Electrical and real-time stroboscopic interferometric measurements of

Jun 4, 1991 - Thus, real-time stroboscopic interferometry provided a direct method for the determination of /. Two different frequency regimes of f we...
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Langmuir 1991, 7, 3127-3137

3127

Electrical and Real-Time Stroboscopic Interferometric Measurements of Bilayer Lipid Membrane Flexoelectricity? Angelio T. Todorov,l Alexander G. Petrov,l Michael 0. Brandt, and Janos H. Fendler* Department of Chemistry, Syracuse University, Syracuse, New York 13244-4100 Received June 4,1991. In Final Form: July 29,1991

Subjectingone side of a glyceryl monooleate (GMO)and phosphatidylcholine(PC)bilayer lipid membrane (BLM) to an oscillating hydrostatic pressure, in the 100-600-Hzrange, resulted in the periodic flexing of Flexoelectricity, the membrane, which manifested in the development of microvolt range potential (Uf). as this phenomenon is termed, was described phenomenologicallyby the flexoelectriccoefficient V, defined as the ratio between Uf and the change of curvature (c) that accompanied the flexing of the membrane. Electrical measurements required the assumption of completely spherical membrane deformation and, thus, provided only an indirect assessment off values for PC and GMO BLMs. In contrast, completely spherical deformation of BLMs was not a required assumption for real-time stroboscopic interferometry. This optical method allowed the determination of both the lateral movements and the two principal radii of curvature of the oscillating BLM. Thus, real-timestroboscopic interferometry provided a direct method for the determination off. Two different frequency regimes off were recognized. At low frequencies (300 Hz), associated with blocked mobility of the surfactant, f values of 16.5 X 10-19and 0.30 X 10-19 C were obtained for PC and GMO BLMs. The C) agreed well with that calculated value for the GMO BLM oscillating at high frequency (0.12 X determined experimentally (0.3 X 10-19 C).

Introduction Generation of a potential difference by the periodic bending of a bilayer lipid membrane (BLM) has been recognized for some time.2-13 Flexoelectricity (or curvatureinduced electricity), as the phenomenon has been termed, manifests in the development of microvolt-range transmembrane potential upon subjecting one side of the BLM to an oscillating hydrostatic pressure a t a given frequency. Flexoelectricity has been treated theoretically by considering the electrical multipole moments of the lipid molecules,4* the effect of charge exchange across the BLM on the curvature elastic moduli,12 and electrostatic^.^ Experimentally, the magnitude of flexoelectricity has been shown to depend upon the structure and charge of the surfactant constituting the BLM, the type and concentration of electrolyte(s) bathing the BLM, the ions adsorbed on the BLM surface, and the extent and frequency that the BLM is bent.7 These experimental observations have led to the phenomenological definition of the flexoelectric coefficient, f, as the ratio between the bending+ Dedicated, with the highest professional respect and deeply felt personal regards, to Professor Arthur W. Adamson. (1) Permanentaddress: Laboratory of Liquid Crystalsand Molecular Electronics, Institute of Solid State Physics, Bulgarian Academy of Sciences, Sofia 1784, Bulgaria. (2) Petrov, A. G. In Physical and Chemical Bases of Biological Information Transfer; Plenum Press: New York, 1975; pp 111-125. (3) Passechnik, V. I.; Sokolov, V. S. Biofizika 1973, 18, 655. (4) Petrov, A. G.; Derzhanski, A. J. Phys. Suppl. 1976,37, 155. (5) Derzhanski, A.; Petrov, A. G.; Pavloff, Y. V. J. Phys. Lett. 1981, 42, 119. (6) Petrov, A. G.; Bivas, I. Prog. Surf. Sci. 1984, 16, 389. (7) Petrov, A. G.; Sokolov, V. S. Eur. Biophys. J . 1986, 13, 139. (8) Derzhanski, A,; Petrov, A. G.; Todorov, A. T. Bulg. J. Phys. 1989, 16, 268. (9) Derzhanski, A. Phys. Lett. A 1989, 139, 170. (IO) Derzhanski, A.; Petrov, A. G.; Todorov, A. T.; Hristova, K. Liq. Cryst. 1990, 7, 439. (11) Petrov, A. G.; Pavloff, Y. V. J . Phys. Suppl. 1979, 40, C3-455. (12) Petrov, A. G.; Seleznev, S. A.; Derzhanski, A. Acta Phys. Pol., A 1979,55, 385. (13) Ochs, A. L.; Burton, R. M. Biophys. J. 1974, 14,473.

