be determined from the rate of closing of these pores, and to determine if a correlation exists between line tension and number of methylene chains for vesicles generated from lipids with homologous acyl chains. We have employed laser ablation to generate small transient pores in the membranes of vesicles derived from the saturated lipids DLPC, DMPC, DPPC, and DSPC with 12, 14, 16, and 18 carbon acyl chains, the unsaturated lipid DOPC with a double bond in each 18 carbon acyl chain, and the natural lipid Egg-PC, which is a mixture of saturated and unsaturated lipids. The rate of pore closing was determined from video microscopy, and the line tension was calculated from this rate under close to physiological conditions of pH and 11 mM MgCl2 without the inclusion of fluorescent dyes in the membrane region. The radius of the * Towhomcorrespondenceshouldbeaddressed.E-mail:[email protected] (S.M.); [email protected] (N. S.).

10.1021/jp7119203 CCC: $40.75

vesicle was constant during the experiments, indicating minimal leakage of the inner fluid. This, to our knowledge, is the first report of a systematic study of the line tension of synthetic vesicles by laser ablation. The significance of transient pores and line tension has been extensively discussed in the literature for model vesicles and cells. Several studies on the measurement of line tension have appeared in the literature, many of which employ micropipette aspiration for the generation of pores.3,11 Other approaches to pore generation have included UV irradiation,1,9,10,12 electroporation,16–18mechanical forces,19–23 and pore-forming peptides and proteins.24–28 Among the various studies reported, those of Brochard-Wyart1,10,12 and Rodriguez9 are of direct relevance to the studies that we have performed on the generation of transient pores and the determination of line tension from the rate of their closing. Brochard-Wyart generated pores as large as 10 µm in diameter in giant unilamellar vesicles of 100 µm diameter prepared from the lipid DOPC and 1% fluorescent dye di6ASPBS or C6-NBD-PC in a 66% glycerol medium.1 The pores were generated by UV irradiation, which increased the membrane tension and eventually resulted in large pores. These pores closed when the irradiation was stopped. The pores formed in several minutes and closed in several seconds. The glycerol medium minimized the inner liquid leakage such that the radius of the vesicle was constant during the process of pore formation and closing. The pore closing was recorded by video microscopy and the line tension determined from the analysis of the images. An average value of 6.9 pN was obtained for the line tension, which increased with varying amounts of cholesterol in the bilayer region.  2008 American Chemical Society

