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Langmuir 1999, 15, 600-606
Lipid Lateral Diffusion in Dilauroylphosphatidylcholine/ Cholesterol Mixed Monolayers at the Air/Water Interface Keiji Tanaka, Patricia A. Manning,† Victor K. Lau,‡ and Hyuk Yu* Department of Chemistry, University of WisconsinsMadison, Madison, Wisconsin 53706 Received July 14, 1998. In Final Form: November 6, 1998 Binary monolayers of L-R-dilauroylphosphatidylcholine (DLPC) and cholesterol were formed at the air/ water interface by the successive addition method with chloroform as the spreading solvent at 296 K. Translational diffusion of a probe lipid in the monolayers as a function of cholesterol fraction was examined by the technique of fluorescence recovery after photobleaching in conjunction with epifluorescence microscopy and the Wilhelmy plate method. A transition from biphasic morphology to a visually homogeneous uniphasic monolayer occurred at surface pressures between 13 and 20 mN‚m-1, depending on the cholesterol fraction in the monolayer. The lateral diffusion coefficient was found to decrease when surface pressure and/or cholesterol fraction were/was increased. The diffusion coefficients of the probe lipid in the homogeneous monolayers were analyzed on the basis of the free area model. The observed retardation of the diffusion is ascribed to an increase in the in-plane surface viscosity of monolayers. In the case of biphasic binary monolayers, the retardation with increasing cholesterol fraction is attributed to the obstacle mediated diffusion as in the effective medium analysis as well as to increasing surface viscosity.
Introduction In 1972 the fluid mosaic model in which lipids form a matrix with isolated proteins randomly embedded in it was introduced by Singer and Nicolson.1 Such a lipid/ protein mosaic is a molecularly thin, fluid film which resembles a two-dimensional oriented viscous solution through which lipids and proteins undergo translational motion via in-plane diffusion. Thus, the in-plane dynamics closely resembles that of smectic liquid crystals.2 The presence of domains in biological membranes has gradually been accepted as an important modification of the fluid mosaic model.3,4 It has also been revealed that domains are implicated as an important factor in the control mechanism for membrane receptor and enzyme activity. This includes fundamental biological processes such as protein patching for cell-cell recognition,5 ligand binding,6 transport,7 catalysis,8 and transmembrane signaling.9 However, little is known about the size, shape, and organization of these domains or their importance in the regulation of dynamic membrane associated processes. Animal cell membranes contain three lipid components such as phospholipids, glycolipids (or sphingolipids), and cholesterol.10,11 Cell membrane composition is widely † ‡
Permanent address: Epoxylite Corp., Irvine, CA. Present address: Medical College of Wisconsin.
(1) Singer, S. J.; Nicolson, G. R. Science 1972, 175, 720. (2) de Gennes, P.-G.; The Physics of Liquid Crystals; Clarendon Press: Oxford, England, 1974; Chapter 1. (3) Edidin, M. Current Topicsin Membranes and Transport; Academic Press: New York, 1990. (4) Jacobson, K.; Sheets, E. D.; Simson, R. Science 1995, 268, 1441. (5) McConnell, H. M.; Watts, T. H.; Weis, R. M.; Brian, A. A. Biochim. Biophys. Acta 1986, 864, 95. (6) Hurley, J. H.; Grobler, J. A. Curr. Opin. Struct. Biol. 1997, 7, 557. (7) Vrhovnik, K.; Kristl, J.; Sentjurc, M.; Smid-Korbar, J. Pharm. Res. 1998, 15, 525. (8) Honger, T.; Jorgensen, K.; Stokes, D.; Biltonen, R. L.; Mouritsen O. G. Methodol. Enzymol. 1997, 286, 168. (9) Maruyama, I.; Mikawa, Y.; Maruyama, H. J. Mol. Biol. 1995, 253, 530. (10) Rouser, G.; Nelson, G. J.; Fleischer, S.; Simon, G. Biological Membranes, Physical Fact and Function; Academic Press: New York, 1968. (11) Houslay, M. D.; Stanley, K. K. Dynamics of Biological Membranes; Wiley: New York, 1982.