0743-7463191/240%3127$02.50/0

,

induced transmembrane potential, Uf, and the change of curvature (c) that accompanies the bending of the membra~~e:~ f = Uf€Eo/2C

(1)

where e, is the absolute dielectric permittivity of vacuum and t is the permittivity of the hydrocarbon region of the BLM. Evaluation o f f requires a knowledge of the amplitude of BLM deformation during the time it is subjected to oscillating hydrostatic pressure. BLM curvatures have been evaluated indirectly from the second harmonics of the bending-induced potential by assuming, necessarily, completelyspherical deformation of an initially flat BLMe7 Precise movements of oscillating BLMs have been determined directly in the present work by real-time stroboscopic interferometry. We have previously utilized two-exposure interferometric holography14J5and optical interferometry16 for the visualization of steady-state hydrostatic-pressure-induced changes of the curvature and lateral position of BLMs. This methodology is extended here to dynamic measurements. Videorecorded real-time movements of oscillating BLM interferometric patterns have permitted the precise evaluation of membrane deformation in terms of changes in the radii of curvature along any two orthogonal axes, thus obviating the need for assuming completely spherical BLM deformation. Simultaneous electrical measurements of Ufled to the first direct determinations of the flexoelectric coefficients of glyceryl monooleate (GMO)and phosphatidylcholine (PC) BLMs in the 100-600-Hz frequency range. (14) Zhao, X. K.; Picard, G.; Fendler, J. H. J. Phys. Chem. 1988,92, 7161. (15) Picard, G.; Schneider-Henriques,3. E.; Fendler, J. H. J. Phys. Chem. 1990,94, 510. (16) Picard, G.; Denicourt,N.;Fendler,J. H. J.Phys. Chem. 1991,95, 3705.

0 1991 American Chemical Society

Todorou et al.

3128 Langmuir,Vol. 7,No. 12, 1991

delay i n the arrival of lrser pulses, mseo

BSZ BLM

-0.50

CCD

W,

Mach-Zehnder interferometer

BSZ

,VIDEO MON

-

1.oo 0.00

0.33

0.67

1.00

1.33

1.67

TIME PERIOD, msec MW

M

Figure 1. Schematics of the experimental setup used for simultaneous electrical and real-time stroboscopic interferometric measurements of BLMs. A Quantronix 4116 Q-switched, mode-locked and pulse-picked NdYAG laser provided secondrepetition. harmonic 532-nm,l2O-ps,40-115 pulses at 50-5000-H~ Delay was provided by a 111AR Avionics Inc. delay generator. A Hewlett-Packard 8116 A function generator was used. The lock in was a Dynatrac 391A Ithaco lock-in amplifier. The switch box was home built. Key: RLC, 1689 M GENRAD digibridge; LS, a commercial 8-Wloudspeaker; BLM, the cell compartment for the bilayer lipid membrane; BS1 and BS2, beam splitters; M1 and M2, mirrors; CCD, an NEC color camera; VCR, a commercial VHS video recorder; VIDEO MON, NEC color monitor; and COMPUTER, a Hewlett-Packard IBM-compatible PC. For comparison, the scheme of a simple Mach-Zehnder interferometer is included.

