polymorphism of lipid-water systemsdutcher/download/handbook of... · chapter 3 polymorphism of...

CHAPTER 3

Polymorphism of Lipid-Water Systems

J.M. SEDDON and R.H. TEMPLER

Department of Chemistry, Imperial College,Exhibition Road, London SW7 2AY, U.K.

1995 Elsevier Science B.V. Handbook of Biological PhysicsAll rights reserved Volume 1, edited by R. Lipowsky and E. Sackmann

97

Contents

1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99

2. Interfacial curvature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

3. Structure of lyotropic phases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105

3.1. Phase identification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105

3.2. Topology determination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107

3.3. Phase dimensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110

3.4. Nomenclature for phase structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110

3.5. Crystalline phases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110

3.6. Ordered lamellar phases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112

3.7. Fluid phases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115

3.8. Isotropic solution phases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120

4. Phase behaviour . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123

4.1. Lyotropic phase diagrams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123

4.2. Phase stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126

4.3. Packing geometry and frustration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126

4.4. Curvature elastic energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129

4.5. Lateral stress profile . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130

4.6. Defects and epitaxiality in phase transitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134

5. Factors affecting lyotropic transitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136

5.1. Types of transition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136

5.2. Effect of lipid chemical structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137

5.3. Lipid mixtures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138

5.4. Solution effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139

5.5. Solute effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139

5.6. Phase metastability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141

5.7. Transition kinetics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141

6. Biological implications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143

6.1. Non-lamellar phases in biology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143

6.2. Membrane fusion and cell signal transduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145

6.3. Homeostatic control of ‘phase stability’ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145

6.4. Bilayer stress profile and regulation of membrane protein activity . . . . . . . . . . . . . . . . 146

6.5. Protein/lipid mixtures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146

7. Open problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146

Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149

98

1. Introduction

This chapter will describe the types of liquid-crystalline phases adopted by lipids inwater, and the factors which control phase stability. Even single lipid systems candisplay a quite extraordinarily rich variety of liquid-crystalline phase structures uponvarying the water content and/or the temperature. These different phases result froman optimization of the hydrophobic effect with a variety of intra- and intermolec-ular interactions, in combination with a number of geometric packing constraints.Examples of lyotropic phase structures are the fluid lamellar Lα phase, fig. 1a, theinverse hexagonal HII phase, fig. 1b, and the inverse bicontinuous cubic phase ofcrystallographic spacegroup Pn3m, fig. 1c.

In this chapter we will deal primarily with the fluid lyotropic phases, since theseare likely to be of the most direct relevance to the structure and function of biomem-branes. The properties of lamellar phases (those based on lipid bilayers) are discussedextensively in various other chapters in this volume; therefore, in this chapter the em-phasis will rather be on the various non-lamellar phases, whose roles in biomembranestructure and function are still controversial and poorly understood. Furthermore wewill focus attention on biological lipids such as phospholipids, rather than dealingwith all surfactant systems. However, much of the behaviour described here is ofquite general relevance to lyotropic systems: most if not all of the structures formedby biological lipids can also be observed in simpler surfactants, under appropriateconditions.

Fig. 1a. Examples of lyotropic structures: Lα fluid lamellar phase.

99

100 J.M. Seddon and R.H. Templer

Fig. 1b. Examples of lyotropic structures: inverse hexagonal HII phase (from [1]).

Fig. 1c. Examples of lyotropic structures: inverse bicontinuous cubic phase Pn3m (from [2]).

Polymorphism of lipid-water systems 101

Although biopolymers such as DNA also form lyotropic liquid crystalline phases,the mechanisms are quite distinct from those applying to amphiphiles, and suchsystems will not be described here. Much of the experimental work on lipid systemshas been performed on pure, well-defined synthetic lipids, although natural lipidextracts from membranes often exhibit the same phase structures, notwithstandingthe fact that they usually consist of very complex mixtures of different lipids.

The structures of the translationally ordered lipid phases have been reviewed anumber of times [1–10], and these articles should be consulted for further details.A recent issue of Chemistry and Physics of Lipids [11] was devoted to the subjectof lipid polymorphism, and an issue of Journal de Physique [12] to geometry andinterfaces, relating mainly to lyotropic liquid crystals. Books have appeared on thesubject of phospholipid bilayers [13] and the physics of amphiphilic layers [14, 15],and theoretical approaches to membrane conformations have been recently reviewed[16, 17].

2. Interfacial curvature

In order to describe and characterize the various lyotropic phases, it is most useful tofocus attention on the interface between the polar and non-polar regions of the phases(i.e. the narrow region where the headgroups are attached to the hydrocarbon chains),corresponding to the plane at which the interfacial tension acts within a monolayer.(By interfacial tension we mean purely the tension at the hydrocarbon/water interface.However, many authors use this term to mean the total net lateral tension, i.e. theyinclude the lateral stress contributions from chain–chain and headgroup–headgrouplateral repulsions and/or attractions.) This interfacial plane should lie close to theneutral surface, i.e. the surface at which there is no change in area per moleculeupon bending. Apart from its area, the interface is characterised by its mean andGaussian curvatures, H and K. These are related to the principal curvatures c1 andc2 at a given point P on the surface, fig. 2, by

H = [c1 + c2]/2, (1)

K = c1c2. (2)

Different phases have different values of mean and/or Gaussian interfacial curva-tures, and these may or may not be uniform at different points on the interface withina single phase. We will adopt the convention that for a lipid monolayer, H > 0 de-notes curvature towards the chain region, whereas H < 0 denotes curvature towardsthe water region; see fig. 2. Note that although this definition for a monolayer isunambiguous, the sign of the mean curvature for a lipid bilayer is arbitrary.

The mean curvature H of a monolayer can be changed simply by bending, withoutstretching the interface. However, changing the Gaussian curvature K necessarilyinvolves stretching (or contracting) the interface (but this could be achieved at con-stant interfacial area if the molecules are free to redistribute laterally). Both of thesetypes of deformation involve associated curvature elastic energy costs.


Fig. 2. Definition of mean curvature H and Gaussian curvature K for a lipid monolayer. R1 andR2, and c1 and c2, are the principal radii of curvature, and the principal curvatures, respectively, at thepoint P . n is the unit normal vector of the surface patch A at point P , directed in the positive z-direction.

Adapted from [1].


Fig. 3. Saddle surface, of (non-uniform) negative Gaussian curvature. From [1].

The Gaussian curvature K is a more fundamental property of the interface than Hsince it determines the qualitative nature of the surface. Surfaces for which K is pos-itive are known as elliptic, and naturally bend round to form closed shells. A micelleor an inverse micelle are examples of this. When either of the principal curvaturesare zero, the Gaussian curvature is zero, and the surface is known as parabolic. Thelamellar and hexagonal phases are examples of this. The third possibility arises whenthe principal curvatures c1 and c2 are of opposite sign, leading to a negative Gaussiancurvature. These surfaces are known as hyperbolic, and an example is the saddlesurface, shown in fig. 3. The Gaussian curvature is most negative at the saddle pointand increases smoothly to zero at the four apices. When the principal curvatures areeverywhere equal in magnitude but opposite in sign, then the surface has zero mean


Fig. 4. An example of an infinite periodic minimal surface: Schwartz’s P-surface.

curvature at all points and is known as a minimal surface. Such surfaces can be ex-tended to fill space, forming infinite periodic minimal surfaces, which form a singleseptum, dividing space into two congruent sub-volumes. An example is the SchwarzP-surface, shown in fig. 4. Thus when K < 0, this leads naturally to the formationof porous structures. The two networks of interpenetrating, non-intersecting poresare either equivalent, as in the P-surface, or are chiral enantiomorphs. The P-surfaceis closely related to two other minimal surfaces, the Schwarz F-surface (sometimesdenoted the D-surface), and the gyroid, or G-surface [18].

It is now generally believed that the bicontinuous cubic phases are based uponsuch underlying minimal surfaces [19–27, 18, 28–30, 12]. The basis of this is thatparallel surfaces on either side of a minimal surface have smaller areas, and hencehave non-zero average mean curvatures, directed away from the minimal surface. Alipid bilayer draped onto such a minimal surface will have a net curvature of eachmonolayer towards the water regions. Thus a system which has a preferred area perheadgroup which is smaller than the preferred area per chain(s) can lower its elasticenergy by deforming from a planar bilayer to a saddle surface; see fig. 5.

3. Structure of lyotropic phases


Fig. 5. A bilayer draped on a saddle surface has a smaller area at the centre of each monolayerhydrocarbon chain region (σ2) than at the bilayer mid-plane (Σ), and an even smaller area (σ1) at each

headgroup region. From [31].

3.1. Phase identification

Diffraction methods, in particular X-ray scattering, are the most reliable way ofcarrying out lipid phase identification. Spectroscopic techniques such as NMR havebeen used by certain authors for phase identification, although this can under certaincircumstances lead to incorrect assignments. Freeze-fracture electron microscopy,when used in conjunction with X-ray diffraction, can yield useful complementarydata [32].

In the characterization of lipid mesophases by diffraction, there are two regionsof the diffraction pattern that are used to identify the phase. The small angle regionidentifies the symmetry and long range organization of the phase, whereas the wideangle region gives information on the molecular packing, or short range organizationof the phase. The signature of a translationally ordered mesophase is the appearanceof one or more sharp (Bragg) peaks in the low-angle region of the diffraction pattern.

The long-range translational ordering of the lipid/water aggregates (bilayers, cylin-ders, micelles, etc) onto 1-, 2- or 3-dimensional lattices gives rise to Bragg reflectionswhose reciprocal spacings (shkl = 1/dhkl) are in characteristic ratios; see fig. 1, forexample:


Lamellar: sl = l/d (Ratios 1, 2, 3, 4, . . .)

Hexagonal: shk = 2(h2 + k2 − hk

)1/2/√

3a(1,√

3, 2,√

7, 3,√

12,√

13, . . .)

Cubic: shkl =(h2 + k2 + l2

)1/2/a

(1,√

2,√

3, 2,√

5,√

6,√

8, 3, . . .)

Once the lattice type has been identified, it is necessary to determine the crystallo-graphic spacegroup [33] to which the phase belongs, from the pattern of systematicabsences in the diffraction pattern. However, this is often not trivial, since usuallyonly a few low-angle Bragg peaks are detected, due to the large thermal disorderinherent in liquid-crystalline phases, which strongly damps the intensities at largerdiffraction angles. In fact, there are a number of examples in the literature whereincorrect phase assignments appear to have been made.

For the 2D phases (hexagonal, rectangular, square, oblique) there are only 17 pos-sible plane groups. For 3D phases there are 230 possible space groups, althoughvery few of these have so far been observed in lyotropic systems. To date, sixdifferent cubic phases have been clearly identified in lipid systems, belonging todifferent spacegroups (it should be noted that totally different phase structures couldin principle have the same spacegroup, although for lipids this usually seems notto occur). A number of other cubic phases have been tentatively identified in var-ious systems. From unaligned samples it is usually only possible to identify thecubic aspect from the systematic absences, leaving an ambiguity about the precisespacegroup. In some cases this ambiguity could be resolved if monodomain sampleswere available, since hkl reflections are not fully permutable for certain spacegroups(i.e. the observed intensity (hkl) may not be equal to that of (khl), the non-cyclicpermutation). Furthermore, complementary freeze-fracture electron microscopy ex-periments can be of help, by showing directly the presence of mirror planes in thephase structure [29, 32].

The intensities of the various Bragg peaks are determined by the distribution ofmatter (electron density) in the unit cell, which is constrained by the symmetry ofthe spacegroup. A symmetry-allowed reflection may nonetheless have zero intensitybecause the unit cell Fourier transform happens to pass through zero at that particulardiffraction angle. If it is possible to deduce the phasing of the structure factors (fromthe intensities of the Bragg peaks) then low-resolution (electron) density maps can bedirectly obtained by Fourier transformation. However, the standard direct methods, orisomorphous replacement, for phasing are not generally suitable for liquid crystallinesystems. In some cases, in particular for lamellar phases, it is possible to use waterswelling experiments to deduce the phasing [34]; in neutron diffraction experiments,the solvent contrast variation technique may be employed [35]. However, for 3Dstructures such as lyotropic cubic phases, the only successful technique so far forphasing the reflections has been to employ a pattern recognition approach [29, 36].

A further major problem with the characterisation of lipid phases is the difficulty ofensuring that the sample is at equilibrium. In part this may be due to the rate at whicha phase comes to equilibrium being very slow. However, a further problem is that thephase itself may be metastable, reverting to more stable forms over a time scale whichcan span seconds to months. For example, both the gel and fluid lamellar phasesof phosphatidylethanolamines are metastable within certain temperature ranges, andwill spontaneously convert to lamellar crystals on incubation [37].


3.2. Topology determination

There are three main aspects to the determination of the topology of a lipid mesophase(we use the term topology here in a very loose sense).

3.2.1. Sign of the interfacial mean curvatureFirstly, it is vital to establish whether the phase is inverse or normal, i.e. whetherthe polar/non-polar interface curves on average towards the water or towards thehydrocarbon region of the phase. With the exception of the lamellar Lα phase, allof the lyotropic liquid-crystalline phases, for example the hexagonal phases, fig. 6,may potentially occur either as type I (normal, oil-in-water) structures, or as type II(inverse, water-in-oil). Surprisingly, because of Babinet’s principle, it is not trivialto determine by diffraction which type one is dealing with. However, there are anumber of approaches which can be used in order to establish it with reasonablecertainty [1, 3]:

a. If a fluid non-lamellar phase is observed to coexist with an excess aqueousphase, this is by itself strong evidence for an inverse, type II structure; type Iphases of lipid systems almost invariably break up into micellar solutionsbeyond a certain limiting water content.

b. If a fluid non-lamellar phase occurs to lower (higher) water content than thelamellar Lα phase, then it is probably inverse (normal). This rule is howeverdangerous, as there are important exceptions to it. For example, the phasediagram of monoolein exhibits two inverse bicontinuous cubic phases on thehigh water side of the Lα phase.

c. If a phase of unknown type (normal or inverse) is adjacent in the phasediagram to a non-lamellar phase of known type, then it almost certainly is thesame type.

d. If the interfacial area per molecule (deduced from diffraction data) is plot-ted against water concentration, it should not decrease with increasing watercontent, if the assumed type is correct.

e. The value of interfacial area per molecule at the water/lipid interface is nor-mally lower (higher) for an inverse (normal) phase than for an adjacent Lαphase, either when the transition is driven by varying the composition, or byvarying the temperature.

f. The variation of the intensities of the Bragg peaks for a range of water contentscan provide unambiguous evidence for whether the phase is normal or inverse.

g. It should in principle be possible to probe phase type by employing neutrondiffraction contrast variation techniques, although as yet this has been littleemployed in structural studies of lipid polymorphism.

3.2.2. GenusSecondly, for complex 3D structures such as cubic phases, it is necessary to establishwhether the phase is bicontinuous or discontinuous (micellar). These two possibilitiesare topologically distinct: the former type has a single ‘surface’, but many holes, thelatter has ns separate surfaces (per unit cell), each free from holes in the interface.Furthermore, bicontinuous phases may have different values of genus.


Fig. 6. Non-lamellar phases may exist as normal (oil-in-water) or inverse (water-in-oil) types. (a) Anexample of the former is the hexagonal phase HI. From [1]. (b) An example of the latter is the hexagonalphase HII. For this phase, water swelling leads to a strong increase in interfacial area per molecule.

From [1].

The genus g of a phase is a fundamental topological property related to the connec-tivity of the surface defining the lipid layers (e.g., a minimal surface for bicontinuouscubic phases). It is defined as the maximum number of non-intersecting closed loopcuts that can be made in the surface without it falling into two parts. For an in-finite periodic minimal surface, the genus is, strictly speaking, infinite. However,the genus per unit cell is well defined, and is determined by using the translationalsymmetry to connect together corresponding surfaces cut by opposite faces of theprimitive translation cell of the surface. Thus the number of topologically distinctholes per unit cell gives the genus g of the phase. For the P , F , and gyroid minimalsurfaces, the genus per unit cell is 3 [38]; in fact they have to have the same valuebecause they are connected by the Bonnet transformation. It should be noted thatthe space group and the primitive translation cell of the underlying minimal surfaceneed not be the same as that of the cubic phase itself. For example the F -surface


underlying the Pn3m (= Q224) cubic phase has space group F43m (= Q216) and hasa primitive translation cell with twice the volume of the Pn3m cubic phase. A mostuseful quantity is the dimensionless area, A0, per conventional unit cell of the cubicphase, which has the values 1.919, 2.345 and 3.091 for the F , P and gyroid minimalsurfaces, respectively. Thus the total area per unit cell at the bilayer centre is givenby a2A0, where a is the conventional unit cell lattice parameter, and the area permolecule at this interface follows directly if the water content of the phase is known.

The Gauss–Bonnet theorem relates the number of disconnected surfaces ns, eachhaving the same genus g, to the surface integral of the Gaussian curvature by:∫ ∫

K dA = 4πns(1− g). (3)

Thus the bicontinuous phases have a negative average Gaussian curvature, whereasfor the micellar cubic phases this quantity is positive.

Within the family of bicontinuous phases, certain spacegroups could correspond toa variety of different structures, having different degrees of connectivity (genus) [30,39]. For example, the cubic phase Im3m (= Q229) could correspond to structuresbased on surfaces of genus per unit cell of 3 (P-surface), 4 (I-WP-surface), 9 (Neoviussurface) or 10 (O,C-TO-surface). In principle it should be possible to distinguishthese from the relative intensities of the observed Bragg peaks, although the formfactors have so far only been calculated for the first of these surfaces [40]. Thediffraction patterns from the bicontinuous cubic phases based on the P-, F- andG-surfaces tend to have quite characteristic intensity distributions [29], and when anunusual intensity distribution is observed, the possibility that a higher genus phase ispresent should be considered. Further evidence may be obtained from considerationof whether the dimensions of the phase are compatible with the composition andthe packing properties of the amphiphile (e.g., maximum molecular length). Suchanalysis suggests that both genus 3 [41] and higher genus cubic phases [42] occurin certain ternary surfactant/oil/water systems.

