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The cubic phases of lipids
Studies in Surface Science and Catalysis 148 Terasaki (Editor) 9 2004 Elsevier B.V. All rights reserved.
The Cubic Phases of Lipids Vittorio Luzzati,* Herv~ Delacroix,* Annette Gulik,* Tadeusz Gulik-Krzywicki,* Paolo Mariani,* and Rodoifo Vargas* *Centre de Gfnftique Molfculaire, kaboratoire Propre du CNRS Associ6 ~ l'Universit6 Pierre et Marie Curie, 91198 Gif-sur-Yvette Cedex, France, tlstituto di Scienze Fisiche and Istituto Nazionale per la Fisica della Materia, Universit'h di Ancona, 60131 Ancona, Italia, and *Centro de Biofisica y Bioqufmica, IVIC, Caracas 19020-A, Venezuela
I. Introduction II. Structure Analysis A. Crystallographic Techniques B. Freeze-Fracture Electron Microscopy C. Lateral Diffusion Studies III. Chemical Properties IV. Structure Representations A. Bicontinuous Phases: Networks of Rods, Convoluted Surfaces B. Micellar Phases V. Orderly Disposal of Short-Range Conformational Disorder: The Chaotic Zones VI. Biological Implications Abbreviations References
1. I N T R O D U C T I O N
Phases with cubic symmetry have been observed in lipid-water systems since the early days of lipid polymorphism, at a time when it seemed all too natural to presume without closer inspection that phases with such high symmetry should consist of spherical micelies of type I or II, orderly packed in a cubic lattice (Luzzati et aL, 1960; Luzzati and Reiss-Husson, 1966). Reprinted from Lipid Polymorphism and Membrane Properties. Volume 44: Current Topics in Membranes. V. Luzzati. H. Delacroix. A. Gulik. T. Gulik-Krzvwicki. P. Mariani and R. Vargas. Tile Cubic Phases of Lipids. pp. 3-24. 1997. with permission from Elsevier.
17
18
Eventually, careful crystallographic analyses revealed that cubic symmetry is the attribute of not one lipid phase but of a large family of phases. Moreover, the structure of these phases, which took quite a few years to determine, turned out to be unexpectedly complex and multifarious. At the date of the present review, seven cubic phases have been identified and their structure (at least tentatively) described:
1. Q23O(space group Ia3d). This was the first of the cubic phases properly identified, and the first whose structure was firmly established (Luzzati and Spegt, 1967; Luzzati et al., 1968b; Delacroix et al., 1990, 1993b). Thc structure (Fig. 1) was originally described in terms of two 3D networks of rods, mutually intertwined and unconnected, with the rods joined co-planarly three by three; each network is chiral, and the two are mirror images of each other. The surfaces of the rods may be visualized to sit at the polar-apolar interface; in some of the systems the interiors of the rods are occupied by the hydrocarbon chains and the interstices are filled by the polar medium (structure of type I), whereas in others the relative distribution of the polar and the apolar media is the reverse (type II). Luzzati et al. (1968c) pointed out that the structure is "bicontinuous," in the sense that it consists of two media of the same polarity, separated by a medium of the opposite polarity, and that the three media are continuous throughout the 3D space. In 1976, Scriven put forward an alternative representation of the structure, in terms of the G-type IPMS (Schwarz, 1880; Schoen, 1970). 2. 0 224 (space group Pn3m). This phase was originally identified and its structure analyzed by Tardieu (1972) (see also Tardieu and Luzzati, 1970).
Q230
Q224
FIGURE 1 Representation of the bicontinuous phases in terms of a pair of 3D networks of rods (drawn respectively in black and white), mutually intertwined and unconnected, that represent the skeletal graphs of the IPMS. Q230: the rods are joined co-planarly three by three. Q224: the rods are joined tetrahedrally four by four.
19 In 1983 Longley and Mclntosh independently observed this phase and put forward a structure in close agreement with Tardieu's early proposal. The structure (Fig. 1), like that of phase Q230 was originally described in terms of two networks of rods, mutually intertwincd and unconnected. The rods in this phase are tetrahedrally joined four by four. This structure, like that of Q230, is bicontinuous and, as pointed out by Longley and Mclntosh (1983), can also bc described in terms of the IPMS (D-type). 3. Q229(space group Im3m). This phase is often mentioned in lipid literature, frequently in three-component systems (lipid-protein-water [GulikKrzywicki et al., 1984; Mariani et aL, 1988]; surfactant-oil-water [Barois et al., 1990; Maddaford and Topragcioglu, 1993]), although Caffrey (1987), Kekicheff and Cabane (1987), and Mirkin (1992) mention phases with this symmetry in a variety of lipid-water systems. The XRS study of a phase of this symmetry belonging to a ganglioside-water system (Gulik et aL, 1995) has shown that the structure consists of identical quasi-spherical micelles packed in the cubic body-centered mode (represented in Fig. 2 in terms of space-filling polyhedra). It is worthwhile to stress that phase Q229 is often presented as a paradigm of the IPMS (P-surface, the "plumber's nightmare" cartoon), a claim that so far lacks firm experimental support (Luzzati et al., 1993; Luzzati, 1995). 4. Q225 (space group Fm3m). This phase has been observed in the system C12EO~2-water (Ct2EOl2 is a polyethylene glycol surfactant) (Mirkin, 1992) and in several ganglioside-water systems (Gulik et al., 1995). The structure, studied by XRS and FFEM methods, has been shown to consist of identical quasi-spherical micelles close-packed in the cubic face-centered mode (represented in Fig. 2 in terms of space-filling polyhedra) (Gulik et al., 1995). 5. Q223 (space group Pm3n). This phase was discovered by Balmbra et aL (1969) in DTAC and studied by Tardieu and Luzzati (1970) in a variety of lipid-water systems. After some hesitation, and in agreement with earlier proposals (Fontell et al., 1985; Eriksson et al., 1987; Charvolin and Sadoc, 1988), XRS (Vargas et al., 1992) and FFEM (Delacroix et aL, 1993a) studies showed that the structure contains two types of micclles, one quasi-spherical the other disk shaped (represented in Fig. 2 in terms of space-filling polyhedra). 6. Q227(space group Fd3m). This phase was discovered by Tardieu (1972) and described by Mariani et al. (1988). The phase has been observed in a variety of lipid-water systems, in all of which the lipid component is highly heterogeneous (Luzzati et aL, 1992). The structure was first, and incorrectly, interpreted in terms of a 3D network of rods and a set of micelles (Mariani et al., 1990); a more recent analysis revealed that, in keeping with an early proposal by Charvolin and Sadoc (1988), the structure contains two types of quasi-spherical micelles (represented in Fig. 2 in terms of space-filling
20
Q225
Q229
( Q223
Q227
FIGURE 2 Representation of the micellar phases in terms of space-filling polyhedra. Q2ZS: face-centered cubic packing of regular rhombic dodecahedra. Q229:body-centered cubic packing of regular truncated octahedra. Q223: primitive cubic packing of distorted dodecahedra and tetradecahedra. Q227: face-centered cubic packing of distorted dodecahedra and hexadecahedra. (Redrawn with permission from Williams, R. [1979]. ""The Geometrical Foundation of Natural Structure." Dover Publications, New York.)
polyhedra) (Luzzati et al., 1992). This structure has been confirmed by a recent FFEM study (Delacroix et al., 1996). 7. Q212 (space group P4~32). This phase was reported in the system monoolein-water-cytochrome C (Mariani et al., 1988). Those authors proposed a structure formed by a 3D network of rods enclosing a set of identical micelles, each of which contains one protein molecule. It is appropriate to mention another phase of a lipid-water system that consists of identical quasi-spherical micelles, in spite of the fact that its symmetry is not cubic but hexagonal (space group P63/mmc) (Clerc, 1996). We discuss in this paper the structural and physical properties of the cubic phases, and also of other lipid phases of lower symmetry, in a search
21 for general criteria applicable to all lipid phases. We also tackle the longlasting problem of the correlations between the chemical composition of the lipid component and the physical structure of the phases. Finally, we envisage the possible biological implications of lipid polymorphism, with special emphasis on the cubic phases.
11. STRUCTURE ANALYSIS Determining the structure of lipid phases, especially those of type ~ (i.e., with a disordered short-range conformation of the hydrocarbon chains), is a peculiar exercise, whose rules are rather different from those that prevail in other areas of structural chemistry. A few techniques are available.
A. CrystaIIographic Techniques Although single crystals can sometimes be obtained (Clerc, 1996), their use is rarely compatible with the requirements of operating at variable and controlled conditions (usually temperature and water content). Most often, therefore, the experiments are performed on polycrystalline aggregates and the X-ray scattering data take the form of Debye-Scherrer rings. As a consequence, the determination of the space group is sometimes ambiguous (Mariani et al., 1988). Moreover, the highly disordered short-range conformation limits the resolution of the scattering data, and the number of observed reflections is small. Determination of the phase angle of the reflections cannot rely upon conventional methods, since heavy atom derivatives are rarely available in lipid systems. Trial-and-error procedures can only be used when the shape of the structure elements is sufficiently simple to be described in terms of simple geometric models (Gulik et al., 1995). In some cases these drawbacks can be overcome by a systematic study as a function of water content; as a rule, however, the concentration range of cubic phases is too narrow to implement that technique. Another approach is based upon a pattern recognition procedure, based on the axiom that, if two phases are available and if their chemical composition (nature of the lipids and water concentration) is the same, then the histograms of the electron density maps, properly normalized in shape and scale, are identical (Luzzati et al., 1988; Mariani et al., 1988: Luzzati et al., 1992; Vargas et al., 1992). The unknown structure of phase X is thus "solved" by seeking the map compatible with the observed amplitude of the reflections whose histogram best agrees with that of the reference phase. Physical and chemical information is then retrieved from that map. By way of
22 verification, it is of the utmost importance to ascertain that the map is compatible with the physical and chemical properties of the system, especially when these properties are not involved in the crystallographic analysis.
