Langmuir 1992,8,563-570
563
Characterization of Lipid Miscibility in Liquid-Expanded Monolayers at the Gas-Liquid Interface J. M.Smaby and H.L. Brock"* The Hormel Institute, University of Minnesota, Austin, Minnesota 55912 Received May 23, 1991. In Final Form: September 3, 1991
A surface solution model for liquid-expanded monolayers at the gas-liquid interface (Smaby, J. M.; Brock", H. L. Langmuir 1991,7,1031-1034)has been extended to include both ideal and experimental surface pressure-area isotherms. Surface potential-area isotherms for liquid-expanded, mixed monolayershave been analyzed by an extensionof the Helmholzequationmodifiedto includean area-independent potential term (Smaby, J. M.; Brockman, H. L. Biophys. J. 1990,58,195).For experimental mixtures which exhibit ideal surface pressure-area behavior, the constant potential term is shown to apportion among species on a fractional area basis. Application of the equations derived to experimental data is computationally straightforward, requiring no a priori assumptions about the size or shape of the lipid molecules. Comparisonof the four unique parameters obtained for each mixed monolayer provides insight into the origins of mixing nonideality. For example, the parameters reasonably indicate that nonideality in mixtures of l-palmitoyl-2-oleoylphosphatidylserine, an anionic lipid, and sphingosine, a cationic lipid, arises from head group interactions/dehydrationrather than steric accommodationin the aliphatic region. Conversely, in the liquid-disorderedstate, nonideal mixing of cholesterol and 1,2-dimyristoyl-phosphatidylcholine appears driven by steric factors which are not evident in the liquid-ordered state. Thus, the analysis of monolayer-deriveddata by the surface solution model provides a useful adjunct to more classical methods of assessing and characterizing lipid miscibility in fluid monolayers.
Introduction The experimental versatility of insoluble lipid monolayers at the gas-liquid interface makes them excellent models for studying the regulation of biological processes1 and for constructing self-assembling structures of technological utility.2 Frequently, these model systems consist of two or more amphipathic species, often with dissimilar structures. Classically,such surfactant mixtures have been characterized on the basis of their surface pressure-molecular area ( F A ) behavior. As recently reviewed: the determination of miscibility and analysis of the mixing properties of two or more surfactants are approached in two ways. One type of analysis applies the surface phase rule4 to the composition dependence of the observable phase transitions between monolayer phases and between monolayer and bulk phases. This analysis is commonly utilized for three types of monolayer phase transitions, gas to liquid-expanded, liquid-expanded to condensed, and liquid-expanded or condensed to bulk. Additional thermodynamic characterization is provided by comparing the composition dependence of the phase transition pressure with that predicted from a model for perfect or regular mixing. However,there is no universally accepted method to make such comparison^.^ Moreover, for the analysis of monolayer to bulk phase transitions, most models assume that in the phase coexistence region in mixed films the partial molar areas of each surfactant in the monolayer, ai,is constant and k n o ~ n , but ~ ' this assumption has not been tested.
* To whom correspondence should be addressed at the Hormel Institute, University of Minnesota, 801 16th Ave. NE,Austin, MN 55912. (1) Verger, R.;Pieroni, G. In Lipids and Membranes: Past, Present and Future; Op den Kemp, J. A. F., Roelofsen, B., Wirtz, K. W. A., Eds; Eleevier Science Publishers B.V.: Amsterdam, 1986; Vol. 153. (2) Kuhn, H. Thin Solid Films 1989, 178, 1. (3) DLirfIer, H.-D. Adu. Colloid Interface Sci. 1990,31, 1. (4) Crisp, D. J. In Surface Chemistry; Butterworths: London, 1949; Vol. 17. (5) Joos, P. Bull. SOC.Chim. Belg. 1969, 78, 207. (6) Motomura, K.; Terazono, T.; Matuo, H.; Matuura, R. J . Colloid Interface Sci. 1976, 57, 52. (7) -0, J. J . Colloid Interface Sci. 1985, 106, 51.
