Pressure Induced Cubic-to-Cubic Phase Transition in Monoolein

J. Phys. Chem. B 2001, 105, 3109-3119

3109

Pressure Induced Cubic-to-Cubic Phase Transition in Monoolein Hydrated System Michela Pisani,† Sigrid Bernstorff,‡ Claudio Ferrero,§ and Paolo Mariani*,† Istituto di Scienze Fisiche and INFM, UniVersita´ di Ancona, Via Ranieri 65, I-60131 Ancona, Italy; Sincrotrone Trieste S.C.p.A. Strada Statale 14, km 163.5, I-34016 BasoVizza (Trieste), Italy, and European Synchrotron Radiation Facility, POB 220, F-380 Grenoble Cedex, France. ReceiVed: April 20, 2000; In Final Form: NoVember 27, 2000

Synchrotron X-ray diffraction has been used to investigate structure, stability, and transformation of the Pn3m bicontinuous cubic phase in the monoolein-water system under hydrostatic pressure. As a first result, it appears that the full-hydration properties of monoolein are strongly related to the pressure. Moreover, the experimental results show the occurrence of a Pn3m to Ia3d cubic phase transition when the mechanical pressure increases to 1-1.2 kbar, depending on the water concentration. The underlying mechanism for the phase transition has been then explored in searching for relationships between the structural parameters derived from the two cubic phases. The emerging picture is a change in the basic geometrical shape of the monoolein molecule during compression. Moreover, the analysis of the position of the pivotal surface indicates that the interface is bending and stretching simultaneously as a function of pressure. Because the lipid concentration is rather low and the external pressure increases the cell sizes, thus reducing the principal curvatures, a tentative analysis of the pressure effects on the energetics of these structures has been exploited. A simple theoretical model based on curvature elastic contributions has been used: calculations show that increasing the pressure the spontaneous curvature H0 of the monoolein tends to zero, whereas the ratio between the monolayer saddle splay modulus and the monolayer splay modulus kG/k increases to 1. Moreover, the curvature elastic energy appears to reduce progressively as a function of pressure, indicating that in these conditions, the curvature elasticity does not dominate the total free energy.

Introduction Phase behavior and structural properties of monoacylglycerides in water have been investigated for a long time, because they exhibit an extended polymorphism.1-6 In particular, monoolein in water shows several mesophases, characterized by a highly disordered conformation of the hydrocarbon chains.1,3,5 The monoolein temperature-concentration phase diagram is reported in Figure 1: a lamellar structure LR, where lipid molecules assemble into stacked sheets, an inverted (type II) hexagonal phase HII, which consists of cylindrical structure elements packed in a 2-D hexagonal lattice, and two bicontinuous inverted cubic phases with space group Pn3m (Q224) and Ia3d (Q230) have been identified.1,3,7 The structure of bicontinuous cubic phases has been described in terms of Infinite Periodic Minimal Surfaces (IPMS),8,9 that is, infinite arrays of connected saddle surfaces with zero mean curvature at every point on the surface. In inverse structures, lipid monolayers are draped across either side of the minimal surface, touching it with their terminal methyl groups; this results in a threedimensional periodic bicontinuous structure, formed by distinct water and lipid volumes. The crystallographic space group of the cubic phase determines the type of the IPMS; in particular, the cubic phases observed in the monoolein-water system (space groups Ia3d and Pn3m) are based on G (Gyroid) and D (Diamond) surfaces, respectively (see Figure 2).3,7,10 * To whom correspondence should be addressed. Tel: 39 071 2204608. Fax: 39 071 2204605. E-mail: [email protected]. † Istituto di Scienze Fisiche and INFM, Universita ´ di Ancona. E-mail: [email protected], [email protected]. ‡ Sincrotrone Trieste S.C.p.A. E-mail: [email protected]. § European Synchrotron Radiation Facility. E-mail: [email protected].

Figure 1. Phase diagram of the monoolein-water system at ambient pressure (redrawn from Briggs et al.5). The concentration c is expressed as weight of water per weight of mixture. Phases are labeled as in the text; FI stands for fluid isotropic.

Pressure effects on lipid structures have been sparingly investigated.11 In the case of monoacylglycerides, the pressuredependent phase behavior has been the object of a few works. Winter and co-workers12 studied the phase behavior of monoolein and monoelaidin in excess water by X-ray and neutron diffraction. It was found that the cubic Pn3m phase observed in monoolein in fully hydrated conditions extends in a pure domain over a large phase region in the temperature-pressure plane (up to 2 kbar at 20 °C). Synchrotron X-ray diffraction was also used to investigate the polymorphism of monoolein at low hydration (water concentration of 0.25 w/w) under hydro-

10.1021/jp001513v CCC: $20.00 © 2001 American Chemical Society Published on Web 03/20/2001

3110 J. Phys. Chem. B, Vol. 105, No. 15, 2001

Figure 2. Representation of the unit cell structure of the Pn3m, symbol Q224 (upper frame) and of the Ia3d, symbol Q230 (lower frame) cubic phases. For reasons of clarity, we show only the bilayer midplane (i.e., the underlying periodic minimal surfaces, D and G, respectively). Courtesy of S. Hyde and S. Ramsden, Department of Applied Mathematics, Australian National University, Canberra, Australia.

