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Sponge-Vesicle Transformation in Binary Mixtures of Ionized Phospholipid Bilayers K. Tajima,† M. Koshinuma,‡ A. Nakamura,§ and N. L. Gershfeld* National Institute of Arthritis, Musculoskeletal, and Skin Diseases, National Institutes of Health, Bethesda, Maryland 20892 Received August 31, 1999. In Final Form: November 23, 1999 The ionized phospholipids NaDLPG and NaDMPG each undergo a transformation from a sponge phase to unilamellar vesicles at a critical temperature T* (Koshinuma; et al. Langmuir 1999, 15, 3430). The present study examines the dependence of T* on composition in aqueous bilayer dispersions of binary mixtures of these lipids. The surface pressure of the saturated solutions show a maximum at T* that is a monotonic function of the lipid composition in the bilayer. The lipid composition in the equilibrium aqueous solution was also measured. At T*, and only at this temperature, the lipid composition of the bilayer and equilibrium solution become identical. These properties are shown to be a natural consequence of the surface pressure maximum at T*, and are indicative of the physical uniqueness of the critical bilayer state. In general, when aqueous dispersions of bilayer-forming multicomponent mixtures of phospholipids exhibit a surface pressure maximum at a critical temperature T*, the lipid composition of the solution and bilayer phases become identical. This property is a characteristic of the general class of indifferent states.
I. Introduction When the sodium salts of dimyristoylphosphatidylglycerol (NaDMPG) and dilauroylphosphatidylglycerol (NaDLPG) are dispersed in water at concentrations exceeding their solubility, and below a critical temperature T*, they form, as bilayers, a viscous, jellylike sponge phase.1,2 At T* the sponge phase transforms into unilamellar vesicles that become progressively more heavywalled as temperatures are raised above T*.2 Changes in conductivity and an increase in light scattering have also been observed in dispersions of NaDMPG at T*.3 Since the solubility of these lipids in water is large enough to be measured quantitatively, their saturated solutions may be used for studying the properties of the physical states that form.2,4 The present study exploits the solubility of these bilayer-forming lipids to examine the influence of lipid composition on T*, and to test a thermodynamic theory that has been used to deduce the solution properties of neutral phospholipid analogues of PG, i.e., phosphatidylcholines with solubilities in water that are too low for quantification. Measurements of the thermodynamic properties of these less soluble lipid bilayers have been restricted to the use of the surface pressure π of the equilibrium surface films formed by aqueous dispersions of these phospholipids.5 In the present study we used the more soluble sodium salts of NaDLPG and NaDMPG to verify that deductions based on surface film properties may also be obtained from analysis of the equilibrium solutions. For mixtures of neutral lipids at T* it has been shown that (∂π/∂T)µi,p ) (∂π/∂µi)T,p ) 0; under these * To whom corrrespondence should be addressed. Address: NIH, Building 6, Room 139, Bethesda, MD20892. E-mail:
[email protected]. † Present address: Kanagawa University, Yokahama , Japan. ‡ Present address: Teikyo Heisei University, Chiba, Japan. § Present address: Nagoya City University, Nagoya, Japan. (1) Koshinuma, M.; Tajima, K.; Nakamura, A.; Gershfeld, N. L. Langmuir 1999, 15, 3430. (2) Gershfeld, N. L.; Stevens, W. B.; Nossal, R. J. Faraday Discuss. Chem. Soc. 1986, 18, 19. (3) Riske, K. A.; Politi, M. J.; Reed, W. F.; LamyFreund, M. T. Chem. Phys. Lipids 1997, 89, 31. (4) Gershfeld, N. L. Biochemistry 1989, 28, 4229. (5) Gershfeld, N. L. J. Phys. Chem. 1989, 93, 5256.
