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The cubic phases
The cubic phases Paolo Mariani Universit~ di Ancona, Ancona, Italy Recent papers dealing with lipid cubic phases are discussed. The image reconstruction of freeze-fracture electron micrographs and fluorescence bleaching techniques are the major experimental novelties. The determination of the structure of the phase Q227 (space group Fd3m) is particularly important and confirms an earlier proposal by Charvolin and Sadoc. Current Opinion in Structural Biology 1991, 1:501-505
Introduction Within the wide variety of phases formed by lipids in the presence of water [1], those with cubic symmetry are the most complex. Cubic phases were discovered in lipid/water systems in the early 1960s [2,3], but only in the past few years has attention been focused on their structure [3--6]. Much theoretical interest has been shown in these phases, especially from the viewpoint of differential geometry [4,7",8",9]. Several authors have discussed the biological implications of cubic structures, with special emphasis on membrane fusion, fat digestion, regulation of lipid composition, transport processes and photosynthesis (reviewed in [3,4,6,7",10,11..]; see also [5,12]). In particular, it has been suggested that lipid polymorphic transitions and cubic phases may be involved in some of the physiological functions of membranes (for a review, see [4]). So far, however, it has been impossible to support with convincing experimental evidence the hypothesis that naturally occurring lipids can form cubic phases under physiological conditions. Nevertheless, there exist numerous reports of the existence of three-dimensional periodic membrane assemblies, which could be related to cubic structures. Details of literature on these periodic conformations from ultrastructural studies of cell membranes and organelles can be found in [10]. Phases with cubic symmetry are now known to be widespread in amphiphilic systems; six cubic phases have been identified so far [3,5], but the list may still be incomplete. As a rule, the phases are named according to their space group. In this review, I use the nomenclature introduced by Luzzati's group: a cubic phase is called Qn, where Q stands for cubic and n is the number of the space group defined by the International Tables for Crystallography [3]. In this review, a number of recent papers dealing with cubic phases of lipid-containing systems, and more generally with lipid polymorphism, will be discussed so as to stress the most important current developments and the results of outstanding interest.
Two important review papers published within the past year are directly relevant to this topic. One [11"'] provides a catalogue of all the cubic phases observed so far in systems containing anionic and cationic detergents, zwitterionic and non-ionic surfactants, and lipids of biological origin (monogtycerides, sphingolipids and phospholipids). The other [7"] focuses on the inverted hexagonal phase, but also reports a large number of phase diagrams, discusses the topological and structural relationships between the different non-lamellar phases, and analyses the thermodynamic properties of lipid phases.
Experimental techniques and methods The general trend has been to improve the analysis of crystallographic data [5,12,13,14"], to perform more sophisticated analyses of electron microscope images [15,-], and to widen the spectrum of experimental techniques [16°',17",18",19].
X-ray and neutron scaltering A significant improvement in crystallographic procedures has been the development of a pattern-recognition approach [13] based upon the axiom that the histogram of the electron-density map is invariant in phases with different structures and the same chemical composition [5,13]. In the past year, the method has been successfully employed in the structure analysis of phase Q227 (v Luzzati et al., unpublished data) and, quite recently, of phase Q223 (R Vargas et al., personal communication). Neutron-scattering techniques have also been applied to the cubic phases [20,21.,22.] but with limited success because of the inadequate quality of the data, especially in contrast to that provided by X-ray-scattering experiments. The experimental techniques could perhaps be improved, in particular by making better use of specific labeling [14.].
Abbreviations DDAB
didodecyl dimethyl ammonium bromide; IPMS~infinite periodic minimal surface.
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Lipid$ Electron microscopy A large number of freeze-fracture electron micrographs of lipid-containing systems with apparent cubic synlmetry have been published [6,9]. Nevertheless, in most cases, the problem of whether the micrographs refer to the original structure of the sample or to some artefact of the freezing process was not resolved. Even when this problem h a s been overcome, the correlations between the electron-microscope images and the structures have not been properly investigated. Recently, the results of extended freeze-fracture electron-microscopy and X-ray-scattering studies of phase Q230 have been reported [15"]. In this case, the structure of the samples was checked by X-ray scattering after the freezing and before the fracture step [23]. The freeze-fracture electronmicroscope images were then analysed using real-space cross-correlation averaging. Moreover, in order to understand the nature of the fracture surfaces, the processed images were compared with the electron-density maps established by the X-ray-scattering analysis.
Self-diffusion measurements The analysis of the translational diffusion coefficients of both the lipid and the water components can provide useful information about the structure of a cubic phase. More precisely, the diffusion properties of a system comprised of two bicontinuous media are likely to be quite different from the diffusion properties of a system containing unconnected micelles. Charvolin and Rigny [24] have introduced NMR pulsedfield gradient methods for that purpose; these have been used largely in the study of cubic phases [6,7",17"]. Anderson and Wennerstrom [18.] have recently discussed the geometric aspects of the interpretation of gradientfield NMR data. In order to analyse the lateral diffusion in cubic phases of known structure, Cribier and co-workers [16-*] have used the modulated fringe-pattern photobleaching technique. The experiment consists of determining the kinetics of fluorescence recovery after flashing a bleaching beam on a sample containing the lipid phase doped with a fluorescent probe. In phases Q224 and Q230, where the structure is bicontinuous, the fluorescent molecules diffused freely, whereas in phases Q227 and Q223, which contain discrete micelles, the fluorescent probes were immobile (S Cribier et al., unpublished data); these conclusions complete and correct an earlier preliminary report [16.*].