variable that depends on the functional differentiation.12 However, there seems to be an invariant in the lipid compositions for all cell memebranes; phosphatidylcholine and cholesterol are the two main components of the lipid. If we are to gain systematic insights into the dynamics of cell membranes, it is of value to start with mixed monolayers of phosphatidylcholine/cholesterol to the extent that there now exists a well-established connection between the dynamics in lipid bilayer membranes and that in the corresponding monolayers at the air/water interface.13 Once such a starting point is accepted, then we come to the cholesterol composition of the monolayer as the primary independent variable of interest. Lateral diffusion in phospholipid monolayers14-17 and bilayers,18 which can be deduced by the fluorescence recovery after photobleaching (FRAP) technique, has been of interest as a measure of the molecular mobility of phospholipids in cell membranes. These studies have also been carried out from a perspective of trnaslational diffusion in two-dimensional systems.19 The lateral diffusion coefficients, D(2), of fluorescence probes in twodimensional systems have been analyzed in detail on the basis of the free area model,20,21 which has its origin in the free volume model in the bulk state.22 In a three-dimensional isotropic medium, the translational diffusion coefficient, D(3), of an isolated spherical particle with a hydrodynamic radius, a, immersed in a (12) Cullis, P. R.; Hope, M. J. Biochemistry of Lipids and Membranes; Benjamin/Cummings: Menlo Park, CA, 1985. (13) Montal, M.; Darszon, A.; Schindler, H. Q. Rev. Biophys. 1981, 14, 1. (14) Rubenstein, J. L. R.; Smith, B. A.; McConnell, H. M. Proc. Natl. Acad. Sci. U.S.A. 1979, 76, 15. (15) Peters, R.; Beck, K. Proc. Natl. Acad. Sci. U.S.A. 1983, 80, 7187. (16) Kim, S.; Yu, H. J. Phys. Chem. 1992, 96, 4034. (17) Tamada, K.; Kim, S.; Yu, H. Langmuir 1993, 9, 1545. (18) Almeida, P. F. F.; Vaz, W. L. C.; Thompson, T. E. Biochemsitry 1992, 31, 6739. (19) Schlicht, L.; Ilgenfritz, G. Physica A 1996, 227, 239. (20) Tra¨uble, H.; Sackmann, E. J. Am. Chem. Soc. 1972, 94, 4499. (21) Galla, H. J.; Hartmann, W.; Theilen, U.; Sackmann, E. J. Membr. Biol. 1979, 48, 215. (22) Cohen, M.; Turnbull, D. J. Chem. Phys. 1959, 31, 1164. (23) Landau, L. D.; Lifshitz, E. M. Fluid Mechanics; Pergamon Press: Elmsford and New York, 1959.
10.1021/la9808869 CCC: $18.00 © 1999 American Chemical Society Published on Web 12/24/1998
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Figure 1. Hydrodynamic models of Saffmann-Delbruck and Hughes-Pailthorpe-White for lateral diffusion of an isolated cylindrical diffusant immersed in a thin film viscous continuum.
viscous continuum with a shear viscosity, η, is given by the Stokes-Einstein relation23
D(3) ) kT/6πηa
(1)
where kT has the usual meaning of thermal energy. For a two-dimensional system, analogous formulations have been proposed by Saffman and Delbruck24 and Hughes et al.25 for an isolated cylinder with a radius, a, and height, h. Both starts with the cylindrical diffusant confined in a flat, molecularly thin, lipid film with a thickness, h, sandwiched between a pair of viscous fluids with a much smaller viscosity but in a very large height and depth than h. Since Saffman and Delbruck’s hydrodynamic model24 assumes that the upper and lower fluids are of the same viscosity, e.g., that of water, it is directly applicable to bilayer systems. On the other hand, HughesPailthorpe-White (HPW) model25 assumes that the upper and lower fluids are of different viscosities, η′ and η′′ but still both are much smaller than η of the lipid film, it is applicable to monolayer systems. Both models with the linear dimensions of the diffusants are illustrated in Figure 1. For HPW model, the following formulation for the diffusion coefficient, D(2), is given
D(2) ) kT/[4π(η′ + η′′)aΛ()]
(2)
where Λ() is numerically evaluated, called a reduced friction coefficient that is a monotonically decreasing function of the parameter , defined as
≡ (a/h)[(η′ + η′′)/η]
(3)
Λ() reaches the asymptotic limit of 2/π when exceeds about 40. In the case of the phospholipid monolayer at the air/water interface, is predicted to be on the order of 0.01 and Λ() almost linearly decreases with increasing in this region, resulting in Λ() ∝ η. An important point here is that D(2) is inversely proportional to the viscosity of the lipid film η when η′ and η′′ are substituted as those (24) Saffman, P. G.; Delbru¨ck, M. Proc. Natl. Acad. Sci. U.S.A. 1975, 72, 3111. (25) Hughes, B. D.; Pailthorpe, B. A.; White, L. R. J. Fluid Mech. 1981, 110, 349.