The second approach to determining component miscibility invclves inspection of the average molecular area at any n (A,) as a function of surfactant mole fraction (Xi).If the components are ideally miscible or totally immiscible within a given monolayer phase, A, versus Xi plots are linear.8 If data plotted in this way are nonlinear, miscibility is qualitatively inferred. However, this type of analysis can be complicated if miscibility gaps exist in the system? A n-independent way to characterize component miscibility in a single surface phase is to model the u-A behavior using an equation of state. The best developed approach is the two-dimensional solution model for soluble1° and insoluble surfactants." In this model, all interactions are presumed to be reflected in the water activity coefficient, while the partial molar area of each lipid species remains constant. The magnitude of the interactions can be estimated using regular solution theory.1° In our experience using n-A data for monolayers of pure lipids with 1-3 aliphatic chains, the simple surface solution model gave a poor description of the data. Standard deviations for u were as high as 2.6 mN/m with an average of 1.48mN/m.12 Much better representation was obtained with a modified form of the equation13with which standard deviations for the test data averaged only 0.11 mN/m. This paper addresses the application of this equation to ideal and real mixed-lipid monolayers mostly of the liquidexpanded type. Departing from previous practice, the analysis does not presume a priori that partial molar areas remain constant in mixtures. This permits assessment of the degree to which nonideal mixing can be attributed to steric accommodation or to specific lipid-lipid-water interactions. The n independence of the partial molar areas obtained will allow testing of the assumption of (8)Goodrich, F. C. Proc. Int. Congr. Surf. Act., 2nd 1967, I, 85. (9) Matuo, H.; Motomura, K.; Matuura, R. Chem. Phys. Lipids 1982, 30, 353. (10) Lucassen-Reynders,E. H. J . Colloid Interface Sci. 1973,42,554. (11) Gaines, G. L., Jr. J. Chem. Phys. 1978, 69,924. (12) Smaby, J. M.; Brock", H. L. Langmuir 1991, 7, 1031. (13) Smaby, J. M.; Brock", H. L. Biophys. J. 1990,58,195.
0143-1463/92/2408-0563$03.00/0Q 1992 American Chemical Society
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564 Langmuir, Vol. 8, No. 2, 1992 constant partial molar areas used in the thermodynamic analyses of monolayer to bulk phase transition data noted above. Also addressed in this paper is the use of surface potential-area behavior (AV-A) to characterize the miscibility of lipids in mixed monolayers and to distinguish between classically ideal miscibility and complete immiscibility. Especially for liquid-expanded films, T-A data alone may not permit assessment of miscibility. This can occur because (i) monolayer collapse pressures for the species are identical, (ii) no liquid-expanded to liquidcondensed transitions are observed, (iii) the gaseous to liquid-expanded phase transition is not experimentally accessible with most commercial film balances, and (iv) average molecular area-composition plots are linear.
involvingthe activity coefficient,lghas recently been shown to be correlated with f1 (In q = 7.1 - 5.2f1) and, therefore, is not unique.12 It is retained as a separate parameter for curve fitting because the relationship between f1 and q has been defined only for pure lipids and is approximate. The classical definition of ideal miscibility for a mixture of lipids at constant a is8
A, = CAi,,Xi i=2
where A, is the average area per lipid molecule in the monolayer at T , Ai,, is the molecular area at A of each of the 2-n lipid species alone (component 1is water), and Xi is its mole fraction relative to all lipid species. Solving eq 1 for A, and substituting it into eq 2 gives
Materials and Methods
n
Monooleoyl-,l,&dioleoyl-,and triacylglycerols,oleic acid, 13,16-cis,cis-docosadienoicacid, oleyl alcohol, oleylmethanol, oleylnitrile, and cholesterol were purchased from NuChek Prep, Inc. (Elysian, MN). Sphingosine was purchased from Sigma Chemical Co. (St. Louis, MO). N-oleylethanolamine was a generous gift from H. H. 0. Schmid of the Hormel Institute. Phospholipids were purchased from Avanti Biochemical (BirThe purity of each lipid was checked by thinmingham, a). layer chromatography and from measured detection limits was shown to be >99%. Solvents, water, and buffers were treated and used as described.13 Surface pressure and potential isotherms were measured as a function of area using a fully automated Langmuir film balance system."J6 All isotherms were measured at 24 O C and in most cases on a subphase of 10 mM phosphate and 0.1 M NaCl at a pH of 6.6. The mixtures containing l-palmitoyl2-oleoyl-sn-3-phosphoglycerol and diacyl-sn-glycero-3-phosphoinositol had 0.1 mM EGTA in the subphase. Mixtures with sphingosine and l-palmitoyl-2-oleoyl-sn-glycero-3-phosphoserine were measured on a subphase of 10 mM citrate and 2.0 M NaCl, pH 5.0. Phase transition pressures ("8) were detected using a combinationof second and third derivatives of T with respect to A.14
Simply, for an ideal mixture A, can-be readily calculated by summing the contributions to A, of the constituent lipids. Thus, over any range of A an ideal FA isotherm for a lipid mixture can be generated from the 3 (n - 1) values of 00, f , and q for the species present and the n 2 mole fractions. The parameter wo in eq 3 is separated from the others so that a parameter i o can be defined such that for any ideal mixture n
io= &Xi
Surface Pressure-Area Behavior. For monolayers of a single lipid species, in the liquid-expanded state, surface pressure (+molecular area (A) isotherms are well described by an equation of state13J6 T
= (skT/o,) In [(l/fl)(l + wl/(A, - ~ , ) ) l
(1)
As defined, A, is the total surface area at A divided by the number of lipid molecules even though water is a component of the interface at all T < a, The parameter w 1 = 9.65A2/moleculeis the area of an interfacial water molecule computed from its bulk ~r0perties.l~ The correctness of using this value for interfacial water is supported by hydration measurements of phospholipids.'s The values of the remaining three ?r-independent parameters 00, f1, and q are determined by the choice of the dividing surface.1° Using a monolayer model of the interface, wo becomes the area of dehydrated lipid (a = a) and f1 is the activity coefficient of the water which comprises the remainder of the interface. Through application of eq 1,the parameter Q, originally included to allow for higher order terms (14) Brockman, H. L.; Jones, C. M.; Schwebke, C. J.; Smaby, J. M.; Jarvis, D. E. J. Colloid Interface Sci. 1980, 78, 502. (15) Brockman, H. L.; Smaby, J. M.; Jarvis, D. E. J. Phys. E Sci. Instrum. 1984, 17, 351. (16) Israelachvili, J. N.; Wennerstrbm, H. Langmuir 1990, 6, 873. (17) Fowkes, F. M. J . Phys. Chem. 1962,66, 385. (18) Scherer, J. R. Proc. Natl. Acad. Sci. U.S.A. 1987,84,7938.