the phases Q224, Q230 (Fig. la) and Q229 are described in terms of two three-dimensional networks of joined rods, mutually intertwined and unconnected. As originally pointed out by Luzzati and co-workers (reviewed in [5] ), these structures are bicontinuous (i.e. both the water and the hydrocarbon media are continuous throughout the structure) and can, moreover, be visualized as topological generalizations of the lipid bilayer ('bicontinuous bilayer' [5]). The structure of phase Q212 is related to that of phase Q230, one network of polar rods being preserved, the other being replaced by a lattice of closed polar micelles [5]. This phase thus consists of two continuous disjoined media - - one apolar (which contains the micelles) and the other polar - - and can be visualized as a three-dimensional generalization of the lipid monolayer ('bicontinuous monolayer' [5]). The last two phases, Q223 and Q227, have been the subject of controversial reports (summarized in [5,11o.]), and only recently have their structures apparently been determined unambiguously. The two phases consist of two types of closed and disjoined micelles embedded in a continuous matrix (V Luzzati et aL, unpublished data; R Vargas et al., unpublished data) [9,19,25-*,26-,27.o]. Because, in the cubic phases, the 'inside' and the 'outside' of the structure elements are topologically distinct, the structures may be either type I (oil-in-water) or type II (water-in-oil). Examples of phase Q230 have been observed both as type I or type II, depending on the chemical composition of the system; in contrast, all the known examples of phases Q212,Q224,Q227 and Q229belong to type II and those of phase Q223 to type I (Fig. lb) [3,5]. As originally suggested by Scriven [28], the bicontinuousbilayer cubic phases can also be described in terms of periodic minimal surfaces [29,30], often referred to as infinite periodic minimal surfaces (IPMSs), i.e. surfaces whose average curvature is zero. In type-lI structures, the minimal surface coincides with the loosely defined locus of the CH 5 ends of the hydrocarbon chains; in type-1 structures, the minimal surface sits in the middle of the water region. There are three basic IPMS types related to the cubic phases: the primitive (P), the diamond (D) and the gyroid (G) [30], which correspond respectively to phases Q229, Q224 and Q230. More recently, Charvolin and Sadoc [25"] have introduced a more general description of the cubic structures (see 'Theoretical approaches' below).
Phase-diagram analysis Structure of cubic phases In lipid phases, the regions occupied by either the polar or the parafl~nic moiety are sometimes visualized as 'structure elements' of simple shapes (e.g. flat lamellae, cylindrical rods and spherical globules). With the cubic phases, a simplified description based on these elements provides a convenient (and widely used [8.*]) framework for discussing the structures [5]. Accordingly,
Many papers were published last year on the phase diagrams of lipid-containing systems that exhibit cubic phases [12,14",26",27°',31",32,33.-35,]. Among these, the structural study of root-cell membranes resistant to water-deficit stress [33"] is worthy of emphasis, as it reported the interesting observation of a cubic phase in a lipid extract resuspended in water, under physicochemical conditions not too remote from those that prevail in viva
The cubic phases Mariani
(a)
o2~O (b)
/l OQ 0 (i)
Q223
Several authors have considered correlations between phase diagrams and chemical composition [7o,11o-,14o]. This is an important problem; nevertheless, the number of systems explored is still too small to draw any general conclusion [5]. With regard to phase Q227, a recent analysis stressed two points (v Luzzati et al., unpublished data). Firstly, Q227 is one of the most common phases in systems containing an ordinary polar lipid (e.g. lecithin or monoglyceride) and either a fatty acid or a diacylglyceride. Secondly, Q227 along with phase Q224 may be particularly relevant to a determination of the biological significance of lipid polymorphism. Ternary systems formed by the surfactant didodecyl dimethyt ammonium bromide (DDAB), water and oil, and especially their cubic domains [36], have been studied extensively during the past year [20,21-,22., 37°,38]. A report of single crystals of a cubic phase, several cubic millimeters in volume and with a mosaic spread of ,-- 1" [22-], is important because these crystals may be suitable for a detailed crystallographic analysis.
Theoretical approaches In 1990, an international conference on geometry and interfaces assembled physicists, chemists, biologists and
(ii)
Fig.
1. Schematic representation of the structures of two cubic phases. (a) Q230 (type II): the structure is described in terms of two three-dimensional networks of rods, joined coplanarly 3 x 3, mutually intertwined and unconnected. The rod interior is filled by water. (b) Q223 (type I): the structure is described as a packing of non-regular polyhedra. (i) The unit cell contains two dodecahedra (0) and six tetrakaidecahedra (0), centred as shown in (ii). The lipid film is supported by the faces of the polyhedra such that each cage delimited by it contains a micellar aggregate.
mathematicians to discuss a variety of problems in which the interfaces play a prominant role [8"]. Several contributions were devoted to the cubic phases, especially in relation to the IPMS [39,°,40°--42°]. Finally some of the suggestions of Charvolin and Sadoc [9,25"°], although published somewhat earlier than 1990, have been confirmed only recently. The basic idea was that all the lyotropic structures can be described in the same geometrical terms, as periodically ordered systems of fluid films separated by interfaces. The structure of these films must reconcile constant interfacial distances and curvatures; when the thermodynamic conditions are such that the interfaces become curved, a typical case of geometrical frustration arises. The introduction into the structure of disclinations (rotation defects) can solve this problem. According to this view, configurations are derivc~xt that have the same topology as that of the cubic phases, which could then be described as structures of disclinations. In particular, the search for space-filling assemblies of non-regular polyhedra has led to two remarkable results [25"]. One is the assembly of dodecahedra and tetrakaidecahedra of space group Pm3n, the other the assembly of dodecahedra and hexakaidecahedra of space group Fd3m. These two structures are those of the phases Q223 and Q227, respectively (V Luzzati et al., unpublished data; R Vargas et aL, unpublished data) [26°,27o.].
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tipids References and recommended reading Papers of special interest, published within the annual period of review, have been highlighted as: • of interest •• of outstanding interest 1.
LUZZAT1 V: X-Ray Diffraction Studies of Lipid-Water Systems.
In Biological Mengaranes edited by Chapman D. London: Academic Press, 1968, pp 71-123. 2.
LUZZATIV, HUSSON F: The Structure of the Liquid Crystalline Phases of Lipid-Water Systems. J Cell Biol 1962, 12:207-219.
3.
LUZZA'nV, MARIAN]P, GUUK-KRZYWICVdT: The Cubic Phases of Lipid-Containing Systems: Physical Structure and Biological Implications. In Physics of An~Aphilic Layers edited by Meunier J, [angevin D, Boccara N. Berlin: Springer.Verlag, 1987, pp 131-137.
4.
LUZZKnV, GUUK A, GUUK-KRZYWlCFdT, TARDmUA: Lipid Poly. morphism Revisited: Structural Aspects and Biological Implications. In L~oids and Membrane~. Past, Present and Future edited by Op den Kamp JAF, Roelofsen B, Wirtz KWA. Amsterdam: Elsevier Science Publishers, 1986, pp 137-151.