B. Freeze-Fracture Electron Microscopy
One of the novelties regarding lipid-water phases is the impact of imagefiltering FFEM. FFEM has been applied to lipid-containing systems for more than 25 years; combined low-temperature XRS and FFEM techniques, moreover, have been introduced (Gulik-Krzywicki and Costello, 1978) to avoid the effects of freezing artifacts. Although the FFEM images of the cubic phases are too complex to provide much useful information upon plain visual inspection, the presence of extended quasi-periodically ordered areas justifies the use of image-filtering techniques based upon correlation averaging (Saxton and Frank, 1977; Frank et al., 1978). The results yield a remarkable wealth of information. Image-filtering procedures have been applied to a variety of cubic phases: the bicontinuous phase Q230 of types I and II (Delacroix et al., 1990, 1993b); the micellar phases Q223 (Delacroix et al., 1993a) and Q225of type I (Gulik et al., 1995), the micellar phase Q227of type II (Delacroix et al., 1996). For structures of type I, in which the fracture occurs at the lipid-water interface, the filtered images display remarkable correlations with the electron density maps (Figs. 3 and 4; see also Delacroix et al., 1990, 1993a). For structures of type II, in which the fracture occurs over the CH3-decorated surfaces, the comparison is less straightforward. Moreover, the images provide valuable information regarding symmetry. For example, Fig. 4 reveals the presence of mirror planes that escape XRS detection and help narrow down the choice of the space group, and also of fourfold mirror planes.
C. Lateral Diffusion Studies
The diffusion properties of different lipid phases, cubic as well as noncubic, are related to the topological and geometric properties of their structures. Field-gradient NMR experiments have demonstrated that the lateral diffusion of the lipid molecules is much easier in phase O 230 than in phase Q223 (Charvolin and Rigny, 1973; Eriksson et al., 1987), whereas in other phases the results are not as clearcut (Hendrykx et al., 1994; Lindblom and Or~idd, 1994: see also Chapter 3, this volume). FRAP experiments have shown that the lateral diffusion is fast in phases O 230 and O 224 and quite slow in phases Q223 and O 227, in keeping with the bicontinuous structure
23
FIGURE 3 FFEM of phase Q230, type I. Fracture plane [211]. (A) Electron micrograph of a rotatory-shadowed replica. Note the presence of subdomains (labeled 0 to 3) corresponding to sequential steps of freeze-fracture. Inset. Correlation average of subdomain 2. (B) Crosscorrelation map showing the relative shift of the different subdomains. (C) Sequence of sections of the electron density map normal to [211] mutually spaced by a/V'6; the dots mark the projection of the origin of the unit cell. Note the similarity between the correlationaveraged motif (inset in panel A) and the corresponding section of the electron density map 2, and also the faithful representation of the sliding of the correlation maps (panel B). (Reprinted with permission from Gulik-Krzywicki. T., and Delacroix, H. [1994]. Combined use of freeze-fracture electron microscopy and X-ray diffraction for the structure determination of three-dimensionally ordered specimens. Biol. Cell 80, 193-201.)
of phases Q230and Q224and the micellar structure of phases (Cribier et al., 1993).
Q223and Q227
!il. CHEMICAL PROPERTIES Phases Q230, Q224, Q229, Q225, and Q223 have b e e n o b s e r v e d in l i p i d - w a t e r systems containing a chemically h o m o g e n e o u s (or m o d e r a t e l y heterogeneous: e.g., egg lecithin) lipid c o m p o n e n t . In contrast, phase Q22V seems to require a mixture of polar (MO, F A salt, PL) and apolar ( F A , D A G ) lipids (Luzzati et al., 1992). Phase Q229 has been r e p o r t e d also in m o r e
24
1 rn
C
rn m
m rn 9
li
r
mmm
m
I
mmm V
D I// F I G U R E 4 FFEM of phase Q223, type I. Fracture plane [100]. (A) Electron micrograph of a rotatory-shadowed replica, with the subdomains (labeled 1 and 2) corresponding to sequential steps of freeze-fracture. (B) Quasi-optical Fourier filtering of the whole frame (panel A) revealing the content and boundaries of the subdomains. Inset, Cross-correlationaveraged motifs, determined over the area labeled respectively 1 and 2 in panel B. Note that motifs 1 and 2 are related to each other by a 90 ~ rotation. (C) Contour plots of the insets of panel B with, in panel D, the corresponding sections of the electron density maps. The mirror planes, shown in panels C and D, distinguish space group Q223 from space group Q218, also compatible with the powder X-ray scattering data. (Reprinted with permission from Delacroix, H., Gulik-Krzywicki, T., Mariani, P., and Luzzati, V. [1993]. Freeze-fracture electron microscope study of lipid systems: The cubic phase of space group Pm3n. J. Mol. Biol. 229, 526-539.)
25 heterogeneous systems (lipid-protein-water [Gulik-Krzywicki et al., 1984; Mariani et al., 1988]; surfactant-oil-water [Barois et al., 1990, Maddaford and Topragcioglu, 1993]). Phase Q212has been observed in only one lipidprotein-water system (Mariani et al., 1988). Phases Q229 and Q225have been observed in lipid-water systems in which the polar headgroups of the lipids are particularly bulky (C12EO12 [Mirkin, 1992]; gangliosides [Gulik et aL, 1995]). Phase Q230, and most likely phase Q229,have been reported of both type I and II, according to the chemical nature of the lipid (Luzzati et aL, 1968c, 1988; Gulik-Krzywicki et al., 1984). All the examples of the other cubic phases reported so far are either of type I (Q225, Q223) or of type II (Q212, Q224, Q227). Phases Q227 and Q223 display some more subtle correlations between chemical composition and phase behavior. In the case of phase Q223, the area-volume ratio of the micelles (Luzzati et aL, 1993) is almost the same in the two micelles. Moreover, since the lipid component is chemically homogeneous in this phase, the conclusion can be drawn that the area per molecule is the same in the two types of micelles. In contrast, and in keeping with the chemical heterogeneity of the lipid moiety, the area-volume ratio takes different values in the two types of micelles of phase Q227 (Luzzati et al., 1993). This observation can be explained by a difference of lipid composition between the two types of micelles, assuming that the area per molecule of the two lipid components is different. These observations have an interesting thermodynamic implication: The chemical potential of the lipid components~which by definition is constant throughout the volume of the phase~is directly related to the area per molecule at the polarapolar interface. Also noteworthy is the fact that in phase Q227 the parameter <(Ap)4> is close to the minimum of all values compatible with the data (Luzzati et al., 1992), whereas in the two examples of phase Q223 it is far from the minimum (Vargas et al., 1992). In other words (Mariani et al., 1988), the "entropy" of the map is close to maximal in the case of phase Q227 and quite far from it in phase Q223. This property, illustrated in Color Plate I, seems to be related to the chemical type (I or II) of the structure. The argument runs as follows. In the absence of heavy atoms, the most conspicuous electron density fluctuations are those associated with the low-density CH3 end groups. In structures of type I the CH3 end groups are clustered in a small volume surrounding the center of the hydrocarbon region; in structures of type II, those groups are instead spread out over a far more extended volume. As a consequence, and other things being equal, the local density of CH3 groups~and thus the amplitude of the electron density
26 fluctuations and the value of <(Ap)4>--is likely to be larger in structures of type I than in structures of type II (see later). These considerations are also relevant to the position of the fracture and to the aspect of the FFEM images in the phases of type I and II, as discussed earlier.
IV. STRUO'URE REPRESENTATIONS A. Bicontinuous Phases: Networks of Rods, Convoluted Surfaces
Two alternative representations, corresponding respectively to Schoen's skeletal graphs and infinite labyrinths (Schoen, 1970), have been proposed to describe the structure of the bicontinuous cubic phases, one in terms of rodlike elements and the other of folded surfaces (reviewed by Mariani et aL, 1988). The rod representation was adopted in the early crystallographic study of phase Q230 for reasons that have lost none of their relevance. This cubic phase was observed originally in the anhydrous fatty acid salts of divalent cations, among a variety of 2D and 3D phases in all of which the cations (and, presumably, the polar headgroups) are clustered in quasi-crystalline linear aggregates (Luzzati et al., 1968b): a rod model of the cubic phase fitted nicely into that picture. Moreover, the number of polar headgroups per length of rod (a parameter easy to determine when the dimensions and symmetry of the unit cell and the partial volumes of the polar and apolar moieties are known) was found to take almost the same value in a variety of rod-containing phases, cubic and also of lower symmetry. Finally, the observed and the calculated intensity of the XRS reflections were found to be in excellent agreement with each other (Luzzati et al., 1968c). On the other hand, many examples of phase Q230 are known whose water content is high (Luzzati et al., 1988). The structure in these cases can be represented in terms of convoluted polar-apolar interfaces~phase Q230 is indeed related to one of the paradigms of IPMS, the gyroid G (also called the G-surface) (see Color Plate I). Q224, the other bicontinuous cubic phase, has been observed with a high water content: its structure has been described sometimes in terms of rods, sometimes of convoluted surfaces. The surface, in this phase, is related to another type of IPMS, the D-surface (reviewed by Hyde, 1990). The use for one and the same phase of a structure representation that varies with the degree of hydration is at odds with the gradual effects of water (see, e.g., the system egg lecithin-water, Luzzati et al., 1968a). It would be more satisfactory to produce physical and chemical arguments,
27 less formal than those invoked by Schoen (1970) and by Charvolin and Sadoc (1988), in support of one or the other of the two representations, or possibly reconciling the two. The problem is even more confusing if the same representation must also take into account the structure of the micellar phases.
B. Miceilar Phases
Several facets of the structure of the micellar phases can be considered.
