3705
J . Phys. Chem. 1991,95, 3705-3715 MO(CO)~(OZ)~ is proposed to be an active species for the stereoselective hydrogenation and isomerization of dienes over Mo(CO),Jzeolite catalysts.10*" It is considered that the Mo(CO)3-OZ bonds are cleaved on contact with diene molecules by a ligand-displacement reaction, producing a M~(CO)~(~'-diene) complex, a possible intermediate for both reactions. Obviously, the increase in the strength of MO(CO)~-OZbonds is deduced to retard the formation of the reaction intermediate, reducing the catalytic activities. This is in conformity with the previous observation~~#* and a generally accepted idea for M(CO)3 (M = Cr, In this respect, zeolite can Mo, W) metal complex be regarded as a solid ligand for a MO(CO)~ moiety. The coordination strength can be easily controlled by varying the zeolite (42) Calderano, F.; Ercoli, R.; Natta, G. Organic Synthesis via Metal Carbonyls; Wender, I., Pino, P., Eds.; Intersciencc: New York, 1968; Vol. 1, P 1 .
cation, the extent of ion exchange, and the Si/Al ratio in the framework. Zeolites can work also as shape- and size-selective ligands. Thus, it is anticipated that zeolites can offer a series of functional matrices for anchoring metal complexes with controlled coordination strength, catalytic activities, and selectivities. Acknowledgment. We thank Professors H. Kuroda and N. Kosugi, who developed the EXAFS analysis programs, and Professor M. Nomura and staff of the Photon Factory, National Laboratory for High Energy Physics, for assistance in measuring EXAFS spectra (Proposal No. 87014). We also thank Dr.A. Maezawa for assistance in the XPS measurements. Part of this work was financially supported by the Ministry of Education, Science, and Culture (Grant-in Aid for Scientific Research, No. 62540334). Registry No. Mo(CO),, 13939-06-5;Li, 7439-93-2; Na, 7440-23-5; CS,7440-46-2.
Simultaneous Electrical and Optical Interferometric Measurements of Pressure- and Applied-Potentiai-Induced Bilayer Lipid Membrane Deformation Cilles Picard, Normand Denicourt, and Janos H. Fendler* DZpartement de Chimie, UniuersitC de MontrPal. C.P. 6128, succursale A , MontrCal. QuCbec, Canada H3C 357 (Received: July 12, 1990; I n Final Form: September 18, 1990)
Hydrostatic-pressure- and transmembrane-potential-induceddeformations of glyceryl monooleate (GMO) and bovine brain phosphatidylserine (PS) bilayer lipid membranes (BLMs) were investigated by simultaneousoptical and electrical measurements. The investigation of a large number of samples established subtle variations in the observable parameters (appearance of concentric optical interference fringes, capacitance, voltage-dependent capacitance, resistivity, and voltagedependent resistivity changes as a function of hydrostatic pressure and applied potential) of separately formed, but otherwise identical BLMs. Simultaneous optical and electrical measurements were performed on given BLM preparations, each of which had relatively small Plateau-Gibbs borders and "survived" for 6 h or longer. Application of 4-21 mN m-2 hydrostatic pressure (Php)resulted in the appearance of concentric optical interference fringes (some of which were transient) which allowed the calculation of translational (lateral) displacements (FJ and curvature changes (F,). Plots of F, values against Phpgave good straight lines from which interfacial tensions (7) of GMO and PS BLMs were calculated to be 0.22 f 0.02 and 0.29 f 0.03 mN m-I, respectively. Treatment of the Ph -induced F, changes also allowed the calculation of the curvature elastic modulus, K%, from which, assuming constant B L h mass density, the surface elastic density modulus, KS ( K = ~ y), and the thickness elastic modulus, K ,were also assessed. This mechanical approach (method M) gave K = 3.99 X 1V2'J, K~ = 2.92 X lo-' N m-1, and K 4 = 3.53 x 104 N m-2 for PS and KRS = 1.26 x 10-2' J, KS = 2.22 x m-1, and Ka,, = 5.46 x 1 0 ' N m-2 for GMO and BLMs. Voltage-dependent capacitance measurements provided an alternative approach (electrical ap roach, , and K ~ Method . E gave K% = 2.89 X method E) to K ~ KS, J, KS = 2.08 X lo4 N m-I, and K 4.01 X l J N m-2 J, KS = 7.62 X lo4 N m-I, and K~~ = 21.5 X 104 N m-2 for GMO%;Ms. The observed for PS and K = 4.84 X voltage-depen%ent,y, and elastic moduli changes were rationalized in terms of surfactant and solvent exchanges between the bilayer and its Plateau-Gibbs reservoir.
10-4~
Introduction In the absence of additives or adventitious impurities, the bimolecular thick (bilayer lipid) membrane, BLM, is an electrical insulator that physically separates two aqueous compartments.'-3 Sensitive electrical measurements across the BLM in the presence of ionophores or reconstituted transport proteins have contributed significantly to our current understanding of impulse and iontransport mechanismsc7 More recently, BLMs have been utilized
as matrices for supporting size-quantized semiconductor and magnetic particles that mimic bulk photoelectrical and magnetooptical device^.^.^ Continued utilization of BLMs for biophysical and solid-state modeling requires an understanding of their physical-mechanical properties. In spite of its importance, only a few reports, appearing in the late 1960s and early 1970s, have been published on BLM interfacial tension.'*'7 Electrical measurements were used in
(1) Fendlcr, J. H. Membrune Mimetic Chemistry; Wiley-Interscience: New York, 1982. (2) Tien, H. T. Bilayer Lipid Membranes (ELM). Theory and Practice; Marccl Dekker: New York, 1974. (3) White, S.H. In Ion Channel Reconstitution; Miller, C., Ed.; Plenum Press: New York, 1986; p 3. (4) Miller, C. Ion Channel Reconstirution; Plenum: New York, 1986. (5) Hille, B. Ionic Channels of Excitable Membranes; Sinaver Associates: Sunderland, MA, 1984. ( 6 ) Sakmann, B.; Neher, E. Single-Chonnel Recordins Plenum: New York, 1983. ( 7 ) Hoppe, W.; Lohmann, W.; Markl, H.; Ziegler, H. Biophysics; Springer: New York, 1983.
(8) Zhao, X. K.; Baral, S.; Rolandi, R.; Fendler, J. H. J . Am. Chem. Soc. 1988,110,1012. Zhao, X. K.; Fendler, J. H. J. Phys. Chem. 1988,92,3350. Yuan, Y.; Tundo, P.; Fendler, J. H. Macromolecules 1989,22,29. Zhao, X . K.; Hew4 P. J.; Fendler, J. H. J. Phys. Chem. 1989, 93, 908. Baral, S.; Fendler, J. H. J . Am. Chem. Soc. 1989,111, 1604. (9) Kutnik, J.; Tien, H. T. Phorochem. Photobiol. 1987, 46, 413. (10) Tien, H. T. J . Phys. Chem. 1967, 71, 3395. ( 1 1 ) Cater, H. G. L.; Simons, R. Biochim. Biophys. Acta 1968,163,234. (12) Moran, A.; Ilani, A. Chem. Phys. Lipids 1970, 4, 169. (13) Wobschall, D. J. Colloid Interfoce Sci. 1971, 36, 385. (14) Redwood, W. R.; Pheiffer, F. R.; Weisbach, J. A,; Thompson, T. E. Biochim. Biophys. Acta 1971, 233, 1 . ( I S ) Haydon, D. A.; Taylor, J. C. Nature 1968, 217, 739. (16) Hand, T.; Haydon, D. A.; Taylor, J. J . Theor. Bioi. 1965, 9, 433.
0022-365419112095-3705$02.50/0 63 1991 American Chemical Society
3706 The Journal of Physical Chemistry, Vol. 95, No. 9, 1991 these studies for monitoring the effects of transmembrane pressure differences, in the 0.1-atm range. Thinness of the BLM (3-5 nm) precluded the utilization of optical methods prior to the general availability of high-powered lasers. We have recently reported measurements of ultrasmall pressure-induced curvature changes by two-exposure interferometric holography.'8 Interferometricholographs were realized by taking two 1-s exposures, ca. 1 min apart, on the same film. The first exposure was taken on the undeformed BLM. The second exposure was taken after a known amount (in the 10-40 mN m-2 range) of hydrostatic pressure had been applied to the membrane. Holograms obtained provided a permanent dfrom which both three-dimensional and temporal information were reconstructed. Concentric optical fringes reconstructed from holograms allowed the precise determinationof BLM deformation. BLM deformation occurring in the time between the two exposures remained inaccessible, however, by two-exposure interferometric holography. Advantage was taken of optical interferometry, in the present study, to obtain continuous information on pressure- and applied-potential-induced deformation of GMO and phosphatidylserine (PS) BLMs. This allowed the first time visualization of both translational (lateral) movement and curvature changes of the BLM. Capacitance and voltage-dependent capacitance, resistivity, and voltage-dependent resistivity changes were determined simultaneously with the optical interferometric measurements.