5.
MARIANIP, LUZZAT1V, DELACROIXH: Cubic Phases of Lipid Containing Systems. Structure Analysis and Biological Implications. J Mol Biol 1988, 204:165-189.
6.
I.INDBLOMG, RILFORS L: Cubic Phases and Isotropic Struc. tures Formed by Membrane Lipids - - Possible Biological Relevance. Biochim Biophys Acta 1989, 988:221-256.
SEDDONJM: Structure of the Inverted Hexagonal (Hn) Phase and Non-Lamelfar Phase Transitions of Lipids. Biochim Bio phys Acta 1990, 1031:1-69. This review is more directly concerned with a non-cubic phase. Nevertheless, lipid polymorphism is discussed and the cubic phases taken into account. The thermodynamic properties of non-bilayer phases are discussed in detail and a very full reference list is provided.
15. **
DELACROIXH, MARIAN1P, GUUK-KRZY~Cm T: Image Analysis of Freeze Fractured Lipid-Water Cubic Phases of Space Group la3d. J Ply3~sique (Colloq) 1990, C7-51:119-129. Image analysis by real-space cross-correlation averaging of X-ray controlled freeze-fracture of the Q230 phase of both types I and 11. The fractures are shown to be in excellent agreement with the electron-density maps, as determined by X-ray-scattering analysis. 16. **
CRIBIERS, BOURDIEU L VARGASR, GUI2K A, LUZZAT1V: Modulated Fringe Pattern Photobleaching Applied to Lipid-Water Cubic Phases: Structural Information. J Physique (Colloq) 1990, C7-51:105--108. The first lateral-diffusion experiments performed on a cubic system by modulated fringe-pattern photobleaching technique are presented. 17. •
ANDERSONDM: A New Technique for Studying Microstruc. tures: 2H NMR Bandshapes of Polymerized Surfactants and Counterions in Microstructures Described by Minimal Surfaces. J Physique (Colloq) 1990, C7-51:1-18. A new way of using NMR to study and characterize bicontinuous cubic and aligned intermediate phases is presented. The 2H-NMR bandshapes for polymerized and deuterated surfactant or counterion are computed for .several model microstructures. 18. •
ANDERSONDM, WENNERSTROM H: Self-Diffusion in Bicontinuous Cubic Phases, L3 Phases and Microemulsions. J Phys Chem 1990, 94:8683-8694. A theoretical framework for the interpretation of self-diffusion pulsedfield gradient NMR experiments is illustrated. An 'obstruction factor' is introduced to derive the effective self-diffusion rate. The approach is applied to a variety of data from the literature. 19.
BURNSJL, COHEN Y, TALMONY: Structure of Cubic Mesomorphic Phases Determined by Low Temperature Transmission Electron Microscopy and Small-Angle X-Ray Scattering. J Phys ~ 1990, 94:5308-5312.
20.
RADIMANS, TOPRAKCIOGLU C, DAI L, FARUQI AR, HJELM RP, DE VAU.ERAA: Structural Features of the Cubic Phase of a Ternary Surfactant System. J Physique (Colloq) 1990, C7-51:375-381.
7. •
8,
INTERNATIONALWORKSHOP ON GEOMETRY AND INTERFACES [COLLOQUIUM]. J Phys~/ue 1990, C7-51. ~ ' s symposium deals with the general problem of the correlations between cubic phases and IPMSs. Other important problems, such as fluctuating membranes, froths, random surface phases and microemulsions, are also discussed. 9.
SAIx~ JF, CHARVOLINJ: Infinite Periodic Minimal Surfaces and Their Crystallography in the Hyperbolic Plane. Acta Crystallogr [A] 1989, 45:10-20.
10.
LARSSON K: Cubic Lipid-Water Phases: Structures and Biomembrane Aspects. J Phys Chem 1989, 93:7304--7314.
11. FONTELLK: Cubic Phases in Surfactant and Surfactant-Like •• Lipid Systems. Colloid Polym Sci 1990, 268:264-285. A very useful summary of the lipid systems in which cubic phases have been reported. 12.
13.
MARIAN1P, RIVASE, LUZZATIV, DELACROIXH: Polymorphism of a Lipid Extract from Pseudomonas fluorescen.~ Structure Analysis of a Hexagonal Phase and of a Novel Cubic Phase o f Extinction Symbol Fd- -. Biochemistry 1990, 29:6799-6810. LUzzKn V, MARIAN1P, DELACRO[XH: X-ray Crystallography at Macromolecular Resolution: a Solution of the Phase Problem. Makromol Chem Macromol Symp 1988, 15:1-17.
SEDDONJM, HOGAN jL, WARRENDER NA, PEBAY-PEYROULAE: Structural Studies of Phospholipid Cubic Phases. Prog Colloid Polym Sci 1990, 81:189-197. An analysis of the correlations between the chemical and physical properties of lipids and the occurrence of cubic phases. The effects of hydrophilicity and of chirality in inducing cubic structures are discussed. The results of neutron-scattering experiments are also presented. 14.
•
21. •
RADIMANS, TOPRAKCIOGLU C, FARUQI AR: Symmetry Transition in the Cubic Phase of a Ternary Surfactant System. J Physique 1990, 51:1501-1508. An X-ray- and neutron-scattering study of the cubic phases of the ternary system water/DDAB/octane. Phases Q224 and Q229 are identified. In considering the topology of these structures, a further transition within the Im3m symmetry is predicted at a higher water content. 22. •
CRUZ MM, VALLERAAM, TOPRAKCIOGLU C: Single Crystals of Cubic Ternary Phases in the DDDAB/D20/Octane System. J Physique (Colloq) 1990, C7-51:109-114. It is shown that single crystals of a cubic phase can be grown in the DDAB/water/octane system. Preliminary X-my and neutron-scattering results are presented. 23.
GUUK-KRzYWlCKIT, COSTELLOMJ: The Use o f Low Temperature X-Ray Diffraction to Evaluate Freezing Methods Used in Freeze-Fracture Electron Microscopy. J Microsc 1978, 112:103-113.
24.
