A reversible abnormal form of myelin: an X-ray scattering study of human sural and rat sciatic nerves.

A sural nerve dissected from a recently dead patient displayed an unusual X-ray diffraction pattern, suggesting that in situ and at the time of the patient's death the myelin sheaths were in a swollen state. Diffraction patterns of the swollen type were also recorded from: (1) a sural nerve from the corpse of a neurologically healthy person after soaking the nerve with Ringer solution at pH 5.5; (2) sciatic nerves dissected from rat cadavers at increasing time after death. In all the cases the swollen patterns reversed to the native type upon superfusion with Ringer solution at pH 7.3. The postmortem effect is to decrease the pH of the fluids surrounding the nerves in the cadavers. Our experiments show that the early postmortem processes have the effect of acidifying PNS nerves and that as a consequence of acidification the myelin sheaths swell.

Physical structure of the excitable membrane of unmyelinated axons: X-ray scattering study and electrophysiological properties of pike olfactory nerve.

The aim of this work was to elicit correlations between physical structure and physiological functions in excitable membranes. Freshly dissected pike olfactory nerves were studied by synchrotron radiation X-ray scattering experiments and their physiological properties were tested by electrophysiological techniques. The scattering spectra contained a sharply oriented equatorial component (i.e. normal to the nerve axis), and an isotropic background. After background subtraction, the equatorial component displayed a weak and fairly sharp spectrum of oriented microtubules, and a strong and diffuse band of almost the same shape and position as the band computed for an isolated myelin membrane. We ascribed this spectrum to the axonal membranes. Under the action of temperature and of two local anesthetics, the spectrum underwent a contraction (or expansion) in the s-direction, equivalent to the structure undergoing an expansion (or contraction) in the direction perpendicular to the plane of the membrane. The main observations were: (i) with increasing temperature, membrane thickness decreased with a thermal expansion coefficient equal to -0.97(+/-0.19) 10(-3) degrees C(-1). The polarity and amplitude of this coefficient are typical of lipid-containing systems with the hydrocarbon chains in a disordered conformation. The amplitude and propagation velocity of the compound action potentials were drastically and reversibly reduced by lowering the temperature from 20 degrees C to 5 degrees C. (ii) Exposing the nerve to two local anesthetics (tetracaine and dibucaine) had the effect of decreasing membrane thickness. Action potentials were fully inhibited by these anesthetics. (iii) Upon depolarization, induced by replacing NaCl with KCl in the outer medium, approximately 25 % of the membranes were found to associate by apposing their outer faces. Electrophysiological activity was reversibly impaired by the KCl treatment. (iv) No detectable structural effect was observed upon exposing the nerves to tetrodotoxin or veratridine. Electrophysiological activity was fully impaired by tetrodotoxin and partially impaired by veratridine. The main conclusions of this work are that axonal membranes yield highly informative X-ray scattering spectra, and that these spectra are sensitive to the functional state of the nerve. These results pave the way to further studies of more direct physiological significance.

Malnutrition and myelin structure: an X-ray scattering study of rat sciatic and optic nerves.

Taking advantage of the fast and accurate X-ray scattering techniques recently developed in our laboratory, we tackled the study of the structural alterations induced in myelin by malnutrition. Our work was performed on sciatic and optic nerves dissected from rats fed with either a normal or a low-protein caloric diet, as a function of age (from birth to 60 days). By way of electrophysiological controls we also measured (on the sciatic nerves) the height and velocity of the compound action potential. Malnutrition was found to decrease the amount of myelin and to impair the packing order of the membranes in the sheaths.

Structural and electrophysiological effects of local anesthetics and of low temperature on myelinated nerves: implication of the lipid chains in nerve excitability.