Even in binary systems such as sodium dodecyl sulphate/water, the structure ofthe Im3m cubic phase reported [43] is uncertain, but appears not to be based on thegenus 3 P-surface [30].

3.2.3. Monolayer or bilayer structureThirdly, for the bicontinuous phases the structure could in principle be based either ona lipid bilayer, or on a monolayer [30]. Note that for the hexagonal and micellar cu-bic phases the structure is normally based on a lipid monolayer. For most biologicallipid systems (at least in the absence of added oil or co-surfactant) the bicontinuousstructures appear to be based on bilayers, whereas for some surfactant or microemul-sion systems, the picture is much less clear, and both types of bicontinuous phasemight occur [30]. For example, in the ternary system didodecyldimethylammoniumbromide/octane/water, there is some evidence for a monolayer cubic phase structurebased on an underlying I-WP minimal surface (of genus 4) [44].


3.3. Phase dimensions

Although a detailed analysis of the diffraction intensities is required to obtain themesophase structure in terms of electron density maps, useful structural informationsuch as the lipid and water layer thicknesses, and the interfacial area per molecule,can be obtained simply from the positions of the diffraction peaks [3]. The thick-nesses are ill-defined to the extent that the water-lipid interface is not completelysharp. For non-lamellar phases the value of area per molecule depends on the po-sition chosen for the interface. Often this is a hypothetical, sharp interface dividingthe lipid layer from the water. If this becomes unrealistic, for example when thelipid headgroups are very elongated, it may be more appropriate to lump the po-lar headgroups together with the water, setting the interface at the polar/non-polarboundary.

Such analysis requires knowledge of the composition of the phase and the densitiesof the water and lipid components. The density of the water is usually assumed tobe the same at a given temperature as that of bulk water, while the density of thelipid may be measured either by the oscillating tube or neutral bouyancy techniques.For more complex structures such as the bicontinuous cubic phases, the variousdimensions may be estimated using results from differential geometry [30].

3.4. Nomenclature for phase structures

The most widely used nomenclature for lyotropic phases is that proposed by Luz-zati [3], and this will be adopted here. The lattice type is denoted by a capital letter,e.g., L for lamellar, H for hexagonal and Q for cubic. Subscripts I and II are usedto denote normal (oil in water) or reversed (water in oil) topology phases. A Greeksubscript is used to denote the chain conformation: c for crystalline, β for orderedgel-like, α for liquid-like, αβ for coexisting gel- and liquid-like regions, and δ for ahelically coiled chain conformation.

A list of the well-established lyotropic phase types is given in table 1. There isactually a family of cubic phases, and those discovered to date, whose structures arewell-established, are listed in table 2.

Table 2

List of the well-established cubic lyotropic phases.

Spacegroup symbol Spacegroup number Cubic aspect Reference

P4332 Q212 3 29Pm3n Q223 5 50Pn3m Q224 4 29Fd3m Q227 15 36Im3m Q229 8 29Ia3d Q230 12 29


Table 1

List of the well-established, translationally ordered lyotropic phases.

Phase Description Reference

Lc 3D lamellar crystals 45L2D

c Lamellar stack of 2D crystalline bilayers 46Lβ Lamellar gel (untitled) 47Lβ′ Lamellar gel (tilted) 47LβI Interdigitated gel 48Lαβ Partial gel 3Lδ Lamellar phase of square-packed, helically-coiled 47, 49

(δ) chainsPβ′ Rippled gel phase 47Pδ Ribbon phase with δ-packed chains 47Lα Fluid lamellar phase 3H Hexagonal 1Hc Hexagonal, complex 3R Rectangular 43M Oblique 43Q Cubic 29T Tetragonal 3Rh Rhombohedral 3

3.5. Crystalline phases

Most phospholipids form crystalline lamellar Lc phases at low temperatures and/orhydrations. These phases exhibit both long- and short-range order in three dimensionsand are therefore true crystals. They may be anhydrous, or may also contain a numberof water molecules of co-crystallization. Many lipid structures have now been solvedby single crystal studies [45].

The molecular conformation in the lamellar crystalline phases of dilauroylphos-phatidylethanolamine (DLPE) [51], and dimyristoylphosphatidylcholine (DMPC) [52]are compared in fig. 7. Although the conformations appear quite similar, methylationof the phospholipid terminal ammonium group does in fact have a profound effect onthe molecular packing and interactions. It is striking that the intermediate methylatedcompound, dilauroylphosphatidyl-N ,N -dimethylethanolamine (dimethyl-DLPE) [53]has a quite different conformation, as shown in fig. 8, with the headgroups beinginterdigitated. All three lipids pack into bilayers, but for DLPE a tight network ofheadgroup-headgroup hydrogen-bonds is formed, fig. 9, with the headgroups parallelto the plane of the layer, whereas DMPC headgroups (lacking any donor groups)interact via bridging water molecules.

Certain lipids when incubated in water at low temperatures, adopt so-called sub-gel phases. These appear to consist of lamellar stacks of two-dimensional crystallinebilayers. For a charged lipid such as phosphatidylglycerol (PG), the crystallinebilayers can be swollen apart in water by electrostatic repulsion [46].


3.6. Ordered lamellar phases

Many lipids adopt lamellar phases at low temperatures in which the hydrocarbonchains are still ordered essentially in the all-trans conformation, but where theyundergo hindered long-axis rotation on a time scale of 100 nsec. The effectivecylindrical symmetry means that the chains pack onto 2D hexagonal lattices. Theheadgroups are normally disordered and the lateral correlations between adjacentlayers are weak or nonexistent.

Such gel phases are normally formed in the presence of water, although this isnot always strictly necessary. The thickness of the water layer depends on factorssuch as the water content and temperature, and the lipid headgroup size, polarityand charge. The maximum water content is often relatively low, with a water layerthickness in the region of 8–16 A, although the gel phases of charged lipids canswell to very large layer spacings.

In the Lβ gel phase, fig. 10a, the hydrocarbon chains are arranged parallel to thelayer normal, with a value close to 20 A2 for the cross-sectional area per chain.The Lβ′ phase, fig. 10b, is a tilted version of Lβ , and different tilt directions withrespect to the underlying hexagonal lattice may occur. The tilting occurs when theheadgroup area packing requirement exceeds twice that of the chains (for diacyllipids): tilting allows the packing mismatch to be accommodated. However, whenthe tilting becomes too great, then the (untitled) interdigitated LβI phase, fig. 10c, mayform, which has a similar cross-sectional area per chain to Lβ , but with approximatelytwice the area available per headgroup.

A gel phase where the lamellae are deformed by a periodic modulation is notuncommon. This Pβ′ ripple phase, fig. 10d, occurs below the Lα phase with temper-ature. It has been observed in phosphatidylcholines [47] and phosphatidylglycerol atneutral pH [56], and in phosphatidylethanolamine [57] and phosphatidic acid [58] at

Fig. 7. Molecular conformation in the lamellar crystal phase of DMPC. From [45].


Fig. 8. Structure of the headgroup-interdigitated lamellar crystal phase of dimethyl-DLPE. The positionsof the L- and D-enantiomers are indicated. From [53].

high pH. The lattice is usually oblique (2D space group p2, No. 2), with the chainsessentially being in the tilted gel-like β′ conformation.

An unusual lamellar Lδ phase has been observed in dry phosphatidylcholines [47,49]. Here the hydrocarbon chains are coiled into helices and are arranged on atwo-dimensional square lattice. The polar headgroups are also arranged on a squarelattice (the length of which is the diagonal of the square lattice of chains), andare oriented perpendicular to the layer, interdigitated with those from the apposed


Fig. 9. Headgroup packing and hydrogen bonding in crystalline DLPE. The molecular area S is38.6 A2. The b and c unit cell parameters are indicated, along with a number of intramolecular

and intermolecular contact distances. From [54].

Fig. 10. Gel phases of lipids: a) Lβ untitled gel; b) Lβ′ tilted gel; c) LβI interdigitated gel; d) Pβ′rippled gel. Adapted from [55].


neighbouring bilayer. A closely related phase denoted Pδ (2D space group cmm,No. 9) is also found in dry phosphatidylcholines. In this phase, the hydrocarbonchains have the δ conformation, and ribbon-like strips of bilayer are packed onto a2D centred rectangular lattice.

3.7. Fluid phases

Upon heating a gel phase lipid, the cross-sectional area per chain characteristicallyincreases to a limiting value of about 21 A2; upon further heating, the chains meltto a liquid-like conformation, transforming usually to the lamellar Lα phase, fig. 11(For some lipid systems the gel phase melts directly to a fluid non-lamellar phase,for example HII or cubic). The interfacial area per molecule expands by 15–30%on transforming to the Lα phase (the expansion is usually smaller for the HII phase,and intermediate for the inverse bicontinuous cubics), and there is the onset ofrapid lateral diffusion (Dtrans ≈ 10−11 m2 sec−1). The Lα phase may be swollen byaddition of water or oil up to certain limiting spacings. For uncharged phospholipids,the maximum water layer thickness is typically in the range of 10–30 A.

Fig. 11. The fluid lamellar Lα phase and its water- and oil-swollen versions.


However, certain lyotropic lamellar phases will swell to extremely large spacings(as large as 5000 A) upon addition of oil or water [59]. The swelling may be drivenelectrostatically (for charged bilayers), but can also result from thermally excitedundulations if the layers are quite flexible. It should be noted that oil-swellingseparates the bilayer into two monolayers.

3.7.1. 2D fluid phasesIf the fluid lipid aggregates consist of indefinitely long cylinders (not necessarily ofcircular cross-section) rather than bilayers, then two-dimensional fluid phases willbe formed. The simplest and best established of these are the normal and inversehexagonal phases HI and HII (2D space group p6m, No. 17) shown in fig. 6. Inthe HI phase the lipids aggregate into circular cylindrical micelles which pack ontothe hexagonal lattice, with a continuous water region filling the volume betweenthe cylinders. In the inverse HII phase on the other hand, the cylinders containwater cores surrounded by the lipid polar headgroups, with the remaining volumecompletely filled by the fluid hydrocarbon chains at an essentially uniform liquidalkane density. Although the HI phase is very common in simple surfactant systems,it tends not to be formed by diacyl phospholipids, although it is observed withincertain hydration ranges in lyso-phospholipids.

The HII phase is very common in phospholipids such as PE, having small weaklyhydrated headgroups, and having attractive headgroup-headgroup interactions [1]. Itis also observed in hydrated phospholipid/amphiphile systems such as PC/fatty acidmixtures [60–64]. Although the vast majority of reported hexagonal phases are basedon aggregates having a single curved lipid layer (monolayer), a more complex type,denoted Hc, has been found in certain systems, whose structure appears to be basedon a hexagonal packing of cylinders formed by curved lipid bilayers [3].

For some systems, the shape of the cylinders may deviate from circular in cross-section, leading to a packing into 2D phases of lower symmetry, such as rectangularor oblique [43].

3.7.2. 3D fluid phasesThe vast majority of three-dimensional fluid phases so far detected are of cubicsymmetry, although rhombohedral, tetragonal and orthorhombic phases of inversetopology have been detected in a few lipid systems at low hydrations [3].

In the rhombohedral phase (space group R3m, No. 166), short segments of lipid/wa-ter cylinders are connected three by three to form planar hexagonal networks, whichstack into a trilayer structure, fig. 12a. The tetragonal phase (space group I422,No. 97) is similar, but the cylinders are connected four by four to form planar squarenetworks, which stack into a body centred tetragonal lattice, fig. 12b. A body-centred orthorhombic phase (space groups mmm, No. 47 or 222, No. 16) has beenobserved in certain anhydrous soap systems [3], but has not as yet been found inphospholipids.

By far the largest family of 3D lyotropic phases are of cubic symmetry. Thesephases may be easily detected by polarising microscopy, since they are opticallyisotropic, and are very viscous, unlike isotropic or micellar solutions. To date five


Fig. 12a. Three-dimensional non-cubic liquid-crystalline phases: rhombohedral (spacegroup R3m).From [1].

centrosymmetric cubic phases have been well characterised in lipid/water systems,along with a further non-centrosymmetric one which occurs in certain lipid/proteinmixtures at low hydration. These phases are listed in table 2, along with theirspacegroup number and cubic aspect. Strictly speaking it is only possible to deducethe cubic aspect from the pattern of systematic absences in the powder-like diffractionpatterns, but it is assumed that the most symmetric spacegroup within a given cubicaspect is the correct one [29].

There appear to be two distinct families of cubic phases. One type is bicontinuous,and is based on underlying periodic minimal surfaces; the other type is micellar,being based on complex packings of discrete micellar aggregates. Both types maybe normal (oil-in-water) or inverse (water-in-oil), although curiously, apart from Ia3d(= Q230), a given spacegroup usually exists as only one type or the other. There aremany other examples of cubic phases that are not yet definitely identified, and it isprobable that more cubic phases remain to be discovered.

In terms of minimal surfaces, the inverse bicontinuous cubic phases Ia3d, Pn3mand Im3m are formed by draping a continuous lipid bilayer onto the gyroid, F- and


Fig. 12b. Three-dimensional non-cubic liquid-crystalline phases: tetragonal (spacegroup I422).From [1].

P-minimal surfaces, respectively. It is interesting that these three surfaces constitutea family of infinite periodic minimal surfaces which are related to each other bythe Bonnet transformation. This means that one surface can be transformed intoeither of the others simply by bending, which leaves the Gaussian curvature at allpoints unchanged, and preserves all angles, distances and areas on the surface [18].However, in our opinion it is unlikely that cubic-cubic transitions occur by a Bonnet-like transformation, which would require unphysical layer self-intersections to occur.

The lattice parameters observed so far for cubic phases fall into the range of 80–270 A, both for ternary surfactant/oil/water systems [42] and for lipid mixtures [65].There are some theoretical grounds for believing that the latter figure may be closeto an upper stability limit [66], but this remains to be established.

Ia3d (= Q230) was the first cubic phase structure to be solved [67]. The inversetype, shown in fig. 13a, is formed by a number of lipid systems, whereas the type I(oil-in-water) version is rather common in surfactant systems. The structure consistsof two interwoven yet unconnected chiral networks of water/lipid cylinders, con-nected coplanarly three by three and separated by the G-minimal surface. Althoughthe two networks are chiral, the cubic phase itself is centrosymmetric.


Fig. 13. Inverse bicontinuous cubic phases: a) Ia3d (= Q230); b) Pn3m (= Q224); c) Im3m (= Q229).The structures for Ia3d and Pn3m are shown in their ‘rod-like’ versions, which should correspond tolow water contents. At higher water contents they will appear more like uniform thickness bilayersdraped on the underlying minimal surface; cf., fig. 1c. Part of the underlying F-surface is shown for the

Pn3m cubic phase. From [1].


Fig. 14. The micellar cubic phase Pm3n (= Q223). The proposed clathrate/micelle structure (a) hasnow been ruled out. It is not yet established which of (b) or (c) is the correct structure. Also shown,between structures b and c, are electron density maps from the system sodium octanoate/p-xylene/water(taken from [29]). The left frame shows a section normal to the 3-fold axis through the point (1/4, 1/4,

1/4), and the right frame shows a section normal to the z-axis at z = 1/4. From [10].


The structure of Pn3m (= Q224) was determined independently by two groups[22, 68]. It consists of two interwoven tetrahedral networks of water channels ar-ranged on a double-diamond lattice, separated by the F-minimal surface; see fig. 13b.The third bicontinuous cubic phase, Im3m (= Q229) has orthogonal networks of wa-ter channels connected six-by-six, and separated by the P-minimal surface, fig. 13c.Pn3m seems always to be inverse, and Im3m is usually so, although one example ofa type I (oil-in-water) Im3m cubic phase has been reported [43].

The cubic phase Pm3n (= Q223) occurs in certain systems adjacent to the micellarsolution, and its structure has been controversial since the original proposal [69]shown in fig. 14a. It is now agreed that the structure in fact consists of a cubicpacking of two types of micelle [70]. There are 2 quasi-spherical, and 6 slightlyasymmetric micelles per unit cell. However, it is not yet fully established whetherthe asymmetric micelles are disk-like, as shown in fig. 14b [50, 71], or rod-like,fig. 14c, with rotational disorder around one of the short axes [72, 73].

The first well-established example of a cubic phase composed of a packing ofdiscrete inverse micelles is the phase Fd3m (= Q227). It has been observed in avariety of hydrated lipid mixtures, such as monoolein/oleic acid [29] and diglyc-eride/phosphatidylcholine mixtures [74]. The structure has recently been solved [36]and is shown in fig. 15. As for the type I micellar cubic phase Pm3n, there aretwo types of aggregate in the unit cell. However, in the case of Fd3m both types ofinverse micelle are quasi-spherical, but of different sizes. There are 8 of the largerand 16 of the smaller inverse micelles per unit cell. It is interesting to note thatsuch a structure was predicted by a topological/geometrical study of the possiblepackings of fluid films [71]. Formation of the Fd3m cubic phase usually needs thepresence of at least two lipid components, one of which is very weakly hydrophilic(e.g., fatty acid, diglyceride, etc). The explanation is probably that this permits apartial segregation of the two lipid components between the two types of micelle,with the less hydrophilic species locating preferentially in the smaller, more stronglynegatively curved inverse micelles.

A chiral cubic phase of spacegroup P4332 (= Q212) has been observed in a ternarylipid/protein/water system [29]. The proposed structure is derived from that of Ia3d:one water/lipid network remains, but the other is replaced by a network of quasi-spherical inverse micelles, within which the protein is located. The fact that thiscubic phase is chiral has fascinating implications. In particular, although ordinaryphospholipids appear not to be sufficiently chiral to form chiral cubic phases [76],more strongly chiral lipids might be found to do so.