Experimental Section Glyceryl monooleate (GMO, Sigma), bovine brain phosphatidylserine (PS, Sigma), and decane (Phillips Petroleum Co.) were used as received. Water was distilled, passed through an ionexchange column (Barnstead), and finally filtered by a Millipore system (water resistivity 18 MQ cm). BLMs were formed across a 1.10 & 0.01 mm diameter conical hole drilled in a 0.52 f 0.01 mm thick black Tefzel film at room temperature (ca. 20 "C). The cone angle with respect to the film surface was determined to be 37O. The Tefzel film was inserted diagonally in a 1 .OO-cm optical path fluorescence cuvette and sealed with silicone rubber glue. The cuvette was filled with 0.10 M KCl solution. BLMs were made by smearing the BLM-forming solution (50 mg of GMO or 25 mg of PS per milliliter of decane) across the Tefzel aperture with a steel needle. The needle was rinsed with methanol after each dipping. Surfactant solutions were maintained in a nitrogen atmosphere between usage. Thinning of the initially formed film to a BLM was monitored by observing the image of the reflected laser light by a video recorder system (NEC, NC-8 CCD color camera; JVC HR 0440U video recorder; and JVC color television). The precise area of the BLM was determined from its video image. Recorded images were digitized by "frame grabbing". Computer contrast enhancements of the digitized images greatly facilitated the counting of the optical interference fringes. The investigation of a large number of samples established subtle variations in the observable parameters (appearance of concentric optical interference fringes, capacitance, voltage-dependent capacitance, resistivity, and voltage-dependent resistivity changes as a function of hydrostatic pressure and applied potential) of separately formed, but otherwise identical, BLMs. It was deemed important, therefore, to perform all needed determinations on the same BLM preparation by simultaneous electrical and spectroscopic measurements. In practice, this restricted the use to BLMs which had relatively small Plateau4ibbs borders (4- R, I0.18 mm) and which "suMved" for 6 h or longer. Details will be illustrated on three such separately prepared GMO and on three such separately prepared PS BLMs (indicated by GMO A, B, and C and PS A, B, and C in Tables 111-VI and in Figure 4). The schematics of the experimental setup used for simultaneous optical interferometry and electrical (capacitance, resistance, H.T.; Diana, A. L. Chem. Phys. Lipids 1968, 2,255. (18) Rad,0.;Schneider-Henriquez, J. E.; Fendler,J. H. J. Phys. Chem. 1990, 94, 510. (17) Tien,
Picard et a]. P2
CCD camera
recorder
j 2
9
monitor
P1
'i
L1
I
He-Ne laser BS 1
BLH
Figure 1. Schematics of the system used for optical interferometry: HtNe, IO-mW, 632.8-nm CW laser; BSl and BS2, beam splitters; L1, lens; M1 and M2, mirrors; P1 and P2, polarizers; BLM, bilayer lipid
membrane. voltage-dependentcapacitance) measurements of BLMs is shown in Figure 1. The He-Ne laser beam (CW, 10 mW, 632.8 nm; Melles-Griot) was divided by a beam splitter (Bsl). The reference beam was reflected by a mirror (Ml) through a polarizer (Pl) toward a second beam splitter (Bs2). The intensities of the object and reference beams were balanced by P1 during thinning and subsequent measurements of the optical interference fringes. The object beam was directly incident onto the BLM, which acted as a mirror and reflected some 0.01% of the incident light to BS2. The superposed reference and object beams were imaged onto the CCD camera target via a lens (Ll), a mirror (M2), a second polarizer (P2), and a second lens with the camera. The function of P2was to adjust the beam intensity for the CCD camera. The incident planar waves curved after reflection from the deformed BLM (Figure 2). This caused a change in the optical path of the object beam and manifested in the appearance of an interference pattern. Perfect parallel alignment of the reference and object beams was found to be absolutely essential for the observation of interference fringes. This requirement is difficult to meet since BLMs never position themselves exactly in the same place in the aperture, and consequently, they reflect the incident beam at random. Strategically, it is simpler to align the BLM in the optical path. This was achieved with a vertically positioned rotator (RSA-I, Newport) that oriented the BLM in the Z axis (normal to the top table). The rotator was mounted on a translator assembly that moved the BLM in the X-Y axes to the aperture at the intersection of the two optical axes. The stacked translators were bolted on another rotator (Daedal, Inc.) which oriented the BLM plane 45" with the optical axes. The entire BLM setup was mounted on a vibration isolation table and covered by a Faraday cage. Hydrostatic pressure was applied by lowering a small piston (part of a Hamilton syringe)I3into the aqueous solution bathing one side (the cis side) of the BLM. Calibration allowed the precise calculation of the volumes of water (in nanoliters) displaced. Hydrostatic pressures were calculated from the volumes of water displaced by the pressure-induced movements of the BLM. Two kinds of volume changes were considered: those due to translational displacement and those which originate in curvature increase (Figure 2). The volume of liquid displaced by the translational motion of the BLM accompanying the lowering of the piston into the cis side (V,) is given by v, = T R ~ F , (1) where R, is the radius of the aperture of the hole of the Tefzel film which supports the BLM (0.55 mm) and F1 is the distance of translational displacement of the BLM accompanying the lowering of the piston into the cis side. The volume of water
The Journal of Physical Chemistry, Vol. 95, No. 9, 1991 3707
Bilayer Lipid Membrane Deformation reflected laser beam
incident laser beam
instrument was used for electrocompression by applying the transmembrane potentials across the BLM.
Results
elec
quartz cuvette
:2Rm
0:
Pressure-Induced Changes of Optical Interference Fringes. A video microscopic image of a typical BLM is shown in Figure 3a. The three optical interference fringes in the lower left-hand side of the BLM indicate that the slight deformation from planarity is limited to an area that is close to a part of the Plateausibbs border. This deformation is likely to originate in the imperfect planarity of the aperture which supports the BLM. A slight lowering of the plunger resulted in the appearance of concentric interference fringes, as seen in Figure 3b. These fringes are the manifestation of hydrostatic-pressure-inducedcurvature change (F,). Transient fringes were also observed and counted during compression. They resulted from translational displacement of the BLM (F,). The concentric optical interference fringes observed were related to geometrical deformation of the BLM as a consequence of the applied hydrostatic pressure, Ph which displaced the BLM from position 1 (flat) to position 2 (iurved), as illustrated in Figure 2. Deformation of the BLM from position 1 to position 2 was probed by the He-Ne laser beam (A = 632.8 nm in air) whose shortened wavelength in the aqueous solution, A,, is given by
X, = A/na
2Ra
Figure 2. Schematics of pressure-inducedand applied-potential-induced BLM deformations. Application of hydrostatic pressure Pb (by lowering a piston into the aqueous solution bathing the cis side of the BLM) displaces the BLM from position 1 to position 2. The displacement involves both translational (lateral) motion (F,)and curvature increase (FJ.As indicated, deformation of the BLM is accompanied by a change in its torus (Plateau4ibbs border). 2R,and 2R, represent the diameters of the aperture of the pinhole in the Tefzel film and that of the membrane (excluding the torus). The object laser beam, incident upon the trans side of the BLM and reflected by it at 4 5 O at a shortened wavelength (eq 5), produces concentric optical interference fringes with the reference laser beam (see Figure 1). Ag/AgCl electrodes, placed in the cis and trans sides of the BLM, allow for continuous electrical measurements.