static pressure up to 10 kbar.13 The results showed a large coexistence of the cubic Ia3d and lamellar LR and Lc phases at all the investigated pressures before the transition to the pure Lc lamellar phase occurs. Even if changes in phase composition of the competing structures were not excluded, the observed phase sequence and unit cell pressure dependence were discussed using simple molecular packing arguments, based on changes in the molecular wedge shape of monoolein.14 By increasing pressure, the lipid chain order parameter is increased, and thus, the monoolein molecular wedge shape reduced. This results in an enlargement of the unit cell size of the cubic phases because of a decreased curvature of the lipid bilayer.12,13 Moreover, the more cylindrical molecular shape leads to the formation of the lamellar LR phase or to the Lc phase, which have the higher lipid packing density. As expected, this structure was detected to be practically incompressible.13 Pressure can be also used as a suitable thermodynamic variable to obtain information on the energetic and stability of lipid phases.11-13 In fact, several attempts to determine the energetic of bicontinuous cubic phases from structural data and to give both a qualitative and a quantitative explanation for their location within the temperature-concentration phase diagram have been reported.15-19 In particular, the curvature elastic energy is believed to be a crucial factor governing the stability of such phases: assuming that bicontinuous cubic phases are correctly described in terms of IPMS, a simple curvature free energy elastic model, which includes a mean and a Gaussian curvature term, has been described.20 Improvements of the original model have been proposed. To correctly describe the interfaces of the cubic phases when the degree and the variance of the mean and Gaussian curvatures are high, the curvature

Pisani et al. elastic energy has been re-expressed as a high order polynomial expansion of the principal curvatures.18 However, it has been also shown that the inhomogeneity in the curvature can give rise to lateral packing frustrations,21 which will be the worst when the lipid concentration is the greatest. A further complicating factor for the description of the energetic of bicontinuous cubic phases with high interfacial curvature is that the distance between sections of monolayers facing each other across a water channel can be quite small. This means that van der Waals attraction and hydration repulsion will play a significant role in stabilizing the phase. Because neither of these effects has been accounted for in any modeling of bicontinuous cubic phases, the meaning of the curvature elastic parameters that can be extracted from structural data remains elusive. According to Templer and co-workers,18 most of the problems mentioned above become less tough when structural data, obtained at low lipid concentrations and from systems with low curvatures, are considered. In this conditions, the terms in the free energy expansion greater than quadratic in the principal curvatures can be neglected and the obtained curvature elastic parameters could become meaningful. In this work, we take advantage of the well-known structural properties of monoolein in order to extensively study the pressure effects on the Pn3m bicontinuous cubic phase over a relatively wide concentration and pressure range. As a Pn3mIa3d cubic-to-cubic phase transition has been detected to be induced by mechanical pressure, the underlying mechanisms for the phase transition have been explored to establish relationships between the structural data derived from the two phases. Because the external pressure increases the cell sizes, reducing the curvatures, a tentative analysis of the curvature elastic parameters to prove theoretical models for the energetic of bicontinuous cubic structures and to understand the pressureinduced phase behavior has finally been carried out. Materials and Methods The monoacylglyceride 1-monoolein was obtained by Sigma Chemical Co. (Milano, Italy) with a purity of >99% and used without further purification. Monoolein-water samples of concentrations ranging from c ) 0.35 to c ) 0.40 (c being the water weight concentration), the range at which the cubic Pn3m phase exists at ambient temperature and pressure, were considered. Samples were prepared by mixing the lipid with appropriate amounts of bidistilled water in small weighing bottles and were equilibrated in the dark for 1 day at ambient temperature and pressure. No water loss was detected before the hydrated lipids were mounted into the pressure cell. Moreover, after the X-ray scattering experiments, the water composition of each sample was checked again by gravimetric analysis. The differences between the nominal and the concentration measured after the pressure cycle were detected to be in the limit of the experimental errors. Diffraction measurements were performed at the SAXS beamline of the Elettra Synchrotron Light Source, Trieste (Italy). The wavelength of the incident beam was λ ) 1.54 Å, and the explored s range extended from 0.005 to 0.05 Å-1 (s ) 2 sinθ/ λ, where 2θ is the scattering angle). An additional wide-angle X-ray scattering (WAXS) detector was used to simultaneously monitor diffraction patterns in the range from 0.11 to 1 Å-1. For pressure experiments, we used the pressure-control system designed and constructed by M. Kriechbaum and M. Steinhart.22 The pressure cell has two diamond windows (3.0 mm diameter and 1 mm thickness) and allows us to measure diffraction patterns at hydrostatic pressures up to 3 kbar.

Phase Transition in Monoolein Hydrated System

J. Phys. Chem. B, Vol. 105, No. 15, 2001 3111

X-ray diffraction measurements were performed at 25 °C for different pressures, from 1 bar to 3 kbar, with steps of about 100 bar. To avoid radiation damage, the exposure time was 2-5 s/frame, and a lead shutter was used to protect the sample from excess radiation within periods where no data were recorded. Particular attention has been devoted to check for equilibrium conditions and for radiation damage: in several cases, measurements were repeated several times (up to 200) at the same constant pressure to account for stability in position and intensity of the Bragg peaks. Accordingly, a gentle compression of the sample, at a rate of 0.5-2 bar/s, was observed to ensure the establish of equilibrium conditions, also in the regions of phase coexistence. In all cases, once stabilized, the pressure (in a few minutes), the X-ray diffraction measurements were repeated at least 2 times, with an interval of at least 5 min. In each experiment, a number of sharp, low angle reflections were observed and their spacings measured following the usual procedure.3,23 In all of the cases discussed in this paper, a diffuse band in the (3-5 Å)-1 region of the scattering curves indicates the disordered (type R) nature of the lipid short-range conformation. Low angle diffraction profiles were indexed using equations which define the spacing of reflections for the different symmetry systems usually observed in lipid phases (lamellar, hexagonal, or 3-dimensional cubic lattices): the indexing problem was easy to solve, because in no case were extra peaks, which can be ascribed to the presence of unknown phases or to crystalline structures, observed. In the present experimental conditions, three different series of low-angle Bragg reflections were observed and indexed according to the Ia3d cubic space group (spacing ratios x6: x8: x14: x16: x20: x22...), to the Pn3m cubic space group (spacing ratios x2: x3: x4: x6: x8: x9: x10...) and to the lamellar one-dimensional symmetry (spacing ratios 1:2:3...). Once the symmetry of the lipid phase was found, the dimension of the unit cell was calculated. In the following, a indicates the unit cell dimension. The other parameter necessary for determining the internal dimensions of the phases is the water (or lipid) volume fraction. The water volume fraction φw was determined as usual3,15,23 from the sample weight composition, using the density of both the monoolein and water, FMO and Fw, respectively