Experimental Section Schematics of the experimental setup used for synchronized electrical and real-time stroboscopic interferometric measurementa of BLMs are shown in Figure 1. Oscillating pressures were applied by an electricallyshielded loudspeaker. The speaker was driven by a function generator (Hewlett-Packard 8116A). The synchronization output of the generator was connected to a lock-in amplifier (Dynatrac 391A, Ithaco) and to a delay generator (111AR Avionics Lab, Inc.). The Ag/AgCl electrodes were connected to a home-built switch box, which allowed switching between the RLC Digibridge (1689 M Genrad) for capacitance measurements or the lock-inamplifier for measuring the potentials generated from the membranes in response to the oscillating hydrostatic pressure. The second-harmonic pulses (532 nm, 120 ps, 40 wJ, 50-5000Hz repetition rate) of a Quantronix4116 Q-switched,mode-locked and pulsed-picked NdYAG laser were used for optical interferometry. The laser beam was divided by a beam splitter (BSl). The reference beam was reflected by a mirror (M2) through a polarizer (P) toward a second beam splitter (BS2), as shown in Figure 1. The intensities of the object and reference beams were balanced by P 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. This arrangement is analogous to that used in the MachZehnder interferometerL7with the exception that mirror 1 is replaced by the BLM (Figure 1). Changes in the optical path of the object beam after reflection from the deformed BLM were (17) Note that AZ, and qy (andR,, Ry,cI, and cy)are used to describe the membrane at any position. When the flexoelectric coefficient is calculated, AZz and AZ values are needed for two different BLM positions-A&, UYl, A&, and AZ* (this allows the calculation of change in curvature). For a static membrane, the two positions are taken to be 'flat" and "flexed". For oscillatingmembranes,they are taken to be the two extremes of oscillation.

Figure 2. Time frames for the laser probe pulses (top) and the oscillating voltage driving the loudspeaker (bottom). In the example shown, frequencies for the oscillating voltage were kept at 300 Hz (Le., 3.33-ms period), while the laser pulses were kept at 298 Hz (Le., at 3.36-ms period). Laser pulses are shown (in the top) to arrive at 0-, 0.32-, 0.55-, 0.71-, 0.85-,0.99-, 1.15-,1.33-, 1.47-,and 1.67-ms delaysand, thus, interrogate different positions of the BLM during its movement. 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 was simpler to align the BLM in the optical path. This was achieved with a horizontally positioned rotator (RSA1,Newport) that rotated the BLM along the 2 axis (normal to the table top). The rotator was mounted on a translator assembly that moved the BLM in the X-Y-2 axes. The rotator and translators were bolted together and placed under a Gimball mount (7330, Inrad), which allowed tilting and a small rotation along the 2 axis. The entire BLM setup was mounted on a vibration isolation table and covered by a Faraday cage. For static images, synchronization was accomplished by keeping the frequency of the oscillating pressure the same as that of the laser pulses. Adding a delay to the synchronization signal (coming from the generator) allowed the observation of the oscillating BLM at different positions. Real-time movements of the BLM were observed by using a second function generator (Global Specialties, Inc.) to oscillate the BLM (Figure 1). When the loudspeaker was driven at a frequencyslightlydifferent from the laser-pulsefrequncy,a slowly oscillatingfringe pattern was produced. In this way it was possible to obtain direct information on the oscillating-pressure-induced movements of the BLM by real-time stroboscopic interferometry. For example, with 298-Hz laser pulses (i.e., at 3.36-ms period) to generate interferograms from a BLM oscillating at 300 Hz, each laser pulse arrived 0.022 ms later in the bending cycle than the previous laser pulse. Thus, each laser pulse captured a slightly different position of the oscillating BLM and a complete cycle of oscillating-pressure-induced BLM motion was observed by 100 pulses. Ten pulses chosen from the 100 at strategic points in time are shown in Figure 2. The use of stroboscopic interferometry slowed down the "apparent" rate of oscillationso that optical interferograms could be continuously videorecorded at the normal speed of a commercial VHS recorder (every 33 ms a BLM interferogram was recorded). A time sequence of images was read fromthe videotape into computer memory with a PC-Vision Plus frame-grabber (Imaging Technology, Inc.). Software for the selective storage of images on hard disks was developed in our laboratory. Each frame was then computer analyzed. The first step of image analysis consisted of setting the scaling factors in the x and y directions. Since the BLM was viewed from an angle, ita circumference was visible as an ellipse (instead of a circle). The x and y dimensions of this ellipse were measured and used (along with the known hole diameter) to calculate x and y scaling factors. These scaling constants were then stored along with each image.

