pressure induced cubic-to-cubic phase transition in monoolein hydrated system

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; SincrotroneTrieste S.C.p.A. Strada Statale 14, km 163.5, I-34016 BasoVizza (Trieste), Italy, and European SynchrotronRadiation 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 thePn3mbicontinuous cubic phase in the monoolein-water system under hydrostatic pressure. As a first result, itappears that the full-hydration properties of monoolein are strongly related to the pressure. Moreover, theexperimental results show the occurrence of aPn3m to Ia3d cubic phase transition when the mechanicalpressure increases to 1-1.2 kbar, depending on the water concentration. The underlying mechanism for thephase transition has been then explored in searching for relationships between the structural parameters derivedfrom the two cubic phases. The emerging picture is a change in the basic geometrical shape of the monooleinmolecule during compression. Moreover, the analysis of the position of the pivotal surface indicates that theinterface is bending and stretching simultaneously as a function of pressure. Because the lipid concentrationis rather low and the external pressure increases the cell sizes, thus reducing the principal curvatures, a tentativeanalysis of the pressure effects on the energetics of these structures has been exploited. A simple theoreticalmodel based on curvature elastic contributions has been used: calculations show that increasing the pressurethe spontaneous curvatureH0 of the monoolein tends to zero, whereas the ratio between the monolayer saddlesplay modulus and the monolayer splay moduluskG/k increases to 1. Moreover, the curvature elastic energyappears to reduce progressively as a function of pressure, indicating that in these conditions, the curvatureelasticity does not dominate the total free energy.

Introduction

Phase behavior and structural properties of monoacylglyc-erides in water have been investigated for a long time, becausethey exhibit an extended polymorphism.1-6 In particular, mo-noolein in water shows several mesophases, characterized by ahighly disordered conformation of the hydrocarbon chains.1,3,5

The monoolein temperature-concentration phase diagram isreported in Figure 1: a lamellar structure LR, where lipidmolecules assemble into stacked sheets, an inverted (type II)hexagonal phase HII, which consists of cylindrical structureelements packed in a 2-D hexagonal lattice, and two bicontinu-ous inverted cubic phases with space groupPn3m (Q224) andIa3d (Q230) have been identified.1,3,7 The structure of bicon-tinuous cubic phases has been described in terms of InfinitePeriodic Minimal Surfaces (IPMS),8,9 that is, infinite arrays ofconnected saddle surfaces with zero mean curvature at everypoint on the surface. In inverse structures, lipid monolayers aredraped across either side of the minimal surface, touching itwith their terminal methyl groups; this results in a three-dimensional periodic bicontinuous structure, formed by distinctwater and lipid volumes. The crystallographic space group ofthe cubic phase determines the type of the IPMS; in particular,the cubic phases observed in the monoolein-water system(space groupsIa3d andPn3m) are based on G (Gyroid) and D(Diamond) surfaces, respectively (see Figure 2).3,7,10

Pressure effects on lipid structures have been sparinglyinvestigated.11 In the case of monoacylglycerides, the pressure-dependent phase behavior has been the object of a few works.Winter and co-workers12 studied the phase behavior of mo-noolein and monoelaidin in excess water by X-ray and neutrondiffraction. It was found that the cubicPn3m phase observedin monoolein in fully hydrated conditions extends in a puredomain over a large phase region in the temperature-pressureplane (up to 2 kbar at 20°C). Synchrotron X-ray diffractionwas also used to investigate the polymorphism of monoolein atlow hydration (water concentration of 0.25 w/w) under hydro-

* 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 ambientpressure (redrawn from Briggs et al.5). The concentrationc is expressedas weight of water per weight of mixture. Phases are labeled as in thetext; FI stands for fluid isotropic.

3109J. Phys. Chem. B2001,105,3109-3119

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

static pressure up to 10 kbar.13 The results showed a largecoexistence of the cubicIa3d and lamellar LR and Lc phasesat all the investigated pressures before the transition to the pureLc lamellar phase occurs. Even if changes in phase compositionof the competing structures were not excluded, the observedphase sequence and unit cell pressure dependence were dis-cussed using simple molecular packing arguments, based onchanges in the molecular wedge shape of monoolein.14 Byincreasing pressure, the lipid chain order parameter is increased,and thus, the monoolein molecular wedge shape reduced. Thisresults in an enlargement of the unit cell size of the cubic phasesbecause of a decreased curvature of the lipid bilayer.12,13

Moreover, the more cylindrical molecular shape leads to theformation of the lamellar LR phase or to the Lc phase, whichhave the higher lipid packing density. As expected, this structurewas detected to be practically incompressible.13