CHARVOUNA, RIGNY P: Pulsed NMR in Dynamically Heterogeneous Systems. J Magn Reson 1971, 4:40-46.
25. CHARVlOL[NJ, SADOCJF: Cubic Phases as Structure of Discli•• nations. Colloid Polym Sci 1990, 268:190-195. Ordered geometrical configurations with bicontinuous or cellular topologies, which optimize the frustration of a periodic system of frustrated fluid films, are analysed. The structures of the two controversial phases Q223 and Q227 are presented in terms of packing of non-regular
polyhedra. 26. •
SEDDONJM: An Inverse Face-Centred Cubic Phase Formed by Diacylglycerol-phosphatidylcholine Mixtures. Bk~Jem/sir3, 1990, 29:7997-8002. A structural analysis of fully hydrated unsaturated diacytglycerol-phosphatidyicholine mixtures. A phase Q227 is identified between an inverse hexagonal phase and an inverse micellar solution. Several problems that can occur in structural studies are discussed.
The cubic phases Mariani 27. **
SEDDONJM, BARTLEEA, MINGINSJ: Inverse Cubic Liquid-Crystalline Phases of Phospholipids and Related Lyotropic Systems. J Phys Condens Matter 1990, 2:SA2.85-SA290. The authors discuss the evidence in favour of the presence of a phase Q227 in hydrated acid-soap mixtures of an unsatured fatty acid with its alkali salt. An analysis o f the average mean curvature of the polar-apolar interface is given in support of a structure of close inverse miceUar aggregates. 28.
SCRIVEN LE: Equilibrium Bicontinuous Structure. Nature 1976, 263:123-125.
29.
SCHWARZHA: Gesammelte Mathematische Abhandlung Vol 1. Berlin: Springer, 1890.
30.
SCHOENAll: Infinite Periodic Minimal Surfaces Without SelfIntersections. NASA Technical Note D5541, National Technical Information Service Document N70-29782, Springfield, VA 22161.
31. •
RAMA KRISHNA YVS, MARSH D: Spin Label ESR and 31p. NMR Studies of the Cubic and Inverted Hexagonal Phases of Dimyristoyl Phosphatidylcholine/Myristic Acid (1:2, Mol/Mol) Mixtures. Biochim Biophys Acta 1990, 1024:89-94. The thermotropic behaviour and the chain dynamics of a dimyristoyi phosphatidylcholine/myristic acid (1:2, mol:mol) mixture are reported, providing evidence for a phase transition from La to non-lamellar phases. The data are consistent with the presence of a cubic and a hexagonal phase. 32.
HEIMBURGT, RYBA NJP, WURZ U, MARSH D: Phase Transition from a Gel to a Fluid Phase of Cubic Symmetry in Dimyristoyl Phosphatidylcholine/Myristic Acid (1:2, mol/mol) Bilayers. Biochim Biophys Acta 1990, 1025:77-81.
33. •
NORBERGP, LARSSONK, LILJENBERGC: A Study of Membrane Lipids from Dehydration-Acclimated Brassica napus Root Cells: Formation of a Cubic Phase Under Physiological Conditions. B i ~ Cell Biol 1990, 68:102-105. A comparison between the phase behaviour of total lipids extracted from microsomal membranes of root cells of control plants of Brassica napus with plants that were exposed to a repeated dehydration stress. 34. •
CLERCM, LrVELtrr AM, SADOCJF: X-Ray Study of Phase Transitions in Amphiphilic Systems. J Physique (Colloq) 1990, C7-51:97-11M. A structural study of the transition between hexagonal and cubic phases, which reveals clear epitaxial relations. Possible fluctuations in the hexagonal phase are shown to play the role of precursor. 35. •
SIEGELDP, BANSCHBACHJL Lameilar/Inverted Cubic (Let/QII Phase Transition in N-Methylated Dioleoylphosphatidyl Ethanolamine. Biochemistry 1990, 29:5975-5981.
A structural and thermodynamic analysis of the formation of type-ll cubic phases (Q224 and Q230) from a lamellar phase. The mechanism of the phase transition is rationalized in terms of the contribution by intermediate structures. 36.
FONTELLJ, JANSSON M: The Relation Between the Cubic Phase and the Neighbouring Solution Phase in Systems of Di(alkyl) Dimethylanunonium Bromide-Hydrocarbon-Water. Prog Colloid Polym Sci 1988, 76:169-175.
37. •
BAROIS P, HYDE S, NINHAM B, DOWLING T: Observation of Two Phases Within the Cubic Phase Region of a Ternary Surfactant Solution. Langmuir 1990, 6:1136-1140. An X-ray-scattering analysis of the cubic region of the DDAB/water/ cyclohexane ternary system. It is shown that the relative intensity of the three visible reflections of phase Qzz9 changes as a function of the chemical composition. 38.
BAROISP, EDAM D, HYDE ST: X-Ray Study of Cubic Phases in Ternary Systems of Surfactant DDAB, Water and Oil. J Physique (Colloq) 1990, C7-51:25--34.
39. ••
CHARVOLINJ, SADOC JF: Structures Built by Amphiphiles and Frustrated Fluid Films. J Physique (Colloq) 1990, C7-51:83--96. A description of the structures that are formed by interfacial films of amphiphilic molecules. A geometrical approach is proposed, leading to a structure of defects. 40. •
BOULIGANDY: Comparative Geometry of Cytomembranes and Water-Lipid Systems. J physique (Colloq) 1990, C7-51:35-52. An analysis of a number of structures observed by electron microscopy in cells. It is shown thai all these structures exist also in the lipid extract in the presence of water. The observed differences are discussed. 41. .
HYDE ST: Curvature and the Global Structure of Interfaces in Surfactant-Water Systems. J Physique (Colloq) 1990, C7-51:209-228, An analysis of the correlations between the global spatial requirements imposed by the composition of the binary system and the local intrinsic geometry of the surfactant film. 42. •
HELFmCHW, RENNSCHUHH: Landau Theory of the LameUarto-Cubic Phase Transition. J Physique (Colloq) 1990, C7-51:189-195. A Landau theory of the transition from cubic to lamellar phases is derived from the analysis of bending elasticity. The occurrence of primitive, diamond and gyroid IPMSs is explained and preliminary criteria for their selection are presented.