7148 J. Phys. Chem. B, Vol. 112, No. 24, 2008 Rodriguez studied the formation and closing of pores on DOPC vesicles containing up to 10% C6-NBD-PC in the aqueous medium without glycerol.9 In these experiments, giant unilamellar vesicles of DOPC were generated by electroformation, and a solution of C6-NBD-PC was added to them. The dye molecules were incorporated in the outer leaflet of the vesicles within minutes by diffusion through nanopores that the author has shown to exist in the bilayer region.8 A 4 mM dithionite solution was added to the vesicles under illumination with a mercury lamp. The dark and photochemical reduction of C6-NBD-PC by dithionite resulted in transient pores that lived for a few seconds to few minutes. Under these experimental conditions, the vesicle liquid leaked, leading to a change in its radius during illumination, and the pores still closed when illumination was discontinued. The leaking velocity was used to determine the line tension, which gave an average value of 2 pN, much smaller than the one determined by BrochardWyart.1 The reduction in line tension was interpreted as due to dithionite reduction of C6-NBD-PC and photosolubilization. These experiments indicate that line tension is influenced by membrane solubilization leading to a change in the vesicle radius. Nevertheless, even a reduced value of the line tension is sufficient to cause pores to close. Rodriguez demonstrated a cascade of pore formation and closing in these studies. These studies have addressed the line tension of the membrane edge that lies in the outer leaflet and at the interface of the vesicle and bulk aqueous medium in vesicles obtained from single lipids. Lipid mixtures and biological membranes possess domains, and theoretical modeling studies of Dan7 and Cohen15 have estimated line tension values between domains and between domains and the continuous phase. These estimates range from 0.1-10 pN. Baumgart and Longo have experimentally shown the line tension values between domains to be similar to the theoretical calculations.29–31 Our studies reported here are complementary to those of Brochard-Wyart and Rodriguez. We have determined the line tension at the membrane edge of vesicles in the aqueous phase formed from lipids with homologous acyl chains and naturally occurring lipid mixtures in the absence of dye molecules by generating transient pores employing laser ablation such that the radius of the vesicle is constant. These studies are discussed here. Materials and Methods Egg-PC, DLPC, DMPC, DPPC, DSPC, and DOPC used in this study were obtained from Avanti Polar Lipids, AL, and used as received. A modified rapid evaporation technique was employed for the generation of vesicles.32 This yielded vesicles of various sizes with a large population of giant vesicles. Single vesicles with diameters around 20 µm were chosen for pore generation and line tension determination. An amount of 4 mg/ mL of a given lipid in a 2:1 chloroform/methanol mixture was added to 1 mL of 11 mM MgCl2 and heated to 65 °C. The vesicles formed rapidly, and the solution was maintained at this temperature for 10 min and cooled to room temperature. A small volume of this solution was added to a well slide and covered with a flat microscope slide for the pore formation studies. All pore formation and closing experiments were performed at the room temperature of 24 ( 1 °C. The home-built apparatus employed for the line tension studies is displayed in Figure 1 and described briefly here. A Nikon TE 2000U inverted microscope was used to image the vesicles under bright field illumination. The microscope is equipped with a spatial light modulator, and light from a 1064 nm CW Nd:YAG laser is allowed through the spatial light

Letters

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

modulator (SLM) to generate a holographic optical tweezer (Arryx Inc.). Up to 200 optical traps with the same light intensity can be generated with this arrangement. The large vesicles (diameter ∼ 20 µm) could be studied without trapping, and a few vesicles of much smaller diameter were studied by trapping. One of the microscope ports was used for a nitrogen-pumped dye laser for ablation and deformation of the vesicles. A Coumarin dye was used to obtain 440 nm laser emission, and Rhodamine 610 dye was used to obtain 626 nm laser emission. The peak laser energy in each case was about 100 µJ. The 440 nm laser was employed for ablation experiments, and the 626 nm laser was used for the deformation experiments. The pore formation and closing, deformation, and return to original shape were recorded with a Sentech STC630 CCD camera at 30 frames/s. The images were analyzed with Videomach software to obtain line tension values. Results and Discussion The transient pores of radius rpore were generated on the membrane edge of vesicles of different lipids with a 440 nm laser such that the radius R of the vesicle did not significantly change during their formation and closing. This may be seen in the movie on the pore formation and closing on the membrane of Egg-PC vesicles included in the Supporting Information. In all cases, the pores could be repeatedly and reproducibly generated rapidly and closed within a few seconds. As discussed by Brochard-Wyart1 and Rodriguez9 the rate of closing of the pore is driven by the competition between the line tension τ and the surface tension σ and is given by eq 1

[

drpore rpore(t) τ σ(t) ) dt 2η rpore(t)

]

(1)

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

R2 ln rpore ≈

-2τ t 3πη

(2)

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

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J. Phys. Chem. B, Vol. 112, No. 24, 2008 7149

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

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

TABLE 1: Line Tension Calculated for Different Giant Vesicles in 11 mM MgCl2 at Room Temperature lipid

carbon chain lengtha

phase transition temp °C

line tension, pN

DLPC DPPC DSPC DOPC Egg-PC

12:0 16:0 18:0 18:1 variable

-1 41 55 -20 no specific phase

2.5 ( 0.3 9.5 ( 1.0 0.8-1.2 ( 0.5 11.4 ( 1.2 32.3 ( 2.0

a

The first number represents the number of carbon atoms in a single acyl chain. The second number denotes saturation (0, no double bonds) and unsaturation (1, one double bond).