of air and water, respectively. When we identify η to the viscosity of the binary monolayers, its surface pressure can be an important controlling variable. Given our binary monolayers of phosphatidylcholine and cholesterol, the composition is another controlling variable since it affects the viscosity of the monolayers, resulting in a change in the magnitude of D(2). The lateral diffusion coefficient D(2) of a probe lipid in the (L-R-dimyristoylphosphatidylcholine, DMPC)/cholesterol mixed monolayers with a composition of 40 mol % cholesterol examined by the dynamic excimer probe method has been reported by Merkel and Sackmann.26 However, their measurement was performed at 293 K whereas the DMPC has the gel-liquid crystal transition temperature of 296.9 K. Given that our focus is the lateral diffusion of fluid lipids as modulated by cholesterol, the temperature distance between the measurement temperature and phase transition should be as wide as possible such that what is being probed is not strongly affected by being in the vicinity of the phase transition. The objective of this study is to investigate lateral diffusion in L-R-dilauroylphosphatidylcholine (DLPC)cholesterol mixed monolayers in fluid state, with the aid of a probe lipid, at the air/water interface. The DLPC has the transition temperature of 271.4 K,27 which is at least 27 °C below than room temperature. We postulate that such a system is a primitive model for the lipid component of animal cell membranes. To the best of our knowledge, this is the first systematic report of such an investigation. Experimental Section Materials and Monolayer Preparation. 1-Acyl-2-[12-[(7nitro-2-1,3-benzoxadiazol-4-yl)amino]dodecanoyl] phosphatidylethanolamine (NBD-PE) and 1-Acyl-2-[12-[(7-nitro-2-1,3-benzoxadiazol-4-yl) amino]dodecanoyl]phosphatidylcholine (NBDPC) which were employed here as fluorescent probes and DLPC were purchased from Avanti Polar Lipids. Cholesterol was purchased from Sigma. All of these were stored at 253 K just prior to use and then used without further purification after leaving them at room temperature for more than 1 h. HPLC grade chloroform was used as the spreading solvent. DLPC/ cholesterol mixed solutions with total concentrations of 0.1-0.2 mM were prepared by mixing each in chloroform. The molar fraction of fluorescent probe in the mixed monolayer for fluorescence microscopic observation and FRAP measurement were 1-2%. It was confirmed that even though the mixed monolayer was in a phase-separated state, the probe molecule was partitioned into both of two phases and any autoquenching of the probes was not occurred. Besides the probe composition was not changed by crossing the phase boundary. Phosphate buffer solutions at pH of 7.0, which are composed of 9.13 × 10-2 M Na2HPO4, 3.87 × 10-2 M NaH2PO4 and 0.1 M NaCl, were used as the subphases of monolayers. Water used here was the housedeionized, further purified by a Milli-Q system with the initial resistivity of greater than 17 MΩ. The monolayer mass density for all measurements was varied by the successive addition method at a controlled room temperature (296.0 ( 0.5 K), under the assumption that spread components form insoluble monolayers without any desorption from the surface into the subphase.28 In our experience with monolayers in fluid state, there is no dependence of surface pressure and diffusion coefficient on the film preparation method.16,17 It is possible however that phase domain size and morphology for the fluid monolayers at an apparent equilibrium state can vary with the film preparation method. Surface Pressure. Experiments were carried out in a Teflon trough with a size of 62.0 or 67.9 cm2, which was housed in a (26) Merkel, R.; Sackmann, E. J. Phys. Chem. 1994, 98, 4428. (27) Mabrey, S.; Sturtevant, J. M. Proc. Natl. Acad. Sci. U.S.A. 1976, 73, 3862. (28) Sauer, B. B.; Yu, H.; Tien, C.; Hager, D. F. Macromolecules 1987, 20, 393.
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acrylate box for humidity control. The relative humidity within the box was kept at 90% or above during all measurements. The surface tension of the bare and monolayer-covered surface were determined by the Wilhelmy technique using a sandblasted platinum plate. The surface tension, γ, was observed as a function of time by a Cahn electrobalance until the time dependence, dγ/dt, reached approximately 10-3 mN‚(m‚s)-1, which is our operational definition of an apparent equilibrium state. Epifluorescence Microscopy. An argon ion laser at a wavelength of 488 nm was used as a light source. Monolayers were visualized through a microscope by a CCD camera and then images were transferred directly to a VCR and recorded on videotape. A Ronchi ruling pattern with a fringe spacing of 34 µm was used to calibrate the image size. The recorded image was subsequently analyzed with an image processor to obtain the area fraction of surface domain. Fluorescence Recovery after Photobleaching. The instrumental setup and the data analysis method were reported earlier in detail.16 A set of recent modifications of the signal acquisition step is described elsewhere.29 Briefly, the lateral diffusion coefficient, D(2), is deduced from the time profile of fluorescence signal envelope which is extracted from the diffenece signal between the depletion profile and recovery profile of the unbleached and bleached regions, respectively. The envelope is commonly observed to be a single exponential when the initial portion as the higher order contributions is truncated away from the fitting.16,29 Thus, the time profile is represented by
V(t) ) V(0) e-t/τ
(4)
1/τ ) D(2)q2
(5)
with
where V(t) is the difference signal amplitute, V(0) is that immediately following the bleaching pulse at 488 nm from an argon ion laster, τ is the relaxation time of the difference signal and q is the spatial wavevector of the Ronchi ruling fringe, imaged on the illuminated area of 473 µm in diameter, equal to 2π/p with p being the imaged ruling spacing. Since q2 dependence of 1/τ was thoroughly checked out and recently reported separately,29 we relied on measurements of τ from a single p at 34 µm. Under these conditions, we can deduce the lateral diffusion coefficient in a range 5 × 10-6 to 5 × 10-10 cm2‚s-1. To attenuate the surface convective flow effect in the area of focal point of the viewing microscope, a cone-shaped Teflon barrier with platinum ring tip was used.16 Once a given monolayer reaches an apparent equilibrium state as specified earlier [dγ/dt e 10-3 mN‚(m‚s)-1], the cone placed under the subphase during the monolayer preparation, is raised until its top rim just touches the monolayer surface. If the convective flow is not arrested or attenuated greatly, smoothly decaying signals cannot be obtained.