P Mariani, Istituto di Fisica Medic'a, Facolth di Medicina e Chirurgia, Universit~ di Ancona, Via Ranieri Monte D'Ago, 60131, Ancona, Italy.
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Introduction Within the wide variety of phases formed by lipids in the presence of water [1], those with cubic symmetry are the most complex. Cubic phases were discovered in lipid/water systems in the early 1960s [2,3], but only in the past few years has attention been focused on their structure [3--6]. Much theoretical interest has been shown in these phases, especially from the viewpoint of differential geometry [4,7",8",9]. Several authors have discussed the biological implications of cubic structures, with special emphasis on membrane fusion, fat digestion, regulation of lipid composition, transport processes and photosynthesis (reviewed in [3,4,6,7",10,11..]; see also [5,12]). In particular, it has been suggested that lipid polymorphic transitions and cubic phases may be involved in some of the physiological functions of membranes (for a review, see [4]). So far, however, it has been impossible to support with convincing experimental evidence the hypothesis that naturally occurring lipids can form cubic phases under physiological conditions. Nevertheless, there exist numerous reports of the existence of three-dimensional periodic membrane assemblies, which could be related to cubic structures. Details of literature on these periodic conformations from ultrastructural studies of cell membranes and organelles can be found in [10]. Phases with cubic symmetry are now known to be widespread in amphiphilic systems; six cubic phases have been identified so far [3,5], but the list may still be incomplete. As a rule, the phases are named according to their space group. In this review, I use the nomenclature introduced by Luzzati's group: a cubic phase is called Qn, where Q stands for cubic and n is the number of the space group defined by the International Tables for Crystallography [3]. In this review, a number of recent papers dealing with cubic phases of lipid-containing systems, and more generally with lipid polymorphism, will be discussed so as to stress the most important current developments and the results of outstanding interest.
Two important review papers published within the past year are directly relevant to this topic. One [11"'] provides a catalogue of all the cubic phases observed so far in systems containing anionic and cationic detergents, zwitterionic and non-ionic surfactants, and lipids of biological origin (monogtycerides, sphingolipids and phospholipids). The other [7"] focuses on the inverted hexagonal phase, but also reports a large number of phase diagrams, discusses the topological and structural relationships between the different non-lamellar phases, and analyses the thermodynamic properties of lipid phases.
Experimental techniques and methods The general trend has been to improve the analysis of crystallographic data [5,12,13,14"], to perform more sophisticated analyses of electron microscope images [15,-], and to widen the spectrum of experimental techniques [16°',17",18",19].
X-ray and neutron scaltering A significant improvement in crystallographic procedures has been the development of a pattern-recognition approach [13] based upon the axiom that the histogram of the electron-density map is invariant in phases with different structures and the same chemical composition [5,13]. In the past year, the method has been successfully employed in the structure analysis of phase Q227 (v Luzzati et al., unpublished data) and, quite recently, of phase Q223 (R Vargas et al., personal communication). Neutron-scattering techniques have also been applied to the cubic phases [20,21.,22.] but with limited success because of the inadequate quality of the data, especially in contrast to that provided by X-ray-scattering experiments. The experimental techniques could perhaps be improved, in particular by making better use of specific labeling [14.].
Abbreviations DDAB
didodecyl dimethyl ammonium bromide; IPMS~infinite periodic minimal surface.
(~) Current Biology Lid ISSN 0959-440X
501
502
Lipid$ Electron microscopy A large number of freeze-fracture electron micrographs of lipid-containing systems with apparent cubic synlmetry have been published [6,9]. Nevertheless, in most cases, the problem of whether the micrographs refer to the original structure of the sample or to some artefact of the freezing process was not resolved. Even when this problem h a s been overcome, the correlations between the electron-microscope images and the structures have not been properly investigated. Recently, the results of extended freeze-fracture electron-microscopy and X-ray-scattering studies of phase Q230 have been reported [15"]. In this case, the structure of the samples was checked by X-ray scattering after the freezing and before the fracture step [23]. The freeze-fracture electronmicroscope images were then analysed using real-space cross-correlation averaging. Moreover, in order to understand the nature of the fracture surfaces, the processed images were compared with the electron-density maps established by the X-ray-scattering analysis.
Self-diffusion measurements The analysis of the translational diffusion coefficients of both the lipid and the water components can provide useful information about the structure of a cubic phase. More precisely, the diffusion properties of a system comprised of two bicontinuous media are likely to be quite different from the diffusion properties of a system containing unconnected micelles. Charvolin and Rigny [24] have introduced NMR pulsedfield gradient methods for that purpose; these have been used largely in the study of cubic phases [6,7",17"]. Anderson and Wennerstrom [18.] have recently discussed the geometric aspects of the interpretation of gradientfield NMR data. In order to analyse the lateral diffusion in cubic phases of known structure, Cribier and co-workers [16-*] have used the modulated fringe-pattern photobleaching technique. The experiment consists of determining the kinetics of fluorescence recovery after flashing a bleaching beam on a sample containing the lipid phase doped with a fluorescent probe. In phases Q224 and Q230, where the structure is bicontinuous, the fluorescent molecules diffused freely, whereas in phases Q227 and Q223, which contain discrete micelles, the fluorescent probes were immobile (S Cribier et al., unpublished data); these conclusions complete and correct an earlier preliminary report [16.*].