slope of the plot of the quantity on the left-hand side as a function of time t. The formation and closing of a 1 µm pore on Egg-PC vesicles is shown over selected time intervals in Figure 2, and the entire process is included as a movie in the Supporting Information. The plot of R2 ln rpore as a function of time is shown in Figure 3, indicating a linear plot as predicted by eq 2. The linearity of this plot supports the assumption that the radius R of the vesicle is constant during the pore formation and closing, and very little of the vesicle fluid leaks out during this process. The line tensions determined for Egg-PC and other vesicles are listed in Table 1. The line tension for DOPC determined in our studies by laser ablation as seen from Table 1 is 11.4 ( 1.2 pN and is higher than the value of 6.9 ( 0.42 pN obtained by BrochardWyart. This author noted that the DOPC lipid obtained from Sigma yielded a value of 6.9 ( 0.42 pN, while the one from Avanti Polar Lipids, the one employed in our studies, yielded a much higher value of 20.7 ( 3.5 pN. It is important to note that the line tension values are sensitive to the source of the lipids and batches from the same source. It is likely that, while we used DOPC from Avanti Polar Lipids, the batch of our samples and that of Brochard-Wyart were different, yielding the different values. All of the lipids in our studies were

purchased at the same time from Avanti Polar Lipids and likely had similar age and the same quality control. Despite the sensitivity of the line tension of vesicles to the source of the lipids, it is worthwhile to examine the trend of the line tension values among lipids with homologous acyl chains. The single lipid vesicles have distinct phases, namely, the gel phase and the fluid phase, and a phase transition temperature which is also listed in Table 1. The membrane regions of the DOPC and DLPC vesicles exist in the fluid phase and those of DPPC and DSPC in the gel phase at room temperature. The membrane region of Egg-PC does not possess well-defined phases and a phase transition temperature. The lipid DOPC and DSPC differ only by the presence of a double bond in each of the 18 carbon acyl chains of DOPC. Evans has shown a linear correlation with a positive slope between (kc/KA)1/2 (kc is the elastic modulus for bending, and KA is the elastic modulus for area stretch) and the thickness of the bilayer region for vesicles generated from lipids with homologous acyl chains.33 In these studies, Evans has shown that the area stretch modulus KA is essentially constant for vesicles derived from lipids with homologous acyl chains which are either completely saturated or have a single double bond. The bending modulus in these studies bears an approximate linear correlation to the number of methylene carbons in the acyl chain. We find a similar linear correlation between the line tension values of DLPC, DPPC, and DOPC within the standard deviations of the experimental values. This result is in agreement with the predicted direct proportionality of the line tension τ on the bending modulus kc.1,9 The line tension values for DLPC, DPPC, and DOPC indicate a (0.7 ( 0.2) pN contribution for each methylene group in the acyl chain of the lipid, keeping in mind that there are two acyl chains in each lipid. It is interesting to find this correlation despite the fact the phases of the membrane regions of the different lipids are not the same at room temperature. The line tension τ is related to the bending rigidity κ and the bilayer thickness e as given in eq 3.1

τ)

πκ e

(3)