3.8. Isotropic solution phases

Although the translationally disordered solution phases such as micellar solutions,microemulsions, or so-called L3 (sponge) phases have so far been mainly associatedwith surfactant systems, we describe them briefly here, since it is likely that lipidsystems in the presence of oil and/or naturally occurring co-surfactants may exhibitanalogous behaviour.

Short chain phospholipids (typically C6 or C8) and lyso-phospholipids form mi-cellar solutions at fairly high dilutions in water [3]. On the other hand, hydrated


Fig. 15. The inverse micellar cubic phase Fd3m (= Q227). From [75].

phospholipids can form inverse micellar solutions in the presence of certain or-ganic solvents such as benzene [77]. Furthermore, at low hydrations in the pres-ence of certain organic solvents such as alkanes, phosphatidylcholines form stiff,non-birefringent gels [78], whose structure appears to consist of entangled flexibleinverse cylindrical micelles [79]. Inverse micellar solutions are also formed by phos-pholipids upon incorporation of large amounts of weakly polar amphiphiles such asdiglycerides [74].

Fig. 16. Structure of the L3 ‘sponge’ phase. The disordered interface may consist of either a bilayer,or an inverse bilayer. From [84].


Microemulsions are isotropic solutions formed by amphiphile/oil/water mixtures[80]. The microstructure can consist of discrete micelles or inverse micelles, butwhen the volume fractions of oil and water are similar, bicontinuous structures tendto form, with the amphiphile forming a monolayer arranged as a random, connectedporous interface between the oil and the water regions. The interface is believed tocorrespond to thermally disordered minimal surfaces [19, 20]. In some microemul-sion systems, stiff gels are formed, which have been found to have a cubic phasestructure. Unlike the bicontinuous lipid cubic phases, the structure appears to bebased on a monolayer rather than a bilayer [44]. However, such monolayer cubicphases might be formed by phospholipids in the presence of organic solvents; workcarried out recently in our laboratory hints at this.

Certain surfactant systems form highly swollen lamellar phases, which may trans-form upon dilution to a so-called L3 or sponge phase [81–83]. This phase is essen-tially a disordered version of the bicontinuous cubic phases: the interface is highlyflexible and thermal excitations break down the long range order of the network ofchannels so that the interface is no longer arranged on a lattice, see fig. 16. Such asponge phase might occur in phospholipid systems in the presence of co-surfactantssuch as pentanol, which should drastically lower the rigidity of the lipid bilayer,thereby enhancing thermally-driven fluctuations.

4. Phase behaviour

Fig. 17. Hypothetical lipid/water binary phase diagram, where the transitions are driven by varyingthe water content. Regions denoted a, b, c and d contain intermediate phases, many of which are cubic.

From [1].


Fig. 18. Binary phase diagram of the phospholipid system: a) dihexadecyl-phosphatidylethanolamine/water; b) didodecyl-phosphatidylethanolamine/water. For this system upon cooling, the Lα phase is

metastable down to 35◦C, and then transforms to a metastable Lβ gel phase. From [76].


4.1. Lyotropic phase diagrams

Water content and temperature are the primary system variables for binary lipid/watersystems. A hypothetical binary lipid/water phase diagram in which the transitionsare driven predominantly by the former, is shown in fig. 17. There is a ‘natural’sequence in which the various possible fluid phases occur, determined by the averagemean curvature of the polar–nonpolar interface [1, 20, 23, 85]. Although the phasediagrams of some surfactants show a striking similarity to regions of the hypotheticaldiagram, phospholipid phase diagrams invariably show a dependence on temperatureas well as hydration. For example, fig. 18 shows the binary phase diagrams inwater for the C16 and C12 saturated ether-linked phosphatidylethanolamines. At hightemperatures, this class of phospholipid tends to adopt the HII phase over a verywide range of water contents. Lowering the chainlength causes the appearance ofthe bicontinuous inverse cubic phases Ia3d, Im3m and Pn3m between the Lα andHII phases.

Curiously, some systems exhibit phase sequences which are not in accord withfig. 17. For example, in monoolein, the inverse bicontinuous cubic phases occur onthe high water side of the lamellar phase [21, 86], even though they are inverse. Itis also possible for an inverse bicontinuous cubic phase such as Ia3d to occur on thelow hydration side of an inverse hexagonal HII phase.

An extensive compilation of binary and ternary phase diagrams has been givenby Ekwall [87], and overviews of phase diagrams of lipid mixtures have been pre-sented [13, 88, 89]. In addition to true binary phospholipid phase diagrams (i.e.lipid/water), it is common in the literature to find the term ‘binary’ used to refer tobinary lipid/lipid mixtures in the presence of an excess water phase. For varioussuch binary lipid mixtures, a range of types of phase diagram are observed, fromperfect mixing to eutectic, peritectic or monotectic behaviour. Generally speaking,deviations from ideal mixing become stronger when the lipids differ strongly inchainlength or headgroup type. A compilation of lipid phase diagrams has beenpublished [90], and databases of lipid transition temperatures and enthalpies, and ofphase diagrams, are currently being assembled [91]. A large number of reviews oflipid phase transitions are available [1, 2, 7–10, 55, 92–100], and these should beconsulted for much detail which will not be covered here.

4.2. Phase stability

The factors responsible for controlling phase stability may be broken down into twotypes, which are interrelated.

Firstly, the transverse interactions between adjacent lipid layers (Van der Waals,hydration, fluctuation, electrostatic) play an important role in stabilizing the structures[13, 101, 102]. In particular, for inverse non-lamellar phases the layer separations(hence lattice parameters) and interfacial curvatures are strongly coupled together.This might provide a mechanism for limiting the shrinking of bicontinuous phases.

Secondly, lateral interactions within a lipid bilayer modulate the preferred inter-facial area per molecule. There is a balance between the hydrophobic effect and


Fig. 19. Balance of lateral interactions across a lipid bilayer. From [103].

any attractive interactions (e.g., hydrogen-bonding), tending to minimize the interfa-cial area, and repulsive chain and headgroup interactions, tending to expand it; seefig. 19. However, the various interactions occur at different depths within the lipidlayer, and this may lead to a tendency for bending, either towards cylindrical orsaddle-like surfaces (of negative Gaussian curvature). The detailed form of the bi-layer stress profile is thus of great importance in determining the lipid polymorphism;see below.

4.3. Packing geometry and frustration

Generally speaking, increasing the temperature will introduce more conformationaldisorder into the hydrocarbon chains, which will tend to expand the interfacial areaper molecule. Conversely, increasing the water content tends to increase the lat-eral repulsions between the headgroups. This also increases the interfacial area permolecule, and hence also the extent of water-hydrocarbon contact. However, this ex-pansion forces the chains to deviate away from their preferred conformational state,which costs energy, and leads to a tendency for each monolayer to curve towards itschain region.

Fig. 20. Frustration in bilayer packing. Adapted from [25].


The ‘stiffness’ of the bilayer to changes in area is given by the area compressibilitymodulus KA, which for phospholipids in the Lα phase typically has values in theregion of 140 mN/m [13]. Within a certain temperature range, such an expansionof area does indeed occur. However, this forces the headgroups further apart thantheir optimal separation (usually any repulsive inter-headgroup terms will be lessaffected by temperature than those in the chain region), increasing the extent ofwater-hydrocarbon contact, which is disfavoured by the hydrophobic effect.

Increased disorder of the chains could be accommodated without an expansion ofthe interface if each monolayer were to curve towards the water region outside it;see fig. 20. However, this would open up voids in the centre of the hydrocarbonchain region which, in the absence of any non-polar solutes, would be energeticallyprohibitively expensive.

Thus in general within a flat lipid bilayer a state of physical frustration will oftenexist, whereby the compromise equilibrium interfacial area per molecule fully satis-fies the packing preference of neither the headgroups nor the chains. For many lipidsthe Lα phase becomes unstable upon heating when the area per molecule exceeds acritical value (which can be as low as 60 A2 for phosphatidylethanolamines), and atransition to an inverse non-lamellar phase occurs.

In transforming to an inverse phase, one possibility is for each lipid monolayer tocurl right round into an inverse cylinder, these then packing onto a 2D hexagonallattice as an HII phase; see fig. 1. However, as is clear from fig. 21, there still

Fig. 21. Packing frustration in the HII phase. From [1].


remains a frustration in the chain packing in that all of the hydrophobic regions mustbe filled at a uniform liquid alkane density, but in order to fill the triangular regionsin the centre (shaded), some of the chains must stretch away from their optimalconformational state. This problem might be partially alleviated by the interfacesof the lipid/water cylinders deforming away from a circular, towards a hexagonalcross-section [104].

Surprisingly, a way does exist for each lipid monolayer to develop a net meancurvature (splay) towards the water, yet without creating potential voids (and hencechain packing problems) within the hydrocarbon region. As may be seen from figs 3and 5, if the bilayer deforms onto a saddle surface (of negative Gaussian curvature),this largely solves the problem, since the ends of the chains of each monolayer meeton the saddle surface without any voids, whilst since the area decreases on movingaway in either direction from the saddle surface, each monolayer has developeda negative mean curvature (i.e. towards the water). By symmetry, since the twomonolayers are equivalent, the saddle surface should have zero mean curvature, i.e.should be a minimal surface. Extending the surface indefinitely through space toform an infinite periodic minimal surface such as the P-surface; see fig. 4, then leadsto the formation of an inverse bicontinuous cubic phase such as Im3m; see fig. 13.

However, draping a bilayer onto an infinite periodic minimal surface does notprovide a complete relief of the packing/curvature frustration. Since the Gaussiancurvature of any infinite periodic minimal surface is not constant along the surface(it is most negative at the saddle points and rises to zero at the apices; see fig. 3),a constant thickness bilayer would not have a uniform (negative) monolayer meancurvature at the polar non-polar interfaces. Conversely, a uniform curvature wouldrequire a non-uniform thickness. Although both of these situations raise the energyof the system, a theoretical analysis [28] has shown that cubic phases can have asmaller amount of frustration than neighbouring lamellar and HII phases, and canthus be expected to occur – as observed experimentally – between these two phases.

4.4. Curvature elastic energy

For large scale single bilayers, or for highly swollen systems, where the layer thick-ness is negligible compared with the dimensions of the bilayer or the layer spacing,the bilayer may be regarded as a thin elastic sheet. The energy cost associated withaltering the mean or Gaussian curvature of this sheet is then given by the values, κand κG, of the mean and Gaussian curvature elastic moduli. In this regime, thermallyexcited (entropic) fluctuations may drive structural or phase transitions, at an elasticenergy cost determined by the two curvature elastic moduli. However, for many bio-logical lipid systems, the phases formed have relatively low hydrations (15–40 wt%),and the layer thickness is then comparable to the layer spacing or lattice parameterof the phase. In this regime, the stress profile across the layer needs to be takeninto account in assessing the two curvature elastic moduli. This profile is liable tovary strongly with physico-chemical conditions such as temperature, hydration, pH,salt concentration, etc, and thus phase transitions in this regime might be driven bychanges to the two curvature elastic moduli.


In the treatment of Helfrich, the curvature elastic energy per unit area of a mono-layer is given [105] by

gcurv = (1/2)κm(c1 + c2 − c0)2 + κmG(c1· c2)

= 2κm(H −H0)2 + κmGK,

(4)

where c1, c2 are the principal curvatures and c0 the spontaneous curvature of themonolayer (taken to be negative for curvature towards the water region), and H andK are the mean and Gaussian interfacial curvatures.

The parameter κm is the monolayer mean curvature elastic modulus, with a valuein the region of 2 × 10−19 J for typical phospholipids. This first term, which isquadratic in H , expresses the energy cost of deforming the monolayer away fromthe equilibrium mean curvature H0 = c0/2. The second term gives the contributionto the free energy of the Gaussian curvature of the monolayer. For a bilayer, thevalue is not simply doubled, but is to first order given [106] by

κbG = 2

(κm

G − 2κmc0t), (5)

where t is the distance of the neutral surface (i.e. the surface of constant area underbending) of either monolayer from the mid-surface of the bilayer under cylindricalcurvature. This term is zero for parabolic surfaces such as planes or cylinders, andthus is not relevant to the case of (flat) lamellar or cylindrical phases. On the otherhand, for elliptic or hyperbolic surfaces the Gaussian term may be important, de-pending on the magnitude of κb

G. However, for lipid systems not only the magnitude,but also the sign of κb

G is not well known, and this could have either the same, or theopposite sign of that for the monolayer κm

G . Negative κbG should tend to favour ellip-

tic surfaces such as bilayer vesicles. Conversely, positive values of κbG should tend

to favour formation of inverse bicontinuous phases based on saddle surfaces. Notethat systems could in principle adopt a cubic phase against an unfavourable negativeGaussian curvature modulus, if there is some other favourable free energy term (e.g.,entropy) which outweighs it. However, for this to occur, κb

G would probably haveto be small in magnitude.

For ternary surfactant/oil/water systems, it has been argued that the favoured phaseis determined largely by the preferred value of interfacial mean curvature, in con-junction with packing constraints induced by the composition and geometry (Stromand Anderson, 1992). Although in such ternary systems the Gaussian curvature en-ergy may play a minor role, this is not necessarily the case in lipid systems. A recentstudy of glycolipid inverse bicontinuous cubic phases finds that κm

G is comparable inmagnitude to κm, and is of negative sign [107].

In the original Helfrich equation for the curvature energy there is an inherentinstability due to the linear dependence on Gaussian curvature K, which is physicallyunrealistic: for a structure of positive κb

G, based on minimal surfaces, it predictsthat the system could lower its free energy by allowing K to become increasinglynegative. This would lead to structures which shrink indefinitely, or which are of


indefinitely high genus. In reality, such phases are frequently stabilized at latticeparameters in the region of 100 A, and with relatively low genus values, such as3 (per translation cell) for the cubic phases Ia3d, Im3m and Pn3m. One sourceof stabilization can arise from inclusion of higher order terms in the expressionfor the curvature elastic energy [106, 108–110]. Inclusion of a term quadratic inK leads to an equilibrium size for the unit cell, and implies a preferred value K0of the bilayer Gaussian curvature. However, it is actually impossible for K to beuniform in a bicontinuous phase, since the underlying minimal surfaces must alwayscontain flat points (where K tends to zero) for the structure to be periodic. The genus3 bicontinuous cubic phases appear to have the smallest relative variation in K alongthe interface, and should therefore tend to be preferred [106]. However, the threegenus 3 cubic phases all have the same variance in K since they are related by theBonnet transformation, and so other factors must determine which of these phasesis the energetically favoured one. The most striking difference is the dimensionlessinterfacial area σ = A/V 2/3, which has the values of 2.3451, 2.4177 and 2.4533 forthe P, F and G surfaces, respectively. This suggests that the phase sequence uponwater dilution should be in the order G–F–P in order to accommodate the increasedvolume of the water, assuming the interfacial area per molecule remains constant.Although the limited data available to date suggests that this sequence is indeed thenatural one in lipid systems, the situation in general is more complicated since thearea per molecule is frequently a strong function of the water content.

4.5. Lateral stress profile

Helfrich has shown that the mean and Gaussian curvature moduli κ and κG aredirectly related, respectively, to the first moment of the stress profile across the lipid

Fig. 22. Schematic lateral stress profile t(z) across a lipid monolayer of thickness d. From [1].


monolayer, and the second moment of the stress profile across the bilayer [105]. Theexpected form of the stress profile t(z) for a lipid monolayer is shown in fig. 22. Thelateral pressure in the chain region is balanced by the residual interfacial tension atthe polar/non-polar interface. There will also be a repulsive (or possible sometimeseven attractive) lateral interaction acting between the polar headgroups.

At the equilibrium area per molecule, the net lateral tension σ, i.e. the integral ofthe stress profile across the monolayer, must equal zero:

σ =

∫t(z) dz = 0. (6)

Fig. 24. Proposed routes for inverse bicontinuous cubic and HII phase formation, via ‘inverted micellarintermediates’ (IMI). For the former phase, the route is proposed also to proceed via so-called ‘interlamel-lar attachments’ (ILA). PILAn

01 and k1(n0

1)2 are the rates of formation of interlamellar attachments andHII phase precursors, respectively. From [115].


Fig. 23. Schematic bilayer stress profile t(z) and its first and second moments. The thickness of thehydrocarbon chain region is 2c, h is the thickness of the interfacial region, σ is the net lateral tension,

τ is the torque tension, and KG is the Gaussian curvature modulus. From [1].

However, in general (as previously discussed) there will be a tendency for the mono-


layer to curve, either towards the water region or towards the hydrocarbon chainregion, depending on whether the interfacial tension is balanced primarily by thechain pressure or the headgroup pressure, respectively. This lateral torque tension τis given by the first moment of the stress profile of the flat monolayer, which is di-rectly related to the product of the spontaneous curvature c0 and the mean curvaturemodulus κ:

τ =

∫zt(z) dz = −κc0, (7)

i.e. in the absence of any applied force, the monolayer will only be flat spontaneouslyif c0 is zero. This approach of Helfrich does not lead to a separation of κ and c0.However, Szleifer and co-workers have shown that k may be obtained from the firstmoment of the variation of the stress profile with mean curvature [111].

For a symmetrical bilayer at its equilibrium area per molecule, the torque tensionτ is always zero by symmetry; see fig. 23. However, the second moment of thebilayer stress profile, which may be equated with the Gaussian curvature modulus:

κG =

∫z2t(z) dz (8)

will not in general be zero.For a bilayer where the interfacial tension is balanced primarily by the chain

pressure, shown schematically in fig. 23, the second moment, and hence κG, willin general be positive, if the origin is set at the centre of the bilayer (note that thissurface certainly does not correspond to the neutral surface upon deforming a bilayerinto a saddle surface: the area per molecule at the mid-plane must increase comparedto the flat bilayer). Thus such a bilayer can lower its elastic energy by deformingonto a saddle-surface (minimal surface at the bilayer centre by symmetry), hencetending to favour the formation of inverse bicontinuous cubic phases. Calculationsof κ and κG show that they depend strongly on the average area per molecule andchainlength [111]. However, we believe that there is still a difficulty in definingwhere to set the origin in evaluating the integrals, since the surface of inextensionfor a bilayer must lie close to the polar/non-polar interface of each monolayer.