X-ray scattering and electrophysiological experiments performed on toad sciatic nerves as a function of the exposure to either low temperature or tetracaine yielded the following results: (i) the main structural effect is to thicken the individual membranes, thus to stiffen the acyl chains and increase the repeat distance of the one-dimensional lattice, phenomena that are typical of lipid-containing systems with disordered chains; (ii) the electrophysiological effect is to decrease the amplitude and velocity of the compound action potential; (iii) the structural and physiological effects of the two agents are practically identical. Since the structural and the electrophysiological parameters have different origins in the nerves (the structure regards the myelin sheath, the electrical signals originate at the nodes of Ranvier) it is inferred that tetracaine and low temperature exert similar effects on the membranes of both the myelin sheath and the nodes of Ranvier. Also, since local anesthetics act by inhibiting the Na+ channels, these observations suggest that the acyl chain conformation modulates the channel function and thus the generation of action potential.

The action of local anesthetics on myelin structure and nerve conduction in toad sciatic nerve.

X-ray scattering and electrophysiological experiments were performed on toad sciatic nerves in the presence of local anesthetics. In vitro experiments were performed on dissected nerves superfused with Ringer's solutions containing procaine, lidocaine, tetracaine, or dibucaine. In vivo experiments were performed on nerves dissected from animals anesthesized by targeted injections of tetracaine-containing solutions. In all cases the anesthetics were found to have the same effects on the x-ray scattering spectra: the intensity ratio of the even-order to the odd-order reflections increases and the lattice parameter increases. These changes are reversible upon removal of the anesthetic. The magnitude of the structural changes varies with the duration of the superfusion and with the nature and concentration of the anesthetic molecule. A striking quantitative correlation was observed between the structural effects and the potency of the anesthetic. Electron density profiles, which hardly showed any structural alteration of the unit membrane, clearly indicated that the anesthetics have the effect of moving the pairs of membranes apart by increasing the thickness of the cytoplasmic space. Electrophysiological measurements performed on the very samples used in the x-ray scattering experiments showed that the amplitude of the compound action potential is affected earlier than the structure of myelin (as revealed by the x-ray scattering experiments), whereas conduction velocity closely follows the structural alterations.

Order-disorder phenomena in myelinated nerve sheaths. VI. The effects of quaking, jimpy and shiverer mutations: an X-ray scattering study of mouse sciatic and optic nerves.

We report the X-ray scattering study of sciatic and optic nerve myelin from shiverer, jimpy and quaking mice mutants and from the corresponding controls. These three mutations are known to affect dramatically central nervous system (CNS) myelin and to induce comparatively minor alterations in peripheral nervous system (PNS) myelin. Scattering experiments and data reduction were carried out using the techniques and algorithms developed in our laboratory and previously applied to several problems involving the structure of myelin. In sciatic nerve the fraction of myelin elementary pairs of membranes (total myelin) decreases in shiverer and quaking nerves (by approximately 30%) but not in jimpy nerves; in all three mutants the fraction of myelin membrane pairs that are not regularly stacked in the sheaths (loose myelin), the average number of membranes per sheath and the packing disorder are the same as in the control nerves; the repeat distance D and the membrane distance Dcyt across the cytoplasmic space increase in shiverer and decrease in jimpy; in quaking, D also decreases and the decrease is smaller than in jimpy and is not specific for Dcyt; small changes are also observed in the electron density profiles. As for the optic nerve the myelin content decreases dramatically in the three mutants; the very weak signal attests to a tiny amount of pairs of membranes structurally similar to normal CNS myelin. It is surprising that the structure of CNS myelin should be almost normal in the absence of the major structural components, namely myelin basic protein (MBP) for shiverer of proteolipid protein (PLP) for jimpy. The question arises whether the composition of the residual pairs of membranes, operationally identified as myelin in the X-ray scattering experiments, mirrors the composition determined by chemical means on the fraction of nerve tissue histologically identified as myelin, or whether in all circumstances it remains approximately the same.

Topological properties of two cubic phases of a phospholipid:cholesterol:diacylglycerol aqueous system and their possible implications in the phospholipase C-induced liposome fusion.