displaced by the increased curvature of the BLM accompanying the lowering of the piston into the cis side, V,, is given by
where Rmis the radius of the BLM (excluding the Plateau4ibbs border) and F, is the distance of the curvature displacement of the BLM accompanying the lowering of the piston into the cis side (see Figure 2). The net volume increase responsible for creating hydrostatic pressure across the BLM which accompanies the lowering of the piston into the cis side (&) is given by vhp
= vp - vt - vc
(3)
where Vpis the total volume of liquid displaced by lowering the piston into the aqueous solution which bathed the cis side of the BLM. However, V, and V,also increase the water level in the trans side; thus the hydrostatic pressure, P,,,,,.due to the differential volume of liquid increase in the cis side, is given by (vhp
- 4 - vc)d&
(4) a, where da is the density of the aqueous solution bathing the BLM (d, = 1 .O g/cm3), g is the gravitational constant (g = 9.8 m/s2), and a, is the surface area of the aqueous solution bathing the cis side of the BLM (a, = 0.462 cm2). Corrections of v h p by V, and V, were on the order of 10%and 196, respectively. Electrical measurements were performed using a Dagan 3900 integrating patch-clamping system. Operating in the voltageclamp mode, current was converted to voltage and was measured with a Kikusui 5021 oscilloscope. The Ag/AgCl electrodes were stored in 3.0 M KCl when not in use. The same Dagan 3900 php
(5)
where n, is the refractive index of the aqueous solution bathing the BLM (n, = 1.33). Deformation of the BLM (F),observed at 45O to the incident laser beam, is related to the number of concentric optical interference fringes, f, by F =fxasin 45O
(6)
F = (fx sin 4So)/n,
(7)
or by The BLM underwent two kinds of pressure-induced motion: curvature increase and lateral translation (Figure 2). These two motions were separated as follows. The number of new concentric fringes that appeared at the center of the BLM during the compression u> was designated to originate in the total deformation of the membrane. The difference between the total number of fringes seen prior and subsequent to immersion of the piston was assigned to the increased curvature of the BLM (f,). These observables allowed the assessment of the fringes related to translational displacement of the BLM which accompanied the lowering of the piston into the cis siae,f,:
h = f -fc
(8)
Appropriate modifications of eq 7 allowed, therefore, the calculation of displacement (see Figure 2) due to curvature, F,, and translational motion changes, F,, accompanying immersion of the piston into the cis side: F, = (f,X sin 4S0)/n, (9)
F, = (f,X sin 4S0)/na
(10)
For each BLM, a set of increasing pressures was applied by immersing the plunger progressively deeper into the aqueous solution bathing the cis side of the membrane. After each immersion (taking 1-2 s to accomplish) and recording the total number of fringes,f (taking a maximum of 1 min to accomplish), the plunger was withdrawn to its original position. A typical set of results appears in Table I. Thus, for example, immersion of a piston (V,) to displace 2.29 X lo-" m3 of liquid corresponded to an increased volume of the BLM curvature (V,)of 1.66 X 10-13 m3 and to an increased volume change due to the translational m3. These changes led motion of the BLM (V,) of 1.27 X to two additional concentric optical interference fringes (f,) and to four fringes ascribable to the translational displacement of the BLM (f,). Thus, the pressure change (ph ) of 4.27 mN/m* corresponded to 1.33 X lod m translationaf displacement (F,) and 0.66 X lo4 m increase of the curvature (F,)of the BLM.
3708 The Journal of Physical Chemistry, Vol. 95, No. 9, 1991
Picard et al.
. I_._-.~
Figure 3. Photographs of frame-grabbed video microscopic images of optical interferometric fringes prior (a, left) and subsequent (b, right) to the application of 17.63 mN/m2 hydrostatic pressure on a BLM prepared from PS. The increase in the total number of concentric optical fringes (difference between those in (a) and (b) = J-) gives the hydrostatic-pressure-induced curvature change of the BLM, F, (eq 9). TABLE I: Pressure-Induced Defomdon of 1 PS BLMo 10" VpP m3 1 OI3 m3 10l2VIP m3 2.29 I .66 1.27 4.58 3.33 1.90 6.88 4.99 2.2 1 9.17 6.65 3.79 11s 8.32 6.33
fc'
ff
2 4 6 8
4 6 7 12 20
1o6F,,g m 1.33 2.00 2.33 4.00 6.66
106Foh m 0.66 1.33 2.00 2.66 3.33
Pbp' mN/m2 4.27 8.8 1 13.5 17.6 21.4
IO "Prepared by smearing a 25.0-mg PS solution in decane (100 mL) across the l.10-mm aperture of the Tefzel film separating the two compartments which contained aqueous 0.10 M KCI. Subsequent to thinning, the diameter (2Rm) and thickness of the hydrocarbon layer (bb) of this
particular BLM (excluding its Plateau-Gibbs border) were determined to be 0.80 mm and 5.63 nm, respectively. It 'lasted" for more than 8 h. Vp is the volume of liquid displaced by lowering the piston into the aqueous solution which bathes the cis side of the BLM. Vc is the volume of water displaced by the increased curvature of the BLM accompanying the lowering of the piston into the cis side (see eq 2). VIis the volume of water displaced by the translational motion of the BLM accompanying the lowering of the piston into the cis side (see eq 1). *f,is the number of fringes due to the increased curvature of the BLM and is determined by taking the difference between the number of fringes seen prior and subsequent to immersion of the piston into the cis side. //I is the number of fringes related to translational displacement of the BLM which accompanied the lowering of the piston into the cis side of the BLM (see eq 8). 'F, is the distance of translational displacement of the BLM accompanying the lowering of the piston into the cis side (see Figure 2). F1values were calculated by substituting appropriate data into eq IO. F, is the distance of the curvature displacement of the BLM accompanying the lowering of the piston into the cis side (see Figure 2). F, values were calculated by substituting appropriate data into eq 9. ' f b p is the hydrostatic pressure due to the differential volume of liquid increase in the cis side. fhp values were calculated by substitution of appropriate data into eq 4.
Withdrawal of the plunger and its reimmersion to displace 4.58 X 10'" m3 of liquid led to the data shown in the second line of Table 1. Data shown in the third, fourth, and fifth line of Table I were obtained analogously. Sets of data, determined for each of the separately prepared BLMs (not shown), were tabulated in a similar manner. Inspection of Table 1 reveals the sensitivity of optical interferometry. Micrometer-range translational displacements (F,) and curvature changes (F,)were clearly distinguishable and separable. F,values appeared to increase linearly with increasing applied hydrostatic pressure. This trend is, however, fortuitous. The extent of translational deformation of the BLM was found
to vary somewhat from preparation to preparation. Unfortunately, in the absence of observable optical fringes in the PlateauGibbs border, its deformation with and/or independent of the BLM . cannot be established. A good relationship was obtained, as expected,l*l4 between the extent of BLM curvature changes and the applied hydrostatic pressure responsible for them. Plots of F, values against Phpfor three separately prepared GMO BLMs and three separately prepared PS BLMs are shown in Figure 4. Values calculated from these plots will be used for the elucidation of the interfacial surface tension and elastic moduli of the BLM, as well as the work performed in bending it (vide infra).
The Journal of Physical Chemistry, Vol. 95, No. 9, 1991 3709
Bilayer Lipid Membrane Deformation
TABLE II: Applied-Potential-InducedDeformtioa of a PS BLMO AV! 10'3V,," lO'*V,,', OC
4od 8W 100'
14W
Fc, m
Php, mN/mZ 4 . W r . ,
.
,
.
,
.
I
.
,
,
m
2 4
4.39 3.48 3.16 3.16 3.13
1.70 3.43 4.29 5.15 6.80
14 11
5
10
6 8
10 10
4.62 3.66 3.33 3.33 3.33
-
0.66 1.33 1.66 2.00 2.66
'PS B BLM; prepared by smearing a 25.0-mg PS solution in decane (100 mL) across the 1.10-mm aperture of the Tefzel film separating the two compartments which contained aqueous 0.10 M KCI. Subsequent to thinning, the diameter (2R,) and thickness of the hydrocarbon layer ( 6 h ) of this particular BLM (excluding its Plateauaibbs border) were determined to be 0.81 mm and 5.41 nm, respectively. It "lasted" for more than 8 h. bAVis the transmembrane potential. 'Php = 7.82 mN/m2. dPhp = 8.13 mN/m2. ' p h p = 8.23 mN/m2. 'Php 8.20 mN/m*. 'Php = 8.14 mN/m2. Vc IS the volume of water displaced by the increased curvature of the BLM accompanying the lowering of the piston into the cis side (see eq 2). 'V,is the volume of water displaced by the translational motion of the BLM accompanying the lowering of the piston into the cis side (see eq 1). jf, is the number of fringes due to the increased curvature of the BLM and is determined by taking the difference between the number of fringes seen prior and subsequent to immersion of the piston into the cis side. is the number of fringes related to translational displacement of the BLM which accompanied the lowering of the piston into the cis side of the BLM (see eq 8). 'F, is the distance of translational displacement of the BLM accompanying the lowering of the piston into the cis side (see Figure 2). F, values were calculated by substituting appropriate data into eq 10. "'FCis the distance of the curvature displacement of the BLM accompanying the lowering of the piston into the cis side (see Figure 2). F, values were calculated by substituting appropriate data into eq 9. TABLE III: Applied-Potential-InducedCurvature Changes of CMO BLMs
Php, mN/m'
Figure 4. (top) Plot of Fc against P h for GMO BLMs prepared by smearing decane solutions of GMO (50 mg in 100 mL) across the 1 . 1 0 " aperture of the Tefzel film separating the two compartments which contained aqueous 0.10 M KCI. Subsequent to thinning, diameters (2R,) and thicknesses of the hydrocarbon layer (&) were determined to be 0.80 mm and 3.79 nm (A), 0.74 mm and 3.57 mm (B); and 0.83 mm and 3.41 nm (C), respectively. (bottom) Plot of F, against Phpfor PS BLMs prepared by smearing decane solutions of PS (25 mg in 100 mL) across the 1 . 1 0 " aperture of the Tefzel film separating the two compartments which contained aqueous 0.10 M KCI. Subsequent to thinning, diameters (2R,) and thicknegses of the hydrocarbon layer (&) were determined to be 0.80 mm and 5.63 nm (A), 0.81 mm and 5.41 mm (B), and 0.74 mm and 5.19 nm (C), respectively. The data used in drawing line A are contained in Table I.