Pressure can be also used as a suitable thermodynamicvariable to obtain information on the energetic and stability oflipid phases.11-13 In fact, several attempts to determine theenergetic of bicontinuous cubic phases from structural data andto give both a qualitative and a quantitative explanation for theirlocation within the temperature-concentration phase diagramhave been reported.15-19 In particular, the curvature elasticenergy is believed to be a crucial factor governing the stabilityof such phases: assuming that bicontinuous cubic phases arecorrectly described in terms of IPMS, a simple curvature freeenergy elastic model, which includes a mean and a Gaussiancurvature term, has been described.20 Improvements of theoriginal model have been proposed. To correctly describe theinterfaces of the cubic phases when the degree and the varianceof the mean and Gaussian curvatures are high, the curvature

elastic energy has been re-expressed as a high order polynomialexpansion of the principal curvatures.18 However, it has beenalso shown that the inhomogeneity in the curvature can giverise to lateral packing frustrations,21 which will be the worstwhen the lipid concentration is the greatest. A further complicat-ing factor for the description of the energetic of bicontinuouscubic phases with high interfacial curvature is that the distancebetween sections of monolayers facing each other across a waterchannel can be quite small. This means that van der Waalsattraction and hydration repulsion will play a significant rolein stabilizing the phase. Because neither of these effects hasbeen accounted for in any modeling of bicontinuous cubicphases, the meaning of the curvature elastic parameters that canbe extracted from structural data remains elusive. According toTempler and co-workers,18 most of the problems mentionedabove become less tough when structural data, obtained at lowlipid concentrations and from systems with low curvatures, areconsidered. In this conditions, the terms in the free energyexpansion greater than quadratic in the principal curvatures canbe neglected and the obtained curvature elastic parameters couldbecome meaningful.

In this work, we take advantage of the well-known structuralproperties of monoolein in order to extensively study thepressure effects on thePn3m bicontinuous cubic phase over arelatively wide concentration and pressure range. As aPn3m-Ia3d cubic-to-cubic phase transition has been detected to beinduced by mechanical pressure, the underlying mechanismsfor the phase transition have been explored to establishrelationships between the structural data derived from the twophases. Because the external pressure increases the cell sizes,reducing the curvatures, a tentative analysis of the curvatureelastic parameters to prove theoretical models for the energeticof bicontinuous cubic structures and to understand the pressure-induced phase behavior has finally been carried out.

Materials and Methods

The monoacylglyceride 1-monoolein was obtained by SigmaChemical Co. (Milano, Italy) with a purity of>99% and usedwithout further purification.

Monoolein-water samples of concentrations ranging fromc) 0.35 toc ) 0.40 (c being the water weight concentration),the range at which the cubicPn3m phase exists at ambienttemperature and pressure, were considered. Samples wereprepared by mixing the lipid with appropriate amounts ofbidistilled water in small weighing bottles and were equilibratedin the dark for 1 day at ambient temperature and pressure. Nowater loss was detected before the hydrated lipids were mountedinto the pressure cell. Moreover, after the X-ray scatteringexperiments, the water composition of each sample was checkedagain by gravimetric analysis. The differences between thenominal and the concentration measured after the pressure cyclewere detected to be in the limit of the experimental errors.

Diffraction measurements were performed at the SAXSbeamline of the Elettra Synchrotron Light Source, Trieste (Italy).The wavelength of the incident beam wasλ ) 1.54 Å, and theexploreds range extended from 0.005 to 0.05 Å-1 (s ) 2 sinθ/λ, where2θ is the scattering angle). An additional wide-angleX-ray scattering (WAXS) detector was used to simultaneouslymonitor diffraction patterns in the range from 0.11 to 1 Å-1.For pressure experiments, we used the pressure-control systemdesigned and constructed by M. Kriechbaum and M. Steinhart.22

The pressure cell has two diamond windows (3.0 mm diameterand 1 mm thickness) and allows us to measure diffractionpatterns at hydrostatic pressures up to 3 kbar.

Figure 2. Representation of the unit cell structure of thePn3m, symbolQ224 (upper frame) and of theIa3d, symbol Q230 (lower frame) cubicphases. 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 AppliedMathematics, Australian National University, Canberra, Australia.

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

X-ray diffraction measurements were performed at 25°C fordifferent pressures, from 1 bar to 3 kbar, with steps of about100 bar. To avoid radiation damage, the exposure time was 2-5s/frame, and a lead shutter was used to protect the sample fromexcess radiation within periods where no data were recorded.Particular attention has been devoted to check for equilibriumconditions and for radiation damage: in several cases, measure-ments were repeated several times (up to 200) at the sameconstant pressure to account for stability in position and intensityof the Bragg peaks. Accordingly, a gentle compression of thesample, at a rate of 0.5-2 bar/s, was observed to ensure theestablish of equilibrium conditions, also in the regions of phasecoexistence. In all cases, once stabilized, the pressure (in a fewminutes), the X-ray diffraction measurements were repeated atleast 2 times, with an interval of at least 5 min.

In each experiment, a number of sharp, low angle reflectionswere observed and their spacings measured following the usualprocedure.3,23 In all of the cases discussed in this paper, a diffuseband in the (3-5 Å)-1 region of the scattering curves indicatesthe disordered (typeR) nature of the lipid short-range conforma-tion. Low angle diffraction profiles were indexed using equationswhich define the spacing of reflections for the differentsymmetry systems usually observed in lipid phases (lamellar,hexagonal, or 3-dimensional cubic lattices): the indexingproblem was easy to solve, because in no case were extra peaks,which can be ascribed to the presence of unknown phases or tocrystalline structures, observed. In the present experimentalconditions, three different series of low-angle Bragg reflectionswere observed and indexed according to theIa3d cubic spacegroup (spacing ratiosx6: x8: x14: x16: x20: x22...), tothe Pn3m cubic space group (spacing ratiosx2: x3: x4:x6: x8: x9: x10...) and to the lamellar one-dimensionalsymmetry (spacing ratios 1:2:3...). Once the symmetry of thelipid phase was found, the dimension of the unit cell wascalculated. In the following,a indicates the unit cell dimension.