Water dispersions of phospholipid:cholesterol:diacylglycerol may, under certain conditions, originate either the lipid- and water-permeable Q224 cubic phase, or the lipid-permeable but water-impermeable Q227 cubic phase. These results are discussed within the framework of the phospholipase C-induced fusion of liposomes [Nieva et al. (1993) Biochemistry 32, 1054]. It is suggested that the cubic phases Q224 and Q227 represent two classes of lipid organization, one promoting, the other hindering the mixing of aqueous contents that is characteristic of membrane fusion. In this context, inverted micelles appear to be the end point of the fusion process, rather than fusion intermediates.

Order-disorder phenomena in myelinated nerve sheaths: V. Effects of temperature on rat sciatic and optic nerves, and structural differences between the two types of nerve.

We describe in this work X-ray scattering and electron microscope studies of rat sciatic and optic nerves as a function of temperature. The scattering experiments were analyzed as described in the previous papers of this series: a variety of parameters were determined, some of which characterize the lattice disorder, others the structure of the motif. The main results are the following. All the parameters determined by the X-ray scattering study vary with temperature and the temperature-dependence is specific for the type of nerve (sciatic or optic). Most of the disorder-related parameters display a minimum or a maximum in the vicinity of physiological temperature (38 degrees C in rat); this observation, strongly supported by the electron microscope study, shows that the degree of organization of myelin is highest near physiological temperature. The structure of the motif, as revealed by the electron density profile, is fairly different in the two types of nerves (in contrast with the assumption made by previous workers); the structure also varies with temperature and the temperature-induced alterations are nerve-type specific. In the two types of nerve the thickness of the lipid bilayer varies with temperature as expected for a lipid-containing system with hydrocarbon chains in the disordered conformation. In sciatic nerve the thickness of the (thinner) cytoplasmic polar layer, which is also the layer most affected by lattice disorder in this type of nerve, decreases dramatically with increasing temperature. In optic nerve, in which lattice disorder predominantly affects the extracellular layer, the thickness of both the cytoplasmic and the extracellular layer is barely affected by temperature.

Cubic phases of lipid-containing systems. A translational diffusion study by fluorescence recovery after photobleaching.

The lateral diffusion coefficient of fluorescent lipid analogues incorporated in four cubic phases of lipid-water systems was determined by the modulated fringe pattern photobleaching technique. In two of the phases, Q230 and Q224, whose structure is bicontinuous, the diffusion is almost as fast as in the fluid lipid bilayers, and is essentially independent of the chemical nature of the probe. In the other two phases, whose structure consists of disjointed hydrocarbon micelles embedded in a water matrix (phase Q223, type I) and of water-containing micelles embedded in a hydrocarbon matrix (phase Q227, type II), the diffusion coefficient is strongly dependent on the chemical structure of the probe and on the topological type (I or II) of the structure. The conclusion is drawn that in the micellar phases the apparent diffusion mirrors the ability of the probe to hop from micelle to micelle.

Freeze-fracture electron microscope study of lipid systems. The cubic phase of space group Pm3n.

The cubic phase Q223 (space group Pm3n) of lipid-water systems has been studied by freeze-fracture electron microscopy. Four types of fracture planes were identified; all display highly ordered two-dimensional domains, each subdivided into subdomains related to each other by displacements and rotations connected to the symmetry of the space group. The images were filtered using cross-correlation averaging techniques and the filtered images were compared with the corresponding planar sections of the electron density map. The similarity of the two distributions was assessed via a mathematical parameter, the matching index, whose values were determined as a function of the apodization of the electron density map and of the position of the plane in the direction normal to the fracture. By definition, the best coincidence corresponds to an extremum of the matching index. Several conclusions were drawn. (1) The structure of the sample is well preserved in the replicas. (2) The "resolution" of the electron microscope experiments is remarkably close to that of the X-ray scattering study. (3) Of the two types of models that have been envisaged for phase Q223, the micellar is found to be in better agreement with the electron micrographs than the cagelike. (4) The symmetry of the space group is faithfully reflected in the electron microscope images; in particular, the presence of mirror planes rules out the non-centric of the two space groups that are compatible with the crystallographic data. (5) The crystallographic orientations of the fracture planes that are most frequently identified coincide with those of the most intense X-ray reflections; this observation was interpreted as an indication that the fracture propagates differently in the hydrocarbon and in the water volumes. (6) The thinner metal deposits in the replicas were found to coincide with the hydrocarbon regions of the fractures. (7) The fracture seems to be planar across the water matrix and the micelles seem to be removed from the replica and replaced by dips.