Applied-Potential-Induced Changes of Optical Interference Fringes. Application of hydrostatic pressure to a BLM that had been subjected to transmembrane potential also resulted in the appearance of concentric optical interference fringes (see Table 11). Some of these fringes were transient and disappeared, while some remained. Fringes were treated similarly to those caused by the application of hydrostatic pressure alone. Thus,f,andf, values were assigned to the applied-potential-inducedcurvature increase (F,) and translational displacement (FJ of the BLM. Hydrostatic pressure was applied to BLMs that were subjected to increasing applied transmembrane potentials. A typical set of results is collected in Table 11. The extent of translational displacement of the BLM (FJ appears to be unaffected by the magnitude of the applied potential in the 40-140-mV range. Application of a potential, regardless of its magnitude, caused approximately 3-pm lateral displacement of the BLM. Increasing transmembrane potentials led to a somewhat larger curvature change of the BLM at a given Php (Table 11). The determined Fc values as functions of curvature changes for several GMO and PS membranes are collected in Tables 111 and IV. These values
1.33 1.83 1.83 2.16 2.16
8.56 8.33 8.46 8.31 8.51
150
2.16
8.45
180 200
2.31
8.45
0 40 80 100
120 140
1.00
8.60
0.67
7.29
1.33 1.47
8.02 7.66
1.33 1.17
7.79 7.60
1.33
7.75
1.33
6.84
1.33
7.66
1.66 1.66
6.96 6.28
Prepared by smearing a 50" GMO solution in decane (100 mL) across the 1.10-mm aperture of the Tefzel film separating the two compartments which contained aqueous 0.10 M KCl. Subsequent to thinning, the diameter (2R,) and thickness of the hydrocarbon layer (6,) of this particular BLM (excluding its Plateau4ibbs border) were determined to be 0.80 mm and 3.79 nm, respectively. It 'lasted" for more than 8 h. bPrepared by smearing a 50" GMO solution in decane (100 mL) across the 1.10-mm aperture of the Tefzel film separating the two compartments which contained aqueous 0.10 M KCI. Subsequent to thinning, the diameter (2R,) and thickness of the hydrocarbon layer (6,) of this particular BLM (excluding its PlateauGibbs border) were determined to be 0.74 mm and 3.57 nm, respectively. It "lasted" for more than 8 h. CPrepared by smearing a 50" GMO solution in decane (100 mL) acrms the 1.10-mm aperture of the Tefzel film separating the two compartments which contained aqueous 0.10 M KCI. Subsequent to thinning, the diameter (ZR,) and thickness of the hydrocarbon layer (6,) of this particular BLM (excluding its PlateauCribbs border) were determined to be 0.63 mm and 3.41 nm, respectively. It "lasted" for more than 8 h. dAV is the transmembrane potential. 'F, is the distance of the curvature displacement of the BLM accompanying the lowering of the piston into the cis side (see Figure 2). Fc values were calculated by substituting appropriate data into eq 9. /Hydrostatic pressure at which AV is applied.
will provide a means for assessing the dependence of y on the applied potential for a given BLM (vide infra). Electrical Measurements. Electrical measurements have been camed out simultaneously with the counting of optical interference
3710 The Journal of Physical Chemistry, Vol. 95, No. 9, 1991 TABLE I V Applied-Potentid-InducedCurvature Changes of PS BLMs A" B* CC
Picard et ai. T
A
I T i
JAS
1 - - - - - - - - - - 1
r0 40 80 100
120 140 150 180 200
1.33
8.81
2.33
8.30
2.00
8.20
3.00
0.67 1.33 1.67 2.00
7.82 8.13 8.23 8.20
2.66
8.14
8.37
0.33 1.33
8.13 8.56
1.33
8.56
1.33 0.67 1.00
8.02 8.10 8.20
"Prepared by smearing a 25" PS solution in decane (100 mL) across the 1.10-mm aperture of the Tefzel film separating the two compartments which contained aqueous 0.10 M KCI. Subsequent to thinning, the diameter (2Rm) and thickness of the hydrocarbon layer (6,) of this particular BLM (excluding its Plateau-Gibbs border) were determined to be 0.80 mm and 5.63 nm, respectively. It 'lasted" for more than 8 h. bPrepared by smearing a 25-mgPS solution in decane (100 mL) across the 1.10-mm aperture of the Tefzel film separating the two compartments which contained aqueous 0.10 M KCI. Subsequent to thinning, the diameter (ZR,) and thickness of the hydrocarbon layer (6,) of this particular BLM (excluding its Plateau-Gibbs border) were determined to be 0.81 mm and 5.41 nm, respectively. It 'lasted" for more than 8 h. CPrepared by smearing a 25-mg PS solution in decane (100 mL) across the 1.10-mm aperture of the Tefzel film separating the two compartments which contained aqueous 0.10 M KC1. Subsequent to thinning, the diameter ( 2 4 , ) and thickness of the hydrocarbon layer (6,) of this particular BLM (excluding its Plateau-Gibbs border) were determined to be 0.74 mm and 5.19 nm, respectively. It 'lasted" for more than 8 h. dAVis the transmembrane potential. 'FCis the distance of the curvature displacement of the BLM accompanying the lowering of the piston into the cis side (see Figure 2). Fc values were calculated by substituting appropriate data into eq 9. /Hydrostatic pressure at which AV is applied.
fringes as functions of hydrostatic pressure and applied transmembrane potential. Thus, capacitances were monitored prior and during thinning of the surfactant to BLM, as well as prior, during, and subsequent to the application of hydrostatic pressure or transmembrane potential. The measured time-dependent capacitance increase to a plateau value is the reflection of the thinning of the surfactant film to a BLM. Once a plateau was reached, the capacitance value remained the same (within f0.296) for 4-6 h, indicating that equilibrium had been reached. All measurements commenced only after the capacitance of a given BLM remained at its equilibrium value for at least 10 min. Furthermore, at the completion of all needed mechanical and electrical measurements, BLM capacitances were remeasured and found to be unaltered (within f0.296) from their equilibrium values. The measured total capacitance, Ct,allowed the BSSeSSment of the thickness of the hydrocarbon layer in the BLM, ah, from
ct = (€0€/6h)&
(11)
where co is the dielectric constant of vacuum (eo = 8.85 X 10-l2 F m-l) and c is the relative permittivity of the hydrocarbon region of the BLM (e = 2.1). The specific capacitances, C,, better express the properties of a given BLM. It is defined as Cs = Ct/& (12) where A, is the surface area of the membrane at its flat position (A, = (3-5) x IO-' m2). C, values remained essentially constant at different hydrostatic pressures. Apparently, the thickness and area of the BLM did not measurably change upon exposure to the ultrasmall hydrostatic pressures used in the present study. A different behavior was found previously on applying hydrostatic pressures in the 10-patm range to the BLM.I2 In fact, changes in C, values as a function of applied pressures were used for assessing BLM interfacial tensions.I2 Specific capacitances determined for GMO BLMs (0.490, 0.520, and 0.545 pF/cm*; Table V) agreed fairly well with values reported previously (0.432 f 0.021,190.390 f 0.018,200.383,21
- expansion
c
\
compression
re
Figure 5. Schematics of elastic moduli. (A) Surface elastic modulus; a given surface area, S, is stretched by isotropic tension, T (eq 24). Stretching is seen to increase the area from that shown in the dotted line to that drawn by the solid line. Adopted from ref 41. (B) Thickness elastic modulus; a given thickness, bh, is compressed by PoG(eq 25). Adopted from ref 41. Compression is seen to decrease the distance and increase the length of a given constant volume from that shown in the dotted line to that drawn by the solid line. (C) One-dimensional illustration of curvature elastic modulus for a BLM. Curving the BLM by hydrostatic pressure, php, stretches the outer and compresses the inner surface relative to the center of the membrane which manifests in extensive tension, T,, at both surfaces in the opposite direction (eq 26).
and 0.406 pF/cm222). For a given GMO or PS BLM, increased transmembrane potential increased the C, values (Table V). These data were used for the elucidation of the thickness elastic (or Young's) modulus, K~ (vide infra). Voltage-dependent current changes were found to be extremely small for PS BLMs (Table VI); apparently they are excellent electrical insulators. Increasing voltages caused pronounced and systematic current increases for a given preparation of GMO BLMs (Table VI). Current-voltage curves for GMO BLMs were found to be ohmic in the flOO mV range. Pronounced deviations from linearity were observed, however, in the -250 to -100 and +lo0 to +250 mV ranges.23 Reproducibility of current densities in separately prepared BLMs, as found previ~usly,~~*I' was rather poor.