1. Packing of Rigid Spheres: Partial Miscibility of Polar Headgroups and Hydrocarbon Chains Knowing the chemical composition, the symmetry, and the unit cell dimension of the lipid-water phase, it is possible to determine the volume of the apolar micelles and, assuming that they are spherical, their radius (Rpar). A puzzling result of this calculation is that Rpar is always larger than the maximum length of the hydrocarbon chains. This anomaly cannot be explained by the polyhedral shape of the micelles nor by some wrinkling of their surface. In fact the critical assumption underlying the calculation is that the polar and apolar regions of the structure are sharply separated from each other. An obvious way to elude the paradox is to allow some of the polar headgroups to dip to some depth inside the hydrocarbon volume or a few of the headgroups to be embedded in the paraffin core of the micelles (Luzzati et al., 1996). Phases Q223 and Q227, which contain two types of micelles, do not lend themselves to this type of analysis.
2. Space-Filling Polyhedra: An Analogy with Foams As depicted in Fig. 2, phases Q225, Q229, Q223, and Q227 can be visualized in terms of space-filling assemblies of polyhedra: rhombic dodecahedra in Q225, truncated octahedra in Q229, a mixture of distorted dodecahedra and tetradecahedra (in the ratio 3:1) in Q223, and a mixture of distorted dodecahedra and hexadecahedra (in the ratio 1:2) in Q227. Three of these space-tilting assemblies (Q225, Q229, and Q223) are sometimes evoked in foams (Wearie, 1994). Foams are similar to the micellar cubic phases in the sense that both systems consist of disjointed cells, containing respectively air or hydrocarbons, separated by septa formed respectively by the hydrated surfactant films or by the hydrated headgroups. In foams, and at the limit of vanishing water content, the geometry of the septa and of their junctions are generally assumed to obey Plateau's conditions: three faces join at each edge with mutual angles equal to 120~
28 four edges meet at each vertex with mutual angles equal to 109028' . As the water content increases, these constraints are expected to relax. According to Wearie (1994), the lowest surface energy at the limit of vanishing water content corresponds to the body-centered packing of Kelvin's tetrakaidecahedra. These space-filling polyhedra derive from the regular truncated octahedra by a subtle distribution of curvature on the hexagonal faces that has the effect of bringing the angles at the vertices (which are of 120 ~ and 90 ~ in the truncated octahedron) closer to tetrahedral. At higher water content the lowest surface energy seems to correspond to the clathrate-like space-filling assembly of distorted dodecahedra and tetradecahedra (phase Q223). In this structure, it must be stressed, the faces meet at angles close to 120~ and each vertex is a quasi-regular tetrahedral junction of four edges (Davidson, 1973). At still higher water content the lowest surface energy seems to correspond to a system of regular rhombic dodecahedra packed in the face-centered cubic mode, much like the micellar phase Q225. This last structure falls short of fulfilling Plateau's conditions: four edges join tetrahedrally at the vertices of each rhombic dodecahedral cell but eight edges join octahedrally at the six other vertices. The structure of the three micellar cubic phases (Gulik et al., 1995) and their sequence Q223 _.~ Q229 ~ 0225 as a function of increasing water content (Mirkin, 1992) are consistent with these theoretical expectations. 3. Infinite Periodic Minimal Surfaces The relevance of the IPMS to the bicontinuous cubic phases stems from the fact that these phases can be thought of as lipid bilayers folded in space according to an IPMS: D-surface in phase Q224, G-surface in phase Q230.The two labyrinths are directly congruent in phase Q224and chirally congruent in Q230. The skeletal graphs of these surfaces coincide with the three- and four-connected systems of rods that are commonly used in the structural description of phases Q230and Q224 (Fig. 1). The center of the bilayer, whose locus is the minimal surface, and the skeletal graph reside respectively in the polar and in the apolar region if the structure is of type I, and the other way around if the structure is of type II (Color Plate I). In contrast, the micellar cubic phases, which subdivide 3D space into an infinite number of disjointed compartments of one polarity embedded in a matrix of the opposite polarity, are by no means bicontinuous. One might thus expect these phases to be utterly unrelated with the IPMS. This is certainly the case for those IPMS whose labyrinths are congruent: the issue is not as clear cut for those IPMS whose labyrinths are not congruent. In particular, two of the IPMS, I-WP and F-RD, display striking correlations with the micellar cubic phases Q229 and Q225. These two surfaces can be visualized by reference to the polyhedra of Fig. 2 and to the pair of noncongruent skeletal graphs.
29
phase Q230
phase H
m
type l
r,
K
"~'~
9
b/l~ II
FIGURE 5 Phases H and Q230: composite representation of the maps Ap(r), of the chaotic zones (green, polar; blue, apolar) and of the polar-apolar interfaces (red). The equidensity lines Ap(r)constant are all equally spaced, with an interval of 0.5; negative values are dotted. Note, in all the cases, the deep troughs near the center of the hydrocarbon regions (see the text) and the fairly flat polar regions; the minimum at the center of the polar region corresponds to the high local concentration of water. The polar-apolar interfaces are assumed to coincide with the equidensity surface A9 = 0. (Phase Q230) Sections normal to the four-fold (plane z = a/8) and to the three-fold axes; these planes contain some of the rods. Note, in the structure of type II, that the electron density troughs fall exactly on the G-surface: in this case, therefore, the IPMS and the apolar chaotic zone coincide. The polar chaotic zone coincides with the networks of rods. (Phase H) Sections normal to the six-fold axes. In H I the polar and the apolar chaotic zones coincide respectively with the hexagonal honeycomb and with the six-fold axes; the opposite is the case in H a . Note that the polar-apolar interfaces are far away from the minimal surfaces (phase Q230) and from the hexagonal honeycomb (phase H). The sections of the G-surface with the two planes of the figure were computed and drawn by Dr. C. Oguey. The bar is 100/~ long. (Reprinted with permission from Luzzati, V., Vargas, R., Mariani, P., Gulik, A., and Delacroix, H. [1993]. Cubic phases of lipid-containing systems: Elements of a theory and biological connotations. J. Mol. Biol. 229, 540-551.) These representations were developed based on the following data:
Lipid
c
T
a
(oc)
(A)
Phase
Type
<(Ao)4>
Reference
DTAC
0.90
20
37.2
H
I
2.90
Vargas et al. (1992)
DTAC
0.90
20
79.6
Q23O
I
2.91
Mariani (unpublished)
PFL
0.65
60
62.9
H
II
1.48
Mariani et al. (1990)
MO
0.66
25
143.0
Q230
II
1.74
Luzzati et al. (1988)
30
phase Q225 ~
,
--
. ,, , ~
~:v ~ ~ : x ~ - L ~
~
~, ' t'l , k~) ~~J ": . . . . . '"~-.S -~- -:-..<"
phase 0 229
.
"~ v~'~
i x~"i ' ~
~'I"1 ~ '" A" '
.
.
.
.
,
,. " " ' -
FIGURE 6 Phases Q225 and Q229, sections [ 100], [ 110], and [ 111 ] through the origin. Notation and scales as in Fig. 5. The traces of the IPMS (red lines) were computed according to yon Schnering and Nesper (1991). The green areas correspond to the sections of the polar labyrinth. (Left) Phase Q225; the IPMS is the F-RD surface, the F-graph is blue, and the RD-graph is green. (Right) Phase Q229;the IPMS is the I-WP surface, the I-graph is blue, and the PW-graph is green. Note that in both cases the IPMS coincides with one of the continuous isodensity lines. Note also that not all of the sections contain elements of the skeletal graphs. The scale bars correspond to 100/~. (Reprinted with permission from Luzzati, V., Delacroix, H., and Gulik, A. [1996]. The micellar cubic phases of lipid-containing systems: Analogies with foams, relations with the infinite periodic minimal surfaces, sharpness of the polar/apolar partition. J. Phys. H (France) 6, 405-418.)
31 Regarding the I-WP surface (Schoen, 1970), one of the graphs (1-graph) is constructed by joining with straight lines all nearest neighbor points of the body-centered cubic lattice; the lines are eight-connected at both ends. The other graph (WP-graph) is the assembly of all the edges of the spacefilling assembly of regular truncated octahedra (see Fig. 2): the edges are four-connected at both ends. As for the F-RD surface (Schoen, 1970), one of the graphs (F-graph) consists of the straight lines joining all nearest neighbor points of the facecentered cubic lattice; the lines are 12-connected at both ends. The other graph (RD-graph) is the assembly of all the edges of a space-filling assembly of regular rhombic dodecahedra (Fig. 2); the edges are 4-connected at one end and 8-connected at the other. The sections [100], [110], and [111] of the two IPMS, computed according to von Schnering and Nesper (1991), are plotted in Color Plate II along with the electron density maps. Most remarkably, in all the cases the relevant IPMS is almost coincident with one particular equi-electron-density surface. In other words, one experimentally defined surface [p(r)= constant] exists whose mean curvature vanishes everywhere. This empirical observation hints at some subtle correlation between the structure of the phases and the IPMS. The structures that correspond to these virtual minimal surfaces (I-WP in Q229, F-RD in Q225) consist of two disjointed 3D labyrinths, one filled by water and the other by the highly hydrated lipid micelles fused together via their hexagonal (in Q229) or quadrilateral (in Q225) faces. The interracial forces, supposed to be exerted on the virtual IPMS and thus to be minimal, would then be applied at an interface separating a polar labyrinth from a labyrinth containing the hydrocarbon chains and a fraction of the polar moiety of the system (Luzzati, 1995). Presumably, in order that the IPMS representation makes physical sense, the size and shape of the labyrinths must be such that water, paraffins, and headgroups properly fit together. All these conditions are not easy to meet; this may be the reason why the micellar cubic phases Q229and Q225 seem to be so rare in lipid-water systems.
V. ORDERLYDISPOSAL OF SHORT-RANGE CONFORMATIONAL DISORDER: THE CHAOTIC ZONES
Many of the ideas explored so far hinge upon the very notion of lipid film and implicitly ascribe to the interfacial interactions a predominant role among all the forces at play in lipid-water phases. The question arises of the chemical nature of the structure elements and of the position of the interface (Luzzati, 1995).