Cubic phases of lipid-containing systems. Elements of a theory and biological connotations.

It has recently been shown that the structure of two of the six cubic phases so far identified in lipid-containing systems is micellar, one (Q223) of type I, the other (Q227) of type II. The micelles of both phases belong to two distinct classes, those of each class being centred at one of the special positions of the space group. From the chemical viewpoint, phase Q227 seems to require a heterogeneous mixture of water-miscible and water-immiscible lipids, whereas phase Q223 has been observed with chemically pure lipids. Also, the area/volume ratio measured at the polar/apolar interface takes the same value in the two types of micelles of phase Q223, different values in those of phase Q227, in keeping with the notion that the area/molecule ratio is closely related to the chemical activity of the lipid components. The topological properties of the micellar phases are profoundly different from those of the bicontinuous phases. The bicontinuous cubic phases (Q230, Q224, Q229) are often presented as paradigms of the infinite periodic minimal surfaces (IPMS). Some authors have generalized that notion and sought in the IPMS a unified theory underlying the entire field of lipid polymorphism. These analogies entertain some confusion between the mathematical concept of surface and the physical notion of interface. A few electron density maps are presented to document the distance that separates the polar/apolar interfaces from the IPMS. The maps also show that some of the geometric singularities (points, lines, surfaces) of the structures coincide with the locus of the CH3 ends of the chains and with the very centre of the water matrix, i.e. with the regions where the short-range disorder is highest. We introduce the expression chaotic zones to designate these regions. In all the lipid phases the chaotic zones are found to occupy special geometric positions, either related to the symmetry elements or to the IPMS. It thus appears that it is energetically more advantageous to adopt an orderly disposal of the short-range disorder than to minimize the area of the polar/apolar interfaces. Finally, regarding the possible biological significance of lipid polymorphism, the point is stressed that among the phases that are observed in equilibrium with excess water (these phases are also the most likely candidates for a biological role) those with a cubic symmetry deserve special attention.(ABSTRACT TRUNCATED AT 400 WORDS)

Order-disorder phenomena in myelinated nerve sheaths. IV. The disordering effects of high levels of local anaesthetics on rat sciatic and optic nerves.

Sequences of 15 minute X-ray scattering spectra were recorded with rat sciatic and optic nerves, superfused with tetracaine-containing Ringer solutions. The spectra were analysed using the algorithm advocated in this series of papers. The main results, as a function of the time of exposure to tetracaine, were: the mean value of the repeat distance increases; its variance decreases; the average number of membrane pairs per coherent domain decreases; the fraction of isolated membrane pairs increases. Eventually, the spectra were observed to give way to the continuous intensity curve of a single, isolated membrane pair. At all stages of the experiment the continuous intensity curves were found to differ from one type of nerve to the other, and to be invariant, for each type of nerve, with respect to the tetracaine treatment. The X-ray scattering study clearly identified the nature of the structural differences between the two types of myelin sheaths: in that of native sciatic nerves, packing disorder preferentially affects the cytoplasmic space of the membrane pair, and tetracaine disrupts the packing in that space; in the myelin of optic nerves it is the external space that is preferentially affected by packing disorder and disrupted by tetracaine. The time-course of the structure parameters showed that, at any stage of the experiment, tetracaine acts preferentially on the more highly disordered regions of the structure and totally disrupts them. These results corroborate earlier conclusions reported in the previous papers of this series. An electron microscope study was also performed on tetracaine-treated nerves: the results, in close agreement with those of the X-ray scattering study, neatly confirm the conclusions given above. In a more general way, the remarkable agreement between the results of the analysis of the X-ray scattering spectra and the electron microscope observations strongly supports the validity of the physical model used in this series of papers and the correctness of the mathematical treatment that we advocate. Finally, the relations between this work and the work of others are discussed. It must be stressed that the present work bears on the toxic rather than on the anaesthetic effects of tetracaine.