Measurements of BLM Flexoelectricity

Figure 3. Schematics of a bent membrane showing definitions of R,, R,, r , and d. Movement of the BLM in the x direction is also shown to define AL, A&, and U,2. The next step involved pinpointing and clarification of the fringes. This was accomplished by using a mouse to draw lines which were superimposed over the image where each fringe appeared. The intensity of each line was used to represent the order of the corresponding fringe and, thus, its relative height. If a time series of images was being analyzed, the most central fringe in each image was designated as the reference fringe. The difference in the order of the reference fringe from one image to the next (which had to be observed while the images were acquired) was used to correlate height between the images. Profiles of the BLM were then produced. The height of a cross section was known at each place where it crossed a fringe line. Intermediate points were interpolated by using a cubic spline function. If necessary,the profile was linearly extrapolated to the edges of the hole. The average edge height was the lateral position of the BLM and was used to measure lateral movements (AL)throughout a time series. A2 values, used to calculate curvature (Figure 3), were determined by subtracting the height at the peak of the profile from the lateral position (thus keeping the lateral position from affecting the calculated curvature). The x axis was chosen as horizontal and they axis as vertical (as seen by the video camera). and AZY1are defined as the height difference between the center of the BLM and its edge along the x and y axes, respectively, prior to flexing. Similarly, A2,z and a Z , 2 are defined as the height difference between the center of the BLM and its edge along the x and y axes, respectively, subsequent to flexing.I7 Next, height information was obtained for every point on the entire image by calculating complete sets of profiles in the x and y cross sections. The two resulting height values ( x and y) for each point were averaged, with interpolated values given precedence over extrapolated ones. The obtained data were stored as a new image in which the intensity of each pixel (notjust those on the fringes) was proportional to its height. This image, which appeared as a shadowed picture of the BLM, contained all of the surface information and was used to generate three-dimensional data files for a surface plotting program (Boeing Graph, Three-D Graphics). A time series of surface plots was generated and stored as images in computer memory for rapid recall. By consecutive display of these images on the screen, a movie was produced that clearly showed thre-dimensional BLM movement. Glyceryl monooleate (GMO; Sigma) L-a-phosphatidylcholine (egg yolk PC; Sigma),and decane (Aldrich)were used as received. Water was purified by a Millipore (Milli-Ro, Milli-Q) system with a final filtration through a Milli-pak 40 filter (0.22 pm). The resistivity of this water was monitored and kept at 18 MQ cm. BLMs were formed across a 0.30 f 0.01 or 1.00 f 0.01 mm diameter conical hole drilled in a black Teflon or a black Delrin film (Curbell, Inc.). The film was pressed diagonally between two compartments with a total internal volume of 5.0 mL. One compartment was closed by a Teflon cap through which oscillating air pressure could be applied via a flexible Teflon pipe. Two Ag/AgCl electrodes were also mounted through the Teflon cap and reached into the two separate compartments containing 0.10 M KCl. BLMs were made by smearingthe BLM-formingsolution (40mgof GMO or PC per milliliter of decane) acrossthe aperture. The needle was rinsed with methanol after each dipping.

Langmuir, Vol. 7, No. 12,1991 3129 Thinning of the membrane to a BLM was monitored by both capacitance measurements and reflectivity. No interference pattern was observed in thick membranes. With thinning, the intensity of reflected light decreased and interference patterns appeared upon the formation of a BLM. Special care was taken to obtain as flat a BLM as possible. Specifically, the size and the geometry of the pinhole in the BLM-supporting Teflon film were carefully optimized. Smoothness at the perimeter of the hole was found to be mandatory. Each pinhole was carefully examined under a microscope prior to its introduction into the cell and BLM formation. Subsequent to the formation of a BLM, the static pressure was equalized on both sides of the membrane by the injection or withdrawal of an appropriate amount (a few microliters) of liquid into one side of the solution bathing the BLM. Observation of a minimum capacitance and a decrease in the number of interference fringes accompanied the pressure equalization and, hence, the flattening of the BLM. Optical interferometric patterns are highly sensitive to any perturbation of the BLM from planarity. By this stringent criterion, none of our BLMs appeared to be absolutely flat. However, deviations were kept to less than 1% of the membrane radius, r. The direction of curvature was established by comparing the optical interference fringes obtained by the application of an oscillating hydrostatic pressure with those induced by deliberately adding and withdrawing small volumes of water from one side of the BLM (i.e., applying static positive and negative pressures).