φw )

c Fw c + (1 - c) FMO

(1)

In the present case, we used FMO ) 0.942 g cm-3 and Fw ) 1.0 g cm-3, respectively,24 under the assumption that densities are largely unaffected by pressure. Even if the previously detected incompressibility of the lamellar phase at high pressure13 ensures that the molecular volumes play a small role in the unit cell variations induced by pressure, it should be point out that using constant partial densities for monoolein and water as a function of pressure imparts a systematic error in the determination of molecular geometry. Results Phase Behavior and Pressure Dependence of the Unit Cell Dimension. Selected low-angle X-ray diffraction patterns, showing a number of reflections, are reported in Figure 3. By analyzing the spacing ratios of the low angle diffraction peaks, the structure of the lipid phases was identified and the unit cell dimensions determined.3 At all the investigated concentrations (from c ) 0.35 to c ) 0.4), the X-ray diffraction profiles confirm the presence of the

Figure 3. Low-angle X-ray diffraction profiles from monoolein samples at concentrations c ) 0.364 (φw ) 0.35), c ) 0.393 (φw ) 0.379) and in excess water. Each experiment has been performed at the indicated pressure. Peaks are indexed according to the cubic Pn3m and Ia3d or to the 1-D lamellar space groups3.

Pn3m cubic phase at ambient pressure.3 However, a different pressure dependent phase behavior was detected for the less hydrated samples and the sample prepared in excess water (c ≈ 0.4, at ambient pressure). As illustrated in Figure 3, in the diffraction profiles of the fully hydrated monoolein sample, a Bragg peak centered at s ) 0.02 Å-1 emerges at a pressure of about 700 bar. The intensity of this peak increases as far as the pressure increases, whereas the Pn3m characteristic reflections reduce in intensity; at ∼1100 bar, only the diffraction peak at about s ) 0.02 Å-1 remains. According to the results reported by Czeslik and co-workers,12 the transition can be ascribed to the conversion from the cubic Pn3m phase to a lamellar phase with a lattice spacing of about 49 Å. As no extra peaks were observed in the wide-angle region, the lamellar phase was identified as a liquid-crystalline LR phase. Remarkably, the Pn3m-LR phase transition occurs over about 400 bar. As it can be deduced from the X-ray diffraction profiles reported in Figure 3, all the samples prepared in less hydrated conditions exhibit a cubic-to-cubic phase transition, from the Pn3m to the Ia3d cubic phase. During compression, at about 1 kbar and within a relatively narrow pressure range, two series of Bragg reflections, which can be properly indexed considering the Pn3m and Ia3d cubic lattices, occur. It should be noticed that scattering data obtained at these intermediate pressures indicate that the two cubic phases coexist in a thermodynamic equilibrium. As shown in Figure 4, in the biphasic region, the intensity and the position of the diffraction peaks measured at constant pressure, do not change as a function of time, at least for the first 60 min. By further increasing the pressure, the Pn3m cubic phase disappears and only the diffraction peaks corresponding to the Ia3d cubic phase are still detected. The typical profile of a pure Ia3d cubic phase is then observed up to about 2 kbar, and no evidence for other phase transitions is stated. This result can be compared with previous measurements on a very dry sample (c ) 0.25), which showed that the region of coexistence of the Ia3d and LR phases extends from very low pressure (a few hundred bar) up to 4.5 kbar.13 In Figure 5, the pressure at which the Pn3m and Ia3d phase transition occurs is reported as a function of concentration. In the graph, the error bars account for the extension of the twophase region. Data are scattered, but the trend is quite clear (see the tentative linear fit to the data in Figure 5); whereas increasing the lipid concentration, the Pn3m-Ia3d transition occurs at lower pressure. Moreover, the limited extent of the cubic-cubic two-phase region (the average value is around 240 bar) should be compared with the one of the lamellar-cubic twophase region.


Pisani et al.

Figure 4. X-ray diffraction profiles from monoolein samples at two different concentrations and at a fixed pressure (top: c ) 0.364, φw ) 0.35, pressure 0.9 kbar; bottom: c ) 0.393, φw ) 0.379, pressure 0.9 kbar) as a function of time. The spectra have been recorded every 5 min.

Figure 5. Composition dependence of the pressure range at which the Pn3m-Ia3d cubic-to-cubic phase transition occurs. For the sample prepared in excess water, the transition is from the Pn3m cubic to LR lamellar phase. Note that this point is plotted versus the nominal sample composition at ambient pressure (see text for more details). The dependence of the phase transition pressure on the water volume fraction is assumed to be linear; the best fit parameters are a0 ) 0.397 kbar and b ) 1.94 kbar φw -1.

The observed variations of the unit cell dimension with the hydrostatic pressure are shown in Figures 6 and 7. According to previous measurements,11-13 the unit cell of the different lipid phases increases during compression. This fact has been related to a continuous change in shape of the lipid molecule due to the increase of the chain order parameter induced by pressure. In the less hydrated conditions (see Figure 6), the unit cell of both the Pn3m and Ia3d cubic phases increases almost linearly as a function of pressure. A linear fit to the data has then been used to determine the pressure dependence da/dP; the obtained values are reported in Figure 8 as a function of concentration. In the Pn3m cubic phase, the da/dP parameter is practically independent of the concentration; the average value is 4.3 ( 1.1 Å kbar-1, which can be satisfactory compared with the value of 7 Å per kbar reported by Czeslik and co-workers.12 In the Ia3d phase, the slope of the a versus P curves is larger and clearly depends on concentration. This strong pressure dependence was not detected in a less hydrated sample (c ) 0.25) previously investigated, but in that case, the Ia3d cubic phase was existing in a biphasic region.13 Therefore, for the sake of confirmation, the unit cell pressure dependence recently ob-