The other parameter necessary for determining the internaldimensions of the phases is the water (or lipid) volume fraction.The water volume fractionφw was determined as usual3,15,23

from the sample weight composition, using the density of boththe monoolein and water,FMO andFw, respectively

In the present case, we usedFMO ) 0.942 g cm-3 andFw ) 1.0g cm-3, respectively,24 under the assumption that densities arelargely unaffected by pressure. Even if the previously detectedincompressibility of the lamellar phase at high pressure13 ensuresthat the molecular volumes play a small role in the unit cellvariations induced by pressure, it should be point out that usingconstant partial densities for monoolein and water as a functionof pressure imparts a systematic error in the determination ofmolecular geometry.

Results

Phase Behavior and Pressure Dependence of the Unit CellDimension. Selected low-angle X-ray diffraction patterns,showing a number of reflections, are reported in Figure 3. Byanalyzing the spacing ratios of the low angle diffraction peaks,the structure of the lipid phases was identified and the unit celldimensions determined.3

At all the investigated concentrations (fromc ) 0.35 toc )0.4), the X-ray diffraction profiles confirm the presence of the

Pn3m cubic phase at ambient pressure.3 However, a differentpressure dependent phase behavior was detected for the lesshydrated samples and the sample prepared in excess water (c≈ 0.4, at ambient pressure). As illustrated in Figure 3, in thediffraction profiles of the fully hydrated monoolein sample, aBragg peak centered ats ) 0.02 Å-1 emerges at a pressure ofabout 700 bar. The intensity of this peak increases as far as thepressure increases, whereas thePn3m characteristic reflectionsreduce in intensity; at∼1100 bar, only the diffraction peak atabouts ) 0.02 Å-1 remains. According to the results reportedby Czeslik and co-workers,12 the transition can be ascribed tothe conversion from the cubicPn3m phase to a lamellar phasewith a lattice spacing of about 49 Å. As no extra peaks wereobserved in the wide-angle region, the lamellar phase wasidentified as a liquid-crystalline LR phase. Remarkably, thePn3m-LR phase transition occurs over about 400 bar.

As it can be deduced from the X-ray diffraction profilesreported in Figure 3, all the samples prepared in less hydratedconditions exhibit a cubic-to-cubic phase transition, from thePn3m to theIa3d cubic phase. During compression, at about 1kbar and within a relatively narrow pressure range, two seriesof Bragg reflections, which can be properly indexed consideringthe Pn3m and Ia3d cubic lattices, occur. It should be noticedthat scattering data obtained at these intermediate pressuresindicate that the two cubic phases coexist in a thermodynamicequilibrium. As shown in Figure 4, in the biphasic region, theintensity and the position of the diffraction peaks measured atconstant pressure, do not change as a function of time, at leastfor the first 60 min. By further increasing the pressure, thePn3mcubic phase disappears and only the diffraction peaks corre-sponding to theIa3d cubic phase are still detected. The typicalprofile of a pureIa3d cubic phase is then observed up to about2 kbar, and no evidence for other phase transitions is stated.This result can be compared with previous measurements on avery dry sample (c ) 0.25), which showed that the region ofcoexistence of theIa3d and LR phases extends from very lowpressure (a few hundred bar) up to 4.5 kbar.13

In Figure 5, the pressure at which thePn3m andIa3d phasetransition occurs is reported as a function of concentration. Inthe graph, the error bars account for the extension of the two-phase region. Data are scattered, but the trend is quite clear(see the tentative linear fit to the data in Figure 5); whereasincreasing the lipid concentration, thePn3m-Ia3d transitionoccurs at lower pressure. Moreover, the limited extent of thecubic-cubic two-phase region (the average value is around 240bar) should be compared with the one of the lamellar-cubic two-phase region.

φw ) c

c + (1 - c)Fw

FMO

(1)

Figure 3. Low-angle X-ray diffraction profiles from monooleinsamples at concentrationsc ) 0.364 (φw ) 0.35), c ) 0.393 (φw )0.379) and in excess water. Each experiment has been performed atthe indicated pressure. Peaks are indexed according to the cubicPn3mand Ia3d or to the 1-D lamellar space groups3.

Phase Transition in Monoolein Hydrated System J. Phys. Chem. B, Vol. 105, No. 15, 20013111

The observed variations of the unit cell dimension with thehydrostatic pressure are shown in Figures 6 and 7. Accordingto previous measurements,11-13 the unit cell of the different lipidphases increases during compression. This fact has been relatedto a continuous change in shape of the lipid molecule due tothe increase of the chain order parameter induced by pressure.In the less hydrated conditions (see Figure 6), the unit cell ofboth thePn3m andIa3d cubic phases increases almost linearlyas a function of pressure. A linear fit to the data has then beenused to determine the pressure dependence da/dP; the obtainedvalues are reported in Figure 8 as a function of concentration.In the Pn3m cubic phase, the da/dP parameter is practicallyindependent of the concentration; the average value is 4.3(1.1 Å kbar-1, which can be satisfactory compared with the valueof 7 Å per kbar reported by Czeslik and co-workers.12 In theIa3d phase, the slope of thea versusP curves is larger andclearly depends on concentration. This strong pressure depen-dence was not detected in a less hydrated sample (c ) 0.25)previously investigated, but in that case, theIa3d cubic phasewas existing in a biphasic region.13 Therefore, for the sake ofconfirmation, the unit cell pressure dependence recently ob-

served25 in equilibrium conditions in a pureIa3d phase at theconcentrationc ) 0.26 and in the pressure range from 1 to 1.2kbar is also reported in Figure 8.