Evans has determined the κ and e values for DOPC to be 0.85 × 10-19 J and 3.69 nm, respectively.33 These values yield a τ value of 7.7 pN, which is smaller than the value of 11.4 pN that we have determined but closer to the value of 6.9 pN reported by Brochard-Wyart1 This agreement is fortuitous considering the fact that lipids from different sources yielded different line tension values. Evans has not reported the κ and e values for all of the lipids in the homologous series of 12-18 carbon atoms in the hydrocarbon chain. We have estimated the κ values for DLPC and DPPC from the reported values to be 0.56 × 10-19 and 0.75 × 10-19 J, respectively. Using eq 3 and the τ values determined in our study and the κ values from Evans’s work, the thickness of the bilayer (e) for DLPC and DPPC is found to be 7 and 2.4 nm, respectively. Both of these values are unrealistic, with the thickness being overestimated in the case of DLPC and underestimated in the case of DPPC, with a more realistic number being 3-4 nm. Several possible factors could contribute to the disagreement between the line tension and bilayer thickness values calculated from eq 3 and the experimental results, namely, (i) eq 3 is obtained for small elastic deformations of the lipid membrane; laser ablation yields pores of 1 µm and larger diameters, which are not small perturbations, (ii) the different lipids result in bilayers in the gel, fluid, or mixed gel and fluid phases at room temperature (Table 1) characteristic of the lipid carbon chain length;

7150 J. Phys. Chem. B, Vol. 112, No. 24, 2008 theoretical models have not considered the influence of different phases on elastic deformation, and (iii) the curvature of vesicles varies with size, influencing the membrane mechanical properties like line tension, bending rigidity, and area stretch modulus, which is manifested in the experimental determinations; theoretical models are based on small vesicles, and the disagreements between values predicted by models and experimental results could result from size effects. A relevant molecular model for understanding variation in the line tension of vesicles generated from a homologous series of lipids is the one proposed by May.34 This model considers the free energy of the lipid molecule at the membrane edge and relates the line tension to the repulsive interactions of the lipid head groups and specifically relates the line tension to the head group interaction parameter B. Line tension is the onedimensional force that overcomes surface tension to facilitate pore closing on the membrane edge. The pore formation perturbs the position of the head groups from their self-assembled equilibrium structure, and pore closing is driven by the return of the head groups from the perturbed to the equilibrium structure. Line tension, which is a manifestation of the return to the equilibrium, can be expected to depend on the head group interaction parameter B. May has generated theoretical curves for the dependence of line tension on B for the vesicles formed from DLPC, DMPC, and DPPC lipids. The B parameter for DLPC corresponding to the line tension that we have measured yields a head group radius of 0.8 Å, which is a reasonable value. However the B value for DPPC yields an unrealistic head group radius of 13.9 Å. It is reasonable to expect the head group radii of DLPC and DPPC to be similar. The line tension for DPPC can be calculated using a head group radius of 0.8 Å from the line tension versus B plots in May’s model. This value is 3.2 pN, almost a third of the value determined by laser ablation (Table 1). The difference between the line tensions of DLPC and DPPC may be rationalized based on the expected differences in the elastic area compressibility modulus of the bilayers of vesicles formed from these lipids. Evans has determined the elastic area compressibility factor for DMPC in the fluid (LR phase) and gel (Lβ phase) to be 144 and 855 dyne/cm, respectively.35 Differences in the values are attributable to the differences in the phases. The bilayers of DLPC and DPPC are in the fluid and gel phases, respectively, at room temperature. As a result, the elastic area compressibility modulus of DPPC vesicles can be expected to be larger than that for DLPC vesicles, analogous to the fluid and gel phases of DMPC. This difference may also explain the much smaller value for the line tension of DPPC vesicles from May’s model compared to the experimental value. The head group interaction parameter B like the elastic area compressibility modulus can be expected to have a strong dependence on the phase of the bilayer region, where the packing of the lipid hydrocarbon chains is a function of their length and temperature. As seen from Table 1, the line tensions of DSPC and EggPC do not fit the approximate linear correlation observed for DLPC, DPPC, and DOPC. The vesicles of DSPC presented an experimental difficulty in terms of following pore formation dynamics, as reproducible results could not be obtained. The value shown in Table 1 is the best value that could be obtained from a limited set of data. One of the difficulties encountered was the irregular behavior of pore closing. In all cases studied except DSPC, the pores closed uniformly over several seconds to yield linear R2 ln rpore versus t plots. The pores on DSPC partially closed over a few seconds and took much longer to