32 The arguments used by the authors who have sought in the IPMS a unified theory underlying lipid polymorphism (reviewed by Hyde, 1990) seem to entertain some confusion between the mathematical notion of surface and the physical concept of film. In the bicontinuous cubic phases the polar-apolar interfaces lie not only at s o m e distance from the IPMS (Charvolin and Sadoc, 1988; Anderson et al., 1988; Hyde, 1990) but in some cases at a distance that is almost as large as is compatible with the space group and the cell dimension. The most striking example is phase Q230 of the anhydrous divalent cation soaps (Luzzati et al., 1968b), in which the polar-apolar interface is very close to the skeletal graph. Similarly, in phases Q227and Q223 the polar-apolar interface, the most likely candidate for a film to which a "surface tension" is to be applied, lies at quite a distance from the polyhedral faces (see Fig. 2). Let us get away from the interface and move deeper into the hydrocarbon and the water media. The short-range conformation of the hydrocarbon chains (above the "melting" temperature) has been the matter of some controversy. In the early days, Hartley (reviewed by Hartley, 1977; Luzzati et al., 1993) produced lucid arguments in support of a highly disordered conformation. After some confusion, the general consensus now seems to be that the chains are highly flexible (reviewed by Charvolin and Hendrikx, 1985) and that the stability of any one structure involves a compromise between the curvature of the polar-apolar interface and the flexibility of the chains (Luzzati and Spegt, 1967; Luzzati, 1968; Charvolin and Sadoc, 1988; Turner and Gruner, 1992; Turner et al., 1992, and references cited therein). More precisely, the lateral order of chain packing is visualized to be high near the polar-apolar interface--to which the chains are anchored----and to decrease gradually as the distance to the interface increases. The hydrocarbon core of the structure, namely the region most distant from the interfaces, is occupied by segments of chains anchored at different interfaces, with a high concentration of CH3 end groups. The packing is inevitably disordered in those regions. A similar picture applies to the water regions. In the highly hydrated phases the water dipoles are strongly oriented in the immediate vicinity of the polar-apolar interfaces; the orientation becomes increasingly disordered as the distance to the interface increases. In the very center of the water region, the orienting effects of the different interfaces cancel out and the disorder probably becomes as high there as in liquid water. We call the regions where the short-range disorder is maximal chaotic zones. These zones, as we now show, occupy special positions (i.e., symmetry elements, IPMS, skeletal graphs) and coincide with the points, lines, and surfaces that play a conspicuous role in the structure representation. By
33 definition, on the other hand, the short-range order is maximal at the polar-apolar interface. The apolar chaotic zones are decorated by the CH3 end groups of the hydrocarbon chains and, as discussed in Section II, coincide with the minima of the electron density maps. By way of illustration, we present a few examples in Color Plate I. In the maps of phase H the minima (and thus the apolar chaotic zones) coincide either with the six-fold axes (structure of type I) or with the hexagonal honeycomb (structure of type II). In phase Q230, type I, the minima fall exactly on the rods of the two networks. In the case of phase Q230, type II, the minima o f the map fall sharply on the Gsurface. This remarkable observation, which applies also to the bicontinuous phase Q224(result not shown), indicates that the chaotic zones are the support of the IPMS. As discussed in Section II, the situation is not quite symmetrical for phases of type I and type II, since the zones within the water matrix where the short-range disorder is maximal are not decorated by electron density maxima or minima. In the micellar cubic phases, on the other hand, the minima in the maps coincide with the centers of the micelles in phase Q225, Q229, and Q223, with the surface of the polyhedra in phase Q227 (results not shown). By analogy with phases Q230 and H (see Color Plate I) we thus conclude that the polar and the apolar chaotic zones coincide respectively with the surface and with the center of the polyhedra in phase Q223, Q225, and Q229 and with the center and the surface of the polyhedra in phase Q227 (see Fig. 2). Over the surface of the polyhedra, moreover, the disorder is likely to be higher along the edges and even higher at the vertices, where two and three quasi-planar chaotic zones meet. Alternatively, should one adopt the IPMS representation of phases Q225 and Q229, then the chaotic zones would coincide with the skeletal graphs RD for the F-RD surface (phase Q225) and I and WP for the I-WP surface (phase Q229). It thus appears that one of the constraints that these structures are bound to fulfill is to orderly distribute the short-range disorder in space. Table I presents a list of the chaotic zones, polar and apolar, for some of the lipid phases whose structures are firmly established. It is worthwhile to end this section with a few comments of general interest: 1. At variance with the widely accepted idea that the IPMS are related to the polar-apolar interfaces, we stress the fact that in the crystallographic sense the positions of the polar-apolar interfaces are in no way remarkable (see Color Plate I; see also Anderson et al., 1988; Turner and Gruner, 1992; Turner et al., 1992).
34
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35 2. We introduce the notion of chaotic zones to designate the geometric singularities (points, lines, surfaces) that coincide with the loci of maximal short-range disorder. 3. We note that orderly disposing short-range disorder seems to bring an important contribution to the energy of the phases, much like minimizing the area of the polar-apolar interfaces. 4. Finally, the notion of chaotic zones has the rewarding effect of ascribing formally equivalent roles to the two alternative representations of the bicontinuous cubic phases~rods or IPMS.
Vl. BIOLOGICALIMPLICATIONS Another important aspect of the cubic phases of lipid-containing systems is their possible biological relevance. In a more general way, the biological significance of lipid polymorphism is a problem often evoked in the past (reviewed by Mariani et al., 1988). The point has also been stressed that, on account of their remarkable topological properties, the bicontinuous cubic phases are far better candidates for biological speculations than the lamellar and the hexagonal phases. Besides, if a biological function is to be ascribed to any of the lipid phases, then that phase is expected to be stable in the presence of excess water, as most biological systems are. Of all lipid phases, four have so far been observed in equilibrium with excess water: lamellar for most phospholipids devoid of a net electrical charge, hexagonal (HII) for some phospholipids (reviewed by Seddon, 1990), cubic Q224for some lipids of biological interest (MO [Mariani et al., 1988]; lipid extract from a thermoacidophilic archaebacterium [Gulik et al., 1985]), and cubic Q227for lipid mixtures of the proper chemical composition (Luzzati et al., 1992). Phase Q224, and its spongy structure, have played a prominent role in biological speculations~for example, the plasma membranes of thermoacidophilic archaebacteria (Luzzati et al., 1987) and the digestion of fats (Mariani et al., 1988). We may also envisage a possible biological significance for phase Q227. Two properties of this phase are relevant to this question. One is chemical composition: phase Q227 contains one (or more) of the most common lipid components of biological membranes (PC, PE), plus one of the usual end products of many a lipid degradation (FA, DAG). The other property is watertightness, associated with the apolar 3D continuum. In contrast, apolar a n d polar continua are present in the bicontinuous phases. This last property suggests a sort of "patch-the-puncture" process, whereby the local formation of phase Q227 might have the effect of repairing the damage of some
36
lipolytic agents. Initially, an enzymatic attack would liberate FA and/or DAG, (locally) destabilize the bilayer, and make the membrane leaky; subsequently, FA and/or DAG would mix with the intact lipids and form a patch of watertight phase Q227 that would eventually stop the leak. A similar process, averting the danger of leaks, could come into play in other processes, for example, membrane budding and fusion, which involve a local disruption of the diffusion barrier. This hypothesis is corroborated by the close chemical and physical similarities of phases Q227 and Q224. The same lipid (e.g., MO) is indeed present in these two phases, and the two phases are stable in the presence of excess water. The addition of FA (or DAG) transforms the bicontinuous structure of Q224, highly permeable to both water and oil, into the water-impermeable Q227. The process could thus be visualized as a switch between two states, one of high and the other of low conductivity, under the control of FA (and/or DAG). In support of these speculations is a study of phospholipase C-induced liposome fusion (Nieva et al., 1995) as well as the frequent observation of lipidic particles in membrane systems undergoing fusion (Verkleij, 1984). Moreover, DAG is known to be an essential component in the signal transmission pathway that cells utilize to recognize and respond to a variety of extracellular signals (Bell and Bums, 1991). This function is indeed preceded by a liberation of DAG that might well induce local and transient alterations of the membrane structure. Finally, the discovery in a wide variety of cells of membrane systems folded in space according to the symmetry of the IPMS (Hyde et al., 1997) is a fascinating generalization of the cubic phases (see also Luzzati et al., 1987). It is also worth mentioning that Delacroix, Nicolas, and GulikKrzywicki have observed that, in the photosomes of some annelids (Harmothoe lunulata), the lattice and symmetry of these "cubic membranes" may well vary with the physiological state of the organelles (in preparation).
Acknowledgments We are grateful to Christophe Oguey for kindly computing the sections of the G-surface of Fig. 5. This work was supported in part by grants from the Association Franceaise pour la Recherche M6dicale, the Ligue Nationale contre le Cancer, and the Association Franqaise contre les Myopathies.