Results and Discussion Surface Pressure-Area Isotherm. Figure 2 shows the surface pressure Π vs area per molecule, A, isotherms for DLPC, cholesterol, and their mixed monolayers with cholesterol fractions of 5-30 mol % at the air/water interface. The inset of Figure 2 displays the cholesterol fraction dependence of average area per a molecule in DLPC/cholesterol mixed monolayers as a function of surface pressure. The replicability of Π at a given area is about 0.5 mN‚m-1 while the precision of Π determination for a given film is better than 0.05 mN‚m-1. Since surface pressure gradually increases with a decrease in the surface area for DLPC and mixed monolayers, this is taken as a signature for the formation of liquid condensed (LC) film from the gas (G) phase via liquid expansion (LE) state. On the other hand, for cholesterol, the surface pressure abruptly increases in the vicinity of the limiting area which is specified by extrapolation to Π ) 0 mN‚m-1 of the (29) Ma, J. Ph.D. Thesis, University of Wisconsin-Madison, 1998.
Figure 2. Surface pressure isotherms of DLPC/cholesterol mixed monolayers at room temperature (296.0 ( 0.5 K): circles, DLPC; triangles up, 5 mol % cholesterol; squares, 10 mol % cholesterol; triangles down, 15 mol % cholesterol; tilted squares, 20 mol % cholesterol; horizontal parallelograms, 25 mol % cholesterol; vertical parallelograms, 30 mol % cholesterol; right triangles, cholesterol. Different symbols are from different experiments under the same conditions. Subphase is a mixed solution composed of 9.13 × 10-2 M Na2HPO4, 3.87 × 10-2 M NaH2PO4 and 0.1 M NaCl and its magnitude of pH is 7.0. The inset shows cholesterol fraction dependence of isobaric area per molecule: (b), Π ) 5 mN‚m-1; (2), Π ) 25 mN‚m-1, where solid and broken lines denote the ideal mixing of isobaric areas, at 5 mN‚m-1and 25 mN‚m-1, respectively.
straight portion of the Π-A curve. Since this is a characteristic behavior for crystalline monolayers such as fatty acids with long alkyl chains,30,31 it seems that the solid film is formed from crystalline domains by fusion.32 The cholesterol monolayer was not stable at Π > ca. 10 mN‚m-1 as reported33 and in fact predictable from its chemical structure. Recently, the two-dimensional crystalline structure of cholesterol monolayers at the air/water interface is reported by Lafont et al. as studied by the atomic force microscopic and grazing incidence X-ray diffraction techniques.33 In contrast to our result, Albrecht et al. has reported a surface pressure higher than 10 mN‚m-1 for the cholesterol monolayer prepared by the compression method without any instabilities.34 The surface pressure at a given area is essentially independent of the film preparation method for fluid monolayers, if each addition for the successive addition method is made after reaching time-independent pressure (an apparent equilibrium) and the compression rate is slow enough to allow the films to reach the equilibrium state. However, the same cannot be said of solid monolayers such as that of cholesterol. Thus, the discrepancy between their Π-A isotherm for cholesterol and ours might be attributed to the difference in the film preparation methods. In the case of the DLPC/cholesterol mixed monolayers, the area corresponding to the isotherm lift-off point, at which the magnitude of Π starts to increase, becomes monotonically smaller with increasing cholesterol fraction; (30) Knobler, C. M. Adv. Chem. Phys. 1990, 77, 397. (31) Kajiyama, T.; Oishi, Y.; Uchida, M.; Takashima, Y. Langmuir 1993, 9, 1978. (32) Slotte, J. P.; Mattjus, P. Biochim. Biophys. Acta 1995, 1254, 22. (33) Lafont, S.; Rapaport, H.; Somjen, G. J.; Renault, A.; Howes, P. B.; Kjaer, K.; Als-Nielsen, J.; Leiserowitz, L.; Lahav, M. J. Phys. Chem. B 1998, 102, 761. (34) Albrecht, O.; Gruler, H.; Sackmann, E. J. Colloid Interface Sci. 1981, 79, 319.