Figure 6. Pressure dependence of the unit cell dimensions of the cubic Pn3m and Ia3d phases in monoolein samples at different composition. The water volume fraction φw is indicated in each frame. The lattice parameter variation per unit pressure (da/dP) is also indicated.

served25 in equilibrium conditions in a pure Ia3d phase at the concentration c ) 0.26 and in the pressure range from 1 to 1.2 kbar is also reported in Figure 8. In the presence of bulk water, the unit cell of the Pn3m cubic phase is found to be strongly pressure dependent (see Figure 7); moreover, the dependence is quadratic. The temperatureconcentration phase diagram of the monoolein in water (see Figure 1) shows that the composition of the fully hydrated Pn3m cubic phase ranges from c ) 0.25 to c ) 0.49 at 92 °C and 0 °C, respectively. Increasing the pressure has the same effect on the lipid as decreasing the temperature. Therefore, we expect that the excess water boundary of the Pn3m phase would change during compression, determining a change in the monoolein full hydration values which can account for the unusual increase of


Figure 7. Pressure dependence of the unit cell dimensions of the cubic Pn3m and lamellar LR phases in the monoolein sample prepared in excess water. The cubic lattice parameter dependence on pressure is quadratic; the best fit parameters are a0 ) 103.5 Å, b ) 12.8 Å kbar-1, and c ) 7.53 × 10-3 Å kbar-2.

J. Phys. Chem. B, Vol. 105, No. 15, 2001 3113 temperature but also to the pressure. Quantitatively, from the fully hydration concentration, we calculate that during compression up to about 1 kbar, the number of water molecules per fully hydrated monoolein molecule increases from about 13 to 24. Structural Parameters. Assuming distinct water and lipid regions within the cell, the internal structural dimensions of lipid-containing phases can be calculated from unit cell dimensions and sample concentrations.3,5,15,23 In the case of cubic bicontinuous phases, a model describing the structure should be considered.9 Here, the lipid monolayer thickness, the curvature parameters, and the lipid cross sectional area have been determined considering that Pn3m and Ia3d cubic structures are described as lipid bilayers draped across the IPMS. According to Turner and co-workers,15 the monolayer thickness l, considered constant throughout the structure, can be calculated using

(1 - φw) ) 2 σ (l /a) + 4/3 π χ (l /a)3

(2)

where σ and χ are the constants for the minimal surface and have values specific to each bicontinuous cubic phase26 (Ia3d: σ ) 3.091, χ ) -8; Pn3m: σ ) 1.919, χ ) -2). The unit cell surface area at the headgroup A, that is, at the lipid-water interface, which is assumed to be parallel to the minimal surface, can be obtained using

A ) A0 (1 + 〈K〉0 l2) Figure 8. Cubic lattice parameter variation per unit pressure (da/dP) versus water volume fraction φw. The lines are only guides to the eye to show the general trends.

where 〈K〉0 is the surface averaged Gaussian curvature on the minimal surface (the surface average is necessary because the curvature of the underlying minimal surface is inhomogeneous) and A0, defined as σa2,is the area of the minimal surface within the unit cell. 〈K〉0 is related to the lattice parameter through the Gauss-Bonnet theorem

〈K〉0 ) 2πχ/(σ a2)

Figure 9. Calculated water weight concentrations of the Pn3m phase of monoolein at full hydration versus pressure.

the lattice parameter. Assuming that the pressure dependence in the Pn3m unit cell is constant and equal to 4.3 Å kbar-1, as detected in the less hydrated samples, the location of the excess water line in the concentration-pressure dependent phase diagram can be obtained. In practice, the 4.3 Å kbar-1 pressure contribution has been subtracted from the experimentally observed unit cell to derive the lattice dimensions that are dependent only on composition. These values have been then converted in water concentration using cell dimensions measured at ambient pressure as a function of water content.5,6 Due to the occurrence of a phase transition at higher pressures, these calculations were performed only in the single-phase region. The final result is reported in Figure 9; up to about 200 bar, the composition of the Pn3m in fully hydrated conditions is quite constant (around cexe)0.395), whereas the excess water boundary increases rather linearly in the pressure range from 200 to 800 bar. Therefore, as expected, the hydration properties of monoolein appear to be strongly related not only to the

(3)

(4)

The area-per-molecule Amol at the lipid-water interface can be obtained by dividing A by the number of lipid molecules in the unit cell, (1 - φw) a3/2V, where V is the lipid molecular volume. Other parameters, that are also necessary to describe a complete curvature free energy for the lipid layer (see below), are the Gaussian 〈K〉 and the mean 〈H〉 curvatures at the lipidwater interface, both averaged over the unit cell. Their values can be calculated using15,26

〈K〉 ) 2πχ/A 〈H〉 ) 2π χ l/A

(5)

Note that the sign of the mean curvature is taken to be negative when the lipid headgroup surface bends toward the aqueous phase. This means that the cross-sectional area per lipid increases from the head to the tail, reducing to zero at the center of the water channel. The area-per-lipid and the curvature parameters can be evaluated on a surface parallel to the minimal surface and at any distance from it (i.e., at any point along the lipid length) only by adjusting the value of l in eqs 3 and 5. This is an important point because it has been observed that in some cases a surface, approximately parallel to the underlying minimal surface, exists about which the average molecular area does not vary upon bending by hydration. This is the neutral surface which has permitted to model the effect of water content on


Pisani et al.