Discussion Simultaneous electrical and optical interferometric characterization of hydrostatic-pressure- and applied-potential-induced changes of BLMs has been the most significant accomplishment of the present work. Treatment of the data presented in the Results section will be the subject of the ensuing discussion. Interfacial surface tensions and curvature elastic, thickness elastic (Young's), and surface elastic moduli (seeFigure 5 ) of GMO and PS BLMs will be elucidated sequentially. Trends in the obtained (19) White, S. H. Eiophys. J . 1970, IO, 1127. (20) Benz, R.; Frahlich, 0.;Liuger, P.;Montal, M. Eiochim. Biophys. Acta 1975, 394. 232. (21) Fettiplace, R.; Andrews, D. M.;Haydon, I. R.J. Membr. Eiol. 1912, IO, 11. (22) White, S. H. Eiophys. J. 1975. I S , 95. (23) Picard, G.; Denicourt, N.;Lee, H. Unpublished results, 1990.
The Journal of Physical Chemistry, Vol. 95, No. 9, 1991 3711
Bilayer Lipid Membrane Deformation TABLE V: Specific Capacitances (C, rF/cmz) of BLM GMO, A# bh.
rima
GMO, Bb GMO, Ce PS, Ad bh, nm9 PS,Be
PS,Cf
0 0.490 3.790 0.520 0.545 0.330 5.630 0.344 0.358
20 0.490 3.790 0.340 5.460 0.362
BLMs at Different Applied Potentiah (AV,
40 0.495 3.760 0.532 0.545 0.380 4.890 0.380 0.393
60 0.495 3.760 0.390 4.760 0.390
80 0.500 3.720 0.532 0.545 0.400 4.640 0.399
C. at AV = 100 0.510 3.640 0.543 0.561 0.410 4.530 0.418
120 0.520 3.570
mV)
140
150 0.540 3.440
0.555 0.577 0.440 4.220 0.436 0.427
0.445
0.470 3.950 0.473 0.462
180 0.567 0.609 0.500 3.720 0.501 0.497
200 0.570 3.260 0.642 0.520 3.570 0.519 0.508
#Prepared by smearing a 50" GMO solution in decane (100 mL) across the 1.10-mm aperture of the Tefzel film separating the two compartments which contained aqueous 0.10 M KCI. Subsequent to thinning, the diameter (2R,) and thickness of the hydrocarbon layer (6,) of this prticular BLM (excluding its Plateau-Gibbs border) were determined to be 0.80 mm and 3.79 nm, respectively. It 'lasted" for more than 8 h. Prepared by smearing a 50-mg GMO solution in decane (100 mL) across the 1 .IO-mm aperture of the Tefzel film separating the two compartments which contained aqueous 0.10 M KCI. Subsequent to thinning, the diameter (2R,) and thickness of the hydrocarbon layer (6h) of this particular BLM (excluding its Plateau-Gibbs border) were determined to be 0.74 mm and 3.57 nm, respectively. It 'lasted" for more than 8 h. CPreparedby smearing a SO-mg GMO solution in decane (100 mL) across the 1.10-mm aperture of the Tefzel film separating the two compartments which contained aqueous 0.10 M KCI. Subsequent to thinning, the diameter (2R,) and thickness of the hydrocarbon layer (6,) of this particular BLM (excluding its Plateau-Gibbs border) were determined to be 0.63 mm and 3.41 nm, respectively. It 'lasted" for more than 8 h. dPrepared by smearing a 25-mg PS solution in decane (100 mL) across the 1.10-mm aperture of the Tefzel film separating the two compartments which contained aqueous 0.10 M KCI. Subsequent to thinning, the diameter (2R,) and thickness of the hydrocarbon layer (6h) of this particular BLM (excluding its Plateau-Gibbs border) were determined to be 0.80 mm and 5.63 nm, respectively. It 'lasted" for more than 8 h. ePrepared by smearing a 25-mg PS solution in decane (100 mL) across the 1.10-mm aperture of the Tefzel film separating the two compartments which contained aqueous 0.10 M KCI. Subsequent to thinning, the diameter (2R,) and thickness of the hydrocarbon layer (6,) of this particular BLM (excluding its Plateau-Gibbs border) were determined to be 0.81 mm and 5.41 nm, respectively. It 'lasted" for more than 8 h. /Prepared by smearing a 25-mg PS solution in decane (100 mL) across the 1.10-mm aperture of the Tefzel film separating the two compartments which contained aqueous 0.10 M KCI. Subsequent to thinning, the diameter (2R,) and thickness of the hydrocarbon layer (6,) of this particular BLM (excluding its Plateau-Gibbs border) were determined to be 0.74 mm and 5.19 nm, respectively. It 'lasted" for more than 8 h. *Thickness of the hydrocarbon layer, calculated by eq 12. TABLE VI: Specific Currents ( J , nA/cmz) of BLMs at Different Applied Potentials (A V, mV) JatAV= BLM 0 20 40 60 80 100 120 GMO, Aa 0 2.0 4.6 7.0 10.6 13.2 16.8 0 4.9 6.4 GMO, Bb GMO,CC 0 1.6 3.2 PS, Ad 0 0.20 0.20 0.20 0.20 -0.20 -0.40 PS, Be 0 0 0 0 -0.37 -0.37 -0.55 PS, Cf 0 0.20 0.50
140
150 24.8
8.70 7.40 -0.55
-0.80 -0.74 -0.20
180 13.4 13.1 -0.6 -1.10 -2.1
200 40.0 16.4 -0.20 -1.10 -1.6
#Prepared by smearing a 50" GMO solution in decane (100 mL) across the 1.10-mm aperture of the Tefzel film separating the two compartments which contained aqueous 0.10 M KCI. Subsequent to thinning, the diameter (ZR,) and thickness of the hydrocarbon layer (6,) of this articular BLM (excluding its Plateau-Gibbs border) were determined to be 0.80 mm and 3.79 nm, respectively. It 'lasted" for more than 8 h. PPrepared by smearing a 50-mg GMO solution in decane (100 mL) across the 1.10-mm aperture of the Tefzel film separating the two compartments which contained aqueous 0.10 M KCI. Subsequent to thinning, the diameter (2R,) and thickness of the hydrocarbon layer ( b h ) of this particular BLM (excluding its Plateau-Gibbs border) were determined to be 0.74 mm and 3.57 nm, respectively. It 'lasted" for more than 8 h. CPreparedby smearing a 50" GMO solution in decane (100 mL) across the 1.10-mm aperture of the Tefzel film separating the two compartments which contained aqueous 0.10 M KCI. Subsequent to thinning, the diameter (2R,) and thickness of the hydrocarbon layer (6,) of this particular BLM (excluding its Plateau-Gibbs border) were determined to be 0.83 mm and 3.41 nm, respectively. It 'lasted" for more than 8 h. "repared by smearing a 25-mg PS solution in decane (100 mL) across the 1 . 1 0 " aperture of the Tefzel film separating the two compartments which contained aqueous 0.10 M KCI. Subsequent to thinning, the diameter (ZR,) and thickness of the hydrocarbon layer (6,) of this particular BLM (excluding its Plateau-Gibbs border) were determined to be 0.80 mm and 5.63 nm, respectively. It 'lasted" for more than 8 h. CPrepared by smearing a 25-mg PS solution in decane (100 mL) across the 1.10-mm aperture of the Tefzel film separating the two compartments which contained aqueous 0.10 M KCI. Subsequent to thinning, the diameter (2R,) and thickness of the hydrocarbon layer ( b h ) of this particular BLM (excluding its Plateauaibbs border) were determined to be 0.81 m m and 5.41 nm, respectively. It 'lasted" for more than 8 h. /Prepared by smearing a 25-mg PS solution in decane (100 mL) across the 1.10-mm aperture of the Tefzel film separating the two compartments which contained aqueous 0.10 M KCI. Subsequent to thinning, the diameter (ZR,) and thickness of the hydrocarbon layer (6,) of this particular BLM (excluding its Plateau-Gibbs border) were determined to be 0.74 mm and 5.19 nm, respectively. It 'lasted" for more than 8 h.