the phases Q224, Q230 (Fig. la) and Q229 are described in terms of two three-dimensional networks of joined rods, mutually intertwined and unconnected. As originally pointed out by Luzzati and co-workers (reviewed in [5] ), these structures are bicontinuous (i.e. both the water and the hydrocarbon media are continuous throughout the structure) and can, moreover, be visualized as topological generalizations of the lipid bilayer ('bicontinuous bilayer' [5]). The structure of phase Q212 is related to that of phase Q230, one network of polar rods being preserved, the other being replaced by a lattice of closed polar micelles [5]. This phase thus consists of two continuous disjoined media - - one apolar (which contains the micelles) and the other polar - - and can be visualized as a three-dimensional generalization of the lipid monolayer ('bicontinuous monolayer' [5]). The last two phases, Q223 and Q227, have been the subject of controversial reports (summarized in [5,11o.]), and only recently have their structures apparently been determined unambiguously. The two phases consist of two types of closed and disjoined micelles embedded in a continuous matrix (V Luzzati et aL, unpublished data; R Vargas et al., unpublished data) [9,19,25-*,26-,27.o]. Because, in the cubic phases, the 'inside' and the 'outside' of the structure elements are topologically distinct, the structures may be either type I (oil-in-water) or type II (water-in-oil). Examples of phase Q230 have been observed both as type I or type II, depending on the chemical composition of the system; in contrast, all the known examples of phases Q212,Q224,Q227 and Q229belong to type II and those of phase Q223 to type I (Fig. lb) [3,5]. As originally suggested by Scriven [28], the bicontinuousbilayer cubic phases can also be described in terms of periodic minimal surfaces [29,30], often referred to as infinite periodic minimal surfaces (IPMSs), i.e. surfaces whose average curvature is zero. In type-lI structures, the minimal surface coincides with the loosely defined locus of the CH 5 ends of the hydrocarbon chains; in type-1 structures, the minimal surface sits in the middle of the water region. There are three basic IPMS types related to the cubic phases: the primitive (P), the diamond (D) and the gyroid (G) [30], which correspond respectively to phases Q229, Q224 and Q230. More recently, Charvolin and Sadoc [25"] have introduced a more general description of the cubic structures (see 'Theoretical approaches' below).
Phase-diagram analysis Structure of cubic phases In lipid phases, the regions occupied by either the polar or the parafl~nic moiety are sometimes visualized as 'structure elements' of simple shapes (e.g. flat lamellae, cylindrical rods and spherical globules). With the cubic phases, a simplified description based on these elements provides a convenient (and widely used [8.*]) framework for discussing the structures [5]. Accordingly,
Many papers were published last year on the phase diagrams of lipid-containing systems that exhibit cubic phases [12,14",26",27°',31",32,33.-35,]. Among these, the structural study of root-cell membranes resistant to water-deficit stress [33"] is worthy of emphasis, as it reported the interesting observation of a cubic phase in a lipid extract resuspended in water, under physicochemical conditions not too remote from those that prevail in viva
The cubic phases Mariani
(a)
o2~O (b)
/l OQ 0 (i)
Q223
Several authors have considered correlations between phase diagrams and chemical composition [7o,11o-,14o]. This is an important problem; nevertheless, the number of systems explored is still too small to draw any general conclusion [5]. With regard to phase Q227, a recent analysis stressed two points (v Luzzati et al., unpublished data). Firstly, Q227 is one of the most common phases in systems containing an ordinary polar lipid (e.g. lecithin or monoglyceride) and either a fatty acid or a diacylglyceride. Secondly, Q227 along with phase Q224 may be particularly relevant to a determination of the biological significance of lipid polymorphism. Ternary systems formed by the surfactant didodecyl dimethyt ammonium bromide (DDAB), water and oil, and especially their cubic domains [36], have been studied extensively during the past year [20,21-,22., 37°,38]. A report of single crystals of a cubic phase, several cubic millimeters in volume and with a mosaic spread of ,-- 1" [22-], is important because these crystals may be suitable for a detailed crystallographic analysis.
Theoretical approaches In 1990, an international conference on geometry and interfaces assembled physicists, chemists, biologists and
(ii)
Fig.
1. Schematic representation of the structures of two cubic phases. (a) Q230 (type II): the structure is described in terms of two three-dimensional networks of rods, joined coplanarly 3 x 3, mutually intertwined and unconnected. The rod interior is filled by water. (b) Q223 (type I): the structure is described as a packing of non-regular polyhedra. (i) The unit cell contains two dodecahedra (0) and six tetrakaidecahedra (0), centred as shown in (ii). The lipid film is supported by the faces of the polyhedra such that each cage delimited by it contains a micellar aggregate.
mathematicians to discuss a variety of problems in which the interfaces play a prominant role [8"]. Several contributions were devoted to the cubic phases, especially in relation to the IPMS [39,°,40°--42°]. Finally some of the suggestions of Charvolin and Sadoc [9,25"°], although published somewhat earlier than 1990, have been confirmed only recently. The basic idea was that all the lyotropic structures can be described in the same geometrical terms, as periodically ordered systems of fluid films separated by interfaces. The structure of these films must reconcile constant interfacial distances and curvatures; when the thermodynamic conditions are such that the interfaces become curved, a typical case of geometrical frustration arises. The introduction into the structure of disclinations (rotation defects) can solve this problem. According to this view, configurations are derivc~xt that have the same topology as that of the cubic phases, which could then be described as structures of disclinations. In particular, the search for space-filling assemblies of non-regular polyhedra has led to two remarkable results [25"]. One is the assembly of dodecahedra and tetrakaidecahedra of space group Pm3n, the other the assembly of dodecahedra and hexakaidecahedra of space group Fd3m. These two structures are those of the phases Q223 and Q227, respectively (V Luzzati et al., unpublished data; R Vargas et aL, unpublished data) [26°,27o.].
503
504
tipids References and recommended reading Papers of special interest, published within the annual period of review, have been highlighted as: • of interest •• of outstanding interest 1.
LUZZAT1 V: X-Ray Diffraction Studies of Lipid-Water Systems.
In Biological Mengaranes edited by Chapman D. London: Academic Press, 1968, pp 71-123. 2.
LUZZATIV, HUSSON F: The Structure of the Liquid Crystalline Phases of Lipid-Water Systems. J Cell Biol 1962, 12:207-219.
3.
LUZZA'nV, MARIAN]P, GUUK-KRZYWICVdT: The Cubic Phases of Lipid-Containing Systems: Physical Structure and Biological Implications. In Physics of An~Aphilic Layers edited by Meunier J, [angevin D, Boccara N. Berlin: Springer.Verlag, 1987, pp 131-137.
4.
LUZZKnV, GUUK A, GUUK-KRZYWlCFdT, TARDmUA: Lipid Poly. morphism Revisited: Structural Aspects and Biological Implications. In L~oids and Membrane~. Past, Present and Future edited by Op den Kamp JAF, Roelofsen B, Wirtz KWA. Amsterdam: Elsevier Science Publishers, 1986, pp 137-151.
5.