conditions the Gibbs-Duhem relations predicted,5 confirming radiotracer studies,6 that the lipid compositions in the bilayer and in the equilibrium surface film are identical. Furthermore, since these are closed systems, it was deduced that dissolved lipid would also have the same composition as the equilibrium surface film and bilayers.5 This deduction could not be verified because the bilayerforming neutral lipids are not sufficiently soluble in water to permit their measurement. In the present study we demonstrate that the water-soluble, ionized, bilayerforming lipids NaDLPG and NaDMPG have similar film properties as the neutral lipids, exhibiting a maximum in the surface pressure at a critical temperature T*; quantitative analysis of the solutions confirms that the composition of the bilayer and equilibrium solution are equal at this temperature. We first derive, from the Gibbs-Duhem equations for a system of binary lipid mixtures of bilayers in equilibrium with solution and surface film, the relationship among the compositions of each of the phases when the surface pressure reaches a maximum at T*. We then demonstrate that the lipid composition of the bilayer and solution follows the predicted thermodynamic relationships. This result is shown to be generally true and independent of the number of lipid components whenever a surface pressure maximum is found. A discussion of the significance of this result for complex mixtures of cell membrane lipids concludes this study. II. Experimental Section A. Materials and Sample Preparation. The sodium salts of dilauroylphosphatidylglycerol (NaDLPG) and dimyristoylphosphatidylglycerol (NaDMPG) (Avanti Polar Lipids, Birmingham, AL), >99 mol %, were used without further purification. Mixtures of these lipids were made by preparing solutions of each component in a solvent consisting of chloroform and methanol (2:1, v/v) and mixing the appropriate ratios to form each required mole fraction. After mixing, the solvent was evaporated overnight under a stream of nitrogen. Water was added to the dried mixtures to a concentration that exceeded the solubility limit of each (6) Tajima, K.; Gershfeld, N. L. Biophys. J. 1985, 15, 203. Fukada, K.; Gershfeld, N. L. J. Phys. Chem. B 1997, 101, 8225.
10.1021/la9911640 CCC: $19.00 © 2000 American Chemical Society Published on Web 01/22/2000
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compound.1 The dispersions were then vortexed and placed in a constant temperature shaking water bath and allowed to equilibrate for a minimum of 4 h; no differences in results were detected for equilibration times that varied from 4 to 24 h. B. Equilibrium Spreading Pressures. The surface pressure of a saturated solution of lipid is the equilibrium spreading pressure, π.7 The temperature dependence of the equilibrium spreading pressure yields thermodynamic properties of the bulk lipid phase.8 Generally the measurement is made by depositing crystals of the lipid on the water surface and, as the lipid spreads to form a monolayer the surface pressure increases. The final surface pressure represents the equilibrium between film and bulk crystal. In the case of NaDLPG and NaDMPG the equilibrium state is the sponge phase,1 a clear, jellylike water-swollen phase that requires several hours to attain. When crystals of the lipids are placed on the water surface, spreading of the lipid to form monolayers was much faster than the rate at which the crystals imbibed water to form the sponge phase. Hence, the surface pressures invariably gave results that were characteristic of partially hydrated crystals and not the equilibrium sponge phase. To obtain films that are in equilibrium with the sponge phase small amounts of concentrated, highly viscous dispersions of the lipids and their mixtures were prepared and were equilibrated at each experimental temperature. The viscous jellies were anchored to the water surface by placing a glass capillary tubing, previously coated with equilibrated sponge phase, in the water surface. A fresh sample was prepared for each experimental temperature. Surface pressures were measured by using the Wilhelmy plate method9 with a sensitivity and reproducibility of (0.2 mN/m. The equilibrium surface pressure is indicated by constant readings for at least 2 h. C. Equilibrium Solubility and Compositions of Bilayer and Solution. To measure the composition of the bilayers and their equilibrium solutions requires separating the two phases and analyzing each for the relative compositions of NaDLPG and NaDMPG. As in previous studies1,2,4 an ultracentrifuge (Beckman model L8-60M) is employed to separate the bulk lipid from the solution using an SW-40 rotor at 40 000 rpm; temperature