The form of the stress profile, and hence the first and second moments, willbe modified by alterations such as changing the lipid chainlength, the headgrouphydrophilicity (e.g., by methylation), or by changing the solution properties such asthe pH or salt concentration.

4.6. Defects and epitaxiality in phase transitions

It has frequently been suggested that transitions to non-lamellar phases occur via theformation of defects such as inverse micelles [94–96]. Siegel has developed a modelfor such transitions, whereby the first step involves the formation of such an ‘in-verted micellar intermediate’ between apposed bilayers [112–114]. Two subsequentoutcomes are possible (in addition to reversion), depending on the particular lipid


Fig. 25. Fusion channel between two bilayers. From [1].

system, fig. 24. Either the inverted micellar intermediate can fuse with neighbouringones to form rod-like inverse micelles, or it can fuse with the surrounding monolay-ers to form an ‘interlamellar attachment’, a fusion channel between the two bilayers.The former outcome should lead to the formation of the HII phase, whereas the lattershould lead to the formation of inverse bicontinuous structures such as cubic phases.The similarity between a fusion channel between two bilayers as shown in fig. 25,and the local structure of the Im3m (= Q229) cubic phase shown in fig. 13c, is in-deed striking. Time-resolved cryo-transmission microscopy appears to have capturedinterlamellar attachment formation and the subsequent assembly into a cubic phase[116].

Defects, possibly corresponding to pores, have indeed been observed in lamellar Lαphases of surfactant systems by X-ray and neutron scattering, particularly when closeto phase boundaries [117–122]. For phospholipids, however, the cost of forming suchholes is expected to be much higher, and it is therefore possible that their densitywould be too low to detect by scattering.

In order to study defects in lipid phases by such scattering experiments, it is nec-essary to obtain monodomain samples, and this has proved to be quite problematical,particularly for more complex structures such as cubic phases. On the other hand,for certain amphiphile systems such as the polyoxyethylene surfactants, monodomaincubic phases grow spontaneously [117, 123–127]. In addition to allowing the studyof defects, such monodomains also permit the study of the epitaxial relationshipsthat exist as one phase transforms into another [124, 126]. For the surfactant hex-aethylene glycol mono-n-dodecyl ether (C12EO6), the crystallographic planes of thelamellar, Ia3d (Q230) cubic, and the HI phases were found to be aligned as shown infig. 26. The (211) planes are in fact the densest planes in the cubic phase. Similarly,well-defined epitaxial relationships have been demonstrated between the various fluidphases observed in the sodium dodecyl sulphate/water system [122].


Fig. 26. Epitaxial relationships between the lamellar Lα, type I cubic Qα (spacegroup Ia3d) and type Ihexagonal Hα phases of a polyoxyethylene surfactant. The crystallographic sections and directions are

denoted by round and square brackets respectively. From [124].

For lipid systems forming inverse phases, much less information is currently avail-able. It is known that the Lα–HII transition occurs with the lamellar (001) planesaligned with the (10) planes of the HII phase [128–130]. For the system monooleoylglycerol, which forms inverse bicontinuous cubic phases, the (001) planes of thelamellar phase were again found to be aligned with the (211) planes of the Ia3dcubic phase [M. Rawiso and J. Charvolin, unpublished observations, 130], althoughthe latter authors also observed occasional alignment with the (220) planes.

5. Factors affecting lyotropic transitions

5.1. Types of transition

There are three main types of phase transition between translationally ordered ly-otropic phases. Firstly, there are transitions between ordered lamellar phases, suchas crystal-crystal, crystal-gel, and gel-gel (e.g., Lβ′–Pβ′). Secondly, there are chain-melting transitions where the lower temperature phase is always lamellar, whereasthe higher temperature phase, which is at least partially fluid, need not be lamellar,and need not even be liquid-crystalline (e.g., it could be a micellar solution). Thirdly,there are transitions where both of the phases are fluid. The transition involves achange of symmetry and/or topology, for example, lamellar-hexagonal, lamellar-cubic, cubic-cubic, etc. Furthermore, in principle any of the translationally ordered


fluid phases can have transitions to isotropic solution phases (micellar solutions ormicroemulsions).

In addition to the usual intensive thermodynamic variables such as temperature andpressure, transitions may also be induced isothermally and isobarically by changes inhydration, pH, salt concentration etc. The sensitivity of a transition to a given per-turbation should be proportional to the free energy shift induced by the perturbation,divided by the transition entropy [13, 131]. Since transitions between fluid phasesinvariably involve small enthalpy (and hence entropy) changes, such transitions tendto be very sensitive to perturbations.

The stability of lipid phases should in principle be affected by electric and magneticfields. The effects of the latter are expected to be very weak since the diamagneticsusceptibility anisotropy of lipids is usually very small (unlike for thermotropic liquidcrystals). Electric fields are much more important, and can bring about membranefusion [132, 133] possibly in part by inducing inverse structures to form in the fusionregions.

Chirality, notwithstanding its paramount importance in Biology, seems to havesurprisingly little effect on lipid phase structure or on phase transitions [134, 135].However, it has recently been found that the chirality of a dialkyl glycolipid doesaffect the transitions to non-lamellar phases for these systems [136].

Hydrostatic pressure is of great importance in the membrane Biology of marinespecies, but also has many powerful effects on most membranes from other species,affecting anaesthesia, permeability, excitability and synaptic transmission [137, 138].However, remarkably little work has so far been carried out on the effects of pressureon lipid polymorphism, particularly on the fluid phases. The gel-fluid transition ofphospholipids increases linearly by approximately 0.02◦C per atm of applied pressure[139, 140]. Effects on increasing the Lα–HII transition are roughly twice as large[141–143]. Perhaps the most striking result (predicted in [1]) is that inverse cubicphases can be induced to form between the Lα and HII phase in certain lipid systemsby application of pressure [144].

5.2. Effect of lipid chemical structure

5.2.1. Hydrocarbon chainsIncreasing the lipid chainlength or the number of chains per polar headgroup has theeffect of strongly increasing the hydrophobicity, and of increasing the chain-chain in-teractions. This drastically lowers the cmc (critical micelle concentration), increasesthe chain-melting temperature (e.g., gel-fluid bilayer), and tends to favour the forma-tion of inverse non-lamellar phases. The Lα–HII transition temperature falls steeplywith increasing chainlength [145, 146]. The published data for the chainlength de-pendence of both the chain-melting, and the Lα–HII transition temperatures are wellfit by the following expression [147, 148]:

Tt = (∆Hinc/∆Sinc)[(n− n0)/(n− n′0)], (9)

where ∆Hinc and ∆Sinc are the incremental values per CH2 group of the transitionenthalpy and entropy; n is the chainlength and n0 and n′0 are the chainlengths atwhich the transition enthalpy and entropy extrapolate to zero.


The presence of cis- or trans-double bonds in the chains has the effect both ofdrastically lowering the gel-fluid transition temperature (typically by approximately60◦C for a cis-unsaturated bond) and of lowering any transitions to inverse non-lamellar phases. The effects depend strongly upon the position of the double bondalong the chain, the maximal effect occurring close to the middle of the chain [149].

For diacyl phospholipids, increasing asymmetry between the lengths of the twochains has the effect of lowering the chain melting transition temperatures [150]. Forsufficiently asymmetric chains, interdigitated gel phases tend to be induced [151–153].

Phospholipid phase behaviour is sensitive to the type of linkage between the chainand the polar headgroup. Ether linkages tend to increase the gel-fluid transitiontemperature by 1–5◦C, can induce the formation of interdigitated gel phases, anddrastically lower the transition temperatures from the fluid lamellar Lα phase toinverse non-lamellar phases [145, 148, 154–158].

5.2.2. HeadgroupsThe chemical structure of lipid headgroups plays a major role in determining thelipid polymorphism. Seemingly minor modifications, such as replacement of a sin-gle proton by a methyl group, can profoundly alter the phase behaviour [1, 2, 9].The crucial underlying factor appears to be the effective polarity of the headgroups[159], although charge (coulombic) and steric effects also play a role. In addition tothe intrinsic hydrophilicity of a lipid headgroup, the effective polarity depends upona number of factors such as the accessibility of different headgroup moieties to water,the possibility for direct headgroup-headgroup bonding, which weakens the interac-tion between the headgroup and water, etc. The latter factor may be responsiblefor the striking differences between the polymorphism of phosphatidylethanolaminescompared to that of phosphatidylcholines [1]. For the former lipid there is the pos-sibility for direct hydrogen-bonding between the headgroups, which is strikinglyapparent in the crystal structure [51, 54], and which may still partially occur in themesophases [160]. For phosphatidylcholines on the other hand, this possibility doesnot exist, and the headgroups interact much more strongly with water. This increasesthe hydration of the phases, modifies their structures, lowers the gel-fluid transitiontemperature, and tends to prevent the appearance of inverse non- lamellar phases forthis latter class of lipid.

The ionic, zwitterionic or non-ionic nature of a lipid headgroup appears to playa secondary role for many biological lipids. Thus the charged lipid phosphatidyl-glycerol has a strikingly similar phase behaviour in excess water [56] to that ofzwitterionic phosphatidylcholine [161]. However, one difference is that the pres-ence of the net charge on the former headgroup leads to an electrostatic swellingof the water layers at high hydrations [50]. Similarly, the polymorphism of certainnon-ionic dialkyl glycolipids [162–164] is quite similar to that of the zwitterionicphosphatidylethanolamines [1]. A striking feature of the glycolipid systems is thatthe phase behaviour is dependent on the stereochemistry of the polar headgroupregion [136]. For phospholipids, on the other hand, chirality does not appear tohave any striking effects on their polymorphism [134]. Although racemic DPPE hasbeen observed to have a more stable dehydrated crystalline form than the L-isomer


[165], such differences do not seem to extend to the fluid phases: no difference wasobserved in the cubic phase formed by racemic dimethyl-DHPE and its chiral 1,2-sncounterpart [76].

5.3. Lipid mixtures

The phase behaviour of lipid mixtures is of interest since it may give valuable insightinto the factors responsible for lyotropic phase stability. Transverse interactions suchas the hydration force between bilayers may be disproportionately modified by form-ing lipid mixtures [166]. Lateral interactions may also be modified in a non-additiveway, with a strong effect on phase stability. Phases of non-uniform interfacial curva-ture may become favoured by the possibility for partial lateral segregation of differentlipid species into regions of different curvature. Regions of two-phase coexistencemay become more extensive, and three-phase coexistence becomes possible. Noveleffects may occur, such as the formation of phases which do not appear for purelybinary lipid/water systems. A further reason for the study of such mixtures is thatbiological membranes normally contain a complex variety of lipids, and this is cer-tainly not accidental but must be related to their function.

Mixing lipids together alters both the tendency for monolayer curvature, and thepacking stresses within the system, and this has large effects on the formation ofnon-lamellar phases [167]. Incorporating a ‘bilayer-forming’ lipid with one whichforms non-lamellar phases has the effect of decreasing the spontaneous monolayercurvature of the latter, tending to stabilize it in the lamellar phase. This is observedfor unsaturated phosphatidylethanolamine (PE) systems upon incorporation of phos-phatidylcholine (PC). However, for certain composition ranges, the mixtures adoptan intermediate curvature structure, forming bicontinuous cubic phases [168, 169].

5.4. Solution effects

In general, increasing hydration tends to lower the chain melting transition temper-atures of lipids, by as much as 50◦C, although there are exceptions to this rule forsome surfactant systems and for certain lipid mixtures. As discussed earlier, withinthe fluid phase region, increasing the water content tends to push the equilibriumtowards phases of less negative/more positive interfacial mean curvature. However,this rule is not always obeyed, for reasons which are not yet well understood.

5.5. Solute effects

There are a number of ways in which solutes can modify the phase equilibria oflipids. In general, polar solutes cause an osmotic dehydration by competing withthe lipid for interaction with water [55]. This tends to favour the formation ofordered phases (gel or crystalline), and may induce inverse non-lamellar phases toform. Furthermore, this effect can be enhanced if the solute binds to the lipidheadgroups, displacing bound water molecules. For charged lipids, ion screeningand binding occur, particularly for divalent or multivalent ions. This leads both toa reduction of electrostatic repulsion, and to dehydration effects. However, some


strongly hydrophilic molecules such as certain halide or organic ions, or alcohols,actually enhance the interfacial hydration upon binding, and these solutes thereforehave opposite effects on the lipid polymorphism.

The effect of pH is complicated by a number of factors [170]. Firstly, the pKa ofionizable groups at the surface of lipid membranes is strongly shifted to higher pHvalues (by as much as 3 pH units) compared to the pKa value for the isolated groupin bulk solution [13, 171]. Secondly, the headgroup hydrophilicity varies with thedegree of ionization, and thus indirect yet important (or even dominant) hydrationeffects are invariably also present as well as the direct electrostatic effects. Thirdly,the strength of any interlipid hydrogen-bonding will depend strongly on the pH. Thenet effect however is that increasing pH almost always lowers the chain-meltingtransition temperature of lipids [170], and increases the transition temperatures toinverse non-lamellar phases [1].

Amphiphilic solutes span a wide range of compounds ranging from long chain fattyacids and alcohols, monoacylglycerols and diacylglycerols, to more rigid moleculessuch as cholesterol. They are frequently soluble in phospholipids up to molar ratiosas high as 2 : 1, even when, like diacylglycerols, they are too weakly amphiphilic toform any lyotropic liquid crystalline phases on their own in water. Such moleculesare very important in membrane biology because they have a range of activities suchas fusion, anaesthesia and cell signalling. Although they all adsorb preferentially withtheir polar groups near the lipid headgroups, and their hydrophobic parts embeddedwithin the hydrocarbon chain region, the effects they have vary widely, dependingon their chemical structure.

Incorporation of long chain fatty acids and alcohols into phospholipid bilayerssuch as PC or PG tends to broaden yet increase the gel-fluid transition tempera-tures [61, 172]. Typically, on reaching a molar ratio of 2 : 1, the transition sharpensas it reaches its maximum temperature, which is in the region of 20–25◦C higher thanthat of the pure phospholipid in water (this temperature is also frequently higher thanthat of the pure solute in water). Such stoichiometric mixtures usually melt directlyfrom the gel phase to non-lamellar phases, either HII [60, 62–64] or bicontinuousinverse cubic [76, 173].

Monoacylglycerols (monoglycerides) such as the fusogen monooleoyl glyceroltend to promote the formation of HII and inverse bicontinuous cubic phases [174–177].This is not altogether surprising since pure monoacylglycerols in water tend to adoptsuch inverse non-lamellar phases [21, 22, 86, 178].

Diacylglycerols also induce the formation of the HII phase upon incorporation inphospholipids [179–185]. At high mole fractions in PC a cubic phase is formed[181] which has been identified as an inverse micellar cubic phase of space groupFd3m [36, 74, 75].

It is well known that cholesterol tends to smear out the gel-fluid transition ofphospholipids, fluidizing the gel phase and ordering the lamellar Lα phase, leadingto enhanced stability of fluid bilayers. However, it also tends to promote formationof inverse phases such as HII, not only in ‘non-lamellar’ phospholipids such as PE[186] but even in PCs, when the chains are polyunsaturated [187].


A non-polar solute may be defined as any molecule (or atom) which partitionspreferentially into the hydrophobic interior of a lipid mesophase. Such solutes rangefrom simple alkanes, aromatic compounds and inert gases, to certain anaesthetics,drugs, peptides and proteins, although strictly speaking the latter group will generallyalso contain limited extents of polar regions. Although phase equilibria in ternarysurfactant/oil/water systems have been studied extensively for many years [87], it isonly relatively recently that the effects of non-polar solutes on lipid polymorphismhave been studied [167, 182, 188, 189, 190–196].

Non-polar molecules exert their effects by partitioning into the hydrocarbon regionsof the lipid phase, increasing the tendency for splay of each monolayer towards thewater (increased tendency for negative mean interfacial curvature of each monolayer).This tends to facilitate the formation of inverse phases. A further important effectis to reduce chain packing constraints by partitioning into the interstices within thehydrocarbon region. This tends to favour the formation of inverse phases such asHII, where there is a significant degree of chain stress due to the necessity to fillthe hydrophobic region at a uniform density. The effects are largest on systemswith small spontaneous curvatures. For example, addition of 5% alkane to a 3/1DOPE/DOPC mixture reduces the Lα–HII transition temperature by as much as55◦C [189]. Even phosphatidylcholines may adopt inverse phases in the presenceof alkanes [190, 191, 193]. The effects of dual-solvent (water and alkane) stress onPC/PE mixtures has been studied in order to remove packing constraints both in thehydrophobic and in the aqueous regions of the phases [195]. The results confirm thatsuch lipid systems minimize their curvature energy, even if this requires separationinto two bulk phases.

5.6. Phase metastability

The study of lipid polymorphism has been hampered by the fact that many of thelipid phases are metastable, reverting in times ranging from seconds to years to morestable, or to true equilibrium phases [197]. A further complication is that the lipidmolecules may be chemically unstable over such long timescales.

Incubation of fully hydrated gel phase PC at low temperature leads to the formationof more ordered ‘sub-gel’ phases [198–202]. These subgel phases contain significantamounts of water and appear to have a crystalline chain packing, although it is notquite clear whether adjacent bilayers are weakly or strongly coupled together. Uponheating, the sub-gel phase undergoes an endothermic transition to the gel phase(usually Lβ′).