Figure 10. Pressure dependence of the structural parameters of the Pn3m and Ia3d cubic phases in monoolein samples at three of the analyzed compositions. The water volume fractions, φw, are indicated at the top of each column. l is the thickness of the lipid monolayer, Amol is the areaper-lipid at the water-lipid interface, and 〈K〉 and 〈H〉 are the average over the unit cell of the Gaussian and of the mean curvature, respectively, calculated at the water-lipid interface. Lines are guides to the eyes to show the general trends.

the geometry of the inverse bicontinuous cubic phases and to calculate the curvature energy as a function of concentration.17,18 In Figure 10, the monolayer thickness (l), the area-permolecule at the headgroup, Amol ) 2 AV/(1 - φw)a3, and the average over the unit cell of the mean and of the Gaussian curvatures at the same surface are shown as a function of pressure for three of the investigated concentrations. It should be noticed that, except for the sample prepared in the presence of excess water, all the calculations have been performed under the assumption that, during a pressure cycle, the water content is the same in all the phases, and equal to the sample nominal concentration. The data obtained from samples prepared in less hydrated conditions clearly confirm that pressure induces a reduction of the curvatures of the lipid layer and a decrease of the cross-sectional monoolein area at the lipid-water interface. Accordingly, the monolayer thickness enlarges. One point should be stressed: the variation of the curvature parameters is rather continuous, even when the phase boundary is crossed. On the contrary, the monolayer thickness and the area-per-molecule at the water-lipid interface show a large discontinuity in correspondence of the Pn3m - Ia3d phase transition. For the sample analyzed in the presence of bulk water, the calculations were performed using the concentration of the fully hydrated Pn3m cubic phase estimated as discussed before and reported in Figure 9. Some of the obtained parameters (see again Figure 10) show an unusual pressure dependence: in particular, the lipid thickness decreases as a function of pressure and, accordingly, the cross-sectional area at the lipid-water interface

increases. Because in the coexistence region a large composition adjustment follows any pressure change, we suggest that hydration effects should overrule the increase of the chain order parameter induced by compression. The concentration dependence of the structural parameters at constant pressure has been also considered. To have illustrative results, we used interpolated Pn3m and Ia3d cells; the results are reported in Figure 11. At all the pressures, the monolayer thickness reduces by increasing the water volume fraction, whereas the area-per-molecule increases. Moreover, the concentration dependence of the 〈K〉 and 〈H〉 parameters indicates that the curvature lowers when the water fraction increases. It is interesting to observe that at the phase transition pressure (see data at 1 kbar), the discontinuity between l and Amol parameters for the Pn3m and the Ia3d phases is confirmed, whereas very similar values for the mean and Gaussian curvatures are observed. To obtain information on the very existence of the neutral surface, we used the cubic equation derived by Templer and co-workers19

()

()

An 3 3 An 2 a2 a + 6A0 V V (1 - φw)

[

()

]

32A03 36πχ Vn 2 + ) 0 (6) (1 - φw) V (1 - φw)3

where An is the molecular area at the pivotal plane, and Vn is


J. Phys. Chem. B, Vol. 105, No. 15, 2001 3115

Figure 11. Composition dependence of the structural parameters of the Pn3m and Ia3d cubic phases calculated at three different pressures. The considered pressures are indicated at the top of each column. Notations and symbols as in the text and Figure 10. It should be noticed that the reported curves have been calculated using Pn3m and Ia3d cubic cells interpolated from experimental data versus concentration and pressure.

the molecular volume between this plane and the end of the chains. Because the pivotal surface is defined to be the location on the molecule whose area is invariant upon isothermal bending and the mass of lipid either side of the pivotal surface remains fixed as the interface bends, eq 6 can be used to derive the pivotal surface geometry (i.e., the An and Vn values) by fitting the unit cell as a function of the water volume fraction. The results of the fitting procedures, performed at different pressures, are reported in the Figures 12 (best fit curves) and 13 (fitting parameters). As a comparison, the fit has been also applied to previous data on the Ia3d phase obtained at ambient pressure and low hydration3; the best fit curve is reported in the insert of Figure 12. Two points can be underlined. First, the fit to high pressure Ia3d data, also performed excluding the point at φw ) 0.379, is far from to be satisfactory. Second, the derived area and volume of the pivotal surface are rather astonishing, especially if compared with the values determined at low hydration and at ambient pressure for the Ia3d cubic phase. In such experimental conditions, the pivotal surface is located at about 9 Å from the IPMS, and the geometrical parameters are An ) 37.0 Å2 and Vn ) 350 Å3 (Vn/V ) 0.56), respectively. This volume compares well with the value of 478 Å3 (Vn/V ) 0.76) reported by Templer and co-workers.18 Fitting the high pressure Ia3d data but also the Pn3m data obtained from ambient to about 1 kbar, it is by contrast derived that the location on the molecule whose area undergoes the smaller variation during bending practically corresponds to the minimal surface. As shown in the Figure 13, the fitted Vn are in fact only few Å3

Figure 12. Best fit curves obtained applying eq 6 to Pn3m and Ia3d data. The corresponding chi-squares are 0.89 (Pn3m data at 1 bar), 0.26 (Ia3d data3 at 1 bar, see the insert), 0.14 (Pn3m, 0.4 kbar), 0.14 (Pn3m, 1 kbar), 2.8 (Ia3d, 1 kbar), 2.4 (Ia3d, 1.4 kbar), 3.4 (Ia3d, 1.8 kbar). The experimental pressures are indicated in each frame.

(Vn/V ≈ 5 × 10-3). This position is extremely unphysical and therefore indicates that it is most likely that the interface is bending and stretching simultaneously under compression.


Figure 13. Pressure dependence of the fitting parameters obtained applying eq 6 to Pn3m and Ia3d data. Vn is the molecular volume between the IPMS and the pivotal plane and An is the molecular crosssectional area at this plane. Open squares refer to volumes obtained fitting Ia3d data with the exclusion of the points at φw ) 0.379 (the corresponding chi-square reduces to 0.17 at 1 kbar, 0.06 at 1.4 kbar and 0.57 at 1.8 kbar). In the lower frame lines are guides to the eyes.