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the isotherm progressively shifts toward the ordinate with increasing cholesterol fraction. A part of this reduction is expected as the cholesterol molecule with a smaller projected molecular cross section compared with DLPC is incorporated into the monolayer. However, an extra reduction in occupied area is also observed, as shown in Figure 2. This phenomenon, negative deviation from the ideal area additivity rule, is known as the condensing effect of cholesterol which enhances the extended conformation of phosphatidylcholine lipid tails,35 resulting in an increase in the viscosity of monolayers. The condensation effect can be easily seen when the Π-A data is replotted as A (area/molecule) against cholesterol fraction under isobaric conditions, i.e., Π fixed, as shown in the inset of Figure 2. To perform epifluorescence microscopic observations and FRAP measurements, it is necessary to incorporate a fluorescence probe into the monolayers. Thus, the effect of the presence of the fluorescence probe on the Π-A isotherm was investigated. Incorporation of the fluorescence probe with a molar ratio smaller than 2% does not alter the isotherms of the DLPC monolayer and DLPC/ cholesterol mixtures. Also, the effect of subphase pH on Π-A isotherms was found to be negligible in the range 7.0-9.0. Phase States. The phase structure of biphasic lipid monolayers is closely related to the lateral diffusion behavior of the probe lipid.17,19 In general, a Π-A isotherm includes information relating the phase state of a monolayer such as LE, LC, and phase transitions. Since it is difficult to delineate the miscibility of the DLPC/ cholesterol mixed monolayers from the isotherms alone, epifluorescence microscopic observations were made at 296.0 ( 0.5 K with the cholesterol fraction ranging up to 60 mol %, using 2 mol % NBD-PE or 1 mol % NBD-PC as a fluorescence probe. Epifluorescence surface patterns were observed to remain constant over a period of at least 5 h. Beyond this, the dye was sufficiently bleached by exciting light to preclude further imaging. Figure 3 shows typical epifluorescence micrographs of the DLPC/cholesterol mixed monolayers at the air/water interface. Immiscibility of the two components, similar to DMPC/cholesterol-mixed monolayers,36 was clearly observed at low surface pressures across the entire range of cholesterol fractions employed here. Since the darker area fraction increases with the increasing cholesterol fraction as shown in Figure 3a-c, we surmise that the nonfluorescence darker region corresponds to a liquidcondensed cholesterol-rich phase. Such an identification of the phase-separated state is also possible by taking into account the previous report that NBD-PE is segregated into the LE regions of biphasic phospholipid/ cholesterol mixed monolayers.32 In the case of Π ) 4 mN‚m-1, the DLPC and cholesterol-rich regions formed well-defined circular domains within a continuous matrix, independent of the cholesterol fraction. When the surface pressure is increased at a given cholesterol fraction, the phase state changes from a well-defined domain/matrix structure, as exemplified in Figure 3b, to a homogeneous one as in Figure 3e, via a domain/matrix structure with elongated domains; such an example is displayed in Figure 3d. Such a miscibility crossover, commonly observed in bulk binary mixtures,37 is no more than an example of upper consolute point in a monolayer system.38 How this (35) Pasenkiewicz-Gierula, M.; Subczynski, W. K.; Kusumi, A. Biochemistry 1990, 29, 4059. (36) Seul, M. Physica A 1990, 168, 198. (37) Sanchez, I. C.; Lacombe, R. H. J. Phys. Chem. 1976, 80, 2352. (38) Slotte, P. J. Biochim. Biophys. Acta 1995, 1238, 118.
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Figure 3. Typical epifluorescence micrographs of DLPC/ cholesterol mixed monolayers at the air/water interface: (a) Π ) 4 mN‚m-1 and 5 mol % cholesterol; (b) Π ) 4 mN‚m-1 and 35 mol % cholesterol; (c) Π ) 4 mN‚m-1 and 40 mol % cholesterol; (d) Π ) 10 mN‚m-1 and 35 mol % cholesterol; (e) Π ) 12 mN‚m-1 and 35 mol % cholesterol.
Figure 4. Phase diagram of DLPC/cholesterol mixed monolayers at 296.0 ( 0.5 K as surface pressure and cholesterol fraction as the variables. The transition from biphasic (gray) to homogeneous (white) monomolecular film is indicated by filled circles. The letters in parentheses correspond to those in Figure 3.
is reflected in observed micrographs may be ascribed to the fact that in higher Π region the lipids are sufficiently condensed throughout the monolayer to prevent selective partitioning of the fluorescence probe. An upper consolute point was observed at Π < 15 mN‚m-1 in the cholesterol fraction range from 10 to 30 mol %. On the other hand, for cholesterol fractions higher than 40 mol %, these points were around 20 mN‚m-1. Figure 4 summarizes the deduced phase diagram of the DLPC/cholesterol mixed monolayer at the air/water interface at 296 K by epifluorescence micrographic observations. Gray and white regions indicate the biphasic and homogeneous states, respectively. The phase boundary is outlined by observation points where the error bars represent uncertainties in Π, and the five letters in parentheses identify the Π-composition coordinates of the five micrographs shown in Figure 3. It is of interest here that the phase diagram of this system is very similar to those for DMPC/cholesterol39 and L-Rdipalmitoylphosphatidylcholine (DPPC)/cholesterol34 mixed (39) Hirshfeld, C. L.; Seul, M. J. Phys. Fr. 1990, 31, 4428.