In the presence of bulk water, the unit cell of thePn3mcubicphase is found to be strongly pressure dependent (see Figure7); moreover, the dependence is quadratic. The temperature-concentration phase diagram of the monoolein in water (seeFigure 1) shows that the composition of the fully hydratedPn3mcubic phase ranges fromc ) 0.25 toc ) 0.49 at 92°C and 0°C, respectively. Increasing the pressure has the same effect onthe lipid as decreasing the temperature. Therefore, we expectthat the excess water boundary of thePn3mphase would changeduring compression, determining a change in the monoolein fullhydration values which can account for the unusual increase of

Figure 4. X-ray diffraction profiles from monoolein samples at twodifferent 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 0.9kbar) as a function of time. The spectra have been recorded every 5min.

Figure 5. Composition dependence of the pressure range at whichthePn3m-Ia3d cubic-to-cubic phase transition occurs. For the sampleprepared in excess water, the transition is from thePn3m cubic to LRlamellar phase. Note that this point is plotted versus the nominal samplecomposition at ambient pressure (see text for more details). Thedependence of the phase transition pressure on the water volume fractionis assumed to be linear; the best fit parameters area0 ) 0.397 kbarandb ) 1.94 kbarφw

-1.

Figure 6. Pressure dependence of the unit cell dimensions of the cubicPn3m andIa3d phases in monoolein samples at different composition.The water volume fractionφw is indicated in each frame. The latticeparameter variationper unit pressure (da/dP) is also indicated.


the lattice parameter. Assuming that the pressure dependencein thePn3m unit cell is constant and equal to 4.3 Å kbar-1, asdetected in the less hydrated samples, the location of the excesswater line in the concentration-pressure dependent phasediagram can be obtained. In practice, the 4.3 Å kbar-1 pressurecontribution has been subtracted from the experimentallyobserved unit cell to derive the lattice dimensions that aredependent only on composition. These values have been thenconverted in water concentration using cell dimensions measuredat ambient pressure as a function of water content.5,6 Due tothe occurrence of a phase transition at higher pressures, thesecalculations were performed only in the single-phase region.The final result is reported in Figure 9; up to about 200 bar,the composition of thePn3m in fully hydrated conditions isquite constant (aroundcexe)0.395), whereas the excess waterboundary increases rather linearly in the pressure range from200 to 800 bar. Therefore, as expected, the hydration propertiesof monoolein appear to be strongly related not only to the

temperature but also to the pressure. Quantitatively, from thefully hydration concentration, we calculate that during compres-sion up to about 1 kbar, the number of water moleculesperfully hydrated monoolein molecule increases from about 13 to24.

Structural Parameters. Assuming distinct water and lipidregions within the cell, the internal structural dimensions oflipid-containing phases can be calculated from unit cell dimen-sions and sample concentrations.3,5,15,23 In the case of cubicbicontinuous phases, a model describing the structure shouldbe considered.9 Here, the lipid monolayer thickness, thecurvature parameters, and the lipid cross sectional area havebeen determined considering thatPn3m and Ia3d cubic struc-tures are described as lipid bilayers draped across the IPMS.

According to Turner and co-workers,15 the monolayer thick-ness l, considered constant throughout the structure, can becalculated using

whereσ and ø are the constants for the minimal surface andhave values specific to each bicontinuous cubic phase26 (Ia3d:σ ) 3.091,ø ) -8; Pn3m: σ ) 1.919,ø ) -2). The unit cellsurface area at the headgroupA, that is, at the lipid-waterinterface, which is assumed to be parallel to the minimal surface,can be obtained using

where⟨K⟩0 is the surface averaged Gaussian curvature on theminimal surface (the surface average is necessary because thecurvature of the underlying minimal surface is inhomogeneous)andA0, defined asσa2,is the area of the minimal surface withinthe unit cell.⟨K⟩0 is related to the lattice parameter through theGauss-Bonnet theorem

The area-per-moleculeAmol at the lipid-water interface can beobtained by dividingA by the number of lipid molecules in theunit cell, (1- φw) a3/2V, whereV is the lipid molecular volume.

Other parameters, that are also necessary to describe acomplete curvature free energy for the lipid layer (see below),are the Gaussian⟨K⟩ and the mean⟨H⟩ curvatures at the lipid-water interface, both averaged over the unit cell. Their valuescan be calculated using15,26

Note that the sign of the mean curvature is taken to be negativewhen the lipid headgroup surface bends toward the aqueousphase. This means that the cross-sectional area per lipid increasesfrom the head to the tail, reducing to zero at the center of thewater channel.