Results BLM Formation and Characterization. Stringent requirements were placed on BLM preparations. Flexoelectric measurements were performed only on BLMs that had relatively small Plateau-Gibbs borders (PG borders

0.06

n

0.01

Y

-0.04 -120

-80

-40

0

40

80

120

Voltage, m V

Figure 6. Capacitance-voltage curves for PC (0)and GMO (A) BLMs in the absence of a transmembrane KCI gradient. Capacitance-voltage curves for a PC BLM in the presence of 0.013 M (+) and 0.025 M (A)transmembrane KC1 gradients.

positions shown in Figure 9 are illustrated in Figure 10. Similar analysis of other real-time stroboscopic interferometric images, obtained for GMO and PC BLMs, were carried out at different frequencies. The calculated curvatures (cxl,cx2, cyl,and cy2) are collected in Tables I11 and IV. The potential of electrode E2 with respect to that of E l (Figures 1 and 7) for a given BLM, being exposed to oscillating pressure a t a given frequency, Uf, was determined routinely and simultaneously with real-time stroboscopic interferometric measurements. The determined

where cxl and cyl are the orthogonal radii of curvature prior to flexing and cx2 and cy2 are the orthogonal radii of curvature subsequent to flexing of the BLM. Flexoelectric coefficients, f, obtained by substituting the Ufvalues (determined by electrical measurements) and the c,l, cx2, cyl, and cy? values (calculated from the corresponding stroboscopic interferograms as described in the Experimental Section) into eq 32, appear in the last column of Tables I11 and IV. Tables I11 and IV also contain values for the displacement of the BLMs (AL)by the applied oscillating pressure. Micrometer-range lateral movements were seen to accompany the oscillating-pressure-induced BLM flexing. The extent of translational deformation was found to vary, however, from preparation to preparation and from frequency to frequency without any discernible trend. A similar situation has been encountered in the optical interferometric investigation of steadystate pressure-induced BLM deformation.16 Limitations of Electrical and Optical Measurements of FlexoelectricCoefficients. It is important to reemphasizethe experimental limitations of the different methods used for the measurements of flexoelectric coefficients. The electric method of assessing the curvature change that accompanies the oscillating-pressureinduced BLM flexing is indirect and requires the assump tion of completely spherical membrane deformation. It permits, however, much greater flexing of the BLMs (Le., the application of much higher oscillating pressure) than that possible in the optical method. Greater flexing is likely to produce a more completely spherical deformation of the BLM. Flexing the BLM to a curvature greater than 330 m-l (Le., A Z r 2 and A Z y 2 of >15 pm) results, however, in the disappearance of the concentric optical interference fringes and renders, therefore, the optical method to be unusable. An inevitable consequence of smaller BLM flexing is the decrease of the potential drop corresponding to the second harmonic of the oscillator (&,) below a detectable level. Limitations of these two methods have precluded the determination of the curvature, and hence the flexoelectric coefficient, by simultaneouselectrical and

3134 Langmuir, Vol. 7,No.12,1991

T O ~ O FetOal. U

Figure 8. Interferograms obtained at selected times during the real-time movements of a GMO BLM (prepared from GMO BLM) exposed to 300-Hzoscillating pressure. The 16 static images, representing a complete movement of BLM, were taken a t t = 0,0.32, 0.45,0.55,0.64,0.71,0.78,0.85,0.91,0.99,1.06,1.15,1.25,1.33,1.47, and 1.67 ms (see Experimental Section and Figure 2 for the position of the laser pulses in bold relative to the BLM movements). The time series of images of the oscillating BLM were read from the videotape and stored as a series of disk files. Height correlation among the images was accomplished by playing the videotape in slow motion and acquiring a new image each time a fringe was created at, or moved past, the center. Thus, the absolute order of the most central fringe increased (or decreased, depending on the direction of movement) by one from each image to the next, indicating its absolute height. Table 111. Flexoelectric Parameters of PC BLMsF Electrical and Real-Time Stroboscopic Interferometric Data Cxl, m-l Cvl, m-l cx2, m-l cv2, WM,, m low,v 1019f:

w, Hz

c

~

100 150 200 250 350 400 450 500 550 600 a

16.589 20.874 13.175 21.703 22.794 17.730 16.826 19.177 19.670 15.052

-39.434 42.861 38.069 43.530 59.709 48.956 51.531 45.756 53.133 43.359

-29.889 -30.299 -36.467 -37.087 -36.595 -34.267 -34.754 -43.730 -43.935 -29.982

O.OO0 O.OO0 -5.028 0.000 -9.199 -3.237 -8.419 -5.689 -5.828 -7.483

4.1 4.2 4.0 4.2 6.2 4.6 4.9 4.9 5.2 4.0

6.1 6.0 6.2 7.1 5.1 5.1 5.2 5.0 4.1 3.0

25.3 22.7 23.8 24.7 14.1 17.4 16.6 15.6 11.9 11.1

Prepared from 40 mg of PC/mL of decane; r = 425.5 pm, Cs = 0.391 A 0.020 pF/cm2. Calculated by means of eq 32.