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monolayers at the air/water interface despite the diference in alkyl chain length as well as gel-liquid crystal transition of phospholipids. We now turn to discuss the domain morphologies in Figure 3. The free energy F of a biphasic monolayer can be described as a balance between the dipolar electrostatic energy and the line tension between the two phases as follows:40
F ) 2πRn[µ2 ln(e2δ/4R) + λ]
(6)
Here n, R, µ, e, δ, and λ are the number of circular noninteracting domains, the radius of a domain, the difference in dipole density between the domain and the surrounding phase, the base of natural logarithm, a distance comparable to the separation between dipoles, and the line tension, respectively. Thus, the predicted equilibrium radius, Req of a circular domain is40 3
2
Req ) (e δ/4) exp(λ/µ )
(7)
When the radius of a lipid domain exceeds the equilibrium radius by a factor of e1/3 or more, it is predicted that the circular domain distorts to various noncircular shapes.41 Benvegnu and McConnell have revealed the surface pressure dependence of Req for a DMPC/cholesterol mixed monolayer.41 As a result, in the case of Π ) 4 mN‚m-1, Req was essentially infinite, whereas in the case of Π > 10.5 mN‚m-1, its magnitude was on the submicrometer scale. The mixed monolayer used here is DLPC, whose alkyl chain length is shorter than that of DMPC by two carbons, while the second component is the same, i.e., cholesterol. If we were to ignore the difference in alkyl chain lengths between DMPC and DLPC, eq 7 for Req can be applied to our system. We base this on the fact that a parallel situation was provided by Perkovic and McConnell for the case of unusual domain shape, cloverleaf, forming at a Π value just above 0 mN‚m-1 for DPPC/dihydrocholesterol and DMPC/dihydrocholesterol monolayers though DPPC and DMPC differ by two carbons,42 and the free energy considerations of eq 6 are not directly connected to the chain length. If so, it is entirely consistent that we observe the well-defined circular domain/matrix morphology at Π ) 4 mN‚m-1, displayed in Figure 3b, and the phase-separated structure with elongated domains at 10 mN‚m-1, as shown in Figure 3d. Lateral Diffusion. The lateral diffusion coefficients D(2) of NBD-PE or NBD-PC in the DLPC/cholesterol mixed monolayers were determined with the FRAP technique. The effect of headgroup structure such as PE and PC on D(2) was found to be negligible within experimental error by using the DLPC monolayers and a mixed monolayer with 15 mol % cholesterol at Π ) 10 mN‚m-1. Results at each composition were reproduced in three independent trials. In every case, the fluorescence difference signal profile was best fit by a single exponential, indicating a single center of mass diffusion rate for the lipids (A ≈ 0.4 nm2) within the binary monolayers averaged over a displacement length that exceeds the cross sectional size of lipids by 4 orders of magnitude, i.e., 34 µm for the fringe spacing vs (0.4)1/2 nm. In the LE/gas coexistence region at Π ≈ 0, the diffusion coefficient increases gradually with decreasing surface area, arising from the diminishing gas domains which can be regarded as semipermeable obstacles, and this was (40) McConnell, H. M. Annu. Rev. Phys. Chem. 1991, 42, 171 (41) Benvegnu, D. J.; McConnell, H. M. J. Phys. Chem. 1992, 96, 6820.
Figure 5. Lateral diffusion coefficient of a probe lipid in DLPC/ cholesterol mixed monolayers as a function of surface pressure at different cholesterol fractions, the symbols are the same as in Figure 2.
discussed in detail elsewhere.16 The surface pressure dependences of the diffusion coefficient at different cholesterol fractions are displayed in Figure 5. Here, the binary monolayers at the homogeneous state at Π > 15 mN‚m-1, were studied at different cholesterol fractions up to 30 mol %, containing 1 mol % of NBD-PC. The data points on the ordinate of the plot in Figure 5, at Π ) 0 mN‚m-1, correspond to the diffusion coefficients obtained at the lift-off points of the isotherms. The standard deviations for replicative determinations of D(2) at Π ) 0 and 30 mN‚m-1 are about 15-20% and 5-10%, respectively. Once the surface pressure reaches the lift-off point from the LE/gas coexistence region and the monolayer moves into the LE state, D(2) decreases sharply with increasing surface pressure, and this is shown in Figure 5. Also, incorporation of cholesterol into the lipid monolayer exerts an additional influence, that is, D(2) decreases progressively as cholesterol is added.43 This is consistent with that for phosphatidylcholine/cholesterol/rhodopsin vesicles44 as well as for a monolayer26 and bilayers composed of lipid and cholesterol.18,45 In the homogeneous monolayers, decrement of D(2) with increasing surface pressure and/or cholesterol fraction can be attributed to increasing the monolayer viscosity. We will shortly return to the viscosity effect. Turning to the differences in the uppermost (pure DLPC) and lowest (30 mol % cholesterol) curves in the plot of D(2) vs Π in Figure 5, we note first that D(2) is more sensitive to Π for the pure DLPC monolayer than for the 30 mol % cholesterol monolayer. In fact, the difference in the diffusion coefficients between the uppermost and lowest curves at Π ) 0 (isotherm lift-off point) is greater by a factor of 2 than that at Π ) 30 mN‚m-1. To understand this, we recall that the pure DLPC monolayer remains in a homogeneous state over the entire range of surface pressure, 0 e Π e 30 mN‚m-1, while the DLPC/cholesterol mixed monolayer goes into a biphasic state at Π < 15 mN‚m-1. Since surface domains behave as semipermeable (42) Perkovic, S.; McConnell, H. M. J. Phys. Chem. B 1997, 101, 381. (43) The cholesterol can be oxidized by ambient air, resulting in changes of domain morphology. Since the time dependence of surface pressure and diffusion coefficient for mixed monolayers was not detected once they reach an apparent equilibrium state, the oxidation effect of cholesterol under our experimental condition is assumed to be negligible, or our experiment is not sensitive to the oxidation. (44) Strause, M.; Litman, B. J. Biochemistry 1988, 27, 7723. (45) Ladha, S.; Mackie, A. R.; Harvey, L. J.; Clark, D. C.; Lea, E. J. A.; Brullemans, M.; Duclohier, H. Biophys. J. 1996, 71, 1364.