Cubic phases of lipid-containing systems. The structure of phase Q223 (space group Pm3n). An X-ray scattering study.

The hexagonal (H) and the cubic (Q223) phases of the systems dodecyltrimethylammonium chloride-water and palmitoyllysophosphatidy choline-water have been studied by X-ray scattering techniques. The signs of the reflections of phase H were determined by a systematic study as a function of the water content, those of phase Q223 were assessed using a pattern recognition approach based upon the axiom that the histograms of the electron density maps of phases Q223 and H, extrapolated to the same concentration and properly normalized in scale and shape, are very similar to each other. In the case of phase Q223, all the sign combinations (the phi-sets) compatible with the observed reflections were generated, and each of the corresponding histograms was compared with the histogram of the map of phase H. One novelty of this work is the use of a highly sensitive criterion to estimate the similarity of the histograms, namely the distance in the six-dimensional space of the moments [mean value of (delta rho)n]1/n, for 3 greater than or equal to n greater than or equal to 8. In the two systems, the use of this criterion has led to the unambiguous choice of one electron density map. The maps show that the structure of phase Q223 consists of disjointed micelles (of type I), belonging to two different classes: those of one class are quasi-spherical in shape and are centered at the points a, those of the other class are disc-shaped and are centred at the points c. The results of this work rule out a structure formed by a cage-like distribution of rods enclosing a set of quasi-spherical micelles and is consistent with previous proposals. This is the second example, after that of phase Q227, of a micellar cubic phases in lipid-containing systems; all the known examples of phase Q223 are of type I, those of phase Q227 of type II.

Lipid polymorphism: a correction. The structure of the cubic phase of extinction symbol Fd-- consists of two types of disjointed reverse micelles embedded in a three-dimensional hydrocarbon matrix.

The X-ray scattering study of a cubic phase of extinction symbol Fd--, recently performed on a lipid extract (PFL) from Pseudomonas fluorescens [Mariani et al. (1990) Biochemistry 29, 6799-6810] has been extended to several other systems, all consisting of mixtures of water-miscible (MO, PC, PE, oleate) and of water-immiscible (FA, DG) lipids, plus water. In all of these systems the cubic phase was observed in the presence of excess water. Some inconsistencies observed between PFL and the other systems, the fact that in PFL one of the reflections of the cubic phase happened to coincide with the strongest reflection of the hexagonal phase, and the finding, in one of the original cubic samples of PFL kept in the cold for more than 3 years, that the intensity of one of the reflections had decreased dramatically all indicated that a nonnegligible amount of a hexagonal impurity was in fact present in the samples of PFL originally thought to contain a pure cubic phase. The intensities were corrected for that impurity and analyzed again using a pattern recognition approach based upon the axiom that the histogram of the electron density maps is invariant with respect to physical structure, when different phases are compared whose chemical composition is the same. The hexagonal phase provided the reference phase for the comparison. The moments mean value of (delta rho)n were used to compare the histograms.(ABSTRACT TRUNCATED AT 250 WORDS)

Order-disorder phenomena in myelinated nerve sheaths. III. The structure of myelin in rat optic nerves over the course of myelinogenesis.

