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The Journal of Physical Chemistry, Vol. 94, No. 2, 1990
Letters
F'OSlllON FROM EDGE OF THE TEFLON HOLE, m m
Figure 3. Photograph taken from a two-exposure interferometric hologram of a GMO BLM (obtained by smearing a solution of 0.08 g of GMO in 1.68 mL of decane across a 1.5-mm pinhole). The second exposure was taken after rotating the BLM by (6.5 f 0.1) X rad (3/8O). I
A 1
I
I
Figure 5. Plots of GMO BLM (obtained by smearing a solution of 0.08 g of GMO in 1.68 mL of decane across a 1.5" pinhole) deformation against the distance from the edge of the Teflon hole sustaining 9.0 (A), 45 (B), and 10 mN/m2 (C) transmembrane pressure. Curve C was taken on a BLM which had an appreciable Plateau-Gibbs border.
1
/B t6
J
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I
I
I
10
20
30
40
PREssURE "/mz
Figure 4. Number of two-exposure interferometric fringes (and, hence, A F values) plotted against the applied pressure for GMO BLMs prepared by smearing a solution of 0.08 g of GMO in 1.68 mL of decane ( 0 )and that of 0.001 3 g in 1.68 mL of decane (*) across a 1.5-mm pinhole. The insert shows the schematics of the deformed BLM.
9 mN/m2 (88.5 natm) pressure sustained across the membrane. At the limit, one-tenth of an interferometric fringe can be detected. This, at X = 5 14.5 nm, corresponds to a lateral deformation of the BLM by 5 1.45 nm! Holographic interferometry provides, therefore, a means for the measurement of BLM deformation with unprecedented sensitivity. The validity of using two-exposure interferometric holograms . for the quantification of BLM deformation has been ascertained by the examination of corresponding holograms obtained by a small rotation of the BLM. As seen in Figure 3, rotation of the BLM by (6.5 f 0.1) X rad (3/8O) between the two exposures resulted in the expected parallel fringes on the Teflon film holder, on the BLM, and less clearly on the Plateau-Gibbs border. The distance between the two parallel fringes (L) on the Teflon film was evaluated to be 82 f 2 pm by calibration taking the diameter of the hole in the Teflon film (1.5 mm) to be the reference.* Correcting for the angle of measurement (45') led to a distance of 1 17 f 3 pm between the two fringes on the Teflon film. This value is in good agreement with that obtained (L = 112 f 2 pm) by substitution into
Figure 6. Photograph taken from a two-exposure interferometric hologram of a G M O BLM (obtained by smearing a solution of 0.08 g of GMO in 1.68 mL of decane across a 1.5" pinhole) which had an appreciable Plateau-Gibbs border and which sustained 10 mN/m2 transmembrane pressure.
to form as flat a BLM as possible in all experiments performed here.9 Increasing the transmembrane pressure resulted in an increased number of concentric fringes in the two-exposure interferometric holographic films (see Figure 2, for example). Plots of the number of fringes, i.e., the extent of BLM deformation, against the pressure applied across the GMO BLMs (formed from two different concentrations of the lipid) are shown in Figure 4. At the usual GMO concentration (0.08 g of GMO in 1.68 mL of decane), the plot is linear whose slope (AF/AP) corresponds to 0.13 f 0.01 pm/(mN/m2). At the very high dilution (0.0013 g of GMO in 1.68 mL of decane), the slope is 0.33 f 0.10 pm/(mN/m2), indicating that the presence of considerable amounts of solvents causes, as expected, different BLM behavior. Surface tension of the BLM, y, was assessed by substituting the value of the slope into the equation
where cp is the angle of rotation. Approximately twice as many fringes are seen in the BLM than in the Teflon film (Figure 3). This is a consequence of the curvature of the BLM resulting from an adventitious pressure differential across the membrane. Identical fringes would be observed in the Teflon film and in the BLM, of course, if they were perfectly in plane. Care was taken
where AP is the pressure difference and d is the diameter of the BLM (1.5 mm). For the 5% GMO BLM investigated here, the obtained surface pressure (y = 1.1 f 0.1 dyn/cm) was found to be in the range previously determined for a variety of BLMs (0.8-3.5 dyn/cm) .3-5 Holography also provides three-dimensional information on membrane deformation. This is best represented by contour diagrams obtained by plotting the extent that the deformation changes along an arbitrary radius from the edge of the Teflon film (Figure 5). It should be noted that the deformation is not always perfectly symmetrical. The shape of the deformed BLM
(8) L and nf were measured by projecting slides (taken of the two-exposure interferometric holograms) onto a screen.
(9) Flatness of the BLMs formed was routinely monitored by observing the laser light reflected from the BLM.