control is maintained from 0 to 45 ( 0.5 °C. For virtually all lipid compositions a pellet of sedimented bilayer was observed after 20 h of centrifugation. Exceptions were noted at temperatures exceeding 30 °C and mole fractions of NaDLPG >0.9, conditions that required much longer centrifugation times to achieve pellet sedimentation.1 We restricted our experiments to conditions that allowed for centrifugation to be completed within 24 h. Aliquots of solutions were taken at various depths in the centrifuge tube and both the phosphorus content10 and fatty acid composition were measured for each aliquot. The latter was obtained by evaporating a portion of the aliquot and converting the dried phospholipids to their fatty acid methyl esters (FAME) using methanolic solutions of BF3 (Alltech Assoc., Inc., Deerfield, IL). The FAME were assayed by gas chromatography (HewlettPackard, model 5880A). Known mixtures of lauric and myristic methyl esters were used as standards. The pellets were collected and dried, and their FAME compositions were also determined. The mole ratio of the two fatty acid methyl esters in each sample is the mole ratio of the two phospholipids in the sample. Analyses were performed in triplicate with an average error for all mole fractions of (2%. Because the partial molar volumes of the two lipids are likely to differ in both bilayer and aqueous solution, the pressures developed along the length of the centrifuge tubes will influence the lipid composition in each of these phases according to the relation11
(
)
M2 2 2 xt3 1 RT ln b ) M3 - V h3 ω (rt - rb2) 2 V h2 x3
bottom of the centrifuge tube; Mi is the molecular weight of the lipid, and ω is the angular velocity, rad/s. We have tested this dependence in the aqueous solutions by measuring the relative concentrations of NaDLPG and NaDMPG as a function of depth in the centrifuge tube, and found that the dependence on r is small and is approximately of the magnitude of the experimental error (see below). However, we found the dependence of the relative mole fractions of the lipids in the bilayer to be significantly greater than the experimental error in FAME determination. Thus, there is a considerable difference between the mole fraction of NaDLPG in the bilayer pellet at the bottom of the centrifuge tube compared with its mole fraction in the bilayer that would be in equilibrium with the solution at the top of the centrifuge tube. These differences vary with composition of the bilayer and temperature. The equilibrium bilayer composition at the top of the centrifuge tube is obtained by subtracting the solution concentrations of each component from the original dispersion concentration. The mole fractions we seek must be for atmospheric pressure, i.e., r ) 0 at the axis of rotation. Since these depend on values of V h i that are not available, we have been able to calculate the mole fractions in the bilayer at r ) 0 from eq 1 by measuring the mole fraction at rb in the pellet, and the value at rt at the top of the tube. From eq 1, ln xi vs r2 is linear, with constant slope (a function of the partial specific volumes); extrapolation to r ) 0 gives the mole fraction at atm pressure. The relevant dimensions of the SW 40 rotor are as follows: rb ) 15.87 cm; rt ) 6.67 cm.
III. Results A. Thermodynamic Relations for Surface Pressures of Bilayer Mixtures of NaDLPG and NaDMPG. Extreme Values of Surface Pressure and the Relation between Lipid Composition in Bilayers and the Equilibrium Solutions. The system we have chosen consists of mixtures of two bilayer-forming lipids in equilibrium with an aqueous solution containing both lipids and with a film at the air/water surface. In this section the relevant Gibbs-Duhem equations for the coexisting binary lipid states are used to derive the relations between lipid compositions in bilayer, film and solution at T*. There are three coexisting bulk phases: vapor, homogeneous bilayer mixture and solution, and four components: water (1), NaDLPG (2), NaDMPG (3), and air, which is here considered to be nitrogen (4). The Gibbs-Duhem equations for this system are for the surface film
- dπ + Sσ dT + Γ1dµ1 + Γ2dµ2 + Γ3dµ3 + Γ4dµ4 + vσ dp ) 0 (2) for the aqueous solution w w w Sw dT + cw 1 dµ1 + c2 dµ2 + c3 dµ3 + c4 dµ4 +
vw dp ) 0 (3) for the vapor
(1)
The variation in composition xi is a function of the partial specific volumes V h i of the lipids in each phase, and the depth r within the centrifuge tube, with t and b signifying the top and (7) Gaines, G. L., Jr. Insoluble Monolayers at Liquid-Gas Interfaces; Interscience Publ.: New York, 1966; pp 140 ff. (8) Eriksson, J. C. J. Colloid Interface Sci. 1971, 37, 659. Gershfeld, N. L. Annu. Rev. Phys. Chem. 1976, 27, 349.