An X-ray scattering study was performed on optic nerves dissected from rats aged from ten days to one year. The spectra were analysed using the procedure described in the previous papers of this series. Each experiment yields the values of a variety of parameters: the average D and the variance sigma D of the repeat distance, the average number mean value of N of motifs per crystallite, the fraction alpha loose of myelin that does not belong to the compact sheaths, the sets [idiff(h/D)] and [imotif(k/2D)] that suffice to define, respectively, the spurious scattering and the continuous intensity curve of the elementary membrane pair. A surprising result is that, in the native optic, as previously found in the swollen sciatic nerves, the stacking disorder affects the external space, whereas in native sciatic nerves the disorder affects the cytoplasmic space. An analysis of the evolution of the structure parameters as a function of the age of the animal and a comparison with the results previously obtained with rat sciatic nerves led to the following conclusions: the structure of the elementary membrane pair is constant throughout myelinogenesis; mean value of N is much smaller in optic than in sciatic nerves; mean value of N and the degree of myelination increase with age in the two types of nerve; D is smaller in optic than in sciatic nerves; in optic nerves, D decreases slightly with age, but in sciatic nerves it increases; sigma D is strongly age-dependent in optic nerves, but almost age-independent in sciatic nerves. In contrast to sciatic, the structure of optic nerve myelin was found to be almost insensitive to hypertonic solutions. Finally, a pair of electron density profiles was selected, quite similar to those selected previously in sciatic nerves, one corresponding to Caspar & Kirschner's the other to Worthington & McIntosh's proposals, neither of which can be ruled out according to the criteria used in this work.

Order-disorder phenomena in myelinated nerve sheaths. I. A physical model and its parametrization: exact and approximate determination of the parameters.

An algorithm is developed for the analysis of the X-ray scattering spectra of lamellar systems, by reference to a precise physical model. The model consists of identical planar lamellae (the motif), all parallel and stacked in a one-dimensional crystal with four types of defect: stacking disorder, finite size of the crystallites, and presence of diffuse and blank scattering. In addition, the spectra are distorted by collimation aberrations. In order to evaluate the effects of these distortions, the following assumptions are made: (1) beyond some point Slimit the intensity curve can be expressed as a function of a (small) number of parameters; (2) the blank scattering, restricted to very small angles, can be identified and eliminated; and (3) the diffuse scattering is entirely defined by the values of idiff(h/D) at the lattice Sh = h/D (h is a positive integer less than or equal to DSlimit). These assumptions lead to an expression of the whole of the intensity curve as a function of a finite number of parameters: the average D and the variance sigma 2D of the repeat distance, the average number [N] of lamellae per crystallite, the set [idiff(h/D)] and the set [imotif(k/2D)] (where k is a positive integer), which defines the structure of the motif. An algorithm is proposed to determine the value of the various parameters. The derivation of the algorithm involves several operations: construction in real space of periodic functions whose motifs are step-sections of the autocorrelation function; expression in reciprocal space, and in terms of the experimental scattering curves, of the Fourier transform of those periodic functions; analysis of the properties of the two functions. The algorithm is tested using a variety of simulated scattering curves whose parameters [imotif(k/2D)], [idiff(2/D)], D, sigma D, [N] (and collimation distortions) are within the range commonly encountered in experimental conditions. The results show that the values of the parameters retrieved by the algorithms are very close to those used in the simulation. The calculations are fast and easy to implement on a computer. The main virtues of the algorithm are (1) to determine the values of all the parameters at once, eliminating most of the intermediate (and questionable) manipulations (separation of signal from noise, discrimination of overlapping reflections, integration of the intensities) and (2) to yield the continuous intensity curve of a single motif.

Order-disorder phenomena in myelinated nerve sheaths. II. The structure of myelin in native and swollen rat sciatic nerves and in the course of myelinogenesis.