The area-per-lipid and the curvature parameters can beevaluated on a surface parallel to the minimal surface and atany distance from it (i.e., at any point along the lipid length)only by adjusting the value ofl in eqs 3 and 5. This is animportant point because it has been observed that in some casesa surface, approximately parallel to the underlying minimalsurface, exists about which the average molecular area does notvary upon bending by hydration. This is the neutral surfacewhich has permitted to model the effect of water content on

Figure 7. Pressure dependence of the unit cell dimensions of the cubicPn3m and lamellar LR phases in the monoolein sample prepared inexcess water. The cubic lattice parameter dependence on pressure isquadratic; the best fit parameters area0 ) 103.5 Å,b ) 12.8 Å kbar-1,andc ) 7.53× 10-3 Å kbar-2.

Figure 8. Cubic lattice parameter variationper unit pressure (da/dP)versus water volume fractionφw. The lines are only guides to the eyeto show the general trends.

Figure 9. Calculated water weight concentrations of thePn3m phaseof monoolein at full hydration versus pressure.

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

A ) A0 (1 + ⟨K⟩0 l2) (3)

⟨K⟩0 ) 2πø/(σ a2) (4)

⟨K⟩ ) 2πø/A

⟨H⟩ ) 2π ø l/A (5)


the geometry of the inverse bicontinuous cubic phases and tocalculate the curvature energy as a function of concentration.17,18

In Figure 10, the monolayer thickness (l), the area-per-molecule at the headgroup,Amol ) 2 AV/(1 - φw)a3, and theaverage over the unit cell of the mean and of the Gaussiancurvatures at the same surface are shown as a function ofpressure for three of the investigated concentrations. It shouldbe noticed that, except for the sample prepared in the presenceof excess water, all the calculations have been performed underthe assumption that, during a pressure cycle, the water contentis the same in all the phases, and equal to the sample nominalconcentration. The data obtained from samples prepared in lesshydrated conditions clearly confirm that pressure induces areduction of the curvatures of the lipid layer and a decrease ofthe cross-sectional monoolein area at the lipid-water interface.Accordingly, the monolayer thickness enlarges. One point shouldbe stressed: the variation of the curvature parameters is rathercontinuous, even when the phase boundary is crossed. On thecontrary, the monolayer thickness and the area-per-molecule atthe water-lipid interface show a large discontinuity in cor-respondence of thePn3m - Ia3d phase transition. For thesample analyzed in the presence of bulk water, the calculationswere performed using the concentration of the fully hydratedPn3m cubic phase estimated as discussed before and reportedin Figure 9. Some of the obtained parameters (see again Figure10) show an unusual pressure dependence: in particular, thelipid thickness decreases as a function of pressure and, accord-ingly, the cross-sectional area at the lipid-water interface

increases. Because in the coexistence region a large compositionadjustment follows any pressure change, we suggest thathydration effects should overrule the increase of the chain orderparameter induced by compression.

The concentration dependence of the structural parametersat constant pressure has been also considered. To have illustra-tive results, we used interpolatedPn3mandIa3d cells; the resultsare reported in Figure 11. At all the pressures, the monolayerthickness reduces by increasing the water volume fraction,whereas the area-per-molecule increases. Moreover, the con-centration dependence of the⟨K⟩ and⟨H⟩ parameters indicatesthat the curvature lowers when the water fraction increases. Itis interesting to observe that at the phase transition pressure(see data at 1 kbar), the discontinuity betweenl and Amol

parameters for thePn3m and theIa3d phases is confirmed,whereas very similar values for the mean and Gaussiancurvatures are observed.

To obtain information on the very existence of the neutralsurface, we used the cubic equation derived by Templer andco-workers19

whereAn is the molecular area at the pivotal plane, andVn is

Figure 10. Pressure dependence of the structural parameters of thePn3m and Ia3d cubic phases in monoolein samples at three of the analyzedcompositions. The water volume fractions,φw, are indicated at the top of each column.l is the thickness of the lipid monolayer,Amol is the area-per-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.

(An

V )3

a3 + 6A0(An

V )2a2

(1 - φw)-

[ 36πø(1 - φw) (Vn

V )2

+32A0

3

(1 - φw)3] ) 0 (6)


the molecular volume between this plane and the end of thechains. Because the pivotal surface is defined to be the locationon the molecule whose area is invariant upon isothermal bendingand the mass of lipid either side of the pivotal surface remainsfixed as the interface bends, eq 6 can be used to derive thepivotal surface geometry (i.e., theAn andVn values) by fittingthe unit cell as a function of the water volume fraction. Theresults of the fitting procedures, performed at different pressures,are reported in the Figures 12 (best fit curves) and 13 (fittingparameters). As a comparison, the fit has been also applied toprevious data on theIa3d phase obtained at ambient pressureand low hydration3; the best fit curve is reported in the insertof Figure 12. Two points can be underlined. First, the fit tohigh pressureIa3d data, also performed excluding the point atφw ) 0.379, is far from to be satisfactory. Second, the derivedarea and volume of the pivotal surface are rather astonishing,especially if compared with the values determined at lowhydration and at ambient pressure for theIa3d cubic phase. Insuch experimental conditions, the pivotal surface is located atabout 9 Å from the IPMS, and the geometrical parameters areAn ) 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 highpressureIa3d data but also thePn3mdata obtained from ambientto about 1 kbar, it is by contrast derived that the location onthe molecule whose area undergoes the smaller variation duringbending practically corresponds to the minimal surface. Asshown in the Figure 13, the fittedVn are in fact only few Å3

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

Figure 11. Composition dependence of the structural parameters of thePn3m and Ia3d cubic phases calculated at three different pressures. Theconsidered pressures are indicated at the top of each column. Notations and symbols as in the text and Figure 10. It should be noticed that thereported curves have been calculated usingPn3m and Ia3d cubic cells interpolated from experimental data versus concentration and pressure.