(4)
i=2
The terms involving f1 and q in eq 3 are not apparently separable, but it can be assumed that functions exist such that f = f(fl,i,Xi) and Q = f(qi,Xi). If this is valid, the PA isotherm for an ideal mixture will be reasonably described by = ( ~ k T / w ,In) [(l/fl)(l + wl/(A, - io)]
(5) Equation 5 has the form of eq 3 and, if empirically correct, would allow the T-A isotherm for an ideal mixture to be described by only three parameters. Furthermore, if eq 5 gives good representation of FA isotherms for noni_deal mixtures, comparison of ideal and actual values of WO, f , and as a function of lipid composition should provide insight into the determinants of the mixing nonideality. In particular, comparison of deviations from ideality for & and f 1 (and hence 4) should qualitatively indicate the extent to which the deviations in A, arise from accommodation of the lipids20themselves versus a loss or gain of water from the interface. Surface Potential-Area Behavior. As recently discussed,13 classical analysis of surface potential (AV) for pure lipids begins with calculation of the surface dipole moment, p l , using the Helmholz equation. The value of p L is usually determined at a single molecular area because at the air-water interface AVgenerally is not proportional to 1/A as predicted by the model. Rather, for films of many pure charged, neutral and zwitterionic lipids in the liquid-expanded state, AV has been shown to obey the equation A
Theory
n
AV = AVO+ 37.70p,/A (6) where AVis measured in millivolts, A in angstroms squared (19) Wolfe, D. H.; Brockman, H. L. Proc. Natl. Acad. Sci. U.S.A. 1988, 85, 4285.
(20) Cadenhead, D. A.; Muller-Landau, F. J. Colloid Interface Sci. 1980, 78, 269.
Lipid Miscibility in Liquid-Expanded Monolayers
Langmuir, Vol. 8, No. 2, 1992 565
Table I. Standard Deviations from Analysis of Ideal and Experimental Surface Pressurs-Potential-Area Isotherms for Equimolar LiDid Mixtures ~~
~_____
ideal isotherms experimentalisotherms lipidsa r range,mN/m std dev w, mN/m std dev AV,mV std dev T,mN/m std dev AV,mV trimyristoleoylglycerol-trieicosadienoleoylglycerol 1-9.4 0.0001 0.0013 0.010 0.484 trioleoylglycerol-l-palmitoyl-2-oleoylGPC 1-14.1 0.0001 0.0018 0.031 0.307 1-13.6 0.0001 0.0003 0.014 0.477 trioleoylglycerol-l,3-dioleoylglycerol l-palmitoyl-2-oleoyl GPS-l-palmitoyl-2-oleoyl GPC 1-43.6 0.0001 0.0092 0.099 1.307 1,3-dioleoylglycerol-1,2-diphytanoylGPC 1-29.0 0.0008 0.0283 0.092 0.425 1-28.8 0.0002 0.0060 0.040 0.374 1,3-dioleoylglycerol-1,2-dioleoylGPE 1,3-dioleoylglycerol-l-palmitoyl-2-oleoylPG 1-31.6 0.0006 0.0367 0.066 0.562 1,3-dioleoylglycerol-bovineliver diacyl PI 1-32.0 0.0004 0.0437 0.044 0.473 13,16-docosadienoicacid-l-palmitoyl-2-oleoylGPC 1-38.8 0.0127 0.651 0.253 0.652 oleylmethanol-l-palmitoyl-2-oleoyl GPC 1-24.2 0.0203 0.0951 0.048 0.499 1-26.0 0.0049 0.0638 0.050 0.605 oleylnitrile-1-palmitoyl-2-oleoylGPC oleyl alcohol-l-palmitoyl-2-oleoylGPC 1-34.9 0.0021 0.171 0.121 0.478 1(3)-monooleoylglycerol-l-palmitoyl-2-oleoylGPC 1-39.4 0.0011 0.0139 0.174 1.428 N-oleylethanolamine-l-palmitoyl-2-oleoylGPC 1-31.5 0.0005 0.0231 0.116 0.916 cholesterol-1,2-dimyistoyl GPC 1-32.1 0.0054 0.0082 0.973 0.520 sphingosine-l-palmityl-2-oleoylGPC 1-41.8 0.0028 0.152 0.135 0.460 sphingosine-l-palmitoyl-2-oleoyl GPS 1-41.8 0.0022 0.0603 0.105 0.419 1(3)-monooleoylglycerol-1,3-dioleoylglycerol 1-29.0 0.0005 0.0026 0.053 0.766 oleic acid-1,3-dioleoylglycerol 1-29.3 0.0004 0.145 0.118 0.433 oleic acid-1(3)-monooleoylglycerol 1-38.4 0.0004 0.0708 0.231 0.425 Abbreviations: GPC,sn-glycero-3-phosphocholine; GPE,sn-glycero-3-phosphoethanolamine;PG,sn-3-phosphoglycerol; PI,sn-glycero3-phoaphoinositol;GPS,sn-glycero-3-phosphoserine.