Discussion The pressure effects on the structure and stability of the Pn3m bicontinuous cubic phase in the monoolein-water system have been investigated using synchrotron X-ray scattering. The observed diffraction data, reported in Figure 3, indicate a different phase behavior for the Pn3m sample prepared in excess water (full hydration condition, c ≈ 0.4 at ambient pressure) and for the Pn3m samples prepared in less hydrated conditions (from c ) 0.4 to c ) 0.34). In excess water, a phase transition from the Pn3m cubic to the lamellar LR phase at about 0.7 kbar has been observed, whereas a Pn3m to Ia3d cubic-to-cubic phase transition occurring when the external pressure increases up to about 1-1.2 kbar was detected in the less hydrated samples (see Figure 5, and compare with the monoolein phase diagram of Figure 1). Moreover, in such conditions, no other phase transitions were detected by further increasing pressure (up to about 2 kbar). Considering that in a very dry monoolein sample (c ) 0.25), a cubic Ia3d - lamellar LR phase coexistence was already observed at few hundred bar and that a transition to the lamellar crystalline Lc phase was detected at about 1.5 kbar,13 it can be concluded that all destabilizing effects induced by pressure are strongly concentration dependent. The absence of the Ia3d structure in the excess water condition, confirming the general finding that this phase is never found as an equilibrium excess water phase for any single component system, should be considered noteworthy. The underlying mechanism for the phase transitions has been then explored in searching for relationships between the structural parameters. The first analysis concerns the dependence of the unit cell on pressure. As evident from Figures 6, 7, and 8 and in complete agreement with previous results,11-13 cell dimensions increase as a function of pressure. This effect has been related to a continuous change in shape of the lipid molecule due to the increase of the chain order parameter induced by pressure. Using very simple molecular packing arguments,14 it can be stated that the monoolein molecular wedge shape decreases as a function of pressure: in both the

Pisani et al. cubic phases, this results in a decreased curvature of the bilayer (see Figure 10) and thus in an enlargement of the unit cell size. The unit cell pressure dependence has been detected to be linear in both Pn3m and Ia3d cubic phases. However, as shown in Figure 8, the slope da/dP is rather different. During compression, the unit cell of the Pn3m phase increases by about 4.3 Å per kbar, independently on concentration, whereas in the Ia3d cubic phase, the pressure dependence appears strongly related to the sample composition, the unit cell increasing from about 4 to 14 Å per kbar when the water volume fraction decreases from 0.4 to 0.26. By contrast, a quadratic pressure dependence was observed for the unit cell of the Pn3m existing in bulk water (see Figure 7). According to the constant da/dP value observed in the Pn3m, we propose that the excess water boundary of this phase would change during compression, so that a large composition adjustment follows any change in pressure (see Figure 9). This fact should have important effects on the spontaneous mean curvature of the monoolein monolayer at a stated pressure (i.e., the mean curvature that the fully hydrated lipid layer would adopt in the absence of external constraints), and then on the energetic and stability of the different phases. The analysis of the pressure dependence of the Ia3d and Pn3m structural parameters (see Figures 10 and 11) strongly confirms the proposed picture for the change in the basic geometrical shape of the monoolein molecule during compression. In particular, the cross-sectional area at the lipid-water interface decreases as a function of pressure, whereas the monolayer thickness correspondingly increases. This pressure effect can be more directly appreciated calculating the cross-sectional area at different distances from the IPMS by adjusting the value of l in eq 3. In Figure 14, a few results are presented: pressure reduces more effectively the cross-sectional area of the lipid near the water-lipid interface, that it is at its terminal methyl group. This indicates that the lateral compressibility reduces moving deeper inside the paraffinic region. Moreover, these calculations also confirm that the location on the molecule whose area shows the smaller variation during bending induced by pressure corresponds to the underlying IPMS. This position for the pivotal surface appears unphysical and suggests that during compression the interface is bending and stretching simultaneously. Finally, it is worthwhile to examine the pressure dependence of the structural parameters in searching for discontinuities (see Figure 10); both l and Amol show a gap when the Pn3m-Ia3d phase boundary is crossed, whereas a progressive variation is found for the Gaussian and mean curvatures. We therefore suggest that the driving force for the phase transition is related to the principal curvatures, which, whatsoever the structure, continuously reduce during compression at all concentrations. As a similar behavior is observed at constant pressures (see Figure 11), we also suggest that the same driving force dictates the Pn3m-Ia3d phase transition observed on dehydration. Energetics: A Tentative Analysis. The lipid concentrations considered in this work are rather low and the external pressure causes an increase of the cell sizes, thus reducing the principal curvatures. A tentative analysis of the curvature elastic parameters has been then exploited to prove theoretical models for the energetic of these lipid structures and to give a reasonable interpretation of the observed phase behavior. So far, no full theoretical description of lipid phase behavior exists, but in the case of bicontinuous cubic phases, the curvature elastic energy is believed to be the crucial term governing their stability in particular at high hydration levels. In a simple model,


J. Phys. Chem. B, Vol. 105, No. 15, 2001 3117 Considering the present data, it appears that the calculations cannot be performed at the area neutral surface, because such a surface, while bending the monolayer both by pressure or by hydration (see Figures 12, 13 and 14), resides pretty well at the underlying IPMS, in a position that is extremely unphysical. Therefore, we calculated the curvature elastic energy with the curvature defined at the headgroup surface, that is, at the lipidwater interface; moreover, we assumed that the lipid-water interface lies parallel to the underlying minimal surface. It can be observed that in these conditions, the magnitude of the Gaussian curvature times the distance to the headgroup surface is much less than 1; therefore, the first-order curvature elastic theory can be used.18 As it stands, eq 7 has three unknowns: k, H0, and kG, whereas the three quantities 〈H〉 , 〈H2〉, and 〈K〉 can be determined from diffraction data.15 Then, the scaled form of surface average curvature elastic energy per lipid molecule 〈µc〉, as defined by Templer and co-workers,18 reads