Letters

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

close completely. These images individually yielded linear R2 ln rpore versus t plots with a break, indicating two different rates of pore closing as displayed in Figure 4. The entire pore closing video is included as Supporting Information. Clearly, the values are much lower than the average value of 11 pN expected based on the contributions from the methylene groups for homologous acyl chains in the lipids. A explanation for the behavior of DSPC may lie in the surface shear viscosity of the vesicle bilayer defined as the ratio of tangential force per unit length of the surface to the rate of strain of the surface as a result of stress. Needham has determined the surface shear viscosities of fully compressed monolayers formed from lipids with 16-24 carbon atoms in their alkyl chains.36 The shear viscosity was almost zero for DPPC, showed a dramatic increase between the monolayers of DPPC and DSPC, and exhibited an almost linear dependence on the reduced temperature Tr (Tr ) Tm - T/Tm, T ) experimental temperature (24 °C) and Tm ) phase transition temperature in °C) for lipids with 18-24 carbon atoms in their alkyl chains. This increase in shear viscosity, which is a measure of the response of the vesicle membrane edge to stress, could have a time-dependent behavior for DSPC. As the pore closes, the rate of strain on the surface changes, leading to approximately two different average time-dependent behaviors. The pores close initially at a slower rate, yielding a line tension of 0.8 pN, and more rapidly after 30% of the pores have closed to yield a line tension of 1.2 pN. This indicates that the membrane around the pore when it is formed is less elastic, with a significant influence of shear viscosity, and becomes more elastic as the pore closes, with a reduced dependence on the shear viscosity. The two values determined from the break in the linear plot of R2 ln rpore versus time can be considered as average values representing nonelastic and elastic behavior of the membrane around the pore. This anomaly vanishes when a double bond is introduced in the alkyl chains, as in DOPC, which seems to have a uniform pore closing behavior as in DLPC and DPPC. The DOPC vesicle bilayer is in the fluid phase at room temperature, and the membrane edge is elastic. The line tension values at the membrane edge for all vesicles formed from single lipids in Table 1, except for Egg-PC, lie in the range of line tension values between domains in the bilayer region of vesicles generated from a mixture of lipids. The line tension between domains is the one-dimensional force that restores the organization of the lipids to maintain the domain structure upon distortion of the vesicle with an external force. It is analogous to the line tension at the membrane edge that facilitates pore closing by restoring the organization of the lipid