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Langmuir, Vol. 15, No. 2, 1999 605 Table 1. ao Used for Figure 6 as a Fitting Parameter and Linear Slope, βa*, Obtained from Figure 6 as a Function of Cholesterol Fraction
Figure 6. A semilogarithmic plot of D(2)/Do(2) vs af-1 for DLPC/ cholesterol mixed monolayers in accord with the free area model (see text): (b, O), DLPC; (2, 4), 5 mol % cholesterol. Data points for mixed monolayers with cholesterol fraction of 10-30 mol % are omitted for clarity; they appear too scattered to obscure the trends to be shown, so we specify the fitting uncertainties of individual lines in Table 1 instead of showing all the data points with error bars. The inset shows the whole view of the plot with the origin. All solid lines indicate the best fitted ones obtained by taking ao as the fitting parameter and collected in Table 1.
or impermeable obstacles in the two-phase region, the diffusion of the probe lipid is restricted to the fluid region that remains fluorescent.17 This means that D(2) is apparently retarded by the effective medium effect 46 as well as the monolayer viscosity effect for the DLPC/ cholesterol mixed system. Thus, it is expected that D(2) difference between the pure DLPC monolayer and binary one at lower surface pressures is much larger than that at Π > 15 mN‚m-1. A more detailed discussion on the dependence on phase state is deferred to a later section. For the moment it suffices to note that a set of the domains acting as the obstacles for lateral diffusion is referred by Saxton as an “archepelago”. 46 The retardation profile of D(2) in the pure DLPC monolayer has been studied in the early 1980s by Peters and Beck,15 and our previous results were in good agreement with theirs.16,17 Here, the free area model of Sackmann, Tra¨uble, and co-workers20,21 is applied to DLPC/cholesterol mixed monolayers in the homogeneous state, by restricting ourselves to Π > 15 mN‚m-1 as is guided by the phase diagram in Figure 4. The lateral diffusion coefficient, D(2) of a rigid cylinder with a crosssectional area ao is expressed as follows:
D(2) ) R exp(-βa*/af)
(8)
Here R is a factor representing the diffusant geometry and its local velocity, af, is the free area per molecule defined as af ) A - ao, a* is the critical free area for a step displacement and β is a factor accounting for the overlap of free area (0.5 < β < 1.0). The preexponential factor, R, in eq 8 can be replaced by Do(2)
D(2) ) Do(2) exp(-βa*/af)
(9)
where Do(2) now assumes the following meaning. It is an extrapolation limit when af f ∞, signifying a hypothetical diffusion coefficient of a probe lipid with the same ao in the limit of infinite dilution at the air/water interface. Figure 6 shows a semilogarithmic plot of D(2)/Do(2) vs af-1. Here, the lateral diffusion coefficient at the lift-off point when Π ≈ 0 is equated to Do(2). Data points for mixed monolayers with cholesterol fraction of 10-30 mol % are omitted for clarity. Solid lines in Figure 6 indicate the (46) Saxton, M. J. Biophys. J. 1982, 39, 165.
cholesterol/mol %
ao/nm2
βa*/nm2
0 (DPLC) 5 10 15 20 25 30
0.42 ( 0.03 0.42 ( 0.03 0.41 ( 0.03 0.39 ( 0.08 0.39 ( 0.06 0.38 ( 0.04 0.36 ( 0.01
0.232 ( 0.004 0.217 ( 0.003 0.177 ( 0.004 0.173 ( 0.007 0.165 ( 0.007 0.161 ( 0.006 0.157 ( 0.004
best semilogarithmically fitted lines with ao as a fitting parameter. In choosing the values of ao as the fitting parameter, we were guided by the monotonic decrease with increasing cholesterol composition upon assuming the area additivity rule between those of DLPC and cholesterol. The inset of Figure 6 shows the whole view of the semilogarithmic plots with the common origin. It should be noted that all solid lines go through the origin within experimental errors, indicating the plausibility of eq 9. We collect in Table 1 the values of ao so chosen with the uncertainties representing the fitting range, and the linear slope, βa* obtained from the slopes in Figure 6. The magnitudes of Do(2), ao and βa* for the pure DLPC monolayer are 1.19 × 10-6 cm2‚s-1, 0.42 nm2, and 0.232 nm2, respectively, which are in good agreement with those by Peters and Beck15 and ours reported ealier.16,17 Both ao and βa* decrease with increasing cholesterol fraction. This means that the surface viscosity increases with an increase in the cholesterol fraction. In terms of the model of HPW, D(2) of a diffusant is inversely proportional to the monolayer viscosity η, as seen in eqs 2 and 3; hence, it seems reasonable to conclude that the decrease in lipid diffusion coefficient with increasing cholesterol fraction arises from the “condensation effect” on DLPC by cholesterol, which in turn incrementally increases the in-plane lateral (quasi-two-dimensional) viscosity of the mixed monolayer. Also, the decrements in the values of ao and βa* with increasing cholesterol fraction are abruptly changed at cholesterol fractions of 15 mol % and 10 mol %, respectively, and then remain almost constant. Thus, it might be predicted that the surface viscosity of the DLPC/cholesterol mixed monolayer is drastically changed at this cholesterol fraction. A more conclusive study of the relation between the monolayer viscosity and cholesterol composition for this system will be carried out soon with our surface canal viscometer.47,48 In the case of the DLPC monolayer, D(2) obtained experimentally deviated from eq 9 at Π < 10 mN‚m-1, which is consistent with a previous finding.15-17 In the case of DLPC/cholesterol mixed monolayers, eq 9 is applicable at a surface pressure range from 15 to 25 mN‚m-1. Although it is difficult to specify the upper limit of applicability of eq 9, it can be plausibly argued that the lower limit must coincide with the phase boundary of the binary monolayer. As shown in Figure 4, the mixed monolayers with cholesterol fractions less than 30 mol % are in a homogeneous state at Π > ca. 15 mN‚m-1, and the lateral diffusion retardation is mainly controlled by available free area in this surface pressure range. We finally come to the effect of phase state. To probe further the effect of phase-separated domains on the lipid lateral diffusion, the system at cholesterol fraction of 50 and 60 mol % which remains biphasic until surface pressure exceeds about 20 mN‚m-1 was examined for D(2). (47) Sacchetti, M.; Yu, H.; Zografi, G. Rev. Sci. Instrum. 1993, 64, 1941. (48) Sacchetti, M.; Yu, H.; Zografi, G. J. Chem. Phys. 1993, 99, 563.