MARIANIP, LUZZAT1V, DELACROIXH: Cubic Phases of Lipid Containing Systems. Structure Analysis and Biological Implications. J Mol Biol 1988, 204:165-189.
6.
I.INDBLOMG, RILFORS L: Cubic Phases and Isotropic Struc. tures Formed by Membrane Lipids - - Possible Biological Relevance. Biochim Biophys Acta 1989, 988:221-256.
SEDDONJM: Structure of the Inverted Hexagonal (Hn) Phase and Non-Lamelfar Phase Transitions of Lipids. Biochim Bio phys Acta 1990, 1031:1-69. This review is more directly concerned with a non-cubic phase. Nevertheless, lipid polymorphism is discussed and the cubic phases taken into account. The thermodynamic properties of non-bilayer phases are discussed in detail and a very full reference list is provided.
15. **
DELACROIXH, MARIAN1P, GUUK-KRZY~Cm T: Image Analysis of Freeze Fractured Lipid-Water Cubic Phases of Space Group la3d. J Ply3~sique (Colloq) 1990, C7-51:119-129. Image analysis by real-space cross-correlation averaging of X-ray controlled freeze-fracture of the Q230 phase of both types I and 11. The fractures are shown to be in excellent agreement with the electron-density maps, as determined by X-ray-scattering analysis. 16. **
CRIBIERS, BOURDIEU L VARGASR, GUI2K A, LUZZAT1V: Modulated Fringe Pattern Photobleaching Applied to Lipid-Water Cubic Phases: Structural Information. J Physique (Colloq) 1990, C7-51:105--108. The first lateral-diffusion experiments performed on a cubic system by modulated fringe-pattern photobleaching technique are presented. 17. •
ANDERSONDM: A New Technique for Studying Microstruc. tures: 2H NMR Bandshapes of Polymerized Surfactants and Counterions in Microstructures Described by Minimal Surfaces. J Physique (Colloq) 1990, C7-51:1-18. A new way of using NMR to study and characterize bicontinuous cubic and aligned intermediate phases is presented. The 2H-NMR bandshapes for polymerized and deuterated surfactant or counterion are computed for .several model microstructures. 18. •
ANDERSONDM, WENNERSTROM H: Self-Diffusion in Bicontinuous Cubic Phases, L3 Phases and Microemulsions. J Phys Chem 1990, 94:8683-8694. A theoretical framework for the interpretation of self-diffusion pulsedfield gradient NMR experiments is illustrated. An 'obstruction factor' is introduced to derive the effective self-diffusion rate. The approach is applied to a variety of data from the literature. 19.
BURNSJL, COHEN Y, TALMONY: Structure of Cubic Mesomorphic Phases Determined by Low Temperature Transmission Electron Microscopy and Small-Angle X-Ray Scattering. J Phys ~ 1990, 94:5308-5312.
20.
RADIMANS, TOPRAKCIOGLU C, DAI L, FARUQI AR, HJELM RP, DE VAU.ERAA: Structural Features of the Cubic Phase of a Ternary Surfactant System. J Physique (Colloq) 1990, C7-51:375-381.
7. •
8,
INTERNATIONALWORKSHOP ON GEOMETRY AND INTERFACES [COLLOQUIUM]. J Phys~/ue 1990, C7-51. ~ ' s symposium deals with the general problem of the correlations between cubic phases and IPMSs. Other important problems, such as fluctuating membranes, froths, random surface phases and microemulsions, are also discussed. 9.
SAIx~ JF, CHARVOLINJ: Infinite Periodic Minimal Surfaces and Their Crystallography in the Hyperbolic Plane. Acta Crystallogr [A] 1989, 45:10-20.
10.
LARSSON K: Cubic Lipid-Water Phases: Structures and Biomembrane Aspects. J Phys Chem 1989, 93:7304--7314.
11. FONTELLK: Cubic Phases in Surfactant and Surfactant-Like •• Lipid Systems. Colloid Polym Sci 1990, 268:264-285. A very useful summary of the lipid systems in which cubic phases have been reported. 12.
13.
MARIAN1P, RIVASE, LUZZATIV, DELACROIXH: Polymorphism of a Lipid Extract from Pseudomonas fluorescen.~ Structure Analysis of a Hexagonal Phase and of a Novel Cubic Phase o f Extinction Symbol Fd- -. Biochemistry 1990, 29:6799-6810. LUzzKn V, MARIAN1P, DELACRO[XH: X-ray Crystallography at Macromolecular Resolution: a Solution of the Phase Problem. Makromol Chem Macromol Symp 1988, 15:1-17.
SEDDONJM, HOGAN jL, WARRENDER NA, PEBAY-PEYROULAE: Structural Studies of Phospholipid Cubic Phases. Prog Colloid Polym Sci 1990, 81:189-197. An analysis of the correlations between the chemical and physical properties of lipids and the occurrence of cubic phases. The effects of hydrophilicity and of chirality in inducing cubic structures are discussed. The results of neutron-scattering experiments are also presented. 14.
•
21. •
RADIMANS, TOPRAKCIOGLU C, FARUQI AR: Symmetry Transition in the Cubic Phase of a Ternary Surfactant System. J Physique 1990, 51:1501-1508. An X-ray- and neutron-scattering study of the cubic phases of the ternary system water/DDAB/octane. Phases Q224 and Q229 are identified. In considering the topology of these structures, a further transition within the Im3m symmetry is predicted at a higher water content. 22. •
CRUZ MM, VALLERAAM, TOPRAKCIOGLU C: Single Crystals of Cubic Ternary Phases in the DDDAB/D20/Octane System. J Physique (Colloq) 1990, C7-51:109-114. It is shown that single crystals of a cubic phase can be grown in the DDAB/water/octane system. Preliminary X-my and neutron-scattering results are presented. 23.
GUUK-KRzYWlCKIT, COSTELLOMJ: The Use o f Low Temperature X-Ray Diffraction to Evaluate Freezing Methods Used in Freeze-Fracture Electron Microscopy. J Microsc 1978, 112:103-113.
24.
CHARVOUNA, RIGNY P: Pulsed NMR in Dynamically Heterogeneous Systems. J Magn Reson 1971, 4:40-46.