List of Abbreviations 1D, etc. DAG DTAC FA FFEM FRAP
Average value of a function A(r) over the unit cell One-dimensional, etc. Diacyl glycerol Dodeeyltrimethylammonium chloride Fatty acid Freeze-fracture electron microscopy Fluorescence recovery after bleaching
37
IPMS L,H, Q" MO NMR PC PE PL
A~r)
Infinite periodic minimal surface without intersection 1-D lameUar, 2-D hexagonal, 3-D cubic phase of space group N~ (International Tables, 1952) Monoolein Nuclear magnetic resonance Phosphatidylcholine Phosphatidylethanolamine Phospholipid Normalized, dimensionless expression of the electron density p(r): A p ( r ) = [p(r) -
Types I and II XRS
The Cubic Phases of Lipids Vittorio Luzzati,* Herv~ Delacroix,* Annette Gulik,* Tadeusz Gulik-Krzywicki,* Paolo Mariani,* and Rodoifo Vargas* *Centre de Gfnftique Molfculaire, kaboratoire Propre du CNRS Associ6 ~ l'Universit6 Pierre et Marie Curie, 91198 Gif-sur-Yvette Cedex, France, tlstituto di Scienze Fisiche and Istituto Nazionale per la Fisica della Materia, Universit'h di Ancona, 60131 Ancona, Italia, and *Centro de Biofisica y Bioqufmica, IVIC, Caracas 19020-A, Venezuela
I. Introduction II. Structure Analysis A. Crystallographic Techniques B. Freeze-Fracture Electron Microscopy C. Lateral Diffusion Studies III. Chemical Properties IV. Structure Representations A. Bicontinuous Phases: Networks of Rods, Convoluted Surfaces B. Micellar Phases V. Orderly Disposal of Short-Range Conformational Disorder: The Chaotic Zones VI. Biological Implications Abbreviations References
1. I N T R O D U C T I O N
Phases with cubic symmetry have been observed in lipid-water systems since the early days of lipid polymorphism, at a time when it seemed all too natural to presume without closer inspection that phases with such high symmetry should consist of spherical micelies of type I or II, orderly packed in a cubic lattice (Luzzati et aL, 1960; Luzzati and Reiss-Husson, 1966). Reprinted from Lipid Polymorphism and Membrane Properties. Volume 44: Current Topics in Membranes. V. Luzzati. H. Delacroix. A. Gulik. T. Gulik-Krzvwicki. P. Mariani and R. Vargas. Tile Cubic Phases of Lipids. pp. 3-24. 1997. with permission from Elsevier.
17
18
Eventually, careful crystallographic analyses revealed that cubic symmetry is the attribute of not one lipid phase but of a large family of phases. Moreover, the structure of these phases, which took quite a few years to determine, turned out to be unexpectedly complex and multifarious. At the date of the present review, seven cubic phases have been identified and their structure (at least tentatively) described:
1. Q23O(space group Ia3d). This was the first of the cubic phases properly identified, and the first whose structure was firmly established (Luzzati and Spegt, 1967; Luzzati et al., 1968b; Delacroix et al., 1990, 1993b). Thc structure (Fig. 1) was originally described in terms of two 3D networks of rods, mutually intertwined and unconnected, with the rods joined co-planarly three by three; each network is chiral, and the two are mirror images of each other. The surfaces of the rods may be visualized to sit at the polar-apolar interface; in some of the systems the interiors of the rods are occupied by the hydrocarbon chains and the interstices are filled by the polar medium (structure of type I), whereas in others the relative distribution of the polar and the apolar media is the reverse (type II). Luzzati et al. (1968c) pointed out that the structure is "bicontinuous," in the sense that it consists of two media of the same polarity, separated by a medium of the opposite polarity, and that the three media are continuous throughout the 3D space. In 1976, Scriven put forward an alternative representation of the structure, in terms of the G-type IPMS (Schwarz, 1880; Schoen, 1970). 2. 0 224 (space group Pn3m). This phase was originally identified and its structure analyzed by Tardieu (1972) (see also Tardieu and Luzzati, 1970).
Q230
Q224
FIGURE 1 Representation of the bicontinuous phases in terms of a pair of 3D networks of rods (drawn respectively in black and white), mutually intertwined and unconnected, that represent the skeletal graphs of the IPMS. Q230: the rods are joined co-planarly three by three. Q224: the rods are joined tetrahedrally four by four.
19 In 1983 Longley and Mclntosh independently observed this phase and put forward a structure in close agreement with Tardieu's early proposal. The structure (Fig. 1), like that of phase Q230 was originally described in terms of two networks of rods, mutually intertwincd and unconnected. The rods in this phase are tetrahedrally joined four by four. This structure, like that of Q230, is bicontinuous and, as pointed out by Longley and Mclntosh (1983), can also bc described in terms of the IPMS (D-type). 3. Q229(space group Im3m). This phase is often mentioned in lipid literature, frequently in three-component systems (lipid-protein-water [GulikKrzywicki et al., 1984; Mariani et aL, 1988]; surfactant-oil-water [Barois et al., 1990; Maddaford and Topragcioglu, 1993]), although Caffrey (1987), Kekicheff and Cabane (1987), and Mirkin (1992) mention phases with this symmetry in a variety of lipid-water systems. The XRS study of a phase of this symmetry belonging to a ganglioside-water system (Gulik et aL, 1995) has shown that the structure consists of identical quasi-spherical micelles packed in the cubic body-centered mode (represented in Fig. 2 in terms of space-filling polyhedra). It is worthwhile to stress that phase Q229 is often presented as a paradigm of the IPMS (P-surface, the "plumber's nightmare" cartoon), a claim that so far lacks firm experimental support (Luzzati et al., 1993; Luzzati, 1995). 4. Q225 (space group Fm3m). This phase has been observed in the system C12EO~2-water (Ct2EOl2 is a polyethylene glycol surfactant) (Mirkin, 1992) and in several ganglioside-water systems (Gulik et al., 1995). The structure, studied by XRS and FFEM methods, has been shown to consist of identical quasi-spherical micelles close-packed in the cubic face-centered mode (represented in Fig. 2 in terms of space-filling polyhedra) (Gulik et al., 1995). 5. Q223 (space group Pm3n). This phase was discovered by Balmbra et aL (1969) in DTAC and studied by Tardieu and Luzzati (1970) in a variety of lipid-water systems. After some hesitation, and in agreement with earlier proposals (Fontell et al., 1985; Eriksson et al., 1987; Charvolin and Sadoc, 1988), XRS (Vargas et al., 1992) and FFEM (Delacroix et aL, 1993a) studies showed that the structure contains two types of micclles, one quasi-spherical the other disk shaped (represented in Fig. 2 in terms of space-filling polyhedra). 6. Q227(space group Fd3m). This phase was discovered by Tardieu (1972) and described by Mariani et al. (1988). The phase has been observed in a variety of lipid-water systems, in all of which the lipid component is highly heterogeneous (Luzzati et aL, 1992). The structure was first, and incorrectly, interpreted in terms of a 3D network of rods and a set of micelles (Mariani et al., 1990); a more recent analysis revealed that, in keeping with an early proposal by Charvolin and Sadoc (1988), the structure contains two types of quasi-spherical micelles (represented in Fig. 2 in terms of space-filling
20
Q225
Q229
( Q223
Q227
FIGURE 2 Representation of the micellar phases in terms of space-filling polyhedra. Q2ZS: face-centered cubic packing of regular rhombic dodecahedra. Q229:body-centered cubic packing of regular truncated octahedra. Q223: primitive cubic packing of distorted dodecahedra and tetradecahedra. Q227: face-centered cubic packing of distorted dodecahedra and hexadecahedra. (Redrawn with permission from Williams, R. [1979]. ""The Geometrical Foundation of Natural Structure." Dover Publications, New York.)
polyhedra) (Luzzati et al., 1992). This structure has been confirmed by a recent FFEM study (Delacroix et al., 1996). 7. Q212 (space group P4~32). This phase was reported in the system monoolein-water-cytochrome C (Mariani et al., 1988). Those authors proposed a structure formed by a 3D network of rods enclosing a set of identical micelles, each of which contains one protein molecule. It is appropriate to mention another phase of a lipid-water system that consists of identical quasi-spherical micelles, in spite of the fact that its symmetry is not cubic but hexagonal (space group P63/mmc) (Clerc, 1996). We discuss in this paper the structural and physical properties of the cubic phases, and also of other lipid phases of lower symmetry, in a search
21 for general criteria applicable to all lipid phases. We also tackle the longlasting problem of the correlations between the chemical composition of the lipid component and the physical structure of the phases. Finally, we envisage the possible biological implications of lipid polymorphism, with special emphasis on the cubic phases.
11. STRUCTURE ANALYSIS Determining the structure of lipid phases, especially those of type ~ (i.e., with a disordered short-range conformation of the hydrocarbon chains), is a peculiar exercise, whose rules are rather different from those that prevail in other areas of structural chemistry. A few techniques are available.
A. CrystaIIographic Techniques Although single crystals can sometimes be obtained (Clerc, 1996), their use is rarely compatible with the requirements of operating at variable and controlled conditions (usually temperature and water content). Most often, therefore, the experiments are performed on polycrystalline aggregates and the X-ray scattering data take the form of Debye-Scherrer rings. As a consequence, the determination of the space group is sometimes ambiguous (Mariani et al., 1988). Moreover, the highly disordered short-range conformation limits the resolution of the scattering data, and the number of observed reflections is small. Determination of the phase angle of the reflections cannot rely upon conventional methods, since heavy atom derivatives are rarely available in lipid systems. Trial-and-error procedures can only be used when the shape of the structure elements is sufficiently simple to be described in terms of simple geometric models (Gulik et al., 1995). In some cases these drawbacks can be overcome by a systematic study as a function of water content; as a rule, however, the concentration range of cubic phases is too narrow to implement that technique. Another approach is based upon a pattern recognition procedure, based on the axiom that, if two phases are available and if their chemical composition (nature of the lipids and water concentration) is the same, then the histograms of the electron density maps, properly normalized in shape and scale, are identical (Luzzati et al., 1988; Mariani et al., 1988: Luzzati et al., 1992; Vargas et al., 1992). The unknown structure of phase X is thus "solved" by seeking the map compatible with the observed amplitude of the reflections whose histogram best agrees with that of the reference phase. Physical and chemical information is then retrieved from that map. By way of
22 verification, it is of the utmost importance to ascertain that the map is compatible with the physical and chemical properties of the system, especially when these properties are not involved in the crystallographic analysis.