Figure 12. Best fit curves obtained applying eq 6 toPn3m and Ia3ddata. 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, 1.8kbar). The experimental pressures are indicated in each frame.


Discussion

The pressure effects on the structure and stability of thePn3mbicontinuous cubic phase in the monoolein-water system havebeen investigated using synchrotron X-ray scattering. Theobserved diffraction data, reported in Figure 3, indicate adifferent phase behavior for thePn3msample prepared in excesswater (full hydration condition,c ≈ 0.4 at ambient pressure)and for thePn3m samples prepared in less hydrated conditions(from c ) 0.4 toc ) 0.34). In excess water, a phase transitionfrom thePn3mcubic to the lamellar LR phase at about 0.7 kbarhas been observed, whereas aPn3m to Ia3d cubic-to-cubic phasetransition occurring when the external pressure increases up toabout 1-1.2 kbar was detected in the less hydrated samples(see Figure 5, and compare with the monoolein phase diagramof Figure 1). Moreover, in such conditions, no other phasetransitions were detected by further increasing pressure (up toabout 2 kbar). Considering that in a very dry monoolein sample(c ) 0.25), a cubicIa3d - lamellar LR phase coexistence wasalready observed at few hundred bar and that a transition to thelamellar crystalline Lc phase was detected at about 1.5 kbar,13

it can be concluded that all destabilizing effects induced bypressure are strongly concentration dependent. The absence oftheIa3d structure in the excess water condition, confirming thegeneral finding that this phase is never found as an equilibriumexcess water phase for any single component system, shouldbe considered noteworthy.

The underlying mechanism for the phase transitions has beenthen explored in searching for relationships between thestructural parameters. The first analysis concerns the dependenceof the unit cell on pressure. As evident from Figures 6, 7, and8 and in complete agreement with previous results,11-13 celldimensions increase as a function of pressure. This effect hasbeen related to a continuous change in shape of the lipidmolecule due to the increase of the chain order parameterinduced by pressure. Using very simple molecular packingarguments,14 it can be stated that the monoolein molecularwedge shape decreases as a function of pressure: in both the

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 belinear in bothPn3mandIa3d cubic phases. However, as shownin Figure 8, the slopeda/dP is rather different. Duringcompression, the unit cell of thePn3mphase increases by about4.3 Å per kbar, independently on concentration, whereas in theIa3d cubic phase, the pressure dependence appears stronglyrelated to the sample composition, the unit cell increasing fromabout 4 to 14 Åper kbar when the water volume fractiondecreases from 0.4 to 0.26. By contrast, a quadratic pressuredependence was observed for the unit cell of thePn3mexistingin bulk water (see Figure 7). According to the constantda/dPvalue observed in thePn3m, we propose that the excess waterboundary of this phase would change during compression, sothat a large composition adjustment follows any change inpressure (see Figure 9). This fact should have important effectson the spontaneous mean curvature of the monoolein monolayerat a stated pressure (i.e., the mean curvature that the fullyhydrated lipid layer would adopt in the absence of externalconstraints), and then on the energetic and stability of thedifferent phases.

The analysis of the pressure dependence of theIa3d andPn3mstructural parameters (see Figures 10 and 11) strongly confirmsthe proposed picture for the change in the basic geometricalshape of the monoolein molecule during compression. Inparticular, the cross-sectional area at the lipid-water interfacedecreases as a function of pressure, whereas the monolayerthickness correspondingly increases. This pressure effect canbe more directly appreciated calculating the cross-sectional areaat different distances from the IPMS by adjusting the value ofl in eq 3. In Figure 14, a few results are presented: pressurereduces more effectively the cross-sectional area of the lipidnear the water-lipid interface, that it is at its terminal methylgroup. This indicates that the lateral compressibility reducesmoving deeper inside the paraffinic region. Moreover, thesecalculations also confirm that the location on the molecule whosearea shows the smaller variation during bending induced bypressure corresponds to the underlying IPMS. This position forthe pivotal surface appears unphysical and suggests that duringcompression the interface is bending and stretching simulta-neously.

Finally, it is worthwhile to examine the pressure dependenceof the structural parameters in searching for discontinuities (seeFigure 10); bothl andAmol show a gap when thePn3m-Ia3dphase boundary is crossed, whereas a progressive variation isfound for the Gaussian and mean curvatures. We thereforesuggest that the driving force for the phase transition is relatedto the principal curvatures, which, whatsoever the structure,continuously reduce during compression at all concentrations.As a similar behavior is observed at constant pressures (seeFigure 11), we also suggest that the same driving force dictatesthe Pn3m-Ia3d phase transition observed on dehydration.