Sv dT + cv1 dµ1 + cv2 dµ2 + cv3 dµ3 + cv4 dµ4 + vv dp ) 0 (4) (9) Gaines, G. L., Jr. Insoluble Monolayers at Liquid-Gas Interfaces; Interscience Publ.: New York, 1966; pp 45 ff. (10) Rouser, G.; Fleischer, S.; Yamamoto, A. Lipids 1970, 5, 494. (11) MacDougall, F. H. Thermodynamics and Chemistry, 3rd ed.; John Wiley & Sons: New York, 1948; pp 348 ff.
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and for the bilayer
Sb dT + cb1 dµ1 + cb2 dµ2 + cb3 dµ3 + cb4 dµ4 + vb dp ) 0 (5) These four equations describe completely the equilibrium states in terms of all the variables of the experimental system. We seek the relationship between the lipid compositions in the coexisting bilayer, film and solution at T* by solving all four equations simultaneously. They contain seven variables: π, p, T, and the chemical potentials µi of the four componentsswater(1), NaDLPG (2), NaDMPG (3), and air, which is assumed to be nitrogen (4). Since the entire system consists of four components and three phases, from the phase rule there are three independent intensive variables that may be arbitrarily chosen to describe the physicochemical state of this equilibrium system. To solve these equations for the surface pressure π we arbitrarily fix three of these variables: p (atmospheric pressure), T (at the critical temperature T*), and set dµ4 as constant. This leaves four unknown variables: π and µi (i ) 1-3) in the four equations (eqs 2-5). Since the concentration of water associated with the surface film and the bilayers cannot be determined, following Defay et al.,12 we define the relative concentration of water in the monolayer as Γ1,1 ) 0 and, by analogy, define the relative concentration in the bilayer13 as cb1,1 ) 0. The lipid and nitrogen concentrations in the films and bilayers are now defined relative to the concentrations of b 13 . water in these states, using the notation Γi,1, and ci,1 With the lipid concentrations in the vapor phase assumed to be zero, eqs 2-5 are solved simultaneously for dπ using determinants.
|
-1 0 dπ 0 0
0 cw 1 cv1 0
Γ2,1 cw 2 0 cb2,1
| |
Γ3,1 cw 3 ) dµ4 0 cb3,1
-Γ4 -cw 4 -cv4 -cb4
0 cw 1 cv1 0
Γ2,1 cw 2 0 cb2,1
Γ3,1 cw 3 0 cb3,1
|
(6)
For neutral phospholipids (∂π/∂cbi )T,p ) (∂π/∂T)µi,p ) 0 at the critical bilayer temperature T*; these conditions occur only with a specific composition that varies with temperature.5 We make the assumption that the ionized phospholipids behave similarly and ask what the lipid compositions are when dπ ) 0; the determinant on the right-hand side of eq 6 is set equal to zero. This condition is met when
Γ3,1 cb3,1
)
Γ2,1
)
cw 2
cb2,1
(7)
and
cw 3 cb3,1
cb2,1
(8)
These are the predicted compositions at T* for the binary (12) Defay, R.; Prigogine, I.; Bellemans, A.; Everett, D. H. Surface Tension and Adsorption; John Wiley & Sons: New York, 1966; pp 26 ff. (13) The relative concentration of component i in the bilayer, by analogy with the definition of the relative surface concentration in the b b w b monolayer,12 is ci,1 ) cbi - cb1(xbi - xw i )/(x1 - x1 ). When i ) 1, c1,1 ) 0. In general, the amount of water in the bilayer is very low, so that the relative concentration of lipid is very close to the actual concentration.
Figure 1. Equilibrium spreading pressures of mixtures of NaDLPG and NaDMPG as a function of temperature and composition. Mole fractions of NaDLPG are calculated on the basis of anhydrous preparations: (O) 1.0; (4) 0.25; (3) 0.5; (2) 0.75; (b) 0.0.