Letters molecules. In other words, the line tension between domains and on the membrane edge are forces that act to restore the self-assembled equilibrium structures of the membrane bilayer. The similarities in the values of line tension at the membrane edge and between domains can be understood on this basis. It was also difficult to generate pores on the vesicles of DMPC as the vesicle either deformed or disintegrated, depending on the energy of the laser beam. A possible reason could be the presence of the DMPC vesicle membrane in both the gel and fluid phases as its phase transition temperature of 23 °C is close to the room temperature. The formation of defects at phase boundaries possibly results in the deformation or disintegration of the vesicle upon pore formation. Egg-PC is a mixture of lipids with saturated and unsaturated acyl chains (34% 16:0, 2% 16:1, 12% 18:0, 32% 18:1, 20% 18:2, and 4% 20:4) and does not possess a phase transition temperature. A weighted average of the line tensions of the different lipids based on the line tensions determined by laser ablation yields a value of 13.2 pN, while an additive value of the line tensions of the vesicles of the main lipid components is 24.8 pN. It is evident from Table 1 that the experimental value of 32.3 pN is much higher than both of these values. The mixture of lipids appears to make the membrane robust and resistant to pore formation by laser ablation. Brochard-Wyart showed that the inclusion of cholesterol in DOPC vesicles increased the value of the line tension, for example, to 14 pN when 30 mol % cholesterol was included in the DOPC membrane.1 They attribute the increase to the increase in the bending modulus and the rigidity of the membrane. The EggPC vesicles only deformed without any pore generation even at the highest energy when a 620 nm laser from Rhodamine 610 was employed. This is included as a movie in the Supporting Information. One of the reviewers has pointed out during the initial review that the lysis tension of Egg-PC is about 3 dyne/cm, while a much larger value may be expected based on the line tension measured by laser ablation. Lysis tension is the force required to lyse the vesicle, while line tension is the force acted to restore self-assembly of the lipid molecules following pore formation. Both of these forces are a function of the bending rigidity, surface shear viscosity, and elastic area compressibility of the lipid bilayer.37–39 The Egg-PC lipid bilayer region is uniform without the presence of domains, despite the fact that it is a mixture of various lipids. Lipid mixtures often result in domains in the membrane region of the vesicles formed from them. Both the lysis tension and line tension are experimentally determined by perturbing the vesicle bilayer by the application of an external force employing micropipette aspiration and laser ablation. The response of the Egg-PC membrane region to such external forces can be complex given its composition of mixed lipids that do not result in domain formation. A better understanding of the lysis and line tensions of Egg-PC could be gained by determining its bending rigidity, surface shear viscosity, and elastic area compressibility. Additionally, the determination of the lysis tension by lysing the vesicle with high laser energy may also provide insight into the lysis and line tensions of the Egg-PC membrane bilayer. Our preliminary studies have clearly shown that laser ablation is a useful method for determining the line tensions of membranes of lipid vesicles in their native form without the need to include fluorescent dyes. We have also shown that line tension is a function of the lipid employed for the generation of vesicles. A correlation between line tension and the number of carbon atoms in the acyl chain has been shown for lipids of