per molecule, and p1 in mi1lideb~es.l~ For a mixture of lipids which are microscopically phase separated at any a, the macroscopic surface potential, AV,, is the areaweighted average of the surface potentials of the coexisting phases.21 For either a film of immiscible components or an ideal mixed monolayer, the area fraction occupied by the ith species at any a is Ai,=Xi/Ar-Multiplying eq 6 for each lipid component by its appropriate area fraction and summing over all components gives n
n
AVr = C A V o , iA i , J i / A , + 3 7 . 7 0 c P * , ~ X ~ / A( 7, ) 112
F 2
Just as eq 3 can be used to generate ideal a-A isotherms from the behavior of the constituent lipids, eqs 7 and 3 can be used together to generate ideal AV,-A, data over a range of a. If for each lipid Ai,=/A,is approximately a independent and we define AVoa = C$2AVo,iAi,,Xi/A, and LLa & s l , i X i , then for a given ideal mixture at all a =
+ 37.7LLa/A,
which is of the same form as eq 6. If a plot of AV versus 1/A, is linear, the AV-A behavior of an ideal mixture can be described by two parameters, Avoa and LLa a t all a. By analogywith the analysis of u-A data, if nonideal mixtures exhibit reasonable linearity of AV versus 1/A, in the a range encompassing the liquid-expandedstate, the source of the nonideality can be identified. Nonclassical AV behavior related to the contribution of AVO has been observed by several researchers, but ikj origins are Because AVOis lipid head group ~pecific,'~ we consider that in ideal mixtures it could apportion with the mole fraction of each component rather than its area fraction. If so, by analogy with the derivation of eq 7 (21)Miller,A,; Helm,C. A.; MBhwald,H.J. Phys. (Paris)1987,48, 693. (22)Taylor,D.M.;Oliveira,0.N.,Jr.; Morgan,H.Thin Solid FiZm 1989,173,L141. (23)Yokoyama, S.;Kbzdy,F.J. J. Biol. Chem.1991,266,4303.
n
n
+
AVr = C A V 0 , , X i 3 7 . 7 0 / A , ~ ~ , , ~ X ~(9) r=2
r=2
Defining AVoX = E=aAVo,iXi and iLx = C p ~ p ~ , i gives Xi for any ideal mixture AVr =
Avt + 37.70 iLx/A,
(10)
where Avox and pLXcan be directly calculated from the AVOand p1 values for the components of the mixture.
Results Analysis of Ideal a-A Isotherms. Using eq 3, u-A isotherms for representative ideal binary lipid mixtures (Table I) in the liquid-expanded state were generated numerically from the parameters and mole fractions describing the components. The range of a over which this calculation is performed (Table I) is arbitrary, but unless otherwise noted, the range is that over which the correspondingexperimental isotherms for the mixture are routinely analyzed.I3 This range is from a = 1mN/m to the r a t which d2a/dA2changes from positive to negative, usually a few millinewtons per meter below the collapse or transition pressure. For many of the mixtures selected, the parent lipids show large difference in one or more of the three fitting parameters.l3 Included in the modeling was cholesterol which, presumably because it exhibita not liquid-expanded but liquid-condensedmonolayer behavior, has values of f1 and q greatly different from acyl lipids showing liquid-expanded behavior. The ideal a-A isotherms were fitted to eq 5 to obtain , QI where the subscript I indicates values of &,I, ~ I J and an ideal isotherm. Also determined were statistical indicators of the goodness of fit,i.e., the standard deviation in a and the largest absolute a residual. As shown in Table I, the fitted curves give nearly perfect representation of the data. The standard deviations and absolute maximum residuals are orders of magnitude lower than those observed for experimental isotherms obtained for single lipid species.12 Also, the parameter values for ideal, mixedlipid isotherms are independent of the a range over which the data are fitted (not shown). These data indicate that,
Smaby and Brockman
566 Langmuir, Vol. 8, No. 2, 1992
6ool 500
30
40
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tJo,I Calculated, A2/ molec. Figure 1. Comparison of ideal limiting molecular ares, &,I, for the mixtures listed in Table I determinedusing eq 4 (calculated) and eq 5 (fitted) as described in the text.