For lipids such as PE, which are more weakly hydrated, the tendency for metasta-bility is very strong, leading to anhydrous crystalline lamellar phases upon incubation[37, 165, 203–208]. The pattern of metastability in fully hydrated L-DLPE is shownin fig. 27, where it is seen that both of the crystalline forms (denoted β1 and β2)observed after incubation have chain melting temperatures higher than that of thegel-fluid phase transition. Thus not only is the gel phase metastable, but also thefluid lamellar Lα phase is metastable below 43◦C [37]. For racemic DL-DPPE, thedehydrated crystalline form is particularly stable, having a chain melting transition


Fig. 27. The pattern of metastability of the fully hydrated Lβ gel and Lα fluid lamellar phases of DLPE.There are two stable dehydrated crystalline forms, denoted β1 and β2. ∆H is shown as the difference

in enthalpy of the lower temperature phases relative to the fluid lamellar Lα phase. From [37].

in water on the initial heating scan at 82◦C [165]. This shows that chirality can bea very significant factor in controlling metastability.

Many other lipid systems exhibit metastability, such as mixed chain PE’s [209],headgroup-methylated PE’s [210]; phosphatidylglycerol [211] and diacyl and dialkylglycolipids [162, 212, 213]. Furthermore, stoichiometric fatty acid/PC (2 : 1) mix-tures also adopt a subgel phase on incubation of the Lβ gel phase at low temperatures[62, 63].

5.7. Transition kinetics

The kinetics of the chain-melting transition of lipids has been studied by a numberof techniques [214–216]. The advent of synchrotron radiation sources has allowedtime-resolved diffraction to be employed to study lipid phase transition kinetics [178,217–225]. Lipid phase transitions are thought to proceed either by nucleation andgrowth mechanisms, by spinodal decomposition, or by martensitic-type transforma-tions [224]. In many cases the rate of the transition may be limited by the speed atwhich water can redistribute, rather than the time required for the lipids to rearrangethemselves [219].


The Lβ–Lα transition of PE is a simple reversible two-state process occurringon the millisecond timescale. However, for phospholipids such as PC, both theLβ′–Pβ′ tilted gel–rippled gel transition and the Pβ′–Lα gel-fluid transition exhibitmore complex multicomponent kinetic behaviour, with relaxation times spanning therange of milliseconds to seconds. Furthermore, on cooling the transitions are muchslower, taking minutes or hours to reach completion. Transitions between moreordered lamellar phases may be slower still.

Lamellar–HII transitions appear to be reversible two-state processes, requiring 1–10 seconds for completion, regardless of whether the lamellar phase is fluid (Lα)[219, 220] or gel (Lβ) [63]. There is still some confusion about the precise sequenceof events which occur during the Lα–HII transition, but it seems that the HII phaseappears within tens of milliseconds, probably initially with the same spacing as thelamellar phase, before swelling to the equilibrium spacing over some seconds [225].However, for small temperature jumps (of the order of 4◦C) the transition becomesmuch slower, requiring as much as one week or more for completion.

To date there have been few studies of the kinetics of transitions involving cubicphases, although in some cases they may be very slow and exhibit considerable hys-teresis. For monoacylglycerols, it was found that cubic-cubic transition times rangedfrom 0.5 sec to 30 minutes [178]. In the case of a lipid extract from the extremethermoacidophile S. solfataricus, it was found to undergo a nearly irreversible tran-sition from the Lα phase to a Pn3m (= Q224) inverse cubic phase on heating [226].For the unsaturated phospholipid DOPE a cubic phase was induced to form by ther-mal cycling, which was then strongly metastable [227]. Similarly, N-methyl-DOPEonly forms cubic phases between Lα and HII when the sample is cooled very slowlyfrom the HII phase [194] or is heated from the lamellar phase at less than 1◦C perhour [228].

6. Biological implications

6.1. Non-lamellar phases in biology

The possible biological implications of lipid polymorphism have been discussed bya number of authors [1, 8, 9, 29, 94–96, 229, 230]. A scheme showing some ofthe ways in which non-lamellar structures may be of relevance to biomembranemorphology and function is given in fig. 28. Although many biomembranes containlarge amounts of lipids which have strong tendencies to form phases such as HII,there are few examples where non-lamellar phases have been definitely identified incells. However, a considerable body of evidence suggests that non-lamellar structuresdo form, for example in membranes of microsomes [231–233], mitochondria [234,235], and in tight junctions between cells [236–238]. Periodically curved bilayerstructures have been observed in the membranes and extracted lipids of the bacteriumStreptomyces hygroscopus [239]. This structure is suggested to be related to a two-dimensional periodic minimal surface. It is interesting to note that the skeletons ofechinoderms such as sea urchins are porous crystalline structures, which appear tobe based on periodic minimal surfaces [240]. For example, the coronal plates of


Fig. 28. Scheme showing some of the possible roles of non-lamellar structures in biomembrane morphol-ogy and function: (1) exocytosis/fusion; (2) interbilayer connection/tight junction; (3) ion permeability.

From [95].

Cidaris rugosa are single crystals, with a structure [241] which is strikingly similarto the lyotropic Im3m (= Q229) cubic phase formed by lipids.

Furthermore, non-lamellar phases do seem to form in certain situations. Forexample, paracrystalline inclusions in retina have been shown to consist of do-mains of HII phase [242]. The plasma membrane of the archaebacterium Sulfolobussolfataricus appears to be based on the inverse bicontinuous cubic phase Pn3m(= Q224) [243]. However, probably the best example of a non-lamellar phase in bi-


ology is the prolamellar body of etiolated chloroplasts, which consists of six-fold orfour-fold interconnected tubular membrane structures [244–247], strikingly similarto the structure elements of the inverse bicontinuous cubic phases Im3m (= Q229)and Pn3m (= Q224). It is interesting to note that the structures of certain membrane-ous organelles in cells, for example in endoplasmic reticulum, bear a quite strikingsimilarity to the L3 sponge phase.

It has been suggested that liquid-crystalline phases, possibly including cubic phases,play a role in the process of fat digestion in vivo. During this process, triglyceride ishydrolysed first to diacylglycerol plus fatty acid, then to monoacylglycerol plus twofatty acid molecules. Studies of phase equilibria of lipid mixtures similar to thosefound in the intestine found that liquid-crystalline phases, as well as an L2 inversemicellar solution were formed, and it was suggested that the latter phase may coexistwith mixed micelles in the human intestine [248]. In other model experiments invitro, it was observed that first a lamellar phase, then a viscous isotropic, presumablycubic, phase was formed as the reaction of lipase with triglyceride proceeded [249].Subsequent freeze-fracture electron microscopy results did not however show anyclear evidence for a cubic phase [250, 251]. Work in our laboratory on a similarmodel system has also failed to find any evidence for cubic phase formation.

A mechanism for how inverse bicontinuous phases such as Pn3m (= Q224) mightbe involved in fat digestion has been proposed [29]. These phases have the importantproperty that all reactants and products, whether polar, non-polar or amphiphilic candiffuse freely across the structure. As the lipolysis proceeds, it would be highlyadvantageous to form such porous structures, rather than impermeable layers suchas in a lamellar phase.

6.2. Membrane fusion and cell signal transduction

Membrane fusion is a very common event in cell membranes, which requires thetransient and localized destabilization of the bilayer structure. It has often beensuggested that non-lamellar phases have a role to play in the underlying molecularmechanism of this process [1, 96, 112–114, 252–255] and evidence is accumulatingin support of this view [115]. It is likely that inverse micellar structures form at thefusion site, lowering the activation barrier for the process. The presence of lipidssuch as phosphatidylethanolamine, having a tendency to adopt inverse non-lamellarphases, should facilitate this process. Furthermore, as previously mentioned, thereis a very close relationship [1, 26, 115] between the structure of a fusion channel,shown in fig. 25, and the structure of an inverse bicontinuous cubic phase suchas Im3m, shown in fig. 13c. Such a channel constitutes a bilayer deformation ofnegative Gaussian curvature. Thus the factors which drive a pure lipid/water systemto undergo lamellar-cubic transitions, and the mechanism of the transition, may bevery similar to some of those involved in membrane fusion in cells.

The activation of phospholipase C, and the subsequent production of diacylglyc-erol in membranes, is associated with transmembrane signal transduction in cells,via activation of protein kinase C [179, 256, 257], and may also be involved inmembrane fusion [180, 185, 258]. It is a striking result that diacylglycerols are


potent promoters of inverse non-lamellar phases in phospholipid systems [180, 181,259]. Although diacylglycerols are too weakly hydrophilic to form any lyotropicmesophases in solution on their own, they can be incorporated in phospholipids suchas phosphatidylcholine up to mole fractions in excess of 0.7, inducing the forma-tion first of the HII phase, and then a cubic phase, with increasing concentration[181]. This latter phase has been shown to be an inverse micellar cubic phase, ofspacegroup Fd3m (= Q227) [75]. An electron microscopy study of the effect oftreatment of PC/PE/cholesterol bilayer membranes with phospholipiase C, has iden-tified structures which appear to be similar or identical to this inverse micellar cubicphase [258].

6.3. Homeostatic control of ‘phase stability’

It was suggested some years ago that cells exhibit ‘homeoviscous adaptation’, wherebythey maintain the ‘fluidity’ of their membranes close to some value which is optimalfor their function [260]. Alternatively it has been proposed that rather than ‘fluidity’,it is the ‘phase stability’ [261, 262] or ‘intrinsic curvature’ [230] of the membranelipids which is carefully regulated. Elegant experiments with Pseudomonas fluo-rescens [261], Acholeplasma laidlawii [262, 263], and Clostridium butyricum [264]have built up quite convincing evidence that cells may indeed regulate their lipidphase behaviour.

6.4. Bilayer stress profile and regulation of membrane protein activity

For mechanical stability, the residual interfacial tension γ that exists on either sideof a lipid bilayer must be balanced by the sum of the lateral pressures πCH in thechain region, and πHG in the headgroup regions [103]. Although most real systemswill have contributions from both regions, the relative contributions may be quitedifferent for different lipids. Thus for example, a strongly hydrated lipid such as PCshould have a relatively large πHG, and hence a small πCH, whereas a more weaklyhydrophilic lipid such as PE should have a smaller πHG and hence a larger πCH.

Thus the stress profile across a bilayer membrane may be modified by changingthe lipid composition (or the state of the lipid headgroups, e.g., by proton or ionbinding). This means that the distribution of lateral stresses at different depths withinthe bilayer will change and, apart from modifying the lipid phase behaviour, mightaffect the conformation and mobility of proteins (or other embedded molecules),thereby modulating their activity.

6.5. Protein/lipid mixtures

Although most of the lyotropic liquid-crystalline phases studied to date have involvedpure hydrated lipids, since real cell membranes invariably contain associated integralor peripheral proteins, it is of great interest to study their effect on lipid polymorphism[229, 265]. For example, the transmembrane channel former gramicidin has beenshown to have a strong tendency to induce HII phase formation in a wide range ofphospholipid systems. However, in general the effects are, not surprisingly, rather


complex: binding or incorporation of proteins sometimes stabilizes the lamellarphase, but sometimes induces non-lamellar HII or cubic phases to form. For example,the peptide melittin induces HII phase formation in the charged lipids phosphatidicacid and PG, but stabilizes the lamellar phase of PE, and causes micellization ofPC. These results clearly indicate that a range of effects such as partial chargeneutralization, headgroup dehydration, protein insertion, etc occur, and these dependsensitively on the chemical structure and physical state of the lipid.

Particularly interesting behaviour has been found for hydrated cytochrome c/mono-acylglycerol mixtures, where a cubic phase of spacegroup P4332 (= Q212) was de-tected at low water content [29]. This cubic phase is derived from the inversebicontinuous cubic phase Ia3d (= Q230), replacing one of the sets of lipid/waterchannels by a network of protein/lipid inverse micelles. The unique feature of thiscubic phase is that it is chiral.

7. Open problems

Apart from the many putative roles of lipid polymorphism in biomembrane structureand function, discussed earlier, and the many remaining problems in our detailedunderstanding of the properties of lipid bilayers, the most pressing unresolved issuesin this area are as follows:

There is still no accurate free energy model for the cubic phases, which cancorrectly predict the phase sequence and relative stability. The relative importanceof the spontaneous curvature c0, and the mean and Gaussian curvature elastic moduliκ and κG in controlling lipid polymorphism are still not well understood. The roleof κG is particularly unclear: its sign is not even well established, and might bedifferent in different lipid systems.

The structures of many cubic and intermediate phases are still unknown. In mostcases progress is hampered by the fact that very few Bragg peaks are observed inthe diffraction patterns.

The possible existence of bicontinuous structures which are of genus higher than3 and/or which are based on monolayers rather than bilayers requires further inves-tigation.

For cubic phases there appears to be a correlation between the sign of the in-terfacial mean curvature (i.e. normal or inverse phases), and which crystallographicspacegroups are observed. For example, amongst micellar cubics, Fd3m (= Q227)is inverse, whereas Pm3n (= Q223) is normal (oil-in-water). Similarly, amongstthe bicontinuous phases, Pn3m (= Q224) and Im3m (= Q229) are usually inverse.On the other hand, Ia3d (= Q230) is commonly observed either as a normal or aninverse cubic phase. It is a mystery whether these correlations have any physicalsignificance.

It is unknown why in some systems ‘incorrect’ phase sequences are sometimesobserved. For example, monoolein transforms from a lamellar to an inverse cubicphase with increasing water content.


It is unclear whether there is a clear distinction between the discontinuous (micel-lar) and the bicontinuous cubic phases, or whether phases exist which are partiallydiscontinuous in one component.

In principle, chiral lipids could form non- centrosymmetric (chiral) cubic phases.In practice, for lipid systems studied to date this does not occur, presumably becausethe molecular chirality is too weak in the hydrated state.

Bicontinuous cubic phases offer a partial solution to the problem of allowingmonolayers to adopt their preferred mean curvature, without requiring a strong vari-ation in the conformational state of molecules in different regions of the phase. It isunclear therefore why they are not more common in excess water, since most lipidsystems will tend to have a non-zero preferred monolayer mean curvature, and thecubic phase could adjust its size to achieve an interfacial mean curvature close tothis value.

The relationship between the macroscopic, elastic properties of lipid layers andthe underlying microscopic interactions needs further clarification.

The limits on the swelling of cubic and other 3D lyotropic phases need to bedetermined. The lower limit for Ia3d appears to correspond to zero water content,since this cubic phase is formed by anhydrous strontium soaps. For Pn3m and Im3mit appears to be much larger, usually in excess of 30 wt% water. The upper limit ofswelling of inverse bicontinuous phases is unclear, although theoretical argumentssuggest that there should be a limit in the region of 300 A, set by the size at whichthermal excitations will destroy the long range order.

Certain cubic phases are metastable, remaining stable for weeks or months aftercooling down below the equilibrium transition temperature to another phase; con-versely, some systems only adopt cubic phases after prolonged incubation or thermalcycling. These phenomena are presumably connected to the complicated topologicaltransformations required at such phase transitions.

The role and use of periodic minimal surfaces in analyzing lipid phase structureand stability will continue to develop, and will contribute towards developing anunderstanding of the mechanism of transitions between non-lamellar phases. It isconceivable that the bilayer within a cubic phase drapes itself not exactly on aminimal surface (zero mean curvature) but rather on a minimal energy surface.

Although it is tempting to invoke Bonnet-like transformations as being involvedin transitions between Ia3d, Pn3m and Im3m cubic phases, such a mechanism wouldrequire layer self-intersection (via fusion events) during the transition, and this maybe unphysical. An alternative mechanism, shown in fig. 29, would involve a contin-uous stretching of the layers during the transition, changing the connectivity of thenodes, followed by a relaxation to the new equilibrium phase. Precisely how such aprocess might proceed is poorly understood.

Much more information is needed on the epitaxial relationships across phaseboundaries, particularly for inverse systems, and on the role of defects in lyotropictransitions, in order to resolve some of these problems.

Finally, the effects of polar, non-polar and amphiphilic solutes on lipid phasebehaviour are still relatively poorly understood.

Much future work will be addressed to resolving these issues.


Fig. 29. Possible mechanism for transitions between bicontinuous cubic phases by layer stretching,without requiring layer intersections. The skeletal graphs of (a) the P-surface, (b) the F-surface, and(c) the gyroid surface are shown. By stretching the 6-connected node of the P-surface along the bodydiagonal direction and adjusting the angles, the graph of the F-surface, with 4-connected nodes, canbe obtained. Stretching these 4-connected nodes then generates the 3-connected nodes of the gyroid

skeletal graph. From [266].


Acknowledgements

This work was supported by grants from the former SERC (U.K.), the Royal Society(London) and Imperial College, London

References1. Seddon, J.M., 1990, Structure of the inverted hexagonal (HII) phase, and non-lamellar transitions

of lipids, Biochim. Biophys. Acta 1031, 1–69.2. Tate, M.W., E.F. Eikenberry, D.C. Turner, E. Shyamsunder and S.M. Gruner, 1991, Nonbilayer

phases of membrane lipids, Chem. Phys. Lipids 57, 147–164.3. Luzzati, V., 1968, X-ray diffraction studies of lipid-water systems, in: Biological Membranes,

Vol. 1, ed. D. Chapman (Academic Press, London) pp. 71–123.4. Shipley, G.G., 1973, Recent X-ray diffraction studies of biological membranes and membrane

components, in: Biological Membranes, Vol. 2, eds D. Chapman and D.F.H. Wallach (AcademicPress, London) pp. 1–89.

5. Charvolin, J. and A. Tardieu, 1978, Lyotropic liquid crystals: Structure and molecular motions,Solid State Phys. Suppl. 14, 209–257.

6. Tiddy, G.J.T., 1980, Surfactant-water liquid crystal phases, Phys. Rep. 57, 1–46.7. Small, D.M., 1986, Handbook of Lipid Research, Vol. 4 (Plenum Press, New York).8. Larsson, K., 1989, Cubic lipid-water phases: Structures and biomembrane aspects, J. Phys. Chem-

istry 93, 7304–7314.9. Lindblom, G. and L. Rilfors, 1989, Cubic phases and isotropic structures formed by membrane

lipids – possible biological relevance, Biochim. Biophys. Acta 988, 221–256.10. Fontell, K., 1990, Cubic phases in surfactant and surfactant-like lipid systems, Colloid Polym. Sci.