Energetics: A Tentative Analysis.The lipid concentrationsconsidered in this work are rather low and the external pressurecauses an increase of the cell sizes, thus reducing the principalcurvatures. A tentative analysis of the curvature elastic param-eters has been then exploited to prove theoretical models forthe energetic of these lipid structures and to give a reasonableinterpretation of the observed phase behavior.

So far, no full theoretical description of lipid phase behaviorexists, but in the case of bicontinuous cubic phases, the curvatureelastic energy is believed to be the crucial term governing theirstability in particular at high hydration levels. In a simple model,

Figure 13. Pressure dependence of the fitting parameters obtainedapplying eq 6 toPn3m and Ia3d data.Vn is the molecular volumebetween the IPMS and the pivotal plane andAn is the molecular cross-sectional area at this plane. Open squares refer to volumes obtainedfitting Ia3d data with the exclusion of the points atφw ) 0.379 (thecorresponding chi-square reduces to 0.17 at 1 kbar, 0.06 at 1.4 kbarand 0.57 at 1.8 kbar). In the lower frame lines are guides to the eyes.


three curvature elastic parameters have been considered byHelfrich to describe the surface curvature energy contributionassociated with the amphiphilic film:20 the spontaneous meancurvatureH0 (the mean curvature that the lipid layer would takeon in the absence of external constraints), the mean curvaturemodulusk and the Gaussian curvature moduluskG. For smallcurvatures, the mean surface energy per unit area is given in afirst approximation by

It should be evident that besides the curvature, there are otherenergetic contributions, such as interlamellar interactions (vander Waals interactions, hydration repulsion and so on) andcontributions associated with the lipid chain packing (stretchingenergy). However, neither of these effects has been accountedfor in any modeling of the bicontinuous cubic phase. Therefore,even if the model suffers from severe limitations and cannotbe fully adequate,18 we will tentatively analyze the curvatureelastic energy contributions for the two cubic phases in thepresent concentration and pressure experimental ranges usingthe energy model description reported by Templer et al.18

Considering the present data, it appears that the calculationscannot be performed at the area neutral surface, because sucha surface, while bending the monolayer both by pressure or byhydration (see Figures 12, 13 and 14), resides pretty well at theunderlying IPMS, in a position that is extremely unphysical.Therefore, we calculated the curvature elastic energy with thecurvature defined at the headgroup surface, that is, at the lipid-water interface; moreover, we assumed that the lipid-waterinterface lies parallel to the underlying minimal surface. It canbe observed that in these conditions, the magnitude of theGaussian curvature times the distance to the headgroup surfaceis much less than 1; therefore, the first-order curvature elastictheory can be used.18

As it stands, eq 7 has three unknowns:k, H0, andkG, whereasthe three quantities⟨H⟩ , ⟨H2⟩, and⟨K⟩ can be determined fromdiffraction data.15 Then, the scaled form of surface averagecurvature elastic energyper lipid molecule⟨µc⟩, as defined byTempler and co-workers,18 reads

To calculate the curvature elastic energy of the two cubic phasesusing eq 8, only the spontaneous curvatureH0 and thekG/kshould be determined. Note that both of them are expected tobe pressure dependent.

According to Templer et al.,18 kG/k andH0 can be obtainedby a numerical fitting procedure. In the present case, bothparameters have been derived analyzing the curvature elasticenergy curves in thePn3mdomain. Calculations were performedin this way: at any pressure, thePn3mcurvature elastic energycurve was calculated as a function of composition in searchingfor reasonableH0 andkG/k pairs giving a minimum in the energycurve at the expected full hydration compositioncexc (see Figure9) and showing a continuous pressure dependence (e.g., linear,quadratic or exponential). In the fitting procedures, the boundsfor the H0 and kG/k parameters were (-0.1, -10-4) Å-1 and(-3, 3), respectively. Moreover, to account for the experimentalerrors, the uncertainty in the full hydration composition wasestimated to be(0.02.

The best fit curves for the curvature elastic energy are reportedas a function of composition (at constant pressure) in the upperframe of Figure 15, whereas in Figure 16, the fittedH0 andkG/k values are plotted as a function of pressure. In the lowerframe of Figure 15, the curvature elastic energy, also calculatedfor theIa3d cubic phase using extrapolatedH0 andkG/k values,is reported as a function of pressure (at constant composition).

As stated by Templer and co-workers,18 the meaning of thecurvature elastic parameters remains elusive, mainly owing tothe inhomogeneity of the Gaussian curvature of the underlyingminimal surface. This means that there are normally regions ofthe bilayer whose curvature is so large that terms in the freeenergy expansion of order higher than the second in the principalcurvatures ought to be included. However, in the present case,the lipid concentrations are quite low and the increased pressurecauses the principal curvatures to reduce. Therefore, we believethat at least two points can be stressed from our results. First,pressure reduces the spontaneous curvatureH0, that is, theintrinsic molecular wedge shape of monoolein vanishes bycompression. This fact is consistent with the conformationalorder induced by pressure and with the related changes in themonoolein hydration properties and accounts for the stabilizationof the lamellar phase at the higher investigated pressures.13

Moreover, the spontaneous curvature calculated at ambient

Figure 14. Pressure dependence of the molecular cross-sectional area,Amol, calculated at different distances from the IPMS for thePn3m andIa3d cubic phases at the two different concentrations indicated in eachframe. Curves are interpolated from the calculated points.