within normal ranges of values o_f the fitting parameters, the assumptions used to define f i and Q in eq 5 are valid even if the analytical expressionsfor them are not apparent. A further test of the applicability of eq 5 is the behavior of the fitting parameter, 00, which should equal &00,iXi (eq 4). As shown in Figure 1,a plot of the fitted values of Go obtained using eq 8 versus the values predicted using eq 4 is linear with all-points near a theoretical line ~ PI can be obtained having a slope of 1. Thus, WOJ, f l , and from ideal isotherms generated using the additivity rule as combined with the basic equation of state, Le., eq 5. Moreover, if eq 5 is applied to experimental data at a given composition, comparison of the values of the ideal and experimental parameters should provide insight into the nature of any mixing nonideality which may occur. Analysis of Ideal A V-A Isotherms. Using the ide-al u-A isotherms generated above with eq 5, ideal AV,-A, isotherms were generated over the same a range shown in Table I using the values of AVOand pL fo_r the parent lipids by application of eq 7. The AV,-l/A, data were linearized using eq 8 and yielded the standard deviations of AV listed in Table I. The coefficient of correlation of eachline was 1.OOO. The largest standard deviation is less than 1 mV, and all lines show excellent linearity. This indicates that, for the variety of lipid mixtures shown, the assumption of an essentially *-independent area fraction for each component is reasonably _correct. An additional test is provided by comparison of p l , l awith iL,~' for each mixture. If, as assumed in the derivation of Eq 8, the A dependence of AVresides only in the I.LLterm, then 111.r~ should equal pL,l' for each mixture. As shown in Figure 2, a plot of pL,f versus i 1 , i x is linear and the points lie close to a theoretical line with a slope of 1.0. The value of c(I,~xat each composition was calculated from the pL values of the parent lipids as defined in the derivation of ~ eq 10, i.e., i l ,=~C:=2~1,iXi. Analysis of Experimental r-A-A V Isotherms. To test the experimental applicability of eqs 5 and 8, the measured a-A-AV isotherms for the equimolar mixtures shown in Table I were analyzed over the same a range as the ideal isotherms described above. The standard deviation in u for each mixture obtained by fitting each u-A isotherm to eq 5 is given in Table I. These average 0.14mN/m. The values are larger than those obtained for the ideal r A isotherms, but are generally the same size as those obtained for the individual c o n s t i t ~ e n t s . ~Eash ~J~ experimental AV-A isotherm was linearized to obtain and AVO,and the coefficient of correlation of each line was 20.999. Note that because eqs 8 and 10 are of the same form, the linearization of experimental AV-A data
200
300
400
500
600
A,I,mDebw Figure 2. Comparison of ideal surface-dipole momenta for the mixtures listed in Table 1. Values of p l , f were calculated by apportioning the area-independent potential term, ~ V Oas, a function of mole fractionusing eqs 9 and 10. Values of pL,f were calculated by apportioning AVO,as a function of area fraction using eqs 7 and 8 as described in the text. makes no assumption as to how AVOis apportioned in experimental mixed monolayers. The standard deviations of A V (Table I) average 0.60mV as compared to an average of 1.03 mV for the component lipid films (not shown). These statistical parameters show that eqs 5 and 8 or 10 can be confidently used to describe the u-A-AV behavior of experimental, as well as ideal, isotherms for lipids in the liquid-expanded state. For each binary system listed in Table I, u-A-AV isotherms were determined over the entire compositional space. Moat show mixing behavior which is ideal or slightly nonideal by the criterion of eq 2. Several of the ideal systems show behavior which allows a test of the two methods for ideal apportionment of AVO. Specifically, ~ each composition are the values of AVof and A V O Jat sufficiently different that their abilities to predict AVOfor experimentally ideal mixtures can be compared. Those systems are 1,3-dioleoylglycerol-oleic acid, l-palmitoyl2-oleoyl-phosphatidylcholine-13,16-cis,cis-docosadienoic acid and 1-palmitoyl-2-oleoyl-phosphatidylcholineoleyl alcohol. Two other systems, consisting of either l(3)monooleoylglycerol or N-oleylethanolamine and 1-palmitoyl-2-oleoyl-phosphatidylcholine, illustrate how AV-A data can help to determine lipid miscibility when ?rt is essentially invariant with Compositionand A,-composition plots are, within experimental error, linear. Extremes of nonideal mixing are represented by the cationiclanionic system sphingosine-l-palmitoyl-2-oleoyl-phosphatidylserine and by mixtures of 