values will then be compared with and contrasted to those reported for monolayers and vesicles. Interfacial Surface Tension of BLMs. Two layers of closely packed surfactants are apposed tail to tail in the BLM. Their polar headgroups are in contact with and hydrated by the aqueous solution bathing the two sides of the membrane. A delicate balance between opposing forces is responsible for maintaining all surfactant assemblies, including BLMs.% The repulsive force between headgroups are counteracted, in part, by the interfacial pressure of the aqueous solution on the surfactants. Since this attractive force (by unit length) is acting in the plane of the monolayer (i.e., one-half layer of the BLM), it is called interfacial surface tension and is designated by ymfor monolayers and by ~
~
~~~~~
(24) Israelachvilli, J. N. Intermolecular and Surface Forces; Academic Press: New York. 1982.
y for BLMs (y = 2 ~ , , , ) .Thermodynamically, ~~ y is defined as
the force (by unit length) required to increase the volume of the spherical cup by an infinitesimally small value, dV,, by stretching it by an infinitesimally small area, dA, at a hydrostatic pressure, php:
PhpdV, = y dA, (13) The relationship between the hydrostatic-pressure- or a p plied-potential-induced curvature deformation (Faand the volume of water displaced by the spherical cup formed (V,)was given (25) Due care should be exercised in consulting the literature for y values. Reported interfacial tensions sometimes refer to monolayers (ym in our notation), sometimes to bilayers ( y in our notation), and sometimes to that between the PlateauGibb border and the bulk aqueous solution. Furthermore, the assumptions used in assessing y values are not always the same or even obvious.
Picard et al.
3712 The Journal of Physical Chemistry, Vol. 95, No. 9, 1991
2 1
0.25
0.20
1
B
Y, mN/m 0.15
A
0.10
'
-
0.05' -50
"
"
0
"
"
"
100
150
200
50
0.01 -50
'
"
0
"
50
'
100
"
150
"
200
'
I
250
250
AV, mV AV, mV
6. Plots of y against transmembranepotential for GMO A, GMO B, and O M 0 C BLMs. See footnotes in Table V for the properties of these BLMs.
in eq 2. The surface area of the cup, A,, corresponding to V, is given by A, = *(Rm2+ F ): (14) and from eq 2, 13, and 14 one obtains
Defining the radius of the curvature of the spherical cup, R, (see Figure Sc) R, =
Rm2 Fc + -2 2F,
and then substituting eq 16 into eq 15 leads to 7 = Ph$d2
(17)
or php
27/Rc
Increasing the transmembrane potential, AK decreased 7 values linearly for GMO and PS BLMs (Figures 6 and 7). Subjecting a given BLM to increasing applied potentials (to electrocompression) also manifested in increased specific capacitances (Table J 7 - can ~ be rationalized in terms V), as reported p r e v i o ~ s l y . ' ~ ~and of changing the complex equilibria prevailing between the BLM and its Plateau-Gibbs border. Serving as a reservoir of surfactants and organic solvent, the Plateau-Gibbs border is responsible for the formation and stability of the BLM. The primary driving force for thinning the initially deposited film to bilayer is the hydrostatic-pressure difference across the BLM (governed by Laplace's law, eq 18). A greater Laplace pressure at the flat part of the membrane than that at its border ensures the flow of surfactants and organic solvent to the Plateau-Gibbs reservoir and, hence, the thinning of the BLM. Application of a transmembrane potential, AV, decreases the BLM thickness (see Table V) by a similar mechanism. It shifts, primarily, the hydrocarbon solvent from the bilayer to the Plateau-Gibbs border. The electric-field-induced pressure change (electrocompression), P,, is given by
(18)
Equation 18 is the well-known Laplace equation for bilayer interfacial tension. Limiting the applied pressure for a monolayer (or one side of the BLM), eq 18 becomes php 4ym/Rc (19) Under our experimental conditions, deformation F, is very small compared to the BLM radius, R, (R, 1 400F,); thus eq 15 can be approximated by Rm2 h' p 7=--
4 Fc In eq 20, Php/Fc is the inverse of the slope of the lines shown in Figure 4. Determination of Rm for each BLM preparation led to mean interfacial surface tensions ( 7 ) of 0.22 0.02 and 0.29 0.03 mN/m for GMO and PS BLMs, respectively. The value of y for GMO BLMs agrees well with that obtained previously by two-exposure interferometric holography (y = 0.2 mN/m)26 or by capacitance measurements as a function of applied hydrostatic pressure (y = 0.35 mN/m).IZ The interfacial surface tension of the charged PS BLM is higher than that of the uncharged GMO. An incomplete understanding of the relationship between surface charge and surface tension and the absence of more extensive data do not warrant undue discussion of this point.
*
Figure 7. Plots of y against transmembrane potential for PS A, PS B, and PS C BLMs. See footnotes in Table V for the properties of these BLMs.
*
(26) y = 0.2 mN/m is obtained after applying corrections for n,, sin 45O, and mast importantly, A , for the value published in ref 15 (7 = 1.1 mN/m).
The implications of eq 21 can be gauged by considering that the application of a 200-mV potential across a 4.0-nm-thick BLM elicits P, = 2.3 X lo4 N m-l (or 0.2 atm) electrocompression. This pressure on the bilayer is orders of magnitude greater than that on the Plateau-Gibbs border and is, once again, responsible for "squeezing out" surfactant and solvent molecules from the bilayer. Indeed, White showed that the mole fraction of ndecane (the organic solvent) in GMO (decane) BLMs decreases in a nonideal manner as a function of increasing applied potential.32 The hydrocarbon thicknesses of GMO BLMs decreases from 3.79 to 3.26 nm upon the application of a 200-mV transmembrane potential (Table V). At the highest potential applied, this value of d h is considerably less than twice the length (I) of the fully extended hydrocarbon chain of a GMO molecule (21 = 4.0 nm). Assuming that e is unaffected by electrocompression, this result must imply surfactant interdigitation and/or bending by extensive kink formation at the C-9 position in GMO. Electrocompression decreased S, for charged PS BLMs, as expected, to a greater extent than for GMO BLMs (Table V). (27) White, S.H. Biochim. Biophys. Acta 1970, 196, 354. (28) White, S. H. Biophys. J . 1974, 14, 155. (29) Wobschall, D. J. Colloid Inrerfoce Sci. 1970,40,417. (30) Crowley, J. M.Biophys. J . 1973, 13, 711. (31) Requena, J.; Haydon, D. A.; Hladley, S.B. Biophys. J. 1975, IS,77. (32) White, S.H. Science 1980, 207, 1075. (33) Alvarez, 0.; Latorre, R.Biophys. J . 1978, 2f, I. (34) White, S. H.; Chang, W. Biophys. J . 1981, 36, 449.