lipid mixtures in bilayers. For neutral phospholipids eq 7 has been verified by radiotracer measurements of the surface density of the lipids.6 Equation 8 signifies that the concentration of each lipid in solution is proportional to its concentration in the bilayer b cw i ) kci,1 (i ) 2, ..., C - 1)
(9)
the relation deduced for neutral lipids.5 In the present study, we demonstrate the validity of eqs 8 and 9 at T* by measuring the composition of the solutions in equilibrium with bilayers composed of mixtures of NaDLPG and NaDMPG as a function of temperature. We begin by showing that the equilibrium spreading pressure of bilayers containing mixtures of NaDLPG and NaDMPG in water have a maximum at a temperature T* that depends on the lipid composition of the bilayer. B. Surface Pressure-Composition-Temperature Relations for Lipid Mixtures in Bilayers and in Solution. Figure 1 shows the surface pressure-temperature relations for NaDLPG and NaDMPG and their mixtures. For each composition a maximum in the surface pressure occurs at a specific temperature T*, and it varies with composition. Thus, the ionized lipids show a T*composition dependence that is similar to the one exhibited by neutral phospholipids.5 According to the results obtained with neutral lipids, a plot of T* as a function of bilayer composition falls on a line, and along this line eq 7 is obeyed. Our present goal is to establish that eq 8 is also valid, i.e., that at T* the lipid compositions in the bilayer and in the equilibrium solution are identical. We have measured bilayer and solution compositions for a number of lipid mixtures at three temperatures: 22, 25, and 28.5 °C. According to the thermodynamic theory presented, at each of these temperatures there will be a single point where the composition of the solution and the bilayer are identical. The results are shown in Figure 2 where, for each temperature, there is a single composition where the bilayer and equilibrium solution are identical; this composition varies with temperature. Since we have derived eqs 7 and 8 assuming that these compositions will occur at the surface pressure maximum (dπ ) 0), the variation of this composition with temperature must lie on the same line describing the T*-composition relation obtained from the surface pressure maximum measurements of Figure 1. Comparison of the results in Figure 2 with those obtained by equilibrium spreading pressures
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Figure 3. T* as a function of composition of NaDLPG and NaDMPG mixtures; mole fraction of NaDLPG calculated excluding water. Since the bilayer and solution lipid compositions are predicted to be identical at each T* (eq 8), no distinction is made between solution and bilayer. T* from: (O) surface pressure maximum (Figure 1); (b) temperature where lipid composition of bilayer and solution are identical (Figure 2). The line is a second-order polynomial fit of all the data; r ) 0.975.
(Figure 1) are shown in Figure 3, where both sets of data fall sensibly on the same line. Along this line, unilamellar vesicles form. Below this line, the sponge phase exists, while above this line multilamellar vesicles form. At 15 °C, below the critical temperature T* for each of the pure components, there is no mixture where the lipid composition of the bilayer and solution are equal (data not shown). Discussion
Figure 2. Comparison of the compositions of mixtures of NaDLPG and NaDMPG in bilayers in equilibrium with B S solutions. nDLPG /nB and nDLPG /nS are the equilibrium lipid fractions of NaDLPG in the bilayer and solutions, respectively, with nB and nS being the corresponding total lipid amounts. Identical lipid compositions in bilayer and solution are indicated by the dashed line. At each temperature there is only one composition where the lipid compositions are equal; it is the composition that is predicted to form the critical bilayer state at the indicated temperature.
Our results show that the surface pressure maximum obtained with dispersions of lipid bilayers is a general phenomenon that occurs with ionized and neutral phospholipids alike. Thus, although neutral phospholipids such as phosphatidylcholines do not form a sponge phase, they share all the other properties associated with the surface pressure maximum at T*. These properties of the bilayers at T* represent a unique condition where unilamellar vesicles form2,6 and where the lipid composition becomes uniform throughout the system of surface film, solution and bilayer. The uniform distribution of lipid also suggests that the interaction between water and the bilayer at T* is distinctly different than the interaction at temperatures above and below T* when conditions are not at criticality. The formation of this singular bilayer state does not depend on the presence of an air/water surface but is a condition of the bilayer at this temperature as evidenced by the presence of special bulk properties at T*. Thus, anomalous lateral diffusion of a fluorescent probe characteristic of probe diffusion at fluid critical points,14 a heat capacity anomaly,15 and special mechanical properties16 have been observed for lipid bilayers at T*. There is an additional property associated with T*. The determinant of the right-hand side of eq 6 is zero at the same time that the determinant on the left is zero. This (14) Jin, A. J.; Edidin, M.; Nossal, R.; Gershfeld, N. L. Biochemistry 1999, 38, 13275. (15) Gershfeld, N. L.; Mudd, C. P.; Tajima, K.; Berger, R. B. Biophys. J. 1993, 65, 1174. (16) Gershfeld, N. L.; Ginsberg, L. J. Membr. Biol. 1997, 156, 279.