1,2-dimyristoyl-phosphatidylcholine with the planar sterol cholesterol. These illustrates how comparison of n-A as well as AV-A fitting parameters can provide insight into the origins of nonideal behavior. For these systems, the results of the analysis (Figures 3-9) are presented in a common format. Unless noted, the values for each parameter are scaled identically to facilitate comparison among figures. For each system, panel a gives the ut-composition phase diagram for the system. Transitions occurring a t very low u values, i.e., gaseous to liquid expanded, were not determined because of the sensitivity limits of the film balance. If more than one ut was detected at any composition, only n-A-AV data obtained at u values less than the lowest ut at that composition were subsequentb analyzed (e.g., Figure 9a). Panel b of each figure shows A, versus composition for A = 1.0 mN/m and two higher u values lower than the lowest ut indicated in the respective panel a. The filled symbols at three compositions in each panel b are actual points from the experimental u-A isotherms, whereas the open
Lipid Miscibility in Liquid-Expanded Monolayers
Langmuir, Vol. 8, No. 2, 1992 561
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symbols were obtained by evaluating the fitted experimental curve at the appropriate r . In every case, good agreement is found between the corresponding filled and open symbols. This confirms the applicability of eq 5 to experimental as well as ideal *-A isotherms shown statistically in Table I. The solid lines connect the end points and show the expected behavior for ideal miscibility of the components. Panels c and d in each figure give the fitted values of wg and 11as a function of composition. The solid lines connect the ideal values of the parameter determined a t each composition for which an experimental point is shown. Panels e and f of each figure give the values of pLI and AVOfor each experimental compositiqn determined by linearization of experimental AV,-lIA, I ~ data. These are compared to ideal _valuesof ~ L , and a V g , ~ a(solid lines) and iLI,lIL and AVOJ' (dashed lines) calculated at each composition. Panel a of Figure 3 shows that r , varies continuously with l,3-dioleoylglycerolcomposition in mixtures with oleic acid. This indicates miscibility of the lipids in all proportions. The &-composition plots show ideal miscibility in spite of the difference in lipid he.$ groups. This . is reflected in the nearly ideal behavior of wg and f ~ The behavior of il shhpys some nonideality relative to both ideal models, but AVOvalues closely follow the ideal curve based on area apportionment. Mixtures of 13,16-cis,cisdocosadienoicacid and 1-palmitoyl-2-oleoylphosphatidylcholine are typical of several fatty acid-phosphatidylcholine system studied (Figure 4). Up to 0.67mole fraction
0.2
0.8
0.4
0.8
0.6
Mol Fraction of Docosadienoic Acid
Mol Fraction of 1 ,bDioieoylglycerol
Figure 3. Analysis summary for mixtures of 1,3-dioleoylglycerol and oleic acid. (a) Phase transition pressures. (b) Average moleculararea,A,,atr= 1(0),12(O),and26(~)mN/mobtained by evaluating fitted experimental curves at each T . For comparison, filled symbols (0,W, A) show experimental data points from?rA isothermsobtainedat0.25,0.50,and0.75molfradions. The solid lines show idtal behavior as dsfined by eq 2. (c) Fitted and ideal WOJ (aslidline). (d) Fitted valuesof experimentalwo(0) values of experimental- 71 (0)and ideal f ~ , l(solid line). (e) ExperimentalvaluesofrL (0),lll~~solidli_n_e),andrl,f (dashed ljne). (0Experimental values of AVO(O),AVo,f (solid line), and AVO,? (dashed line). End points are averages of values from three or four a-A-AV isotherms.
0.6
&
Figure 4. Analysis summary for mixtures of 13,16-cis,cis-docosadienoicacid and l-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine. The legend is the same as Figure 3 except for panel b r = 1 (0,O), 20 (0, m), and 40 (A,A) mN/m.
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Mol Fraction of Oleyl Alcohol
Figure 5. Analysis summary for mixtures of oleyl alcohol and l-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine. The legend is the same as Figure 3 except for panel b: T = 1 (0, O), 15 (0, W), and 30 (A,A) mN/m.
of fatty acid, the phase diagram does not indicate if the components are miscible in the monolayer phase. This is in part attributable to the formation of the well-known 1:2 complex of fatty acid to phosphatidylcholine in the
568 Langmuir, Vol. 8, No. 2,1992
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Figure 8. Analysis summary for mixtures of sphingosine and l-palmitoyl-2-oleoyl-sn-glycero-3-phosphoserine. The legend is the same as Figure 3 except for panel b: ?r = 1 (0, e),16 (0, m), and 34 (A,A) mN/m.