B. Freeze-Fracture Electron Microscopy
One of the novelties regarding lipid-water phases is the impact of imagefiltering FFEM. FFEM has been applied to lipid-containing systems for more than 25 years; combined low-temperature XRS and FFEM techniques, moreover, have been introduced (Gulik-Krzywicki and Costello, 1978) to avoid the effects of freezing artifacts. Although the FFEM images of the cubic phases are too complex to provide much useful information upon plain visual inspection, the presence of extended quasi-periodically ordered areas justifies the use of image-filtering techniques based upon correlation averaging (Saxton and Frank, 1977; Frank et al., 1978). The results yield a remarkable wealth of information. Image-filtering procedures have been applied to a variety of cubic phases: the bicontinuous phase Q230 of types I and II (Delacroix et al., 1990, 1993b); the micellar phases Q223 (Delacroix et al., 1993a) and Q225of type I (Gulik et al., 1995), the micellar phase Q227of type II (Delacroix et al., 1996). For structures of type I, in which the fracture occurs at the lipid-water interface, the filtered images display remarkable correlations with the electron density maps (Figs. 3 and 4; see also Delacroix et al., 1990, 1993a). For structures of type II, in which the fracture occurs over the CH3-decorated surfaces, the comparison is less straightforward. Moreover, the images provide valuable information regarding symmetry. For example, Fig. 4 reveals the presence of mirror planes that escape XRS detection and help narrow down the choice of the space group, and also of fourfold mirror planes.
C. Lateral Diffusion Studies
The diffusion properties of different lipid phases, cubic as well as noncubic, are related to the topological and geometric properties of their structures. Field-gradient NMR experiments have demonstrated that the lateral diffusion of the lipid molecules is much easier in phase O 230 than in phase Q223 (Charvolin and Rigny, 1973; Eriksson et al., 1987), whereas in other phases the results are not as clearcut (Hendrykx et al., 1994; Lindblom and Or~idd, 1994: see also Chapter 3, this volume). FRAP experiments have shown that the lateral diffusion is fast in phases O 230 and O 224 and quite slow in phases Q223 and O 227, in keeping with the bicontinuous structure
23
FIGURE 3 FFEM of phase Q230, type I. Fracture plane [211]. (A) Electron micrograph of a rotatory-shadowed replica. Note the presence of subdomains (labeled 0 to 3) corresponding to sequential steps of freeze-fracture. Inset. Correlation average of subdomain 2. (B) Crosscorrelation map showing the relative shift of the different subdomains. (C) Sequence of sections of the electron density map normal to [211] mutually spaced by a/V'6; the dots mark the projection of the origin of the unit cell. Note the similarity between the correlationaveraged motif (inset in panel A) and the corresponding section of the electron density map 2, and also the faithful representation of the sliding of the correlation maps (panel B). (Reprinted with permission from Gulik-Krzywicki. T., and Delacroix, H. [1994]. Combined use of freeze-fracture electron microscopy and X-ray diffraction for the structure determination of three-dimensionally ordered specimens. Biol. Cell 80, 193-201.)
of phases Q230and Q224and the micellar structure of phases (Cribier et al., 1993).
Q223and Q227
!il. CHEMICAL PROPERTIES Phases Q230, Q224, Q229, Q225, and Q223 have b e e n o b s e r v e d in l i p i d - w a t e r systems containing a chemically h o m o g e n e o u s (or m o d e r a t e l y heterogeneous: e.g., egg lecithin) lipid c o m p o n e n t . In contrast, phase Q22V seems to require a mixture of polar (MO, F A salt, PL) and apolar ( F A , D A G ) lipids (Luzzati et al., 1992). Phase Q229 has been r e p o r t e d also in m o r e
24
1 rn
C
rn m
m rn 9
li
r
mmm
m
I
mmm V
D I// F I G U R E 4 FFEM of phase Q223, type I. Fracture plane [100]. (A) Electron micrograph of a rotatory-shadowed replica, with the subdomains (labeled 1 and 2) corresponding to sequential steps of freeze-fracture. (B) Quasi-optical Fourier filtering of the whole frame (panel A) revealing the content and boundaries of the subdomains. Inset, Cross-correlationaveraged motifs, determined over the area labeled respectively 1 and 2 in panel B. Note that motifs 1 and 2 are related to each other by a 90 ~ rotation. (C) Contour plots of the insets of panel B with, in panel D, the corresponding sections of the electron density maps. The mirror planes, shown in panels C and D, distinguish space group Q223 from space group Q218, also compatible with the powder X-ray scattering data. (Reprinted with permission from Delacroix, H., Gulik-Krzywicki, T., Mariani, P., and Luzzati, V. [1993]. Freeze-fracture electron microscope study of lipid systems: The cubic phase of space group Pm3n. J. Mol. Biol. 229, 526-539.)
25 heterogeneous systems (lipid-protein-water [Gulik-Krzywicki et al., 1984; Mariani et al., 1988]; surfactant-oil-water [Barois et al., 1990, Maddaford and Topragcioglu, 1993]). Phase Q212has been observed in only one lipidprotein-water system (Mariani et al., 1988). Phases Q229 and Q225have been observed in lipid-water systems in which the polar headgroups of the lipids are particularly bulky (C12EO12 [Mirkin, 1992]; gangliosides [Gulik et aL, 1995]). Phase Q230, and most likely phase Q229,have been reported of both type I and II, according to the chemical nature of the lipid (Luzzati et aL, 1968c, 1988; Gulik-Krzywicki et al., 1984). All the examples of the other cubic phases reported so far are either of type I (Q225, Q223) or of type II (Q212, Q224, Q227). Phases Q227 and Q223 display some more subtle correlations between chemical composition and phase behavior. In the case of phase Q223, the area-volume ratio of the micelles (Luzzati et aL, 1993) is almost the same in the two micelles. Moreover, since the lipid component is chemically homogeneous in this phase, the conclusion can be drawn that the area per molecule is the same in the two types of micelles. In contrast, and in keeping with the chemical heterogeneity of the lipid moiety, the area-volume ratio takes different values in the two types of micelles of phase Q227 (Luzzati et al., 1993). This observation can be explained by a difference of lipid composition between the two types of micelles, assuming that the area per molecule of the two lipid components is different. These observations have an interesting thermodynamic implication: The chemical potential of the lipid components~which by definition is constant throughout the volume of the phase~is directly related to the area per molecule at the polarapolar interface. Also noteworthy is the fact that in phase Q227 the parameter <(Ap)4> is close to the minimum of all values compatible with the data (Luzzati et al., 1992), whereas in the two examples of phase Q223 it is far from the minimum (Vargas et al., 1992). In other words (Mariani et al., 1988), the "entropy" of the map is close to maximal in the case of phase Q227 and quite far from it in phase Q223. This property, illustrated in Color Plate I, seems to be related to the chemical type (I or II) of the structure. The argument runs as follows. In the absence of heavy atoms, the most conspicuous electron density fluctuations are those associated with the low-density CH3 end groups. In structures of type I the CH3 end groups are clustered in a small volume surrounding the center of the hydrocarbon region; in structures of type II, those groups are instead spread out over a far more extended volume. As a consequence, and other things being equal, the local density of CH3 groups~and thus the amplitude of the electron density
26 fluctuations and the value of <(Ap)4>--is likely to be larger in structures of type I than in structures of type II (see later). These considerations are also relevant to the position of the fracture and to the aspect of the FFEM images in the phases of type I and II, as discussed earlier.
IV. STRUO'URE REPRESENTATIONS A. Bicontinuous Phases: Networks of Rods, Convoluted Surfaces
Two alternative representations, corresponding respectively to Schoen's skeletal graphs and infinite labyrinths (Schoen, 1970), have been proposed to describe the structure of the bicontinuous cubic phases, one in terms of rodlike elements and the other of folded surfaces (reviewed by Mariani et aL, 1988). The rod representation was adopted in the early crystallographic study of phase Q230 for reasons that have lost none of their relevance. This cubic phase was observed originally in the anhydrous fatty acid salts of divalent cations, among a variety of 2D and 3D phases in all of which the cations (and, presumably, the polar headgroups) are clustered in quasi-crystalline linear aggregates (Luzzati et al., 1968b): a rod model of the cubic phase fitted nicely into that picture. Moreover, the number of polar headgroups per length of rod (a parameter easy to determine when the dimensions and symmetry of the unit cell and the partial volumes of the polar and apolar moieties are known) was found to take almost the same value in a variety of rod-containing phases, cubic and also of lower symmetry. Finally, the observed and the calculated intensity of the XRS reflections were found to be in excellent agreement with each other (Luzzati et al., 1968c). On the other hand, many examples of phase Q230 are known whose water content is high (Luzzati et al., 1988). The structure in these cases can be represented in terms of convoluted polar-apolar interfaces~phase Q230 is indeed related to one of the paradigms of IPMS, the gyroid G (also called the G-surface) (see Color Plate I). Q224, the other bicontinuous cubic phase, has been observed with a high water content: its structure has been described sometimes in terms of rods, sometimes of convoluted surfaces. The surface, in this phase, is related to another type of IPMS, the D-surface (reviewed by Hyde, 1990). The use for one and the same phase of a structure representation that varies with the degree of hydration is at odds with the gradual effects of water (see, e.g., the system egg lecithin-water, Luzzati et al., 1968a). It would be more satisfactory to produce physical and chemical arguments,
27 less formal than those invoked by Schoen (1970) and by Charvolin and Sadoc (1988), in support of one or the other of the two representations, or possibly reconciling the two. The problem is even more confusing if the same representation must also take into account the structure of the micellar phases.
B. Miceilar Phases
Several facets of the structure of the micellar phases can be considered.
1. Packing of Rigid Spheres: Partial Miscibility of Polar Headgroups and Hydrocarbon Chains Knowing the chemical composition, the symmetry, and the unit cell dimension of the lipid-water phase, it is possible to determine the volume of the apolar micelles and, assuming that they are spherical, their radius (Rpar). A puzzling result of this calculation is that Rpar is always larger than the maximum length of the hydrocarbon chains. This anomaly cannot be explained by the polyhedral shape of the micelles nor by some wrinkling of their surface. In fact the critical assumption underlying the calculation is that the polar and apolar regions of the structure are sharply separated from each other. An obvious way to elude the paradox is to allow some of the polar headgroups to dip to some depth inside the hydrocarbon volume or a few of the headgroups to be embedded in the paraffin core of the micelles (Luzzati et al., 1996). Phases Q223 and Q227, which contain two types of micelles, do not lend themselves to this type of analysis.