stroboscopic interferometric measurements on the same BLM in the present set of investigations. Under the conditions of electrical measurements, interferometric fringes could not be observed, and under the conditions of optical measurements, U2wcould not be determined. Fortunately, flexing-induced transmembrane potentials (Uf) were within the range of adequate sensitivity, in both the electrical and optical methods. Taking these limitations together, we believe that the optical method has provided more precise values for the flexoelectric coefficients (Tables I11 and IV) than those obtained by the indirect electric measurements (Tables I and 11).

Discussion Establishing the precise three-dimensional topography of BLMs prior, during, and subsequent to their exposure to oscillating hydrostatic pressures a t controlled frequencies has been the most significant accomplishmentof the present work. Real-time stroboscopic interferometry allowed a sensitive measurement of flexoelectric coefficients and provided the first experimental evidence for the lateral displacement of the BLM. Although GMO is neutral and BC is zwitterionic, the positive ends of the dipoles of these molecules are oriented toward their hydrocarbon chains. Indeed, recent explicit

Langmuir, Vol. 7, No. 12,1991 3135

Measurements of BLM Flexoelectricity

Figure 9. Typical computer-enhanced interferograms of the oscillating GMO BLM (shown in Figure 8) at t = 0 ms (a, top left), t = 0.91 ms (b, top right), and t = 1.67 (c, bottom) ms delays. At these positions, the GMO BLM is seen to be displaced from its center in the x: direction AZxl = 3.42 pm (a), M X 2 = 0.96 p m (b), and A Z x 2 = -1.44 pm (c); and from the y direction AZyl = 0 pm (a), AZ,, = -1.93 pm (b), and U Y 2 = -4.39 pm (c). Notice the difference in scales between x: (0-300 pm) and A Z x 2 or AZ, (-4 to +4 pm). Table IV. Flexoelectric Parameters of GMO BLMs9 Electrical and Real-Time StroboscoDic Interferometric Data 100 15d

200 250 300 350 450 500 600 650 a

149.077 169.912 319.422 186.674 175.629 378.687 168.210 104.062 242.766 281.004

189.477 -47.665 265.658 256.543 226.093 368.040 195.573 156.618 299.859 302.687

-145.080 -159.689 -152.519 -203.018 -197.219 -171.836 -160.846 -218.048 -177.424 -167.719

-169.634 -189.958 -22 1.183 -209.613 -287.058 -160.494 -156.979 -211.934 -216.679 132.645

3.2 0.90 5.5 5.1 4.9 5.7 4.5 0.89 0.81 3.97

1.6 1.2 2.0 2.5 2.0 1.0 0.6 0.7 0.6 0.5

0.87 0.91 0.74 1.04 0.80 0.33 0.31 0.36 0.22 0.29

Prepared from 40 mg of GMO/mL of decane; r = 147 pm, Cs = 0.387 pF/cm2. Calculated by means of eq 32.

calculations indicated a positional variation of the interaction energy of GMO from -16 kcal mol-1 in the headgroup region to +24 kcal mob1 in the terminal methyl groups.27 This calculation is in accord with the proposed

electrostatic potential difference between the middle of the BLM and its two aqueous interfaces (A@ = $'h (27) Wang, J.; Pullman, A. Biochim. Biophys. Acta 1990,1024,lO.

3136 Langmuir, Vol. 7,No. 12,1991

Todorou et al.