606 Langmuir, Vol. 15, No. 2, 1999
Figure 7. Surface pressure dependence of lipid lateral diffusion coefficient in DLPC/cholesterol mixed monolayers: (b), 50 mol % cholesterol; (O), 60 mol % cholesterol. The inset shows surface pressure vs area where experimental data are not shown for clarity in representing the trends: (s), 50 mol % cholesterol; (---), 60 mol % cholesterol. Shaded areas stand for the range of phase boundary (abbreviated as PB) on Π in the abscissa of the main plot and in the ordinate of the inset.
Tanaka et al.
ranges. Once the binary monolayer attains a homogeneous region by increasing surface pressure, a probe lipid can diffuse over the whole surface, resulting in D(2) being influenced by monolayer viscosity alone. At the upper consolute point from the biphasic monolayer to the homogeneous phase, D(2) might increase by virtue of disappearance of the domain effect if an increment of the surface viscosity with increasing surface pressure is relatively modest. We thus such as to propose that D(2) temporarily increases with increasing surface pressure at the vicinity of the upper consolute point, even though there is no signature relating to the upper consolute point on isotherm as shown in the inset. Although the phase separation effect on the lateral diffusion coefficient, twodimensional random walk with obstacles, is of keen interest, there are many other questions that are raised by this study. More specifically, to understand this issue, the in-plane surface viscosity and domain fraction, i.e., phase composition, as a function of surface pressure should be studied. The random walk in the two dimensions with obstacles for pure DLPC monolayers in gas-LE coexistence region was reported earlier17 in detail by the model of Saxton, a diffusion in an archepelago.48 Conclusions
Figure 8. Schematic representation of the lateral diffusion of a probe lipid in the DLPC/cholesterol mixed monolayers: (A) monolayer in a biphasic state with cholesterol-rich domains acting as obstacles; (B) monolayer in a homogeneous state.
Figure 7 and its inset show the dependence of surface pressure on D(2) and Π-A isotherms, respectively, at 50 and 60 mol % of cholesterol. Here the mixed monolayers contained 2 mol % of NBD-PE. Our discussion of the results displayed in Figure 7 is qualitative at best since we have not systematically determined the domain fraction, i.e., phase composition, as a function of surface pressure. As seen clearly, D(2) decreases monotonically with increasing surface pressure to a point. At the surface pressure range from 15 to 20 mN‚m-1, a notable increase was observed in D(2). When the monolayer is in a biphasic state, the cholesterol-rich domains are expected to behave as impermeable obstacles for the lipid diffusion. A cartoon to represent the situation is provided in Figure 8. In the cases of Π e 15 mN‚m-1, the area fraction of the domain is about 50 ( 10%. Thus, the depression in D(2) by the phase effect is remarkable at these surface pressure
The FRAP technique was applied to evaluate the lateral diffusion coefficient of a probe lipid in the DLPC/cholesterol mixed monolayers. The lateral diffusion coefficient decreases with an increase in surface pressure and cholesterol fraction, and that in the homogeneous state is analyzed on the basis of the free area model. Cholesterol in the monolayer affects the diffusion by two distinct mechanisms of (1) increasing surface viscosity as seen in the homogeneous monolayers and (2) domain formation which reduces the available diffusion trajectory, as seen in the heterogeneous monolayers. Acknowledgment. This was in part supported by the Eastman Kodak Professorship and NSF grants (DMR9203289 and DMR9711226) awarded to H.Y. and a Biophysics Training Grant of NIH (No. 5T32 GM08293) awarded to P.A.M. Dr. Marcus Cicerone is gratefully acknowledged for improving the optical configuration of the FRAP instrument, and we are grateful for helpful discussions with Prof. George Zografi and our colleagues Jingwen Ma, Zhihao Yang, and Steven P. Mecca. Finally, we are indebted to Todd Strother for his careful reading of the manuscript. LA9808869