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Figure 7. Analysis summary for mixtures of 1(3)-monooleoylglycerol and l-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine. The legend is the same as Figure 3 except for panel b: ?r = 1 (0, O ) , 20 (0, m), and 42 (A,A) mN/m.
Figure 9. Analysis summary for mixtures of cholesterol and 1,2-dimyristoyl-sn-glycero-3-phosphocholine. The legend is the same as Figure 3 except for panel b: ?r = 1 (0,a),20 (u,m), and 40 (A,A) mN/m. All points are averages of 2-4 isotherms.
collapsed phase and possibly in the m o n ~ l a y e r . If ~ ~a separate phase of the complex is formed in the monolayer phase, it is certainly not reflected in any of the T-A data
for the liquid-expanded state (Figure 4, panels b-d). The surface potential data for this ideal system provide _a good test for AVO apportionment. The ideal values for are indistinguishable from each other and from the experimentally derived points. In contrast, the ideal AVOvalues
(24) Smaby, J.
M.;Brockman, H.L. Biophys. J. 1986, 48,701.
Langmuir, Vol. 8, No. 2, 1992 569
Lipid Miscibility in Liquid-Expanded Monolayers
are distinct and the experimental points are best correlated with the area apportionment model. A similarly definitive test of AVOapportionment is provided by mixtures of oleyl (Figalcohol and l-palmitoyl-2-oleoylphosphatidylcholine ure 5). This system also shows the type of complex formation (panel a) described p r e v i o u ~ l y . ~ ~ Another useful application of this method of analysis is illustrated by Figures 6 and 7. Each system shows linearity of A, versus composition within experimental uncertainty. This indicates either ideal miscibility or total immiscibility of the components (Figures 6b and 7b). Which occurs cannot be definitely evaluated because the phase diagrams (Figures 6a-and 7a)jhow nearly constant ?rt. However, inspection of p1 and AVOdata (Figures 6e,f and AVO and 7e,O shows nonideal behavior of both relative to either ideal model for AVOapportionment. Thus, the potential parameters can indicate the miscibility of the components when it cannot be clearly assessed by more classical means. The cationic lipid sphingosine and the anionic lipid 1palmitoyl-2-oleoylphosphatidylserinemix nonideally, as indicated by the minimum in ?rt for the transition from the liquid-5xpanded to a more condensed state (Figure 8a) and by A,-composition plots (Figure 8b). Insight into the nature of this nonideality is prpvidedby inspection of the c9mposition dependence of wo and f1 (Figure 8c,d). The wo parameter, which should describe the behavior of the dehydrated lipids, shows almost no deviation from ideal mixing, whereas 71, the primary interaction parameter, shows a large deviation relative to other systems. also shows a large deviation from ideal The value of i1 behavior which is maximal aro_und an equjmolar composition. Such behavior off1 andpl, but not WO, is consistent with the nonideality arising from chargelhydration changes a t the lipid-water interface rather than any geometric accommodation of the apolar portions of the lipid molecules. A complex, nonideal system of biological relevance is cholesterol-dimyristoylphosphatidylcholine. Cholesterol alone exhibits liquid-condensed ?r-A behavior, but can be analyzed in the manner described. However,the standard errors associated with the parameters are large, and therefore, results must be interpreted cautiously. Nevertheless, in mixtures with dimyristoylphosphatidylcholine, reasonable analyses can be obtained, particularly in the biologically relevant range of 0-50 mol % cholesterol. From prior studies using fluorescencemicroscopy and compressibilities, the miscibility characteristics of the system are k n ~ w n Above . ~ ~ 50 ~ mol ~ ~% cholesterol, the lipids are immiscible. From -10 to -50 mol %, ?r-dependent immiscibility between liquid-disordered and liquidordered phases occurs, but at 50 mol % only the liquidordered phase is present. Analysis of ?r-A-AV data for the system reveals several interesting features. As often noted, the maximal change in A, with composition occurs when only the liquid-condensed phase is present at about 50 mol % (Figure Sb). However, the geometric parameter & shows maximal deviation around 20 mol % cholesterol (Figure Sc). At 50 mol % ,where A, deviates maximally, GOhas returned to ideal values. Moreov_er,note that the absolute magnitude of the change in wo at 20 mol % cholesterol, -6 Az,is comparable to the absolute changes in A, at the same composition. This suggests that the driving force for the deviation in A, up to 20 mol % cholesterol is steric accommodation of cholesterol in the
rl
apolar portion of the disordered phosphatidylcholine. At 50 mol % cholesterol, Le., in the liquid-ordered state, the condensation in A, appears to arise largely from the phospholipid chain becoming more condensed relative to the disordered state. This permits a closer approach of the molecules, but steric accommodation, as reflected by WO, is absent. That head group interactions are not a major contributor to A, changes and that water-structure is not perturbed are suggested by the ideality of f1 over the entire range of compositions between 0 and 50% f1 (Figure 9d). Note, however, that the scale of f1 is considerably compressed relative to Figures 3-8 because of the high value of f1 for cholesterol. Additional evidence that this head group dehydration does not perturb water structure between 0 and 50 mol % cholesterol comes from the and AVO,which should potential parameters. Both reflect water as well as lipid dipolar structure and ~rientation;~are ideal relative to the area apportionment model for AVO. Note again, however, that the scale for AVOis somewhat more compressed than in Figures 3-8 due to scatter of the values at high mole fractions of cholesterol.