268, 264–285.11. Chemistry and Physics of Lipids (Special Issue), Vol. 57, 1990.12. Dubois-Violette, E. and B. Pansu (eds), 1990, International Workshop on Geometry and Interfaces,

in: J. Phys. (Paris) Colloq. C7, Vol. 51.13. Cevc, G. and D. Marsh, 1987, Phospholipid Bilayers: Physical Principles and Models (Wiley, New

York).14. Meunier, J., D. Langevin and N. Boccara (eds), 1987, Physics of Amphiphilic Layers (Springer,

Berlin).15. Lipowsky, R., D. Richter and K. Kremer (eds), 1992, The Structure and Conformation of Am-

phiphilic Membranes (Springer, Berlin).16. Lipowsky, R., 1991, The conformation of membranes, Nature 349, 475–481.17. Prost, J. and F. Rondolez, 1991, Structures in colloidal physical chemistry, Nature (Suppl.) 350,

11–23.18. Andersson, S., S.T. Hyde, K. Larsson and S. Lidin, 1988, Minimal surfaces and structures: From

inorganic and metal crystals to cell membranes and biopolymers, Chem. Rev. 88, 221–242.19. Scriven, L.E., 1976, Equilibrium bicontinuous structure, Nature 263, 123–125.20. Scriven, L.E., 1977, Equilibrium bicontinuous structures, in: Micellization, Solubilization, and

Microemulsions, Vol. 2, ed. K.L. Mittal (Plenum, New York) pp. 877–893.21. Hyde, S.T., S. Andersson, B. Ericsson and K. Larsson, 1984, A cubic structure consisting of a lipid

bilayer forming an infinite periodic minimal surface of the gyroid type in the glycerolmonooleat-water system, Z. Krystallogr. 168, 213–219.

22. Longley, W. and T.J. McIntosh, 1983, A bicontinuous tetrahedral structure in a liquid-crystallinelipid, Nature 303, 612–614.

23. Charvolin, J., 1985, Crystals of interfaces: the cubic phases of amphiphile/water systems, J. Phys.(Paris) Colloq. C3 46, 173–190.

24. Mackay, A.L., 1985, Periodic minimal surfaces, Nature 314, 604–606.25. Sadoc, J.F. and J. Charvolin, 1986, Frustration in bilayers and topologies of liquid crystals of

amphiphilic molecules, J. Phys. (Paris) 47, 683–691.


26. Helfrich, W. and W. Harbich, 1987, Equilibrium configurations of fluid membranes, in: Physics ofAmphiphilic Layers, eds J. Meunier, D. Langevin and N. Boccara (Springer, Berlin) pp. 58–63.

27. Charvolin, J. and J.F. Sadoc, 1987, Periodic systems of frustrated fluid films and bicontinuous cubicstructures in liquid crystals, J. Phys. France 48, 1559–1569.

28. Anderson, D.M., S.M. Gruner and S. Leibler, 1988, Geometric aspects of the frustration in thecubic phases of lyotropic liquid crystals, Proc. Nat. Acad. Sci. USA 85, 5364–5368.

29. Mariani, P., V. Luzzati and H. Delacroix, 1988, Cubic phases of lipid-containing systems. Structureanalysis and biological implications, J. Mol. Biol. 204, 165–189.

30. Hyde, S.T., 1989, Microstructure of bicontinuous surfactant aggregates, J. Phys. Chem. 93, 1458–1463.

31. Bouligand, Y., 1990, Comparative geometry of cytomembranes and water-lipid systems, J. Phys.(Paris) 51(C7), 35–52.

32. Gulik-Krzywicki, T., L.P. Aggerbeck and K. Larsson, 1984, The use of freeze-fracture and freeze-etching electron microscopy for phase analysis and structure determination of lipid systems, in:Surfactants in Solution, Vol. 1, eds K. Mittal and B. Lindman (Plenum, New York) pp. 237–257.

33. International Tables for Crystallography, 1983, Vol. A, ed. T. Hahn (D. Reidel, Dordrecht).34. Franks, N.P. and Y.K. Levine, 1981, Low-angle X-ray diffraction, in: Membrane Spectroscopy,

ed. E. Grell (Springer, Berlin) pp. 437–487.35. Zaccai, G. and B. Jacrot, 1983, Small angle neutron scattering, Annu. Rev. Biophys. Bioeng. 12,

139–157.36. Luzzati, V., R. Vargas, A. Gulik, P. Mariani, J. M. Seddon and E. Rivas, 1992, Lipid polymorphism:

A correction. The structure of the cubic phase of extinction symbol Fd– consists of two types ofdisjointed reverse micelles embedded in a 3D hydrocarbon matrix, Biochemistry 31, 279–285.

37. Seddon, J.M., K. Harlos and D. Marsh, 1983, Metastability and polymorphism in the gel and fluidbilayer phases of dilauroyl phosphatidylethanolamine, J. Biol. Chem. 258, 3580–3854.

38. Schoen, A.H., 1970, Infinite periodic minimal surfaces without self-intersections, NASA TechnicalNote TD-5541.

39. Hyde, S.T., 1990, Curvature and the global structure of interfaces in surfactant-water systems,J. Phys. (France) 51(C7), 209–228.

40. Anderson, D.M., H.T. Davis, L.E. Scriven and J.C.C. Nitsche, 1990, Periodic surfaces of prescribedmean curvature, Adv. Chem. Phys. 77, 337–396.

41. Barois, P., S.T. Hyde, B.W. Ninham and T. Dowling, 1990, Observation of two phases within thecubic phase region of a ternary surfactant, Langmuir 6, 1136–1140.

42. Strom, P. and D.M. Anderson, 1992, The cubic phase region in the system didodecylmethylammo-nium bromide-water-styrene, Langmuir 8, 691–709.

43. Kekicheff, P. and B. Cabane, 1987, Between cylinders and bilayers: structures and intermediatemesophases of the SDS/water system, J. Phys. (Paris) 48, 1571–1583.

44. Radiman, S., C. Toprakcioglu and A.R. Faruqi, 1990, Symmetry transition in the cubic phase of aternary surfactant system, J. Phys. France 51, 1501–1508.

45. Pascher, I., M. Lundmark, P.-G. Nyholm and S. Sundell, 1992, Crystal structures of membranelipids, Biochim. Biophys. Acta 1113, 339–373.

46. Blaurock, A.E. and T.J. McIntosh, 1986, Structure of the crystalline bilayer in the subgel phase ofphosphatidylglycerol, Biochemistry 25, 299–305.

47. Tardieu, A., V. Luzzati and F.C. Reman, 1973, Structure and polymorphiam of the hydrocarbonchains of lipids: A study of lecithin-water phases, J. Mol. Biol. 75, 711–733.

48. Ranck, J.L., T. Keira and V. Luzzati, 1977, A novel packing of the hydrocarbon chains in lipids:The low temperature phases of dipalmitoyl phosphatidylglycerol, Biochim. Biophys. Acta 488,432–441.

49. Doucet, J., A.M. Levelut and M. Lambert, 1983, X-ray study of single domains of 1,2-dipalmitoyl-sn-phosphatidylcholine with less than 5% water, Acta Crystallogr. B39, 724–731.

50. Vargas, R., P. Mariani, A. Gulik and V. Luzzati, 1992, The cubic phases of lipid-containing systems.The structure of phase Q223 (space group Pm3n): An X-ray scattering study, J. Mol. Biol. 225,137–145.


51. Elder, M., P. Hitchcock, R. Mason and G.G. Shipley, 1977, A refinement analysis of the crystal-lography of the phospholipid, 1,2-dilauroyl-DL-phosphatidylethanolamine, and some remarks onlipid-lipid and lipid-protein interactions, Proc. R. Soc. London Ser. A 354, 157–170.

52. Pearson, R.H. and I. Pascher, 1979, The molecular structure of lecithin dihydrate, Nature 281,499–501.

53. Pascher, I. and S. Sundell, 1986, Membrane lipids: Preferred conformational states and their inter-play. The crystal strucure of dilauroylphosphatidyl-N,N- dimethylethanolamine, Biochim. Biophys.Acta 855, 68–78.

54. Hauser, H., I. Pascher, I.H. Pearson and S. Sundell, 1981, Preferred conformation and molecularpacking of phosphatidylethanolamine and phosphatidylcholine, Biochim. Biophys. Acta 650, 21–51.

55. Cevc, G., 1991, Isothermal lipid phase transitions, Chem. Phys. Lipids 57, 293–307.56. Watts, A., K. Harlos, W. Maschke and D. Marsh, 1978, Control of the structure and fluidity of

phosphatidylglycerol bilayers by pH titration, Biochim. Biophys. Acta 510, 63–74.57. Stumpel, J., K. Harlos and H. Eibl, 1980, Charge-induced pretransition in phosphatidylethanolamine

multilayers: the occurrence of ripple structures, Biochim. Biophys. Acta 599, 464–472.58. Harlos, K., J. Stumpel and H. Eibl, 1979, Influence of pH on phosphatidic acid multilayers:

A rippled structure at high pH values, Biochim. Biophys. Acta 555, 409–416.59. Safinya, C.R., D. Roux, G.S. Smith, S.K. Sinha, P. Dimon, N.A. Clark and A.M. Bellocq, 1986,

Steric interactions in a model multimembrane system: a synchrotron X-ray study, Phys. Rev. Lett.57, 2718–2721.

60. Marsh, D. and J.M. Seddon, 1982, Gel-inverted hexagonal (Lα-HII) phase transitions in phos-phatidylethanolamines and fatty acid-phosphatidylcholine mixtures, demonstrated by 31P NMRspectroscopy and X-ray diffraction, Biochim. Biophys. Acta 690, 117–123.

61. Boggs, J.M., G. Rangaraj and K.M. Koshy, 1986, Effect of hydrogen-bonding and non-hydrogenbonding long chain compounds on the phase transition temperatures of phospholipids, Chem. Phys.Lipids 40, 23–34.

62. Koynova, R.D., A.I. Boyanov and B.G. Tenchov, 1987, Gel-state metastability and nature of theazeotropic points in mixtures of saturated phosphatidylcholines and fatty acids, Biochim. Biophys.Acta 903, 186–196.

63. Koynova, R.D., B.G. Tenchov, P.J. Quinn and P. Laggner, 1988, Structure and phase behaviourof hydrated mixtures of L-dipalmitoylphosphatidylcholine and palmitic acid. Correlations betweenstructural rearrangements, specific volume changes and endothermic events, Chem. Phys. Lipids48, 205–214.

64. Cevc, G., J.M. Seddon, R. Hartung and W. Eggert, 1988, Phosphatidylcholine-fatty acid membranes,I. Effects of protonation, salt concentration, temperature, and chain-length on the colloidal and phaseproperties of mixed vesicles, bilayers, and non-lamellar structures, Biophys. Acta 940, 219–240.

65. Templer, R.H., K.H. Madan, N.A. Warrender and J.M. Seddon, 1992, Swollen lyotropic cubicphases in fully hydrated mixtures of monoolein, dioleoylphosphatidylcholine and dioleoylphos-phatidylethanolamine, in: Structure and Conformation of Amphiphilic Membranes. Springer Pro-ceedings in Physics, eds R. Lipowsky and D. Richter (Springer, Heidelberg) pp. 262–265.

66. Bruinsma, R., 1992, Elasticity and excitations of minimal crystals, J. Phys. II France 2, 425–451.67. Luzzati, V. and P.A. Spegt, 1967, Polymorphism of lipids, Nature 215, 701–704.68. Tardieu, A., 1972, PhD thesis, Universite de Paris-Sud.69. Tardieu, A. and V. Luzzati, 1970, Polymorphism of lipids. A novel cubic phase: A cage-like

network of rods with enclosed spherical micelles, Biophys. Acta 219, 11–17.70. Fontell, K., K.K. Fox and E. Hansson, 1985, On the structure of the cubic phase I1 in some

lipid-water systems, Mol. Cryst. Liq. Cryst. Lett. 1, 9–17.71. Charvolin, J. and J.F. Sadoc, 1988, Periodic systems of frustrated fluid films and micellar cubic

structures in liquid crystals, J. Phys. (Paris) 49, 521–526.72. Eriksson, P.-O., L. Rilfors, G. Lindblom and G. Arvidson, 1985, Multicomponent spectra from

31P NMR studies of the phase equilibria in the system dioleoylphosphatidylcholine-dioleoylphosphati-dylethanolamine-water, Chem. Phys. Lipids 37, 357–371.


73. Eriksson, P.-O., G. Lindblom and G. Arvidson, 1987, NMR studies of micellar aggregates in1-acyl-sn-glycerophosphocholine systems. The formation of a cubic liquid crystalline phase,J. Phys. Chem. 91, 846–853.

74. Seddon, J.M., 1990, An inverse face-centred cubic phase formed by diacylglycerol-phosphatidyl-choline mixtures, Biochemistry 29, 7997–8002.

75. Seddon, J.M., E.A. Bartle and J. Mingins, 1990, Inverse cubic liquid-crystalline phases of phos-pholipids and related lyotropic systems, J. Phys.: Condens Matter 2, SA285–SA290.

76. Seddon, J.M., J.L. Hogan, N.A. Warrender and E. Pebay-Peyroula, 1990, Structural studies ofphospholipid cubic phases, Prog. Colloid Polym. Sci. 81, 189–197.

77. Luisi, P.L., 1985, Enzymes hosted in reverse micelles in hydrocarbon solution, Angew. Chem. Int.Ed. Engl. 24, 439–528.

78. Scartazzini, R. and P.L. Luisi, 1988, Organogels from lecithins, J. Phys. Chem. 92, 829–833.79. Schurtenberger, P., L.J. Magid, J. Penfold and R. Heenan, 1990, Shear aligned lecithin reverse

micelles: A small-angle neutron scattering study of the anomalous water-induced micellar growth,Langmuir 6, 1800–1803.

80. de Gennes, P.G. and C. Taupin, 1982, Microemulsions and the flexibility of oil/water interfaces,J. Phys. Chem. 86, 2294–2304.

81. Porte, G., J. Appel, P. Bassereau and J. Marignan, 1989, Lα to L3: A topology driven transitionin phases of infinite fluid membranes, J. Phys. France 50, 1355–1347.

82. Cates, M.E. and D. Roux, 1990, Random bilayer phases of dilute surfactant solutions, J. Phys.Condens. Matter 2, SA339–SA346.

83. Strey, R., R. Schomacker, D. Roux, F. Nallet and U. Olsson, 1990, Dilute lamellar and L3 phasesin the binary water-C12E5 system, J. Chem. Soc. Faraday Trans. 86, 2253–2261.

84. Strey, R., J. Winkler and L. Magid, 1991, Small-angle neutron scattering from diffuse interfaces,1. Mono- and bilayers in the water-octane-C12E5 system, J. Phys. Chem. 95, 7502–7507.

85. Winsor, P.A., 1968, Binary and multicomponent solutions of amphiphilic compounds. Solubiliza-tion and the formation, structure, and theoretical significance of liquid crystalline solutions, Chem.Rev. 68, 1–40.

86. Lutton, E.S., 1965, Phase behaviour of aqueous systems of monoglycerides, J. Am. Oil Chem.Soc. 42, 1068–1070.

87. Ekwall, P., 1975, Composition, properties and structures of liquid crystalline phases in systems ofamphiphilic compounds, Adv. Liq. Cryst. 1, 1–142.

88. Lee, A.G., 1977, Lipid phase transitions and phase diagrams, II. Mixtures involving lipids, Biochim.Biophys. Acta 472, 285–344.

89. Lee, A.G., 1978, Calculation of phase diagrams for non-ideal mixtures of lipids, and a possible non-random distribution of lipids in lipid mixtures in the liquid-crystalline phase, Biochim. Biophys.Acta 507, 433–444.

90. Marsh, D., 1987, Handbook of Lipid Bilayers (CRC Press, Boca Raton, FL).91. Caffrey, M., D. Moynihan and J. Hogan, 1991, A database of lipid phase transition temperatures

and enthalpy changes, Chem. Phys. Lipids 57, 275–291.92. Lee, A.G., 1977, Lipid phase transitions and phase diagrams, I. Lipid phase transitions, Biochim.

Biophys. Acta 472, 237–281.93. Silvius, J.R., 1982, Lipid phase transitions, in: Lipid–Protein Interactions, Vol. 2, eds P.C. Jost and

O.H. Griffith (Wiley, New York) pp. 239–281.94. Cullis, P.R., M.J. Hope, B. de Kruijff, A.J. Verkleij and C.P. Tilcock, 1985, Structural properties

and functional roles of phospholipids in biological membranes, in: Phospholipids and CellularRecognition, ed. J.F. Kuo (CRC Press, Boca Raton, FL) pp. 1–59.

95. Cullis, P.R., M.J. Hope and C.P.S. Tilcock, 1986, Lipid polymorphism and the roles of lipids inmembranes, Chem. Phys. Lipids 40, 127–144.

96. de Kruijff, B., P.R. Cullis, A.J. Verkleij, M.J. Hope, C.J.A. van Echteld and T.F. Taraschi, 1985,Lipid polymorphism and membrane function, in: The Enzymes of Biological Membranes, 2ndedition, ed. A.N. Martinosi (Plenum, New York) pp. 131–204.

97. Tilcock, C.P.S., 1986, Lipid polymorphism, Chem. Phys. Lipids 40, 109–125.


98. Gruner, S.M., 1989, Stability of lyotropic phases with curved interfaces, J. Phys. Chem. 93,7562–7570.

99. Marsh, D., 1991, General features of phospholipid phase transitions, Chem. Phys. Lipids 57, 109–120.

100. Seddon, J.M. and G. Cevc, 1993, Lipid polymorphism: Structure and stability of lyotropic meso-phases of phospholipids, in: Phospholipids Handbook, ed. G. Cevc (Marcel Dekker, New York)pp. 403–454.