The Journal of Physical Chemistry, Vol. 95, No. 9, 1991 3713
Bilayer Lipid Membrane Deformation Surfactants in the Plateau-Gibbs border form reverse micelles (and other large aggregates) and, most importantly, along with the organic solvent, determine the chemical potentials of the bilayer. The chemical potential of the surfactant in the Plateau-Gibbs border, p, and that in a standard state, po, is given by (22) p = po + R T In cfc,) where c, and f are the concentration of the surfactant and its activity coefficient in the Plateau-Gibbs border. Equation 22 is related to interfacial surface tension of the BLM, y, by the Gibbs equation dy = -r dp (23) where I' is the interfacial concentration of the lipid. The observed decreases of y with increasing transmembrane potential (Figures 6 and 7 ) are simple to rationalize. They are a direct consequence of the Gibbs equation (eq 23). Increasing chemical potentials of the surfactant in the Plateau-Gibbs border (increasing p values), the consequenceof electrocompression (i.e., "squeezing" surfactants to the Plateau-Gibbs border), elicits a linear decrease of y. Elastic Moduli of BLMs. The fundamental mechanical properties of any material are described by its surface elastic modulus ( K ~ ) , thickness elastic (Young's) modulus ( K ~ ) , and curvature elastic modulus (K,) which are defined by eq 24, 25, and 26, respectively (see Figure 5 ) :
= s(aT/as)T (24) where ai is the surface tension variation of a surface area of the BLM, S, at temperature T K4 = h(aPec/a&t)T,V (25)
TABLE VII: Pressure-Idwed CWV8huv m a h 8 php.6
mN/m2 4.27 8.81 13.5 17.6 21.4
106Fc: m 0.66 1.33 2.00 2.66 3.33
K&
= aM,/a(l/Rc)
(26)
where M , is the bending moment and R , is the radius of the curvature. Two different approaches were used in the present work for obtaining the elastic moduli of BLMs. The first approach (mechanical approach, method M) relied on the K, values determined from the observed hydrostatic-pressure-inducedBLM curvature changes (eq 20). The other two elastic moduli ( K and ~ ~ K ~ are ) then calculated from the obtained K values by making appropriate assumptions. In the second approaa (electrical approach, method E),advantage is taken of voltage-dependent capacitance measurements to determine K ~ this, ; in turn, leads to estimates of the other two elastic moduli ( K and ~ K ~ by ) making a different set of assumptions. Modifications of eq 24-26 for BLMs affords the needed relationships for the first approach. Specifically, by definition MR, =
Tc6h
(27)
where T, is the extensive tension (see Figure 5c) which relates to the BLM surface elastic modulus by Tc KS(h/2Rc) Substituting eq 27 and 28 into eq 26 gives
(28)
J
2.86 11.4 25.7 45.6 71.4
BW' lPM&/ N 1.70 3.41 5.10 6.81 8.53
and M is the difference between the pressure applied to the outer (Po) and the inner ( P i ) monolayer of the BLM AP = Po - Pi (33) and Po = 2ym/Roc Pi = 2ym/Ric
(34)
where %,and Rkare the radii of curvature of the outer and inner monolayer of the BLM, respectively. Typical W, T , and M , values assessed for a PS BLM are illustrated in Table VII. It is important to recognize the extremely small values associated with T , M,, and W. The energy required for deforming the BLM by increasing its curvature by F, = 1-2 pm is in the order of J! Clearly this ultrasmall energy deposition is nonperturbing. Since (35)
substitution of eq 16 into eq 33 leads to
AP
N
8y&f?/Rm4
(36)
and substitution of eq 35 and 36 into eq 30 and dividing by the work per the spherical cup area results in (37)
and35 K&
= y6h2/2
(38)
which, with eq 29, shows that the BLM interfacial tension is equal to its surface elastic modulus KS
= Ks6h2/2 (29) as unknown. K , can be considered to be related to the energy of twisting of the BLM (w)
1Oi27c,' N/m 3.03 6.05 9.09 12.1 15.2
'PS A BLM; prepared by smearing a 25" PS solution in decane (100 mL) across the 1.10-mm aperture of the Tefzel film separating the two compartments which contained aqueous 0.10 M KCI. Subsequent to thinning, the diameter (ZR,) and thickness of the hydrocarbon layer (6,) of this particular BLM (excluding its Plateau-Gibbs border) were determined to be 0.80 mm and 5.63 nm, respectively. It "lasted" for more than 8 h. bPbp is the hydrostatic pressure due to the differential volume of liquid increase in the cis side. pbp values were calculated by substitution of appropriate data into eq 4. cFcis the. distance of the curvature displacement of the BLM accompanying the lowering of the piston into the cis side (see Figure 2). Fcvalues were calculated by substituting appropriate data into eq 9. "Work performed on curving the BLM (see eq 30). 'Extensive tension (see cq 28). /Bending moment (see eq 27).
KS
where aP, is the variation of normal stress that changes the thickness ahh, at constant temperature T and volume V, and
l@'W,d
=
(39)
and, if the total volume of the BLM (including its Plateau-Gibbs
KR,
Equation 29 has K, and
K~
sH;wldW = M , d ( 2 / R C )= 2 ~ , / R 2
(30)
or
w=APv where V is the volume of the deformed BLM
v = A,&
(32)
(35) Mechanics treats materials as continuous in three dimensions and gives elastic constants in units of force per units of cross-sectionalarea (dyn cm-2, N m-2, erg cm-), or J m-)). Since the thickness of the BLM (6, = 4.0 nm) is on the order of molecular dimensions, it is beat considered a8 a twdimensional contin~um.'~Accordingly, its surface elastic modulus, KS, has units of dyn an-',N m-I, erg cm-2, or J m-2. Dividing KS by the thickness of the membrane and assuming the nw.9 density of the BLM to be constant give& by definition ( 37), the thickness elastic modulus, K ~ in, units of dyn cm-*, N nr2, erg cm?, or J m-). These are the customary units of the hulk compressibility modulus to which they can, therefore, be compared. Similarly, by definition, the curvature or bending elastic modulus of the BLM (K&) IS obtained by multiplying KS by 6b2/2 (eq 29);thus, the units of KGare dyn an, N m, erg, or J.
3714 The Journal of Physical Chemistry, Vol. 95, No. 9, 1991
Picard et al.
TABLE VIII: Elastic Moduli of BLMs 1068:
BLM
PS A# PS Bh PS C' PS mean GMO AI GMO Bk GMO C' GMO mean
pF/(cm mV2) 3.49 (31.7) 3.65 (21.4) 3.17 (21.9) 1.89 2.25 1.41
IO'KS,~ N/m
method Me 2.67 2.80 3.29 2.92 1.83 2.91 1.92 2.22
method Ef 1.95 (0.17) 1.95 (0.28) 2.36 (0.29) 2.08 6.36 6.10 10.4 7.62
1O4~Jh,e N/m2 method Me method Ef 4.56 3.47 (0.30) 5.18 3.61 (0.52) 6.85 4.97 (0.61) 5.53 4.01 4.83 16.8 5.91 17.1 5.63 30.6 5.46 21.5
1 0 2 ' N~ m~ (or ~ J) method M' 4.07 4.10 3.79 3.99 1.31 1.34 1.12 1.26
method Ef 3.09 (0.27) 2.86 (0.41) 2.72 (0.33) 2.89 4.58 3.87 6.08 4.87
oSlopes of specific capacitances against the square of applied potential (eq 41). Plots of the data for PS BLMs resulted in two slopes (see Figure 8 and Discussion), values for the first of which are given in parentheses. bSurface elastic modulus = y; see eq 39. See ref 35 for units. eThickness elastic modulus; see eq 40. See ref 35 for units. dCurvature elastic modulus, see eq 38. See ref 35 for units. eObtained by the mechanical approach treating the data by eqs 42, 40, and 39 (see Discussion). /Obtained by the electrical approach treating the data by eqs 42, 40, and 39 (see Discussion). Plots of the data for PS BLMs resulted in two slopes (see Figure 8 and Discussion), values for the first of which are given in parentheses. ,#Prepared by smearing a 25-mg PS solution in decane (100 mL) across the 1.10-mm aperture of the Tefzel film separating the two compartments which contained aqueous 0.10 M KCl. Subsequent to thinning, the diameter (2R,) and thickness of the hydrocarbon layer (6,) of this particular BLM (excluding its Plateau-Gibbs border) were determined to be 0.80 mm and 5.63 nm, respectively. It 'lasted" for more than 8 h. Prepared by smearing a 25" PS solution in decane (100 mL) across the 1 . 1 0 " aperture of the Tefzel film separating the two compartments which contained aqueous 0.10 M KCl. Subsequent to thinning, the diameter (2R,) and thickness of the hydrocarbon layer (6,) of this particular BLM (excluding its Plateau-Gibbs border) were determined to be 0.81 mm and 5.41 nm, respectively. It 'lasted" for more than 8 h. 'Prepared by smearing a 25-mg PS solution in decane (100 mL) across the 1.10-mm aperture of the Tefzel film separating the two compartments which contained aqueous 0.10 M KCl. Subsequent to thinning, the diameter (2R,) and thickness of the hydrocarbon layer (6,) of this particular BLM (excluding its Plateau-Gibbs border) were determined to be 0.74 mm and 5.19 nm, respectively. It 'lasted" for more than 8 h. 'Prepared by smearing a 50" GMO solution in decane (100 mL) across the 1.10-mm aperture of the Tefzel film separating the two compartments which contained aqueous 0.10 M KCl. Subsequent to thinning, the diameter (ZR,) and thickness of the hydrocarbon layer (6,) of this particular BLM (excluding its PlateauCribbs border) were deterGMO solution in decane (100 mL) mined to be 0.80 mm and 3.79 nm, respectively. It 'lasted" for more than 8 h. kPrepared by smearing a 50" across the 1 .lO-mm aperture of the Tefzel film separating the two compartments which contained aqueous 0.10 M KCI. Subsequent to thinning, the diameter (2R,) and thickness of the hydrocarbon layer (6,) of this particular BLM (excluding its PlateauCribbs border) were determined to be 0.74 mm and 3.57 nm, respectively. It 'lasted" for more than 8 h. 'Prepared by smearing a 50-mg GMO solution in decane (100 mL) across the 1.10-mm aperture of the Tefzel film separating the two compartments which contained aqueous 0.10 M KCI. Subsequent to thinning, the diameter (2R,) and thickness of the hydrocarbon laver (bk) of this particular BLM (excluding its Plateau-Gibbs border) were determined to be 0.83 mm and 3.41 nm, . respectively. It 'iasted" for m&e than 8 h.