〈µc〉 ) (2 A V/(1 - φw) a3) [〈(H - H0)2〉 + kG/k 〈K〉] ) Amol [(1+ kG/k) 〈(H - H0)2〉 + (1 - kG/k)(〈H2〉 - 〈K〉)] (8)

Figure 14. Pressure dependence of the molecular cross-sectional area, Amol, calculated at different distances from the IPMS for the Pn3m and Ia3d cubic phases at the two different concentrations indicated in each frame. Curves are interpolated from the calculated points.

three curvature elastic parameters have been considered by Helfrich to describe the surface curvature energy contribution associated with the amphiphilic film:20 the spontaneous mean curvature H0 (the mean curvature that the lipid layer would take on in the absence of external constraints), the mean curvature modulus k and the Gaussian curvature modulus kG. For small curvatures, the mean surface energy per unit area is given in a first approximation by

〈gbend〉 ) 2 k 〈(H - H0)2〉 + kG 〈K〉 ) 2 k (〈H2〉 - 2 H0 〈H〉 + H0)2〉 + kG 〈K〉

(7)

It should be evident that besides the curvature, there are other energetic contributions, such as interlamellar interactions (van der Waals interactions, hydration repulsion and so on) and contributions associated with the lipid chain packing (stretching energy). However, neither of these effects has been accounted for in any modeling of the bicontinuous cubic phase. Therefore, even if the model suffers from severe limitations and cannot be fully adequate,18 we will tentatively analyze the curvature elastic energy contributions for the two cubic phases in the present concentration and pressure experimental ranges using the energy model description reported by Templer et al.18

To calculate the curvature elastic energy of the two cubic phases using eq 8, only the spontaneous curvature H0 and the kG/k should be determined. Note that both of them are expected to be pressure dependent. According to Templer et al.,18 kG/k and H0 can be obtained by a numerical fitting procedure. In the present case, both parameters have been derived analyzing the curvature elastic energy curves in the Pn3m domain. Calculations were performed in this way: at any pressure, the Pn3m curvature elastic energy curve was calculated as a function of composition in searching for reasonable H0 and kG/k pairs giving a minimum in the energy curve at the expected full hydration composition cexc (see Figure 9) and showing a continuous pressure dependence (e.g., linear, quadratic or exponential). In the fitting procedures, the bounds for the H0 and kG/k parameters were (-0.1, -10-4) Å-1 and (-3, 3), respectively. Moreover, to account for the experimental errors, the uncertainty in the full hydration composition was estimated to be (0.02. The best fit curves for the curvature elastic energy are reported as a function of composition (at constant pressure) in the upper frame of Figure 15, whereas in Figure 16, the fitted H0 and kG/k values are plotted as a function of pressure. In the lower frame of Figure 15, the curvature elastic energy, also calculated for the Ia3d cubic phase using extrapolated H0 and kG/k values, is reported as a function of pressure (at constant composition). As stated by Templer and co-workers,18 the meaning of the curvature elastic parameters remains elusive, mainly owing to the inhomogeneity of the Gaussian curvature of the underlying minimal surface. This means that there are normally regions of the bilayer whose curvature is so large that terms in the free energy expansion of order higher than the second in the principal curvatures ought to be included. However, in the present case, the lipid concentrations are quite low and the increased pressure causes the principal curvatures to reduce. Therefore, we believe that at least two points can be stressed from our results. First, pressure reduces the spontaneous curvature H0, that is, the intrinsic molecular wedge shape of monoolein vanishes by compression. This fact is consistent with the conformational order induced by pressure and with the related changes in the monoolein hydration properties and accounts for the stabilization of the lamellar phase at the higher investigated pressures.13 Moreover, the spontaneous curvature calculated at ambient


Figure 15. Composition and pressure dependence of the curvature elastic energy 〈µc〉 obtained by the numerical fitting procedure described in the text. Upper frame: best fit curvature elastic energy curves in the Pn3m domain at different pressures. The symbols indicate the experimental points. Lower frame: curvature elastic energy curves calculated using eq 8 as a function of pressure at different compositions. The φw values are indicated in the legend. Below 1 kbar, energies refer to the Pn3m data, whereas above 1 kbar the 〈µc〉 values have been calculated considering the Ia3d data using extrapolated H0 and kG/k parameters.

pressure (H0 ) - 0.018 Å-1) is in significant agreement with that measured by Vacklin and co-workers27 at the pivotal surface in the monoolein HII phase at 37 °C. In this phase, relieving almost all the packing stress by adding 9-cis-tricosene, they found H0 ) -0.025 Å-1, whereas when the packing stress was not completely relieved (i.e., in the presence of tricosane), the measurements led to a nonphysical location of the pivotal surface and a H0 value of about -0.017 Å-1.27 The second point concerns the ratio between the Gaussian and the mean curvature module. The kG/k is positive and increases as a function of pressure from a value of about 0.14 to about 1, obtained by extrapolation at 1.8 kbar of pressure. Because k is expected to be always positive, the positive value of kG is qualitatively consistent with the detected phase behavior, dominated at any pressure by cubic phases.15 The kG/k calculated at ambient pressure can be compared with the corresponding values of 0.024, determined in the Ia3d phase of monoolein by Chung and Caffrey,17 and of 0.05 and -0.10, recalculated by Templer and co-workers18,27 in the same system considering different H0 values, at the pivotal surface. The discrepancy in sign is significant, but, as already discussed,18 small changes in the spontaneous curvature can lead to large changes in the ratio of the curvature moduli. The last comment concerns the continuous decreasing of the curvature elastic energy of the two cubic phases as a function of pressure (see Figure 15). Because the energy of the system is indeed expected to increase by compression,13 it appears that the curvature elasticity does not dominate the total free energy. Other contributions should be included to obtain a complete description of the free energy; interbilayer forces may play a

Pisani et al.