101. Rand, R.P. and V.A. Parsegian, 1989, Hydration forces between phospholipid bilayers, Biochim.Biophys. Acta 988, 351–376.

102. Israelachvili, J.N., 1991, Intermolecular and Surface Forces, 2nd edition (Academic Press, London).103. Israelachvili, J.N., S. Marcelja and R. Horn, 1980, Physical principles of membrane organization,

Q. Rev. Biophys. 13, 121–200.104. Nayaran, O., P.T.C. So, D.C. Turner and S.M. Gruner, 1990, Volume constriction in a lipid-water

liquid crystal using high pressure X-ray diffraction, Phys. Rev. A 42, 7479–7482.105. Helfrich, W., 1981, Amphiphilic mesophases made of defects, in: Physics of Defects, eds R. Balian,

M. Kleman and J.P. Poirier (North-Holland, Amsterdam) pp. 715–755.106. Helfrich, W. and H. Rennschuh, 1990, Landau theory of the lamellar-to-cubic phase transition,

J. Phys. (France) 51(C7), 189–195.107. Turner, D.C., Z.G. Wang, S.M. Gruner, D.A. Mannock and R.N. McElhaney, 1992, A structural

study of the inverted cubic phases of didodecyl-alkyl-b-D-glucopyranosyl-rac-glycerol, J. PhysiqueII 2, 2039–2063.

108. Hyde, S.T., I.S. Barnes and B.W. Ninham, 1990, Curvature energy of surfactant interfaces confinedto the plaquettes of a cubic lattice, Langmuir 6, 1055–1062.

109. Fogden, A., S.T. Hyde and G. Lundberg, 1991, Bending energy of surfactant films, J. Chem. Soc.Faraday Trans. 87, 949–955.

110. Ljunggren, S. and J.C. Eriksson, 1992, Minimal surfaces and Winsor II microemulsions, Langmuir8, 1300–1306.

111. Szleifer, I., D. Kramer, A. Ben-Shaul, W.M. Gelbart and S.A Safran, 1990, Molecular theory ofcurvature elasticity in surfactant films, J. Chem. Phys. 92, 6800–6817.

112. Siegel, D.P., 1986, Inverted micellar intermediates and the transitions between lamellar, cubic andinverted hexagonal lipid phases, I. Mechanism of the Lα-HII phase transitions, Biophys. J. 49,1155–1170.

113. Siegel, D.P., 1986, Inverted micellar intermediates and the transitions between lamellar, cubicand inverted hexagonal lipid phases, II. Implications for membrane-membrane interactions andmembrane fusion, Biophys. J. 49, 1171–1183.

114. Siegel, D.P., 1986, Inverted micellar intermediates and the transitions between lamellar, cubicand inverted hexagonal amphiphile phases, III. Isotropic and inverted cubic state formation viaintermediates in transitions between Lα-HII phases, Chem. Phys. Lipids 42, 279–301.

115. Ellens, H., D.P. Siegel, D. Alford, P.L. Yeagle, L. Boni, L.J. Lis, P.J. Quinn and J. Bentz, 1989,Membrane fusion and inverted phases, Biochemistry 28, 3692–3703.

116. Siegel, D.P., J.L. Burns, M.H. Chestnut and Y. Talmon, 1989, Intermediates in membrane fu-sion and bilayer/nonbilayer phase transitions imaged by time-resolved cryo-transmission electronmicroscopy, Biophys. J. 56, 161–169.

117. Rancon, Y. and J. Charvolin, 1988, Fluctuations and phase transformations in a lyotropic liquidcrystal, J. Phys. Chem. 92, 6339–6344.

118. Holmes, M.C. and J. Charvolin, 1984, Smectic-nematic transition in a lyotropic liquid crystal,J. Phys. Chem. 88, 810–818.

119. Boden, N., S.A. Corne, M.C. Holmes, P.H. Jackson, D. Parker and K.W. Jolley, 1986, Order-disorder transitions in solutions of discoid micelles, J. Phys. (Paris) 47, 2135–2144.

120. Kekicheff, P., B. Cabane and M. Rawiso, 1984, Structural defects of a lamellar lyotropic mesophase:A neutron scattering study, J. Physique Lett. 45, 813–821.

121. Hendrikx, Y., J. Charvolin, P. Kekicheff and M. Roth, 1987, Structural fluctuations in the lamellarphase of sodium decyl sulphate / decanol / water, Liq. Cryst. 2, 677–687.


122. Kekicheff, P. and B. Cabane, 1988, Crystallography of systems with long periods: A neutronscattering study of sodium dodecyl sulphate / water mesophases, Acta Crystallogr. B44, 395–406.

123. Rancon, Y. and J. Charvolin, 1987, Displacement disorder in a liquid crystalline phase with cubicsymmetry, J. Phys. (Paris) 48, 1067–1073.

124. Rancon, Y. and J. Charvolin, 1988, Epitaxial relationships during phase transformations in a ly-otropic liquid crystal, J. Phys. Chem. 92, 2646–2651.

125. Clerc, M., A.M. Levelut and J.F. Sadoc, 1990, X-ray study of phase transitions in amphiphilicsystems, J. Phys. (France) 51(C7), 97–104.

126. Clerc, M., A.M. Levelut and J.F. Sadoc, 1991, Transitions between mesophases involving cubicphases in the surfactant-water systems. Epitaxial relations and their consequences in a geometricalframework, J. Phys. II France 1, 1263–1276.

127. Sotta, P., 1991, Equilibrium shape of lyotropic cubic monocrystals, J. Phys. II France 1, 763–772.128. Gruner, S.M., K.J. Rothschild and N.A. Clark, 1982, X-ray diffraction and electron microscope

study of phase separation in rod outer segment photoreceptor membrane multilayers, Biophys. J.39, 241–251.

129. Gruner, S.M., K.J. Rothschild, W.J. DeGrip and N.A. Clark, 1985, Co-existing lyotropic liquidcrystals: Commensurate, faceted and co-planar single hexagonal (HII) domains in lamellar photre-ceptor membranes, J. Phys. (Paris) 46, 193–201.

130. Templer, R.H., N.A. Warrender, R. Meadows and J.M. Seddon, 1992, Epitaxial relationships be-tween adjacent phases in hydrated monoolein, in: Structure and Conformation of AmphiphilicMembranes. Springer Proceedings in Physics, eds R. Lipowsky and D. Richter (Springer, Heidel-berg) pp. 230–233.

131. Trauble, H., M. Teubner, P. Wooley and H. Eibl, 1976, Electrostatic interactions at charged lipidmembranes, 1. Effects of pH and univalent cations on membrane structure, Biophys. Chem. 4,319–346.

132. Zimmermann, U., 1982, Electric field-mediated fusion and related electrical phenomena, Biochim.Biophys. Acta 694, 227–277.

133. Zimmermann, U., 1983, Electrofusion of cells: Principles and industrial potential, Trends Biotech-nol. 1, 149–155.

134. Arnett, E.M., J.M. Gold, N. Harvey, E.A. Johnson and L.G. Whitesell, 1988, Stereoselective recog-nition in phospholipid monolayers, in: Biotechnological Applications of Lipid Microstructures, edsB.P. Gaber, J.M. Schnur and D. Chapman (Plenum, New York) pp. 21–36.

135. Andelman, D., 1989, Chiral discrimination and phase transitions in Langmuir monolayers, J. Am.Chem. Soc. 111, 6536–6544.

136. Mannock, D.A., R.N.A.H. Lewis, R.N. McElhaney, M. Akiyama, H. Yamada, D.C. Turner andS.M. Gruner, 1992, The effect of the chirality of the glycerol backbone on the bilayer and nonbilayerphase transitions in the diastereomers of di-dodecyl-D-glucopyranosyl glycerol, Biophys. J. 63,1355–1368.

137. Lever, M.J., K.W. Miller, W.D.M. Paton and E.B. Smith, 1971, Pressure reversal of anaesthesia,Nature 231, 368–371.

138. MacDonald, A.G., 1984, The effects of pressure on the molecular structure and physiologicalfunctions of cell membranes, Philos. Trans. R. Soc. London B304, 47–68.

139. Liu, N.I. and R.L. Kay, 1977, Redetermination of the pressure dependence of the lipid bilayerphase transition, Biochemistry 16, 3484–3486.

140. Wong, P.T.T., 1986, Phase behaviour of phospholipid membranes under high pressure, Physica 139and 140B, 847–852.

141. Yager, P. and E.L. Chang, 1983, Destabilization of a lipid non-bilayer phase by high pressure,Biochim. Biophys. Acta 731, 491–494.

142. Chang, E.L. and P. Yager, 1983, Effect of high pressure on a lipid non-bilayer phase, Mol. Cryst.Liq. Cryst. 98, 125–129.

143. Shyamsunder, E., P. Botos and S.M. Gruner, 1989, Comment on: X-ray diffraction study of theeffects of pressure on bilayer to nonbilayer lipid membrane phase transitions, J. Chem. Phys. 90,1293–1295.

144. So, P.T.C., 1992, PhD thesis, Princeton University.


145. Seddon, J.M., G. Cevc, R.D. Kaye and D. Marsh, 1984, X-ray diffraction study of the polymorphismof hydrated diacyl and dialkyl phosphatidylethanolamines, Biochemistry 23, 2634–2644.

146. Lewis, R.N.A.H., D.A. Mannock, R.N. McElhaney, D.C. Turner and S.M. Gruner, 1989, Effect offatty acyl chain length and structure on the lamellar gel to liquid-crystalline and lamellar to reversedhexagonal phase transitions of aqueous phosphatidylethanolamine dispersions, Biochemistry 28,541–548.

147. Marsh, D., 1991, Analysis of the chainlength dependence of lipid phase transition tempera-tures: Main and pretransitions of phosphatidylcholines; main and non-lamellar transitions of phos-phatidylethanolamines, Biochim. Biophys. Acta 1062, 1–6.

148. Seddon, J.M., G. Cevc and D. Marsh, 1983, Calorimetric studies of the gel-fluid (Lβ -Lα) andlamellar-inverted hexagonal (Lα-HII) phase transitions in dialkyl- and diacylphosphatidylethanol-amines, Biochemistry 22, 1280–1289.

149. Barton, P.G. and F.D. Gunstone, 1975, Hydrocarbon chain packing and molecular motion in phos-pholipid bilayers formed from unsaturated lecithins, J. Biol. Chem. 250, 4470–4476.

150. Cevc, G., 1991, How membrane chain-melting phase transition temperature is affected by the lipidchain asymmetry and degree of unsaturation: An effective chain-length model, Biochemistry 30,7186–7193.

151. Mattai, J., P.K. Sripada and G.G. Shipley, 1987, Mixed chain phosphatidylcholine bilayers: Struc-ture and properties, Biochemistry 26, 3287–3297.

152. Wang, Z., H. Lin and C. Huang, 1990, Differential scanning calorimetry study of a homologousseries of fully hydrated saturated mixed chain C(X):C(X+6) phosphatidylcholines, Biochemistry29, 7072–7076.

153. Lin, H., Z. Wang and C. Huang, 1991, The influence of acyl chain-length asymmetry on the phasetransition parameters of phosphatidylcholine dispersions, Biochim. Biophys. Acta 1067, 17–28.

154. Laggner, P., K. Lohner, G. Degovics, K. Muller and A. Schuster, 1987, Structure and thermody-namics of the dihexadecylphosphatidylcholine-water system, Chem. Phys. Lipids 44, 31–60.

155. Lohner, K., A. Schuster, G. Degovics, K. Muller and P. Laggner, 1987, Thermal phase behaviourand structure of hydrated mixtures between dipalmitoyl- and dihexadecylphosphatidylcholines,Chem. Phys. Lipids 44, 61–70.

156. Kim, J.T., J. Mattai and G.G. Shipley, 1987, Gel phase polymorphism in ether-linked dihexade-cylphosphatidylcholine bilayers, Biochemistry 26, 6592–6598.

157. Kim, J.T., J. Mattai and G.G. Shipley, 1987, Bilayer interactions of ether- and ester-linked phos-pholipids: Dihexadecyl- and dipalmitoylphosphatidylcholines, Biochemistry 26, 6599–6603.

158. Haas, N.S., P.K. Sripada and G.G. Shipley, 1990, Effect of chain linkage on the structure ofphosphatidylcholine bilayers, Biophys. J. 57, 117–124.

159. Cevc, G., 1987, How membrane chain melting properties are regulated by the polar surface of thelipid bilayer, Biochemistry 26, 6305–6310.

160. Boggs, J.M., 1987, Lipid intermolecular hydrogen bonding: Influence on structural organizationand membrane function, Biochim. Biophys. Acta 906, 353–404.

161. Janiak, M.J., D.M. Small and G.G. Shipley, 1979, Temperature and compositional dependence ofthe structure of hydrated dimyristoyl lecithin, J. Biol. Chem. 254, 6068–6078.

162. Kuttenreich, H., H.-J. Hinz, M. Inczedy-Marcsek, R. Koynova, B. Tenchov and P. Laggner, 1990,Polymorphism of synthetic 1,2-O-dialkyl-3-O-β-D-galactosyl-sn-glycerols of different alkyl chainlengths, Chem. Phys. Lipids 47, 245–260.

163. Sen, A., S.-W. Hui, D.A. Mannock, R.N.A.H. Lewis and R.N. McElhaney, 1990, The physicalproperties of glycosyl diacylglycerols, 2. X-ray diffraction studies of a homologous series of1,2-di-O-acyl-3-O-(α-D-glucopyranosyl)-sn-glycerols, Biochemistry 29, 7799–7804.

164. Hinz, H.-J., H. Kuttenreich, R. Meyer, M. Renner, R. Frund, R. Koynova, A.I. Boyanov andB.G. Tenchov, 1991, Stereochemistry and size of headgroups determine structure and phase be-haviour of glycolipid membranes: Densitometric, calorimetric and X-ray studies, Biochemistry 30,5125–5138.

165. Tenchov, B.G., A.I. Boyanov and R.D. Koynova, 1984, Lyotropic polymorphism of racemic di-palmitoylphosphatidylethanolamine. A differential scanning calorimetry study, Biochemistry 23,3553–3558.


166. Rand, R.P., N. Fuller, V.A. Parsegian and D.C. Rau, 1988, Variation in hydration forces betweenneutral phospholipid bilayers: Evidence for hydration attraction, Biochemistry 27, 7711–7722.

167. Tate, M.W. and S.M. Gruner, 1987, Lipid polymorphism of mixtures of dioleoylphosphatidyletha-nolamine and saturated and monosaturated phosphatidylcholines of various chain lengths, Bio-chemistry 26, 231–236.

168. Boni, L.T. and S.W. Hui, 1983, Polymorphic phase behaviour of dilinoleoylphosphatidylethanol-amine and palmitoyloleoylphosphatidylcholine mixtures: Structural changes between hexagonal,cubic and bilayer phases, Biochim. Biophys. Acta 731, 177–185.

169. Eriksson, P.-O., G. Lindblom and G. Arvidson, 1985, NMR studies of 1- palmitoyllysophosphatidyl-choline in a cubic liquid crystal with a novel structure, J. Phys. Chem. 89, 1050–1053.

170. Cevc, G., 1990, Membrane electrostatics, Biochim. Biophys. Acta 1031, 311–382.171. Fernandez, M.S. and P. Fromhertz, 1977, Lipoid pH indicators as probes of electrical potential and

polarity in micelles, J. Phys. Chem. 81, 1755–1761.172. Mabrey, S. and J. Sturtevant, 1977, Interaction of saturated fatty acids into phosphatidylcholine

bilayers, Biochim. Biophys. Acta 486, 444–450.173. Heimburg, T., N.J.P. Ryba, U. Wurz and D. Marsh, 1990, Phase transition from a gel to a fluid

phase of cubic symmetry in dimyristoylphosphatidylcholine / myristic acid (1:2, mol/mol) bilayers,Biochim. Biophys. Acta 1025, 77–81.

174. Hope, M.J. and P.R. Cullis, 1981, The role of non-bilayer lipid structures in the fusion of humanerythrocytes induced by lipid fusogens, Biochim. Biophys. Acta 640, 82–90.

175. Tilcock, C.P.S. and D. Fisher, 1982, Interactions of glycerol monooleate and dimethylsulphoxidewith phospholipids: A differential scanning calorimetry and 31P-NMR study, Biochim. Biophys.Acta 685, 340–346.

176. Gutman, H., G. Arvidson, K. Fontell and G. Lindblom, 1984, 31P and 2H NMR studies of phaseequilibria in the three component system: Monoolein-dioleoylphosphatidylcholine-dioleoylphos-phatidylethanolamine, in: Surfactants in Solution, Vol. 1, eds K.L. Mittal and B. Lindman (Plenum,New York) pp. 143–152.

177. Nilsson, A., A. Holmgren and G. Lindblom, 1991, Fourier-transform infrared spectroscopy studyof dioleoylphosphatidylcholine and monooleoylglycerol in lamellar and cubic phases, Biochemistry30, 2126–2133.

178. Caffrey, M., 1987, Kinetics and mechanism of transitions involving the lamellar, cubic, invertedhexagonal, and fluid isotropic phases of hydrated monoglycerides monitored by time-resolvedX-ray diffraction, Biochemistry 26, 6349–6363.

179. Dawson, R.M.C., R.F. Irvine, J. Bray and P.J. Quinn, 1984, Long-chain unsaturated diacylglyc-erols cause a perturbation in the structure of phospholipid bilayers rendering them susceptible tophospholipase attack, Biochem. Biophys. Res. Commun. 125, 836–842.

180. Das, S. and R.P. Rand, 1984, Diacylglycerol causes major structural transitions in phospholipidbilayer membranes, Biochem. Biophys. Res. Commun. 124, 491–496.

181. Das, S. and R.P. Rand, 1986, Modification by diacylglycerol of the structure and interaction ofvarious phospholipid bilayer membranes, Biochemistry 25, 2882–2889.