border) can be considered incompressible (i.e., the mass density of the BLM remains constant)
Availability of precise y values (the first approach, method M) has provided entirely new experimental access for the determination of BLM elastic moduli. In particular, it allowed their assessment from pressure-induced BLM deformations measured exclusively by optical interferometry. Electrocompression measurements offered an alternative route (the second approach, method E) to the measurement of BLM elastic moduli. BLM specific capacitances have been shown to relate to the applied transmembrane potential by'9*27.28
c, = c,, + j3v
(41) Typical plots of the data according to eq 41 are shown in Figure 8. Intercepts of these plots (CsJ define the specific capacitances at zero applied potential. (These values are slightly different than those measured directly and shown in Table V at V =O.) Slopes of plots of the data according to eq 41,& is related to the thickness elastic (Young's) modulus by K 4 = (1 /B)(Co2f2/24l3) (42) B values for the different PS and GMO BLMs are collected in
Table VIII. As seen in Figure 8, plots of the data for PS GMO resulted in two straight lines which, in turn, gave two sets of j3, KS, ~ hand , K& values (also collected in Table VIII). It is tempting to speculate that electrocompression of charged BLMs occurs in two steps; the first step is the reorganization of the surface charges, and the second is the "squeezing out" of the surfactant and solvent molecules from the bilayer to the Plateau-Gibbs border. It is this latter process which corresponds to the second slope and to elastic moduli which are then comparable to those obtained from mechanical measurements (Table VIII). The agreement between the elastic moduli obtained by method M and method E for PS BLMs is quite satisfactory. Electrocompression measurements of GMO BLMs led, however, to consistently higher elastic moduli than those obtained from me-
chanical measurements (Table VIII). This is hardly surprising in view of the different assumptions used in these two approaches. Previously determined K~ values for GMO (4.16 X lo4 N m-2),28,45 phosphatidylcholine(3.46 X 10" N m-2),6 and oxidized cholesterol (3.72 X lo4 N m-2)27BLMs agree well with those reported in Table VIII. K values reported for bilayer lipidic vesicles [(0.4-2) X J]k38 are some 3 orders of magnitude greater than the corresponding curvature elastic modulus of BLMs (Table VIII). Curvature elasticity depends on the extent to which the individual monolayers are free to slide relative to one another in lipidic bilayers and B L M S . ~ ~It' is not unreasonable to assume that the Plateau-Gibbs border favors the lateral movements of the two monolayers and that this imposes less resistance to bending in BLMs than that available in unconfined lipidic bilayers where the surfactant and solvent molecules cannot be drained away so easily from the bilayer. Application of transmembrane potential had modest effects on the BLM interfacial tension and elastic moduli (Table IX). The decreased elastic moduli in the +40 to +140 mV range is the consequence of decreased solvent content of the bilayer by electrocompression. Conclusion Conceptually, bilayer lipid membranes can be considered to be halves of flattened vesicles. Alternatively, they can be looked (36) Sakurai, I.; Kawamura, Y. Biochim. Biophys. Acta 1983, 735, 189. (37) Schneider, M. B.; Jenkins, J. T.; Webb, W. W. Biophys. J. 1984,45, 891. (38) Servuss, R. M.; Harbich, W.; Helfrich, W. Biochim. Biophys. Acfa 1976,436,900. (39) Evans, E. A.; Skalak, R. Mechanics and Thermodynamics of Biomembranes; CRC Press: Boca Raton, FL, 1980. (40)Evans, E.; Needham, D. J. Phys. Chem. 19%7,91,4219. (41) Evans, E. In Phospholipid Bilayers; Cevc, G., Marsch, D., Eds.; Wiley: New York, 1978; p 347. (42) Kwak, R.; Evans, E. A. Biophys. J. 1981,35, 367. (43) Evans, E. A.; Kwak, R. Biochemistry 1982, 21,4874. (44) Evans, E. A.; Simon, S . Biophys. 1. 1975, 15, 850. (45) Andrews, D. M.; Manev, E. D.; Haydon, D. A. Spec. Discuss. Faraday Soc. 1970, 1,46. (46) White, S. H.; Thompson, T. E. Biochim. Biophys. Acta 1973, 323, 7.
The Journal of Physical Chemistry, Vol. 95, No. 9, 1991 3715
Bilayer Lipid Membrane Deformation
0 40 80 100 140
o . I " ' ~ " " ' " " ' " " ' " " ' " 0
10000
20000
30000
40000
50000
v z , mv2 . .
0.60
0.55
-
0.50
-
0
,
.
I
.
.
10000
,
.
I
.
.
20000
vf
.
.
I
.
30000
.
..
I
. ' . '
40000
50000
mV2
for GMO A (top) and P!3 B BLMs (bottom). See footnotes in Table V for the properties of these BLMs.
Figure 8. Plot of Cs against
upon as composites of two monolayers. Indeed, BLMs are formed, in the Montal-Mueller method," by joining the hydrocarbon tails of two monolayers. Furthermore, monolayers have been shown to form from vesicles injected into the aqueous s ~ b p h a s e ~and .'~ vesicle to monolayer to BLM transformations have also been established.'"J2 There are pronounced differences, however, among vesicles, monolayers, and BLMs. Thus,in large surfactant vesicles, in the absence of hydrostatic pressure differences between their interiors and exteriors, the bifacial surface tension is zero. In contrast, surface pressures of 40-60 mN m-' need to be applied for compressing monolayers at air-water interfaces to their (47) Montal, M.; Mueller, P. Proc.Natl. Acad. Sci. USA. 1972.69,3561. (48) Schindler, H. Blochim. Bfophys. Acta 1979, 555, 316. (49) Heyn, S.-P.; Egger, M.;Gaub, H. E. J. P h p . Chem. 1990,94,5073. (50) Schindler, H.; Quast, V.Proc.N d . Acad. Sci. U S A . 1980,77,3052. (51) Schindler, H.; Rosenbusch, J. P.Proc. Not/. Acad. Sci. U.S.A. 1978, 75. 3751. (52) Salcsse, C.; Ducharme, D.; Leblanc, R. M. Btophys. J. 1987,52,351.
4.79 8.13 9.32 10.2 11.9
2.86 3.00 2.21 1.66 1.10
1.95 2.51 2.03 1.68 1.25
3.61 5.13 4.36 3.78 3.00
5.29 4.97 4.79 4.56 4.25
2.86 2.43 2.23 2.03 1.78
O P S B BLM; prepared by smearing a 25.0-mg PS solution in decane (100 mL) across the 1.10-mm aperture of the Tefzel film separating the two compartments which contained aqueous 0.10 M KCI. Subsequent to thinning, the diameter (2R,) and thickness of the hydrocarbon layer (6h) of this particular BLM (excluding its Plateau-Gibbs border) were determined to be 0.81 mm and 5.41 nm, respectively. It "lasted" for more than 8 h. Elastic moduli were measured and calculated by method E. See Table I1 for additional information. bApplied transmembrane potential. See footnotes c-g in Table I1 for Php,values at given transmembrane potentials. Work performed on curving the BLM (see eq 30). dCurvature elastic modulus (eq 38). See ref 35 for units. CSurface elastic modulus, KS, = y (eq 39). See ref 35 for units. /Thickness elastic modulus (eq 40). See ref 35 for units. rExtensive tension (see eq 28). *Bending moment (see eq 27).
well-packed, two-dimensional condensed states. BLM interfacial surface tensions determined in the present work (y = 0.2-0.3 mN m-l) are very much smaller than those expected from corresponding monolayer values or from the surface energies of their components. (Typical hydrocarbon-water surface tensions are on the order of 50 mN m-'.) Similarly,the elastic moduli of BLMs differed markedly from those determined or assessed for lipidic bilayers or vesicles (vide supra). The unique behavior of BLMs is the consequence of the Plateau-Gibbs border, which acts as a reservoir. Stability of BLMs, their interfacial tensions, and elastic moduli are primarily determined by the free energy difference (AGrb) of the surfactant and solvent molecules between their two extreme locations-in the bilayer and in the Plateau-Gibbs reservoir. There are numerous parameters, of course, that influence AGh and are, in turn, responsible for rendering, as it was found here, each BLM to be somewhat distinct. It is important, therefore, to characterize each BLM as fully as possible. The combined electrical and optical measurements developed here have opened the door to simultaneous mechanical and molecular level investigations of the BLM-vesicle fusion mechanism, an area of our current and intensive scrutiny. Note Added in Proof: We became aware of the work of Abidor et al. (Abidor, I. G.; Glazunov, I. Yu.; Leikin, S.L.; Chizmadzhev, Yu. A. Biol. Membr. 1986, 3, 621 (in Russian)) in which k , values of 1.5-3.0 J were reported for BLMs prepared from decane solutions of phosphatidylethanolamine. These values are remarkably similar to our measurements for PS BLMs (see Table VIII). Acknowledgment. Support of this work by a grant from the Natural Sciences and Engineering Research Council of Canada is gratefully acknowledged. Regism NO. GMO, 1 1 1-03-5.