2. Space-Filling Polyhedra: An Analogy with Foams As depicted in Fig. 2, phases Q225, Q229, Q223, and Q227 can be visualized in terms of space-filling assemblies of polyhedra: rhombic dodecahedra in Q225, truncated octahedra in Q229, a mixture of distorted dodecahedra and tetradecahedra (in the ratio 3:1) in Q223, and a mixture of distorted dodecahedra and hexadecahedra (in the ratio 1:2) in Q227. Three of these space-tilting assemblies (Q225, Q229, and Q223) are sometimes evoked in foams (Wearie, 1994). Foams are similar to the micellar cubic phases in the sense that both systems consist of disjointed cells, containing respectively air or hydrocarbons, separated by septa formed respectively by the hydrated surfactant films or by the hydrated headgroups. In foams, and at the limit of vanishing water content, the geometry of the septa and of their junctions are generally assumed to obey Plateau's conditions: three faces join at each edge with mutual angles equal to 120~
28 four edges meet at each vertex with mutual angles equal to 109028' . As the water content increases, these constraints are expected to relax. According to Wearie (1994), the lowest surface energy at the limit of vanishing water content corresponds to the body-centered packing of Kelvin's tetrakaidecahedra. These space-filling polyhedra derive from the regular truncated octahedra by a subtle distribution of curvature on the hexagonal faces that has the effect of bringing the angles at the vertices (which are of 120 ~ and 90 ~ in the truncated octahedron) closer to tetrahedral. At higher water content the lowest surface energy seems to correspond to the clathrate-like space-filling assembly of distorted dodecahedra and tetradecahedra (phase Q223). In this structure, it must be stressed, the faces meet at angles close to 120~ and each vertex is a quasi-regular tetrahedral junction of four edges (Davidson, 1973). At still higher water content the lowest surface energy seems to correspond to a system of regular rhombic dodecahedra packed in the face-centered cubic mode, much like the micellar phase Q225. This last structure falls short of fulfilling Plateau's conditions: four edges join tetrahedrally at the vertices of each rhombic dodecahedral cell but eight edges join octahedrally at the six other vertices. The structure of the three micellar cubic phases (Gulik et al., 1995) and their sequence Q223 _.~ Q229 ~ 0225 as a function of increasing water content (Mirkin, 1992) are consistent with these theoretical expectations. 3. Infinite Periodic Minimal Surfaces The relevance of the IPMS to the bicontinuous cubic phases stems from the fact that these phases can be thought of as lipid bilayers folded in space according to an IPMS: D-surface in phase Q224, G-surface in phase Q230.The two labyrinths are directly congruent in phase Q224and chirally congruent in Q230. The skeletal graphs of these surfaces coincide with the three- and four-connected systems of rods that are commonly used in the structural description of phases Q230and Q224 (Fig. 1). The center of the bilayer, whose locus is the minimal surface, and the skeletal graph reside respectively in the polar and in the apolar region if the structure is of type I, and the other way around if the structure is of type II (Color Plate I). In contrast, the micellar cubic phases, which subdivide 3D space into an infinite number of disjointed compartments of one polarity embedded in a matrix of the opposite polarity, are by no means bicontinuous. One might thus expect these phases to be utterly unrelated with the IPMS. This is certainly the case for those IPMS whose labyrinths are congruent: the issue is not as clear cut for those IPMS whose labyrinths are not congruent. In particular, two of the IPMS, I-WP and F-RD, display striking correlations with the micellar cubic phases Q229 and Q225. These two surfaces can be visualized by reference to the polyhedra of Fig. 2 and to the pair of noncongruent skeletal graphs.
29
phase Q230
phase H
m
type l
r,
K
"~'~
9
b/l~ II
FIGURE 5 Phases H and Q230: composite representation of the maps Ap(r), of the chaotic zones (green, polar; blue, apolar) and of the polar-apolar interfaces (red). The equidensity lines Ap(r)constant are all equally spaced, with an interval of 0.5; negative values are dotted. Note, in all the cases, the deep troughs near the center of the hydrocarbon regions (see the text) and the fairly flat polar regions; the minimum at the center of the polar region corresponds to the high local concentration of water. The polar-apolar interfaces are assumed to coincide with the equidensity surface A9 = 0. (Phase Q230) Sections normal to the four-fold (plane z = a/8) and to the three-fold axes; these planes contain some of the rods. Note, in the structure of type II, that the electron density troughs fall exactly on the G-surface: in this case, therefore, the IPMS and the apolar chaotic zone coincide. The polar chaotic zone coincides with the networks of rods. (Phase H) Sections normal to the six-fold axes. In H I the polar and the apolar chaotic zones coincide respectively with the hexagonal honeycomb and with the six-fold axes; the opposite is the case in H a . Note that the polar-apolar interfaces are far away from the minimal surfaces (phase Q230) and from the hexagonal honeycomb (phase H). The sections of the G-surface with the two planes of the figure were computed and drawn by Dr. C. Oguey. The bar is 100/~ long. (Reprinted with permission from Luzzati, V., Vargas, R., Mariani, P., Gulik, A., and Delacroix, H. [1993]. Cubic phases of lipid-containing systems: Elements of a theory and biological connotations. J. Mol. Biol. 229, 540-551.) These representations were developed based on the following data:
Lipid
c
T
a
(oc)
(A)
Phase
Type
<(Ao)4>
Reference
DTAC
0.90
20
37.2
H
I
2.90
Vargas et al. (1992)
DTAC
0.90
20
79.6
Q23O
I
2.91
Mariani (unpublished)
PFL
0.65
60
62.9
H
II
1.48
Mariani et al. (1990)
MO
0.66
25
143.0
Q230
II
1.74
Luzzati et al. (1988)
30
phase Q225 ~
,
--
. ,, , ~
~:v ~ ~ : x ~ - L ~
~
~, ' t'l , k~) ~~J ": . . . . . '"~-.S -~- -:-..<"
phase 0 229
.
"~ v~'~
i x~"i ' ~
~'I"1 ~ '" A" '
.
.
.
.
,
,. " " ' -
FIGURE 6 Phases Q225 and Q229, sections [ 100], [ 110], and [ 111 ] through the origin. Notation and scales as in Fig. 5. The traces of the IPMS (red lines) were computed according to yon Schnering and Nesper (1991). The green areas correspond to the sections of the polar labyrinth. (Left) Phase Q225; the IPMS is the F-RD surface, the F-graph is blue, and the RD-graph is green. (Right) Phase Q229;the IPMS is the I-WP surface, the I-graph is blue, and the PW-graph is green. Note that in both cases the IPMS coincides with one of the continuous isodensity lines. Note also that not all of the sections contain elements of the skeletal graphs. The scale bars correspond to 100/~. (Reprinted with permission from Luzzati, V., Delacroix, H., and Gulik, A. [1996]. The micellar cubic phases of lipid-containing systems: Analogies with foams, relations with the infinite periodic minimal surfaces, sharpness of the polar/apolar partition. J. Phys. H (France) 6, 405-418.)
31 Regarding the I-WP surface (Schoen, 1970), one of the graphs (1-graph) is constructed by joining with straight lines all nearest neighbor points of the body-centered cubic lattice; the lines are eight-connected at both ends. The other graph (WP-graph) is the assembly of all the edges of the spacefilling assembly of regular truncated octahedra (see Fig. 2): the edges are four-connected at both ends. As for the F-RD surface (Schoen, 1970), one of the graphs (F-graph) consists of the straight lines joining all nearest neighbor points of the facecentered cubic lattice; the lines are 12-connected at both ends. The other graph (RD-graph) is the assembly of all the edges of a space-filling assembly of regular rhombic dodecahedra (Fig. 2); the edges are 4-connected at one end and 8-connected at the other. The sections [100], [110], and [111] of the two IPMS, computed according to von Schnering and Nesper (1991), are plotted in Color Plate II along with the electron density maps. Most remarkably, in all the cases the relevant IPMS is almost coincident with one particular equi-electron-density surface. In other words, one experimentally defined surface [p(r)= constant] exists whose mean curvature vanishes everywhere. This empirical observation hints at some subtle correlation between the structure of the phases and the IPMS. The structures that correspond to these virtual minimal surfaces (I-WP in Q229, F-RD in Q225) consist of two disjointed 3D labyrinths, one filled by water and the other by the highly hydrated lipid micelles fused together via their hexagonal (in Q229) or quadrilateral (in Q225) faces. The interracial forces, supposed to be exerted on the virtual IPMS and thus to be minimal, would then be applied at an interface separating a polar labyrinth from a labyrinth containing the hydrocarbon chains and a fraction of the polar moiety of the system (Luzzati, 1995). Presumably, in order that the IPMS representation makes physical sense, the size and shape of the labyrinths must be such that water, paraffins, and headgroups properly fit together. All these conditions are not easy to meet; this may be the reason why the micellar cubic phases Q229and Q225 seem to be so rare in lipid-water systems.
V. ORDERLYDISPOSAL OF SHORT-RANGE CONFORMATIONAL DISORDER: THE CHAOTIC ZONES
Many of the ideas explored so far hinge upon the very notion of lipid film and implicitly ascribe to the interfacial interactions a predominant role among all the forces at play in lipid-water phases. The question arises of the chemical nature of the structure elements and of the position of the interface (Luzzati, 1995).