J. Phys. Chem. B, Vol. 112, No. 24, 2008 7151 homologous chains. The line tension values have been rationalized based on the existing molecular models of the vesicle bialyer region. The behavior of vesicles of mixed lipids such as Egg-PC is more complex. Further studies to understand the line tensions of vesicles of single and mixed lipid systems determined by pore generation by laser ablation are underway. Acknowledgment. This research was supported by the W. M. Keck Foundation when the authors were at Western Michigan University, Kalamazoo, MI. We would like to thank the reviewers of the manuscript for bringing to our attention important experimental and theoretical investigations in the literature that enabled us to provide better rationale for our results. Supporting Information Available: Movies of the pore closing at the membrane edge of Egg-PC and DSPC vesicles following laser ablation. This information is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Karatekin, E.; Sandre, O.; Guitouni, H.; Borghi, N.; Puech, P. H.; Brochard-Wyart, F. Biophys. J. 2003, 84, 1734. (2) Umeda, T.; Suezaki, Y.; Takiguchi, K.; Hotani, H. Phys. ReV. E 2005, 71, 011913. (3) Ly, H. V.; Longo, M. L. Biophys. J. 2004, 87, 1013. (4) Baumgart, T.; Hess, S. T.; Webb, W. W. Nature 2003, 425, 821. (5) Baumgart, T.; Das, S.; Webb, W. W.; Jenkins, J. T. Biophys. J. 2005, 89, 1067. (6) Zhelev, D. V.; Needham, D. Biochim. Biophys. Acta 1993, 1147, 89. (7) Towles, K. B.; Dan, N. Langmuir 2007, 23, 13053. (8) Rodriguez, N.; Heuvingh, J.; Pincet, F.; Cribier, S. Biochim. Biophys. Acta 2005, 1724, 281. (9) Rodriguez, N.; Cribier, S.; Pincet, F. Phys. ReV. E 2006, 74, 061902. (10) Puech, P. H.; Borghi, N.; Karatekin, E.; Brochard-Wyart, F. Phys. ReV. Lett. 2003, 90, 128304. (11) Melikyan, G. B.; Matinyan, N. S.; Arakelian, V. B. Biochim. Biophys. Acta 1990, 1030, 11. (12) Karatekin, E.; Sandre, O.; Brochard-Wyart, F. Polym. Int. 2003, 52, 486. (13) Brockman, H. Chem. Phys. Lipids 1994, 73, 57. (14) Basanez, G.; Shinnar, A. E.; Zimmerberg, J. FEBS Lett. 2002, 532, 115. (15) Akimov, S. A.; Kuzmin, P. I.; Zimmerberg, J.; Cohen, F. S. Phys. ReV. E 2007, 75, 011919. (16) Genco, I.; Gliozzi, A.; Relini, A.; Robello, M.; Scalas, E. Biochim. Biophys. Acta 1993, 1149, 10. (17) Bier, M.; Chen, W.; Gowrishankar, T. R.; Astumian, R. D.; Lee, R. C. Phys. ReV. E 2002, 66, 062905. (18) Akinlaja, J.; Sachs, F. Biophys. J. 1998, 75, 247. (19) Riveline, D.; Zamir, E.; Balaban, N. Q.; Schwarz, U. S.; Ishizaki, T.; Narumiya, S.; Kam, Z.; Geiger, B.; Bershadsky, A. D. J. Cell Biol. 2001, 153, 1175. (20) Opsahl, L. R.; Webb, W. W. Biophys. J. 1994, 66, 75. (21) Moroz, J. D.; Nelson, P. Biophys. J. 1997, 72, 2211. (22) Griffin, M. A.; Engler, A. J.; Barber, T. A.; Healy, K. E.; Sweeney, H. L.; Discher, D. E. Biophys. J. 2004, 86, 1209. (23) Evans, E.; Ritchie, K.; Merkel, R. Biophys. J. 1995, 68, 2580. (24) Ye, J. S.; Zheng, X. J.; Leung, K. W.; Chen, H. M.; Sheu, F. S. J Biochem. (Tokyo) 2004, 136, 255. (25) Thundimadathil, J.; Roeske, R. W.; Guo, L. Biopolymers 2006, 84, 317. (26) Sobko, A. A.; Kotova, E. A.; Antonenko, Y. N.; Zakharov, S. D.; Cramer, W. A. FEBS Lett. 2004, 576, 205. (27) Coutinho, A.; Silva, L.; Fedorov, A.; Prieto, M. Biophys. J. 2004, 87, 3264. (28) Abrunhosa, F.; Faria, S.; Gomes, P.; Tomaz, I.; Pessoa, J. C.; Andreu, D.; Bastos, M. J. Phys. Chem. B 2005, 109, 17311. (29) Ly, H. V.; Longo, M. L. Biophys. J. 2004, 87, 1013. (30) Baumgart, T.; Hess, S. T.; Feigenson, G. W.; Webb, W. W. Biophys. J. 2003, 84, 326a. (31) Baumgart, T.; Hammond, A. T.; Sengupta, P.; Hess, S. T.; Holowka, D. A.; Baird, B. A.; Webb, W. W. Proc. Natl. Acad. Sci. U.S.A. 2007, 104, 3165. (32) Moscho, A.; Orwar, O.; Chiu, D. T.; Modi, B. P.; Zare, R. N. Proc. Natl. Acad. Sci. U.S.A. 1996, 93, 11443.

7152 J. Phys. Chem. B, Vol. 112, No. 24, 2008 (33) Rawicz, W.; Olbrich, K. C.; McIntosh, T.; Needham, D.; Evans, E. Biophys. J. 2000, 79, 328. (34) May, S. E. Phys. J. E 2000, 3, 37. (35) Needham, D.; McIntosh, T. J.; Evans, E. Biochemistry 1988, 27, 4668. (36) Kim, D. H.; Costello, M. J.; Duncan, P. B.; Needham, D. Langmuir 2003, 19, 8455. (37) Evans, E.; Needham, D. J. Phys. Chem. 1987, 91, 4219.

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