L=
X
sin
cp
sin ( 4 5 O )
(2)
J . Phys. Chem. 1990, 94, 5 13-5 15 is close to a spherical cap. Decreasing the distance from the center (0.75 mm from the edge of the Teflon film) results in a curvilinear decrease of the number of interference fringes observed for GMO BLMs sustaining I O and 45 mN/m2 transmembrane pressures. Fitting straight lines to the initial slopes of lines A and B in Figure 5, the degrees of curvature (a in the insert of Figure 4) of the BLMs deformed by IO and 45 mN/mZ were assessed to be 0.1' and 0.4', respectively. These curvatures are some 2 orders of magnitude smaller than those previously m e a s ~ r e d . ~ - ~ Important information on Plateau-Gibbs border deformation has also been obtained in the present work. A typical photograph of a two-exposure interferometric hologram obtained for a GMO BLM having an appreciable Plateau-Gibbs border is shown in Figure 6. The pressure applied across this BLM was 9 mN/m2. The Plateau-Gibbs border is seen to have a greater number of fringes (1 1) than the BLM itself (3). Obviously, global deformation is not uniform; the bilayer portion is distorted less than the surrounding Plateau-Gibbs border upon the application of a transmembrane pressure gradient. It is therefore important to use BLMs whose Plateau-Gibbs borders are minimal. The different behavior of the Plateau-Gibbs border and the BLM also
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manifests in their contour diagrams (see Figure 5C). In the presence of an appreciable torus, pressure-induced deformation of the BLM is no longer symmetrical.
Conclusion Two-exposure interferometric holograms have been shown to provide a permanent record of three-dimensional and temporal information on ultrasmall-pressure-induced BLM deformation. The presence of excess solvent or an unusually large torus can also be deduced from these holograms. The method provides a means for probing biophysically important membrane processes with unprecedented sensitivity. Applications of interferometric holography for monitoring subtle electrical, magnetic, photolytic, chemical, and biochemical changes in BLMs prepared from lipids and surfactants are the subject of our current and intensive scrutiny. Acknowledgment. Support of this research by a grant from the Natural Sciences and Engineering Research Council (NSERC) of Canada is gratefully acknowledged. We thank Mr. Jean Beliveau for helpful discussions.
Statistical Mechanical Calculation of Inhomogeneously Broadened Absorption Line Shapes in Solution Roger F. Loring Department of Chemistry, Baker Laboratory, Cornell University, Ithaca, New York 14853 (Received: October 30, 1989)
A general relation is derived between the inhomogeneously broadened absorption spectrum of a solute at infinite dilution in a solvent and an equilibrium free energy of solvation. This relation permits the techniques of equilibrium fluid theory to be applied to the calculation of solvation effects in absorption line shapes. A model calculation is presented in which the mean spherical approximation is used to predict the line shape of a polar solute in a polar solvent. Significant deviations from dielectric continuum theory are found.
The characterization of electronic states in liquids is fundamental to the understanding of chemical processes in solution. Steady-state absorption and fluorescence measurements have long been used to probe solvent perturbations of the electronic states of a solute Such measurements are conventionally interpreted with theories in which the solute is represented by a point dipole at the center of a spherical cavity, which is surrounded by a continuous dielectric medium.'" In such treatments, the solvent-induced shift of the peak of either the fluorescence spectrum or the absorption spectrum is calculated using secondorder perturbation theory. The local electric field at the solute, which is associated with the polarization of the medium by the solute, enters as an input to the perturbation theory and is calculated by using classical electrostatics. This procedure yields ( 1 ) Mataga, N.; Kubata, T. Molecular Interactions and Electronic Spectra; Marcel Dekker: New York, 1970. (2) Lippert, E. In Organic Molecular Phorophysics; Birks, J. B., Ed.; Wiley: New York, 1975. (3) Itskovitch, E. M.; Ulstrup, J.; Vorotyntsev, M. A. In The Chemical Physics of Soloarion; Part C; Elsevier: Amsterdam, 1985. (4) Bayliss, N . S. J . Chem. Phys. 1950, 18, 292. (5) Ooshika, Y. J . Phys. Soc. Jpn. 1954, 9, 594. (6) McRae, E. G. J . Chem. Phys. 1957,61, 562. ( 7 ) Bakshiev, N . G . Opr. Spectrosc. 1964, 16, 446. (8) Marcus, R. A. J . Chem. Phys. 1965, 43, 1261. (9) Okamoto, B. Y.; Drickamer, H. G. Proc. Narl. Acad. Sei. U S . A 1974, 71, 2671.
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a relation between the solvent-induced line shift and properties of the solute (dipole moments, polarizabilities, cavity radius) and of the solvent (dielectric constant). The predicted dependence of the line shift on solvent dielectric constant is in reasonable agreement with numerous measurements for polar and nonpolar solutes and solvents.'sZ However, it is sometimes found that in order to fit experimental data, the cavity radius, which may be regarded as an adjustable parameter, must be assumed to depend on the thermodynamic state of the s o l ~ e n t . ~ The J ~ continuum model should provide a qualitatively correct description of the contribution to the line shift of long-ranged electrostatic interactions between solute and solvent. The cavity is introduced into the theory to represent the effects of short-ranged repulsions between the solute and solvent molecules. The practical necessity of allowing the cavity radius to depend on the thermodynamic state of the solvent indicates that the repulsive interactions are not included in a consistent way. It is clearly desirable to develop an approach in which both short-ranged and long-ranged solute-solvent interactions are treated on a molecular level. Several recent theoretical treatments of the absorption spectrum of a polarizable solute in a polarizable solvent have employed concepts and techniques of modern fluid theory to improve upon the dielectric continuum a p p r o a ~ h . ' ~Schweizer '~ and Chandler (10) Chandler, D.; Schweizer, K. S.; Wolynes, P.G. Phys. Reu. Lett. 1982, 49, 1100.
0 1990 American Chemical Society