32 The arguments used by the authors who have sought in the IPMS a unified theory underlying lipid polymorphism (reviewed by Hyde, 1990) seem to entertain some confusion between the mathematical notion of surface and the physical concept of film. In the bicontinuous cubic phases the polar-apolar interfaces lie not only at s o m e distance from the IPMS (Charvolin and Sadoc, 1988; Anderson et al., 1988; Hyde, 1990) but in some cases at a distance that is almost as large as is compatible with the space group and the cell dimension. The most striking example is phase Q230 of the anhydrous divalent cation soaps (Luzzati et al., 1968b), in which the polar-apolar interface is very close to the skeletal graph. Similarly, in phases Q227and Q223 the polar-apolar interface, the most likely candidate for a film to which a "surface tension" is to be applied, lies at quite a distance from the polyhedral faces (see Fig. 2). Let us get away from the interface and move deeper into the hydrocarbon and the water media. The short-range conformation of the hydrocarbon chains (above the "melting" temperature) has been the matter of some controversy. In the early days, Hartley (reviewed by Hartley, 1977; Luzzati et al., 1993) produced lucid arguments in support of a highly disordered conformation. After some confusion, the general consensus now seems to be that the chains are highly flexible (reviewed by Charvolin and Hendrikx, 1985) and that the stability of any one structure involves a compromise between the curvature of the polar-apolar interface and the flexibility of the chains (Luzzati and Spegt, 1967; Luzzati, 1968; Charvolin and Sadoc, 1988; Turner and Gruner, 1992; Turner et al., 1992, and references cited therein). More precisely, the lateral order of chain packing is visualized to be high near the polar-apolar interface--to which the chains are anchored----and to decrease gradually as the distance to the interface increases. The hydrocarbon core of the structure, namely the region most distant from the interfaces, is occupied by segments of chains anchored at different interfaces, with a high concentration of CH3 end groups. The packing is inevitably disordered in those regions. A similar picture applies to the water regions. In the highly hydrated phases the water dipoles are strongly oriented in the immediate vicinity of the polar-apolar interfaces; the orientation becomes increasingly disordered as the distance to the interface increases. In the very center of the water region, the orienting effects of the different interfaces cancel out and the disorder probably becomes as high there as in liquid water. We call the regions where the short-range disorder is maximal chaotic zones. These zones, as we now show, occupy special positions (i.e., symmetry elements, IPMS, skeletal graphs) and coincide with the points, lines, and surfaces that play a conspicuous role in the structure representation. By
33 definition, on the other hand, the short-range order is maximal at the polar-apolar interface. The apolar chaotic zones are decorated by the CH3 end groups of the hydrocarbon chains and, as discussed in Section II, coincide with the minima of the electron density maps. By way of illustration, we present a few examples in Color Plate I. In the maps of phase H the minima (and thus the apolar chaotic zones) coincide either with the six-fold axes (structure of type I) or with the hexagonal honeycomb (structure of type II). In phase Q230, type I, the minima fall exactly on the rods of the two networks. In the case of phase Q230, type II, the minima o f the map fall sharply on the Gsurface. This remarkable observation, which applies also to the bicontinuous phase Q224(result not shown), indicates that the chaotic zones are the support of the IPMS. As discussed in Section II, the situation is not quite symmetrical for phases of type I and type II, since the zones within the water matrix where the short-range disorder is maximal are not decorated by electron density maxima or minima. In the micellar cubic phases, on the other hand, the minima in the maps coincide with the centers of the micelles in phase Q225, Q229, and Q223, with the surface of the polyhedra in phase Q227 (results not shown). By analogy with phases Q230 and H (see Color Plate I) we thus conclude that the polar and the apolar chaotic zones coincide respectively with the surface and with the center of the polyhedra in phase Q223, Q225, and Q229 and with the center and the surface of the polyhedra in phase Q227 (see Fig. 2). Over the surface of the polyhedra, moreover, the disorder is likely to be higher along the edges and even higher at the vertices, where two and three quasi-planar chaotic zones meet. Alternatively, should one adopt the IPMS representation of phases Q225 and Q229, then the chaotic zones would coincide with the skeletal graphs RD for the F-RD surface (phase Q225) and I and WP for the I-WP surface (phase Q229). It thus appears that one of the constraints that these structures are bound to fulfill is to orderly distribute the short-range disorder in space. Table I presents a list of the chaotic zones, polar and apolar, for some of the lipid phases whose structures are firmly established. It is worthwhile to end this section with a few comments of general interest: 1. At variance with the widely accepted idea that the IPMS are related to the polar-apolar interfaces, we stress the fact that in the crystallographic sense the positions of the polar-apolar interfaces are in no way remarkable (see Color Plate I; see also Anderson et al., 1988; Turner and Gruner, 1992; Turner et al., 1992).
34
o
.o
o o
o
m
o [-,
..~
8
N~
8
8~8
8
0
8
8
E o 0
8
E --
o
.~
0
8
~
0
~
e4 e4 -~ ~
0
~
~
~
0
~
.u
~
~'~
--.
0
8
.u
~
m
8
o
~
.~..
~
0
8
8
8 ~ - - ~ 8 ~ 8 ~ 8 ~
~
0
..~
8
8
~~~.~.~.~.~.~~
0
~'c
.
.~_
o
e,i
8~
9- -
~
E o E
am
,-2,~
~g
~
E= ~.~_
'~
~.~-~ ~ ~ ~ ~.~.
0
,,o~, o~Z~ ! Z "-~T~
"N ~ 0
35 2. We introduce the notion of chaotic zones to designate the geometric singularities (points, lines, surfaces) that coincide with the loci of maximal short-range disorder. 3. We note that orderly disposing short-range disorder seems to bring an important contribution to the energy of the phases, much like minimizing the area of the polar-apolar interfaces. 4. Finally, the notion of chaotic zones has the rewarding effect of ascribing formally equivalent roles to the two alternative representations of the bicontinuous cubic phases~rods or IPMS.
Vl. BIOLOGICALIMPLICATIONS Another important aspect of the cubic phases of lipid-containing systems is their possible biological relevance. In a more general way, the biological significance of lipid polymorphism is a problem often evoked in the past (reviewed by Mariani et al., 1988). The point has also been stressed that, on account of their remarkable topological properties, the bicontinuous cubic phases are far better candidates for biological speculations than the lamellar and the hexagonal phases. Besides, if a biological function is to be ascribed to any of the lipid phases, then that phase is expected to be stable in the presence of excess water, as most biological systems are. Of all lipid phases, four have so far been observed in equilibrium with excess water: lamellar for most phospholipids devoid of a net electrical charge, hexagonal (HII) for some phospholipids (reviewed by Seddon, 1990), cubic Q224for some lipids of biological interest (MO [Mariani et al., 1988]; lipid extract from a thermoacidophilic archaebacterium [Gulik et al., 1985]), and cubic Q227for lipid mixtures of the proper chemical composition (Luzzati et al., 1992). Phase Q224, and its spongy structure, have played a prominent role in biological speculations~for example, the plasma membranes of thermoacidophilic archaebacteria (Luzzati et al., 1987) and the digestion of fats (Mariani et al., 1988). We may also envisage a possible biological significance for phase Q227. Two properties of this phase are relevant to this question. One is chemical composition: phase Q227 contains one (or more) of the most common lipid components of biological membranes (PC, PE), plus one of the usual end products of many a lipid degradation (FA, DAG). The other property is watertightness, associated with the apolar 3D continuum. In contrast, apolar a n d polar continua are present in the bicontinuous phases. This last property suggests a sort of "patch-the-puncture" process, whereby the local formation of phase Q227 might have the effect of repairing the damage of some
36
lipolytic agents. Initially, an enzymatic attack would liberate FA and/or DAG, (locally) destabilize the bilayer, and make the membrane leaky; subsequently, FA and/or DAG would mix with the intact lipids and form a patch of watertight phase Q227 that would eventually stop the leak. A similar process, averting the danger of leaks, could come into play in other processes, for example, membrane budding and fusion, which involve a local disruption of the diffusion barrier. This hypothesis is corroborated by the close chemical and physical similarities of phases Q227 and Q224. The same lipid (e.g., MO) is indeed present in these two phases, and the two phases are stable in the presence of excess water. The addition of FA (or DAG) transforms the bicontinuous structure of Q224, highly permeable to both water and oil, into the water-impermeable Q227. The process could thus be visualized as a switch between two states, one of high and the other of low conductivity, under the control of FA (and/or DAG). In support of these speculations is a study of phospholipase C-induced liposome fusion (Nieva et al., 1995) as well as the frequent observation of lipidic particles in membrane systems undergoing fusion (Verkleij, 1984). Moreover, DAG is known to be an essential component in the signal transmission pathway that cells utilize to recognize and respond to a variety of extracellular signals (Bell and Bums, 1991). This function is indeed preceded by a liberation of DAG that might well induce local and transient alterations of the membrane structure. Finally, the discovery in a wide variety of cells of membrane systems folded in space according to the symmetry of the IPMS (Hyde et al., 1997) is a fascinating generalization of the cubic phases (see also Luzzati et al., 1987). It is also worth mentioning that Delacroix, Nicolas, and GulikKrzywicki have observed that, in the photosomes of some annelids (Harmothoe lunulata), the lattice and symmetry of these "cubic membranes" may well vary with the physiological state of the organelles (in preparation).
Acknowledgments We are grateful to Christophe Oguey for kindly computing the sections of the G-surface of Fig. 5. This work was supported in part by grants from the Association Franceaise pour la Recherche M6dicale, the Ligue Nationale contre le Cancer, and the Association Franqaise contre les Myopathies.
List of Abbreviations 1D, etc. DAG DTAC FA FFEM FRAP
Average value of a function A(r) over the unit cell One-dimensional, etc. Diacyl glycerol Dodeeyltrimethylammonium chloride Fatty acid Freeze-fracture electron microscopy Fluorescence recovery after bleaching
37
IPMS L,H, Q" MO NMR PC PE PL
A~r)
Infinite periodic minimal surface without intersection 1-D lameUar, 2-D hexagonal, 3-D cubic phase of space group N~ (International Tables, 1952) Monoolein Nuclear magnetic resonance Phosphatidylcholine Phosphatidylethanolamine Phospholipid Normalized, dimensionless expression of the electron density p(r): A p ( r ) = [p(r) -
Types I and II XRS
]/[ 2]m
-
Structures with the hydrocarbon chains inside the structure elements (oil-inwater) and vice versa (water-in-off) X-ray scattering
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38
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