The origin of flexoelectricity has been discussed in terms of an asymmetric redistribution of the charges (fc), the dipoles p), and the quadrupoles (fp) of the surfactants in the flexed BLM

f=f“+P+P

L

(33)

The absence of appreciable surface charges for flat GMO and PC BLMs (see Results) does not exclude the possibility of adsorption of more (or less) charges on one side of the flexed BLM. This will, in turn, create a transmembrane charge when the BLM flexes and contribute to f“. Similarly, stretching (or compressing) of one of the monolayers can result in an asymmetrical conformationaland/ or hydration of the surfactant headgroups. This will, in turn, create a change in the transmembrane dipole moment when the BLM flexes and contribute to fd in eq 33. The origin of fq is more complex and its contribution to f (eq 33) is expected to be less significant than those made by f“ and P. Two limiting frequency regimes have been recognized in flexoele~tricity.~-l~ At the low frequencies (o 5 300 Hz), lateral mobility of the surfactants and their exchange between the torus and one of the monolayers occur during (or a t a time scale comparable to) the flexing of the BLM. In this “free” regime, governed by f F , flexing of the BLM is tantamount to the bending of two uncoupled monolayers. At high frequencies (o> 400 Hz), flexing of the BLM is faster than the lateral mobility of the surfactant. In this “blocked” regime, governed by$, both monolayers in the BLM can be considered to flex in unison. The two limiting frequency regimes of the flexoelectric coefficients have been experimentally realized for both the PC and the GMO BLMs in the optical measurements (see Tables I11 and IV). Mean F and $ values of 24.1 X and 16.5 X C were obtained for PC BLMs. For GMO BLMs, the obtained mean and fs values were 0.87 X and 0.30 X C, respectively. In contrast, f values determined by electrical measurementswere 1 order of magnitude higher and increased with increasing frequencies to a plateau value (Tables I and 11). The higher values obtained for PC than for GMO BLMs are likely to be a reflection of the more positive A+ value of the phosph~lipid.~~ The dipolar flexoelectric contribution to f, assuming blocked surfactant exchange, can be calculated by8

I

F

Figure 10. Three-dimensionalpresentations of the oscillating GMO BLM at t = 0 ms (a, top), t = 0.91 ms (b, middle), and t = 1.67 (c,bottom)ms;i.e.,correspondingto the computer images shown in Figure 9. Notice the difference in the scales. = J?1- 1c/s2when A$ = - 1c/s2= 0 and tC/h is the electrostatic potential at the hydrophobic region in the middle of the BLM).28p29Furthermore, the A+ values of PC membranes were proposed to be some 200 mV more positive than that of GMO membranes.29 ~~~~

(28) Haydon, D. A.; Myers, V. B. Biochim. Biophys. Acta 1973,307, 429. (29) Andersen, 0. S. In Membrane Transport in Biology; Concepts and Models; Giebisch,G.,Tosteston, D. C., Ussing, H. H., Eds.; SpringerVerlag: Heidelberg, Germany, 1978; Vol. I, p 369.

where p is the normal component of the dipole moment per lipid, dp/dA is its derivative with respect to the area, A, is the headgroup area of the surfactant in the planar state, and d is the membrane thickness (see Figure 3). Substituting p = 300 mD and d = 46 X m for GM028 C. This value into eq 34, we obtained fdB = 0.12 X is in much better agreement with the flexoelectric coefficient determined experimentally by real-time stroboscopic interferometry (f = 0.3 X C) than with that obtained by electrical measurements (f = 9.0 X lO-l9 C). Furthermore, the oscillating-pressure-induceddipole redistribution appears to be primarily responsible for the observed flexoelectric coefficient. Methodologies developed here open the door to systematic investigations of mechanosensitive ion transport and impulse transmission in membrane biology, as well as to the exploitation of flexoelectricity in artificial systems. Flexoelectricity in BLMs is a unique mechanoelectric phenomenon simultaneously involving two degrees of freedom of the molecular system-electrical and mechan-

Measurements of BLM Flexoelectricity

ical. Utilization of this phenomenon should allow, at least conceptually, the construction of molecular elements with mechanical input-electric output and/or with electrical input-mechanical output, thus permitting the fabrication of supramolecular sensors and/or actuators. Theoretical, experimental, and practical ramifications of these concepts are currently being actively pursued in our laboratories.

Langmuir, Vol. 7 , No. 12,1991 3137

Acknowledgment. Support of this work by a grant from the National Science Foundation is gratefully acknowledged. A.T.T. thanks the Bulgarian Ministry of Science a d Education (Project 587) for partial support. Registry No. GMO,25496-72-4.