rl
Discussion This paper has presented an analysis of ?r-A-AV data from mixed monolayers in the liquid-expanded state. The analysis is phenomenological in that ideal behavior is defined in terms of the properties of the pure components. As for any analysis of monolayer behavior, the u-A-AV data should be equilibrium values. For the systems described in Table I, with the exception of cholesterolphosphatidylcholine mixturesz8, this is generally true in that below rt isotherms are reversible. The interpretation of the results is model specific and depends on the choice of the dividing surface. The reasonableness of the convention used, i.e., A = wo when all water is removed, has been shown earlier13in that wo values are consistent with the cross-sectional areas of the lipid molecules (Figures 3-9c). For films with chains in a disordered state, interactions should be governed primarily by the lipid head groups and their interactions with water and dissolved solutes.z9 This was demonstr_ated by the nonideal composi_tiondependence of thefl, p1, and AVOparameters but not 00 when oppositely charged lipids were mixed (Figure 8c-e). In contrast, for lipids like cholesterol and phosphatidylcholine with differently shaped apolar moieties, accommodation contributes to the stabilization of the interface by allowing a closer packing of the lipids.zo Thus, application of the r-A analysis described provides a more detailed understanding of the deviations of ?r-A data from classically ideal behavior than plots of A versus composition alone. Such knowledge is useful for analysis of ?rt data and challenges the common assumption that at collapse lipids have a constant partial molar area in mixtures.k7 However, Figures 3-8 show that the assumption is reasonable for lipids all having linear aliphatic groups in a disordered state. AV-A data have seldom been used to characterize lipid miscibility. I t waa recently recognized that even uncharged lipids in the liquid-expanded state require an areaindependent potential term, AVO,in addition to p l for a complete description of this AV-A b e h a v i ~ r . ' ~This * ~ ~has been extended herein to cover lipid mixtures. Unclear (27) Coleman, R.; Lowe, P. J.; Billington, D. Biochim. Biophys. Acta 1980,599, 294.
(25) Subrammiam, S.; McConnell, H. M. J . Phys. Chem. 1987, 91, 1715. (26) Hirshfeld, C. L.; Seul, M. J. Phys. (Paris) 1990,51, 1537.
(28) Cadenhead, D. A.; Kellner, B. M. J.; Phillips, M. C. J. Colloid Interface Sci. 1976, 57, 224. (29) Cevc, G.Biochemistry 1987,26, 6305.
570 Langmuir, Vol. 8, No. 2, 1992
was the form in which AVOshould be apportioned in the interface. Following on the classical Helmholzdescription of AV,2l AVOshould be reasonably distributed on the basis of the area fraction of each species in the interface. On the other hand, AVOis species specific13with values from -70 to +lo0 mV (e.g., Figure 3). This suggested that it was determined by the head group per se and might apportion on a mole fraction basis. However, as shown in the experimental systems in which the ideal models can be distinguished (Figures 3-5), straightforward area fraction apportionment of AVOJ, Le., eq 8, seems more appropriate. This is consistent with the suggestion that AVOarises from an epitaxial ordering of water molecules in the interface.13 The usefulness of AV-A analysis for characterizing miscibility in the liquid-expanded state is exemplified in Figures 6 and 7. For those systems, ideal miscibility cannot be ckarly distinguished from immiscibility by either 7rt or A variations with composition. In summary, the surface solution analysis of lipid mono-
Smaby and Brockman
layers in the liquid-expanded monolayer state is applicable to mixtures as well as pure lipids. Its application T-AAV data is straightforward and leads to physically reasonable results. In biological membranes most lipids are in a chain-disordered, i.e., liquid-crystalline, state. Thus, results obtained by surfaces solution analysis of monolayers in the liquid-expanded state can provide insight into how lipid-lipid-water interactions can regulate biological processes occurring in membranes. For technological applications, which generally utilize more condensed lipids, studies of analogues with disordered acyl chains can help isolate and characterize those head groupwater interactions which regulate packing in more condensed states.
Acknowledgment. This work was supported by USPHS Grant HL08214 and the Hormel Foundation. The technical assistance of C. Perleberg and M. Conway in the preparation of this paper is greatly acknowledged.