182. Epand, R.M., 1985, Diacylglycerols, lysolecithin, or hydrocarbons markedly alter the bilayer tohexagonal phase transition temperature of phosphatidylethanolamines, Biochemistry 24, 7092–7095.

183. Epand, R.M. and R. Bottega, 1988, Determination of the phase-behaviour of phosphatidylethanol-amine admixed with other lipids and the effects of calcium chloride – implications for proteinkinase-C regulation, Biochim. Biophys. Acta 944, 144–154.

184. Siegel, D.P., J. Banschbach and P.L. Yeagle, 1989, Stabilization of HII phases by low levels ofdiglycerides and alkanes: Calorimetric, and X-ray diffraction study, Biochemistry 28, 5010–5019.

185. Siegel, D.P., J. Banschbach, D. Alford, H. Ellens, L.J. Lis, P.J. Quinn, P.L. Yeagle and J. Bentz,1989, Physiological levels of diacylglycerols in phospholipid membranes induce membrane fusionand stabilize inverted phases, Biochemistry 28, 3703–3709.

186. Noordam, P.C., C.J.A. van Echteld, B. de Kruijff and A. Verkleij, 1980, Barrier characteristics ofmembrane model systems containing unsaturated phosphatidylethanolamines, Chem. Phys. Lipids27, 221–232.


187. Dekker, C.J., W.S.M. van Kessel, J.P.G. Klom, J. Pieters and B. de Kruijff, 1983, Synthesis andpolymorphic phase behaviour of polyunsaturated phosphatidylcholines and phosphatidylethanol-amines, Chem. Phys. Lipids 33, 93–106.

188. Hornby, A.P. and P.R. Cullis, 1981, Influence of local and neutral anaesthetics on the polymorphicphase preferences of egg yolk phosphatidylethanolamine, Biochim. Biophys. Acta 647, 285–292.

189. Kirk, G.L. and S.M. Gruner, 1985, Lyotropic effects of alkanes and headgroup composition on theL(alpha)-HII lipid liquid crystal phase transition: Hydrocarbon packing versus intrinsic curvature,J. Phys. France 46, 761–769.

190. Sjolund, M., G. Lindblom, L. Rilfors and G. Arvidson, 1987, Hydrophobic molecules in lecithin-water systems, 1. Formation of reversed hexagonal phases at high and low water contents, Biophys.J. 52, 145–153.

191. Sjolund, M., L. Rilfors and G. Lindblom, 1989, Reversed hexagonal phase formation in lecithin-alkane-water systems with different acyl chain unsaturation and alkane length, Biochemistry 28,1323–1329.

192. Lindblom, G., L. Rilfors, I. Brentel, P.-O. Eriksson, G. Wikander, G. Arvidson and A. Wieslander,1987, Effect of hydrophobic, amphiphilic and peptide molecules on phase structure and dynamicsof membrane lipids, Chem. Scr. 27B, 221–227.

193. Lindblom, G., M. Sjolund and L. Rilfors, 1988, Effect of n-alkanes and peptides on the phaseequilibria in phosphatidylcholine-water systems, Liquid Crystals 3, 783–790.

194. Gruner, S.M., M.W. Tate, G.L. Kirk, P.T.C. So, D.C. Turner, D.T. Keane, C.P.S. Tilcock andP.R. Cullis, 1988, X-ray diffraction study of the polymorphic behaviour of N-methylated di-oleoylphosphatidylethanolamine, Biochemistry 27, 2853–2866.

195. Rand, R.P., N. Fuller, S.M. Gruner and V.A. Parsegian, 1990, Membrane curvature, lipid seg-regation, and structural transitions for phospholipids under dual-solvent stress, Biochemistry 29,76–87.

196. Lohner, K., 1991, Effects of small organic molecules on phospholipid phase transitions, Chem.Phys. Lipids 57, 341–362.

197. Tenchov, B., 1991, On the reversibility of the phase transitions in lipid-water systems, Chem. Phys.Lipids 57, 165–177.

198. Chen, S.C., J.M. Sturtevant and B.J. Gaffney, 1980, Scanning calorimetric evidence for a thirdphase transition in phosphatidylcholine bilayers, Proc. Nat. Acad. Sci. USA 77, 5060–5063.

199. Ruocco, M.J. and G.G. Shipley, 1982, Characterization of the sub-transition of hydrated dipalmi-toylphosphatidylcholine, Biochim. Biophys. Acta 684, 59–66.

200. Finegold, L. and M.A. Singer, 1986, The metastability of saturated phosphatidylcholines dependson the acyl chain length, Biochim. Biophys. Acta 855, 417–420.

201. Lewis, R.N.A.H., N. Mak and R.N. McElhaney, 1987, A differential scanning calorimetric studyof the thermotropic phase behaviour of model membranes composed of phosphatidylcholines con-taining linear saturated fatty acyl chains, Biochemistry 26, 6118–6126.

202. Yang, C.P., M.C. Wiener and J.F. Nagle, 1988, New phases of DPPC/water mixtures, Biochim.Biophys. Acta 945, 101–104.

203. Chang, H. and R.M. Epand, 1983, The existence of a highly ordered phase in fully hydrateddilauroylphosphatidylethanolamine, Biochim. Biophys. Acta 728, 319–324.

204. Mantsch, H.H., S.C. Hsi, K.W. Butler and D.G. Cameron, 1983, Studies on the thermotropicbehaviour of aqueous phosphatidylethanolamines, Biochim. Biophys. Acta 728, 325–330.

205. Chowdry, B.Z., G. Lipka, A.W. Dalziel and J.M. Sturtevant, 1984, Multicomponent phase transi-tions of diacyl phosphatidylethanolamines, Biophys. J. 45, 901–904.

206. Wilkinson, D.A. and J.F. Nagle, 1984, Metastability in the phase behaviour of dimyristoylphos-phatidylethanolamine bilayers, Biochemistry 23, 1538–1541.

207. Xu, H., F.A. Stephenson, H. Lin and C. Huang, 1988, Phase metastability and supercooledmetastable state of diundecanoylphosphatidylethanolamine bilayers, Biochim. Biophys. Acta 943,63–75.

208. Koynova, R. and H.-J. Hinz, 1990, Metastable behaviour of saturated phosphatidylethanolamines:A densitometric study, Chem. Phys. Lipids 54, 67–72.


209. Mason, J.T. and F.A. Stephenson, 1990, Thermotropic properties of saturated mixed acyl phos-phatidylethanolamines, Biochemistry 29, 590–598.

210. Mulakutla, S. and G.G. Shipley, 1984, Structure and thermotropic properties of phosphatidyletha-nolamine and its N-methyl derivatives, Biochemistry 23, 2514–2519.

211. Wilkinson, D.A. and T.J. McIntosh, 1986, A subtransition in a phospholipid with a net charge,dipalmitoylphosphatidylglycerol, Biochemistry 25, 295–298.

212. Reed, R.A. and G.G. Shipley, 1987, Structure and metastability of N-lignocerylgalactosylsphingo-sine (cerebroside) bilayers, Biochim. Biophys. Acta 896, 153–164.

213. Mannock, D.A., R.N.A.H. Lewis, A. Sen and R.N. McElhaney, 1988, The physical properties ofglycosyldiacylglycerosls. Calorimetric studies of a homologous series of 1,2–di-O-di-3-O-(β-D-glucopyranosyl)-sn-glycerols, Biochemistry 27, 6852–6859.

214. Tsong, T.Y., 1974, Kinetics of the crystalline to liquid-crystalline phase transition of dimyristoylL-(alpha)-lecithin bilayers, Proc. Nat. Acad. Sci. USA 71, 2684–2688.

215. Strehlow, U. and F. Jahnig, 1981, Electrostatic interactions at charged lipid membranes. Kineticsof the electrostatically triggered phase transition, Biochim. Biophys. Acta 641, 301–310.

216. Grunewald, B., 1982, On the phase transition kinetics of phospholipid bilayers. Relaxation exper-iments with detection of fluorescence anisotropy, Biochim. Biophys. Acta 687, 71–78.

217. Ranck, J.L., L. Letellier, E. Schechter, B. Krop, P. Pernot and A. Tardieu, 1984, X-ray analysisof the kinetics of Escherichia coli lipid and membrane structural transitions, Biochemistry 23,4955–4961.

218. Caffrey, M. and D.H. Bilderback, 1984, Kinetics of the main phase transition of hydrated lecithinmonitored by real-time X-ray diffraction, Biophys. J. 45, 627–631.

219. Caffrey, M., 1985, Kinetics and mechanism of the lamellar gel – lamellar liquid-crystal and lamellar/ inverted hexagonal phase transition in phosphatidylethanolamine: A real-time X-ray diffractionstudy using synchrotron radiation, Biochemistry 24, 4826–4844.

220. Laggner, P., K. Lohner and K. Muller, 1987, X-ray cinematography of phospholipid phase trans-formations with synchrotron radiation, Mol. Cryst. Liq. Cryst. 151, 373–388.

221. Caffrey, M., 1989, The study of lipid phase transition kinetics by time-resolved X-ray diffraction,Annu. Rev. Biophys. Biophys. Chem. 18, 159–186.

222. Gruner, S.M., 1987, Time-resolved X-ray diffraction of biological materials, Science 238, 305–312.223. Caffrey, M., R.L. Magin, B. Hummel and J. Zhang, 1990, Kinetics of the lamellar and hexago-

nal phase transitions in phosphatidylethanolamine. Time-resolved X-ray diffraction study using amicrowave-induced temperature jump, Biophys. J. 58, 21–29.

224. Laggner, P. and M. Kriechbaum, 1991, Phospholipid phase transitions: Kinetics and structuralmechanisms, Chem. Phys. Lipids 57, 121–145.

225. Tate, M.W., E. Shyamsunder, S.M. Gruner and K. D’Amico, 1992, Kinetics of the lamellar-inversehexagonal phase transition determined by time-resolved X-ray diffraction, Biochemistry 31, 1081–1092.

226. Gulik, A., V. Luzzati, M. de Rosa and A. Gambacorta, 1985, Structure and polymorphism ofbipolar isopranyl ether lipids from archaebacteria, J. Mol. Biol. 182, 131–149.

227. Shyamsunder, E., S.M. Gruner, M.W. Tate, D.C. Turner, P.T.C. So and C.P.S. Tilcock, 1988,Observation of inverted cubic phase in hydrated dioleoylphosphatidylethanolamine membranes,Biochemistry 27, 2332–2336.

228. Siegel, D.P. and J. Banschbach, 1990, Lamellar/inverted cubic (Lα/QII) phase transition in N-me-thylated dioleoylphosphatidylethanolamine, Biochemistry 29, 5975–5981.

229. de Kruijff, B., P.R. Cullis, A.J. Verkleij, M.J. Hope, C.J.A. van Echteld, T.F. Taraschi, P. vanHoogevest, J.A. Killian, A. Rietveld and A.T.M. van der Steen, 1985, Modulation of lipid poly-morphism by lipid-protein interactions, in: Progress in Protein–Lipid Interactions, eds A. Wattsand J.J.H.H.M de Pont (Elsevier, Amsterdam) pp. 89–142.

230. Gruner, S.M., 1985, Intrinsic curvature hypothesis for biomembrane lipid composition – a role fornonbilayer lipids, Proc. Nat. Acad. Sci. USA 82, 3665–3669.

231. Stier, A., S.A.E. Finch and B. Bosterling, 1978, Non-lamellar structure in rabbit liver microsomalmembranes, FEBS Lett. 91, 109–112.


232. de Kruijff, B., A.M.H.P. van den Besselaar, P.R. Cullis, H. van den Bosch and L.L.M. van Deenen,1978, Evidence for isotropic motion of phospholipids in liver microsomal membranes, Biochim.Biophys. Acta 514, 1–8.

233. de Kruijff, B., A. Rietveld and P.R. Cullis, 1980, 31P-NMR studies on membrane phospholipids inmicroscomes, rat liver slices and intact perfused rat liver, Biochim. Biophys. Acta 600, 343–357.

234. Green, D.E., 1972, Membrane proteins: A perspective, Ann. NY Acad. Sci. 95, 150–172.235. Cullis, P.R., B. de Kruijff, M.J. Hope, R. Nayar, A. Rietveld and A.J. Verkleij, 1980, Structural

properties of phospholipids in the rat liver inner mitochondrial membrane, Biochim. Biophys. Acta600, 625–635.

236. Kachar, B. and T.S. Reese, 1982, Evidence for the lipidic nature of tight junction strands, Nature296, 464–466.

237. Pinto da Silva, P. and B. Kachar, 1982, On tight-junction structure, Cell 28, 441–450.238. Verkleij, A.J., 1980, The nature of the intramembrane particle, Proc. Electr. Microsc. Soc. Am.

38, 688–691.239. Meyer, H.W., W. Richter and J. Gumpert, 1990, Periodically curved bilayer structures observed

in hyphal cells or stable L-form cells of a Streptomyces strain, and in liposomes formed by theextracted lipids, Biochim. Biophys. Acta 1026, 171–178.

240. Donnay, G. and D.L. Pawson, 1969, X-ray diffraction studies of echinoderm plates, Science 166,1147–1150.

241. Nissen, H.-U., 1969, Crystal orientation and plate structure in echinoid skeletal units, Science 166,1150–1152.

242. Corless, J.M. and M.J. Costello, 1981, Paracrystalline inclusions associated with the disk mem-branes of frog retinal rod outer segments, Exp. Eye Res. 32, 217–228.

243. Luzzati, V., A. Gulik, M. de Rosa and A. Gambacorta, 1987, Lipids from Sulfolobus solfactaricus,life at high temperature and the structure of membranes, Chem. Scr. B 27, 211–219.

244. Gunning, B.E.S., 1965, The greening process in plastids, I. The structure of the prolamellar body,Protoplasma 60, 111–130.

245. Simpson, D.J., 1978, Freeze-fracture studies on barley plastid membranes, I. Wild-type etioplast,Carlsberg Res. Commun. 43, 145–170.

246. Israelachvili, J.N. and J. Wolfe, 1980, The membrane geometry of the prolamellar body, Proto-plasma 100, 315–321.

247. Murakami, S., N. Yamada, M. Nagano and M. Osumi, 1985, Three-dimensional structure of theprolamellar body in squash etioplasts, Protoplasma 128, 147–156.

248. Borgstrom, B., 1985, The micellar hypothesis of fat digestion: must it be revisited?, Scand. J.Gastroenterol. 20, 389–394.

249. Patton, J.S. and M.C. Carey, 1979, Watching fat digestion, Science 204, 145–148.250. Rigler, M.W. and J.S. Patton, 1983, The production of liquid crystalline product phases by pancre-

atic lipase in the absence of bile salts, Biochim. Biophys. Acta 751, 444–454.251. Rigler, M.W., R.E. Honkanen and J.S. Patton, 1986, Visualization by freeze fracture, in vitro and

in vivo, of the products of fat digestion, J. Lipid Res. 27, 836–857.252. Rand, R.P., 1981, Interacting phospholipid bilayers: measured forces and induced structural changes,

Annu. Rev. Biophys. Bioeng. 10, 277–314.253. Prestegard, J.H. and M.P. O’Brien, 1987, Membrane and vesicle fusion, Annu. Rev. Phys. Chem.

38, 383–411.254. Bentz, J. and H. Ellens, 1988, Membrane fusion – kinetics and mechanisms, Coll. Surf. 30, 65–112.255. Verkleij, A.J., 1984, Lipidic intramembranous particles, Biochim. Biophys. Acta 779, 43–63.256. Nishizuka, Y., 1984, The role of protein kinase-C in cell-surface signal transduction and tumour

promotion, Nature 308, 693–698.257. Berridge, M.J., 1987, Inositol triphosphate and diacylglycerol: Two interacting second messengers,

Annu. Rev. Biochem. 56, 159–193.258. Burger, K.N.J., J.-L. Nieva, A. Alonso and A.J. Verkleij, 1991, Phospholipase C activity-induced

fusion of pure lipid model membranes. A freeze fracture study, Biochim. Biophys. Acta 1068,249–253.


259. Ortiz, A., J. Villalain and J.C. Gomez-Fernandez, 1988, Interaction of diacylglycerols with phos-phatidylchioline vesicles as studied by differential scanning calorimetry and fluorescence probemeasurements, Biochemistry 27, 9030–9036.

260. Sinesky, M., 1974, Homeoviscous adaptation – a homeostatic process that regulates the viscosityof membrane lipids in Escherichia coli, Proc. Nat. Acad. Sci. USA 71, 522–525.

261. Cullen, J., M.C. Phillips and G.G. Shipley, 1971, The effects of temperature on the compositionand physical properties of the lipids of Pseudomonas fluorescens, Biochem. J. 125, 733–742.

262. Lindblom, G., I. Brentel, M. Sjolund, G. Wikander and A. Wieslander, 1986, Phase equilibria ofmembrane lipids from Acholeplasma laidlawii: Importance of a single lipid forming nonlamellarphases, Biochemistry 25, 7502–7510.

263. Wieslander, A., A. Christiansson, L. Rilfors and G. Lindblom, 1980, Lipid bilayer stability inmembranes. Regulation of lipid composition in Acholeplasma laidlawii as governed by molecularshape, Biochemistry 19, 3650–3655.

264. Goldfine, H., N.C. Johnston, J. Mattai and G.G. Shipley, 1987, Regulation of bilayer stability inClostridium butyricum: Studies on the polymorphic phase behaviour of the ether lipids, Biochem-istry 26, 2814–2822.

265. Tournois, H. and B. de Kruijff, 1991, Polymorphic phospholipid phase transitions as tools tounderstand peptide-lipid interactions, Chem. Phys. Lipids 57, 327–340.

266. Sadoc, J.F. and J. Charvolin, 1989, Infinite periodic minimal surfaces and their crystallography inthe hyperbolic plane, Acta Crystallogr. A45, 10–20.

polymorphism of lipid-water systemsdutcher/download/handbook of... · chapter 3 polymorphism of...

Documents