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signifies that there are an infinite number of solutions to eq 6 that involve the compositions of the lipids in the various equilibrium phases. The significance of this result may be more easily recognized if the masses of the individual components are substituted for the concentrations in eq 6. For this closed system, where the total amount of each component is fixed, a complete description of the state requires fixing the amount of each component in all of the equilibrium phases. While the physicochemical state of this system is completely described by T*, p, and µi, the amount of lipid in each state cannot be ascertained. There are an infinite number of combinations of the masses of each of the coexisting phases that will satisfy eqs 7 and 8. Accordingly a transfer of material from bilayer to surface or solution will not change the composition of any of the equilibrium phases, although the masses of each of the coexisting phases will change. For example, if the area of the air/water interface is increased, lipid from the bilayer and/or solution would be transferred to the surface to maintain the equilibrium surface pressure without any change in composition of any of the phases. Moreover, if the vapor space is increased and water from the solution evaporates to maintain equilibrium partial pressure, some of the dissolved lipid will necessarily precipitate as bilayer to maintain equilibrium. Again this transfer of lipid from solution to bilayer will occur without any change in lipid composition. This condition exists only at T*. Other physicochemical systems, such as the azeotropes, exhibit this property; these have been called states of indifference,17 and the critical bilayer state is another example of this general class of systems. As we have seen and have confirmed by more conventional solution methods, the surface pressure maximum provides a rigorous and general method for identifying T*. This approach has been applied to bilayer dispersions of the multicomponent lipid mixtures from cell membranes; a unique surface pressure maximum and a corresponding T* have been obtained for each of these (17) Prigogine, I.; Defay, R.; Everett, D. H. Chemical Thermodynamics; Longmans Green and Co.: London, 1954; pp 468 ff.
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complex mixtures.18 In each instance T* has been shown to equal the growth or physiological temperature Tg of the cells from which the lipids have been obtained. With (dπ/ dT) ) 0 at T*, equivalent relations among the components of the complex mixtures as in eq 9 may be derived.19 It is now also evident why each of these complex lipid mixtures yields only a single critical temperature. For C components in a complex mixture of membrane lipids and P bulk phases there are C - P + 2 independent intensive variables that must be fixed to describe the physicochemical state of the dispersed state of the system. At T* there are the C - 2 relations of eq 9 among the components leaving 4 - P variables remaining to be defined. For a dispersion of membrane lipids with P ) 3 (air, solution, and bilayer) this leaves only one intensive variable that may be arbitrarily chosen, independent of the number of components. Therefore, with constant (atmospheric) pressure and a constant bilayer lipid composition, the temperature of the surface pressure maximum, T*, a singularity, completely defines the state of the system. In practice, T* may be obtained by maintaining a fixed lipid composition and varying the temperature as shown in Figure 1 and as observed with the more complex lipid mixtures.18 The critical point occurs at the surface pressure maximum or at the point when each lipid component in solution is proportional to its composition in the bilayer phase. Alternatively, the temperature may be kept constant, and the composition of one of the lipid components varied until dπ ) 0, at a minimum, maximum, or horizontal point of inflection; at this point the lipid components will conform to eq 9, and the temperature will be T* for this composition. LA9911640 (18) Gershfeld, N. L. Biophys. J. 1986, 50, 457. Ginsberg, L.; Gilbert, D. L.; Gershfeld, N. L. J. Membr. Biol. 1991, 119, 65. Ginsberg, L.; Gershfeld, N. L. Neurosci. Lett. 1991, 130, 133. Tremper, K. E.; Gershfeld, N. L. J. Membr. Biol. 1999, 171, 47. (19) Defay, R.; Prigogine, I.; Bellemans, A.; Everett, D. H. Surface Tension and Adsorption; John Wiley & Sons: New York, 1966; pp 118 ff.