Figure 16. Pressure dependence of the fitted values for the spontaneous mean curvature, H0, and the ratio between the Gaussian and the mean curvature module, kG/k, obtained in the Pn3m phase by the numerical fitting procedure described in the text. The lines are quadratic fits to the data and have been prolonged in the Ia3d pressure domain to suggest the possible trend.

significant role, but especially stretching, that occurs during compression, could be the major responsible for free energy changes, as suggested by previous measurements.13 In the present model, neither of these effects has been accounted for; this point merits to be further investigated. Conclusion In this work, the structural properties, stability, and transformation of the Pn3m bicontinuous cubic phase observed in monoolein-water system have been investigated over a wide concentration range as a function of pressure up to 2 kbar. A phase transition to the Ia3d bicontinuous cubic phase has been detected when the mechanical pressure increases up to 1-1.2 kbar. To explore the underlying mechanism for this transition, a simple theoretical model based on curvature elastic contributions has been used to derive the energetics of the two bicontinuous cubic phases. Even if chain packing and other contributions are ignored, or assumed to change minimally across phase transitions, the free energy curvature model is found to give qualitative indication about the stability of the cubic phases in the pressure-concentration phase diagram. As clearly stated by Czeslik and co-workers,12 an appropriate understanding of the stability and transformation of lipid phases when pressure and concentration vary would require a detailed analysis of all interactions involved. A deeper knowledge of the relationship between the lipid molecular structure and the thermodynamic parameters is as well needed. Although the present analysis is not exhaustive, the authors are persuaded that the reported experimental data might help to disentangle different free energy contributions in further theoretical approaches. Acknowledgment. We gratefully acknowledge H. Muller (Chemical Laboratory of ESRF, Grenoble, France) for supplying

Phase Transition in Monoolein Hydrated System freshly synthesized monoolein samples and H. Amenitsch (Institute of Biophysics and X-ray Structure Research, Austrian Academy of Sciences, Graz, Austria) for the valuable help and support during measurements. We also thank M. Kriechbaum (Institute of Biophysics and X-ray Structure Research, Austrian Academy of Sciences, Graz, Austria) and M. Steinhart (Institute of Macromolecular Chemistry, Academy of Sciences of the Czech Republic, Prague, Czech Republic) for their incisive help in setting up the pressure control system on the beamline. This work was supported by grants from the INFM, Italy. References and Notes (1) Hyde, S. T.; Andersson, S.; Ericsson, B.; Larsson, K. Z. Kristallogr. 1984, 168, 213-219. (2) Caffrey, M. Biochemistry 1987, 26, 6349-6363. (3) Mariani, P.; Luzzati, V.; Delacroix, H. J. Mol. Biol. 1988, 204, 165-189. (4) Briggs, J.; Caffrey, M. Biophys. J. 1994, 66, 377-381. (5) Briggs, J.; Chung, H.; Caffrey, M. J. Physique II (France) 1996, 6, 723-731. (6) Mariani, P.; Rustichelli, F.; Saturni, L.; Cordone, L. Eur. Biophys. J. 1999, 28, 294-301. (7) Longley, W.; McIntosh, T. J. Nature 1983, 303, 612-614. (8) Scriven, L. E Nature 1976, 263, 123-125. (9) Luzzati, V.; Vargas, R.; Mariani, P.; Gulik, A.; Delacroix, H. J. Mol. Biol. 1993, 229, 540-551. (10) Schoen, A. H. NASA Technical Note 1970, TND-5541, Washington, DC.

J. Phys. Chem. B, Vol. 105, No. 15, 2001 3119 (11) Winter, R.; Erbes, J.; Czeslik, C.; Gabke, A. J. Phys. Condens. Matter. 1998, 10, 11 499-11 518. (12) Czeslik, C.; Winter, R.; Rapp, G.; Bartels, K. Biophysical, J. 1995, 68, 1423-1429. (13) Mariani, P.; Paci, B.; Bosecke, P.; Ferrero, C.; Lorenzen, M.; Caciuffo, R. Phys. ReV. E. 1997, 54, 5840-5843. (14) Israeachvili, J. N. Intermolecular and Surface Forces; Academic Press: New York, 1992. (15) Turner, D. C.; Wang, Z.-G.; Gruner, S.; Mannock, D. A.; McElhaney, R. N. J. Phys. II (France) 1992, 2, 2039-2063. (16) Templer, R. H.; Seddon, J. M.; Warrender, N. A. Biophys. Chem. 1994, 49, 1-12. (17) Chung, H.; Caffrey, M. Nature 1994, 368, 224-226. (18) Templer, R. H.; Turner, D. C.; Harper, P.; Seddon, J. M. J. Phys. II (France) 1995, 5, 1053-1065. (19) Templer, R. H.; Seddon, J. M.; Warrender, N. A.; Syrykh, A.; Huang, Z.; Winter, R.; Erbes, J. J. Phys. Chem. B 1998, 102, 7251-7261. (20) Helfrich, W. Z. Naturforsch. 1973, 28c, 693-703. (21) Kozlov, M. M. Langmuir 1992, 8, 1541-1547. (22) Steinhart, M.; Kriechbaum, M.; Pressl, K.; Amenitsch, H.; Laggner, P.; Bernstorff, S. ReV. Sci. Instr. 1999, 70, 1540-1545. (23) Luzzati, V. Biological Membranes; Chapman, D., Ed.; Academic Press: London, 1968, Chapter 3. (24) Handbook of Chemistry and Physics; Lide, D. R., Ed.; CRC Press: Boca Raton, Florida, 1996. (25) Mariani, P.; Pisani, M., unpublished. (26) Anderson, D. M.; Gruner, S. M.; Leibler, Proc. Natl. Acad. Sci. U.S.A. 1988, 85, 5364-5368. (27) Vacklin, H.; Khoo B. J.; Madan, K. H.; Seddon, J. M.; Templer, R. H. Langmuir 2000, 16, 4741-4748.

Pressure Induced Cubic-to-Cubic Phase Transition in Monoolein

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