The algorithm described in the accompanying paper was applied to X-ray scattering experiments performed with rat sciatic nerves, either as a function of the age of the animal (4 to 30 days), or with adult nerves swollen in non-isotonic media. The results were all consistent with the model of disorder used in the theoretical treatment. The algorithm leads, in one step, from the data to the numerical values of the parameters, avoiding all intermediate manipulation. For each experiment a variety of parameters was determined: the average D and the variance sigma 2D of the repeat distance, the average number [N] of motifs per crystallite, the set [idiff(h/D)], which defines the diffuse scattering, the fraction alphaloose of myelin that does not belong to the compact sheaths, and the set [imotif (k/2D)], which suffices to define the continuous intensity curve of the motif imotif(s). Note the remarkable wealth of information, especially by contrast with conventional analyses which, as a rule, only yield the values of D and of the set [imotif(h/D)] (insufficient to determine the function imotif(s]. The function imotif(s) and the parameters D and sigma D (and thus the local structure of the myelin sheaths) were shown to be almost invariant in the course of myelinogenesis; what varies is mainly the total amount of myelin in the nerve and the number of membranes per sheath. Swelling agents have a dramatic influence on the X-ray scattering spectra, but in spite of the conspicuous variation of D, sigma D and [N] the structure of the motif is invariant. The structure of the motif was shown to be quite different in the native and in the swollen samples; the stacking disorder appears to involve mainly the cytoplasmic space in native myelin, the external space in swollen nerves. The very notion of electron density profile, when disorder is present, is discussed. Two criteria were proposed to select the "best" signs of the reflections: two sets came out at almost the same rank, one corresponding to Caspar & Kirschner's the other to Worthington & McIntosh's proposals, neither of which can be ruled out according to the criteria used in this work.

Polymorphism of a lipid extract from Pseudomonas fluorescens: structure analysis of a hexagonal phase and of a novel cubic phase of extinction symbol Fd--.

The phase diagram of the Pseudomonas fluorescens lipid extract is unusual, in the sense that it displays a cubic phase straddled by a hexagonal phase. The hexagonal phase was studied over an extended concentration range, and the reflections were phased on the assumption that the structure contains circular cylinders of known radius. The cubic phase, whose extinction symbol is Fd--, was analyzed by reference to space group No. 227 (Fd3m). The phases of the reflections were determined by using a novel pattern recognition approach, based upon the notion that the average fourth power of the electron density contrast mean value of (delta r)4 is dependent on chemical composition but not on physical structure, provided that the function delta r(r) satisfies the constraints mean value of (delta r) = 0 and mean value of (delta r)2 = 1. As a further constraint, a shape normalization is used, in the form of a Gaussian apodization of the intensities, which has the effect of normalizing the curvature of the autocorrelation function at the origin. We analyzed two cubic samples of different composition: for each of them we generated all the phase combinations compatible with the X-ray scattering data and we searched for those whose mean value of (delta r)4 best agrees with the hexagonal phase. Taking advantage of the favorable properties of the phase diagram, we carefully explored the effects of various parameters; we concluded that the chemical composition of the phases being compared must be identical, that the X-ray scattering data should not be truncated artificially, and that the apodization must be mild so that the curvature takes a value intermediate between those corresponding to the raw data of the two phases. When all these precautions were taken, mean value of (delta r)4 was found to be remarkably invariant; this conclusion is important in view of the possible usefulness of the novel technique in tackling ab initio--and at very low resolution--structural problems of more general interest. The structure of the cubic phase consists of a 3D network of rods joined tetrahedrally 4 by 4 according to a diamond lattice and of a family of quasi-spherical disjointed micelles; the core of the rods and of the micelles is polar, and the interstices are filled by the hydrocarbon chains (structure of type II). All the dimensions (diameter of rods and micelles, area per chain at the polar/apolar interface) are consistent with the chemical properties of the system.(ABSTRACT TRUNCATED AT 400 WORDS)