25. CHARVlOL[NJ, SADOCJF: Cubic Phases as Structure of Discli•• nations. Colloid Polym Sci 1990, 268:190-195. Ordered geometrical configurations with bicontinuous or cellular topologies, which optimize the frustration of a periodic system of frustrated fluid films, are analysed. The structures of the two controversial phases Q223 and Q227 are presented in terms of packing of non-regular
polyhedra. 26. •
SEDDONJM: An Inverse Face-Centred Cubic Phase Formed by Diacylglycerol-phosphatidylcholine Mixtures. Bk~Jem/sir3, 1990, 29:7997-8002. A structural analysis of fully hydrated unsaturated diacytglycerol-phosphatidyicholine mixtures. A phase Q227 is identified between an inverse hexagonal phase and an inverse micellar solution. Several problems that can occur in structural studies are discussed.
The cubic phases Mariani 27. **
SEDDONJM, BARTLEEA, MINGINSJ: Inverse Cubic Liquid-Crystalline Phases of Phospholipids and Related Lyotropic Systems. J Phys Condens Matter 1990, 2:SA2.85-SA290. The authors discuss the evidence in favour of the presence of a phase Q227 in hydrated acid-soap mixtures of an unsatured fatty acid with its alkali salt. An analysis o f the average mean curvature of the polar-apolar interface is given in support of a structure of close inverse miceUar aggregates. 28.
SCRIVEN LE: Equilibrium Bicontinuous Structure. Nature 1976, 263:123-125.
29.
SCHWARZHA: Gesammelte Mathematische Abhandlung Vol 1. Berlin: Springer, 1890.
30.
SCHOENAll: Infinite Periodic Minimal Surfaces Without SelfIntersections. NASA Technical Note D5541, National Technical Information Service Document N70-29782, Springfield, VA 22161.
31. •
RAMA KRISHNA YVS, MARSH D: Spin Label ESR and 31p. NMR Studies of the Cubic and Inverted Hexagonal Phases of Dimyristoyl Phosphatidylcholine/Myristic Acid (1:2, Mol/Mol) Mixtures. Biochim Biophys Acta 1990, 1024:89-94. The thermotropic behaviour and the chain dynamics of a dimyristoyi phosphatidylcholine/myristic acid (1:2, mol:mol) mixture are reported, providing evidence for a phase transition from La to non-lamellar phases. The data are consistent with the presence of a cubic and a hexagonal phase. 32.
HEIMBURGT, RYBA NJP, WURZ U, MARSH D: Phase Transition from a Gel to a Fluid Phase of Cubic Symmetry in Dimyristoyl Phosphatidylcholine/Myristic Acid (1:2, mol/mol) Bilayers. Biochim Biophys Acta 1990, 1025:77-81.
33. •
NORBERGP, LARSSONK, LILJENBERGC: A Study of Membrane Lipids from Dehydration-Acclimated Brassica napus Root Cells: Formation of a Cubic Phase Under Physiological Conditions. B i ~ Cell Biol 1990, 68:102-105. A comparison between the phase behaviour of total lipids extracted from microsomal membranes of root cells of control plants of Brassica napus with plants that were exposed to a repeated dehydration stress. 34. •
CLERCM, LrVELtrr AM, SADOCJF: X-Ray Study of Phase Transitions in Amphiphilic Systems. J Physique (Colloq) 1990, C7-51:97-11M. A structural study of the transition between hexagonal and cubic phases, which reveals clear epitaxial relations. Possible fluctuations in the hexagonal phase are shown to play the role of precursor. 35. •
SIEGELDP, BANSCHBACHJL Lameilar/Inverted Cubic (Let/QII Phase Transition in N-Methylated Dioleoylphosphatidyl Ethanolamine. Biochemistry 1990, 29:5975-5981.
A structural and thermodynamic analysis of the formation of type-ll cubic phases (Q224 and Q230) from a lamellar phase. The mechanism of the phase transition is rationalized in terms of the contribution by intermediate structures. 36.
FONTELLJ, JANSSON M: The Relation Between the Cubic Phase and the Neighbouring Solution Phase in Systems of Di(alkyl) Dimethylanunonium Bromide-Hydrocarbon-Water. Prog Colloid Polym Sci 1988, 76:169-175.
37. •
BAROIS P, HYDE S, NINHAM B, DOWLING T: Observation of Two Phases Within the Cubic Phase Region of a Ternary Surfactant Solution. Langmuir 1990, 6:1136-1140. An X-ray-scattering analysis of the cubic region of the DDAB/water/ cyclohexane ternary system. It is shown that the relative intensity of the three visible reflections of phase Qzz9 changes as a function of the chemical composition. 38.
BAROISP, EDAM D, HYDE ST: X-Ray Study of Cubic Phases in Ternary Systems of Surfactant DDAB, Water and Oil. J Physique (Colloq) 1990, C7-51:25--34.
39. ••
CHARVOLINJ, SADOC JF: Structures Built by Amphiphiles and Frustrated Fluid Films. J Physique (Colloq) 1990, C7-51:83--96. A description of the structures that are formed by interfacial films of amphiphilic molecules. A geometrical approach is proposed, leading to a structure of defects. 40. •
BOULIGANDY: Comparative Geometry of Cytomembranes and Water-Lipid Systems. J physique (Colloq) 1990, C7-51:35-52. An analysis of a number of structures observed by electron microscopy in cells. It is shown thai all these structures exist also in the lipid extract in the presence of water. The observed differences are discussed. 41. .
HYDE ST: Curvature and the Global Structure of Interfaces in Surfactant-Water Systems. J Physique (Colloq) 1990, C7-51:209-228, An analysis of the correlations between the global spatial requirements imposed by the composition of the binary system and the local intrinsic geometry of the surfactant film. 42. •
HELFmCHW, RENNSCHUHH: Landau Theory of the LameUarto-Cubic Phase Transition. J Physique (Colloq) 1990, C7-51:189-195. A Landau theory of the transition from cubic to lamellar phases is derived from the analysis of bending elasticity. The occurrence of primitive, diamond and gyroid IPMSs is explained and preliminary criteria for their selection are presented.
P Mariani, Istituto di Fisica Medic'a, Facolth di Medicina e Chirurgia, Universit~ di Ancona, Via Ranieri Monte D'Ago, 60131, Ancona, Italy.
505