⟨gbend⟩ ) 2 k ⟨(H - H0)2⟩ + kG ⟨K⟩

) 2 k (⟨H2⟩ - 2 H0 ⟨H⟩ + H0)2⟩ + kG ⟨K⟩ (7)

⟨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)


pressure (H0 ) - 0.018 Å-1) is in significant agreement withthat measured by Vacklin and co-workers27 at the pivotal surfacein the monoolein HII phase at 37°C. In this phase, relievingalmost all the packing stress by adding 9-cis-tricosene, theyfoundH0 ) -0.025 Å-1, whereas when the packing stress wasnot completely relieved (i.e., in the presence of tricosane), themeasurements led to a nonphysical location of the pivotal surfaceand aH0 value of about-0.017 Å-1.27

The second point concerns the ratio between the Gaussianand the mean curvature module. ThekG/k is positive andincreases as a function of pressure from a value of about 0.14to about 1, obtained by extrapolation at 1.8 kbar of pressure.Becausek is expected to be always positive, the positive valueof kG is qualitatively consistent with the detected phase behavior,dominated at any pressure by cubic phases.15 ThekG/k calculatedat ambient pressure can be compared with the correspondingvalues of 0.024, determined in theIa3d phase of monoolein byChung and Caffrey,17 and of 0.05 and-0.10, recalculated byTempler and co-workers18,27 in the same system consideringdifferent H0 values, at the pivotal surface. The discrepancy insign is significant, but, as already discussed,18 small changesin the spontaneous curvature can lead to large changes in theratio of the curvature moduli.

The last comment concerns the continuous decreasing of thecurvature elastic energy of the two cubic phases as a functionof pressure (see Figure 15). Because the energy of the systemis indeed expected to increase by compression,13 it appears thatthe curvature elasticity does not dominate the total free energy.Other contributions should be included to obtain a completedescription of the free energy; interbilayer forces may play a

significant role, but especially stretching, that occurs duringcompression, could be the major responsible for free energychanges, as suggested by previous measurements.13 In thepresent 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 trans-formation of thePn3m bicontinuous cubic phase observed inmonoolein-water system have been investigated over a wideconcentration range as a function of pressure up to 2 kbar. Aphase transition to theIa3d bicontinuous cubic phase has beendetected when the mechanical pressure increases up to 1-1.2kbar. To explore the underlying mechanism for this transition,a simple theoretical model based on curvature elastic contribu-tions has been used to derive the energetics of the twobicontinuous cubic phases. Even if chain packing and othercontributions are ignored, or assumed to change minimallyacross phase transitions, the free energy curvature model isfound to give qualitative indication about the stability of thecubic phases in the pressure-concentration phase diagram.

As clearly stated by Czeslik and co-workers,12 an appropriateunderstanding of the stability and transformation of lipid phaseswhen pressure and concentration vary would require a detailedanalysis of all interactions involved. A deeper knowledge ofthe relationship between the lipid molecular structure and thethermodynamic parameters is as well needed. Although thepresent analysis is not exhaustive, the authors are persuadedthat the reported experimental data might help to disentangledifferent free energy contributions in further theoretical ap-proaches.

Acknowledgment. We gratefully acknowledge H. Muller(Chemical Laboratory of ESRF, Grenoble, France) for supplying

Figure 15. Composition and pressure dependence of the curvatureelastic energy⟨µc⟩ obtained by the numerical fitting procedure describedin the text. Upper frame: best fit curvature elastic energy curves inthe Pn3m domain at different pressures. The symbols indicate theexperimental points. Lower frame: curvature elastic energy curvescalculated using eq 8 as a function of pressure at different compositions.Theφw values are indicated in the legend. Below 1 kbar, energies referto the Pn3m data, whereas above 1 kbar the⟨µc⟩ values have beencalculated considering theIa3d data using extrapolatedH0 and kG/kparameters.

Figure 16. Pressure dependence of the fitted values for the spontaneousmean curvature,H0, and the ratio between the Gaussian and the meancurvature module,kG/k, obtained in thePn3m phase by the numericalfitting procedure described in the text. The lines are quadratic fits tothe data and have been prolonged in theIa3d pressure domain to suggestthe possible trend.


freshly synthesized monoolein samples and H. Amenitsch(Institute of Biophysics and X-ray Structure Research, AustrianAcademy of Sciences, Graz, Austria) for the valuable help andsupport during measurements. We also thank M. Kriechbaum(Institute of Biophysics and X-ray Structure Research, AustrianAcademy of Sciences, Graz, Austria) and M. Steinhart (Instituteof Macromolecular Chemistry, Academy of Sciences of theCzech Republic, Prague, Czech Republic) for their incisive helpin setting up the pressure control system on the beamline. Thiswork was supported by grants from the INFM, Italy.

References and Notes

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pressure induced cubic-to-cubic phase transition in monoolein hydrated system

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