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Shape Transitions and Lattice Structuring of Ceramide-Enriched Domains Generated by Sphingomyelinase in Lipid Monolayers

Steffen Härtel ^* , María Laura Fanani ^* and Bruno Maggio ^*

^* Departamento de Química Biológica-CIQUIBIC, Facultad de Ciencias Químicas-CONICET, Universidad Nacional de Córdoba, Ciudad Universitaria, Córdoba, Argentina; and Centro de Estudios Científicos, Valdivia, Chile

Correspondence: Address reprint requests to Dr. Bruno Maggio, Departamento de Química Biológica-CIQUIBIC, Facultad de Ciencias Químicas, Universidad Nacional de Córdoba, Ciudad Universitaria, 5000 Córdoba, Argentina. Tel.: 054-351-4334-168; Fax: 054-351-4334-074; E-mail: bmaggio{at}dqb.fcq.unc.edu.ar.

	ABSTRACT

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS AND DISCUSSION CONCLUSIONS APPENDIX: DEFINITIONS SUPPLEMENTARY MATERIAL ACKNOWLEDGEMENTS REFERENCES

 
Sphingomyelinases (SMases) hydrolyze the membrane constituent sphingomyelin (SM) to phosphocholine and ceramide (Cer). Growing evidence supports that SMase-induced SMCer conversion leads to the formation of lateral Cer-enriched domains which drive structural reorganization in lipid membranes. We previously provided visual evidence in real-time for the formation of Cer-enriched domains in SM monolayers through the action of the neutral Bacillus cereus SMase. In this work, we disclose a succession of discrete morphologic transitions and lateral organization of Cer-enriched domains that underlay the SMase-generated surface topography. We further reveal how these structural parameters couple to the generation of two-dimensional electrostatic fields, based upon the specific orientation of the lipid dipole moments in the Cer-enriched domains. Advanced image processing routines in combination with time-resolved epifluorescence microscopy on Langmuir monolayers revealed: 1), spontaneous nucleation and circular growth of Cer-enriched domains after injection of SMase into the subphase of the SM monolayer; 2), domain-intrinsic discrete transitions from circular to periodically undulating shapes followed by a second transition toward increasingly branched morphologies; 3), lateral superstructure organization into predominantly hexagonal domain lattices; 4), formation of super-superstructures by the hexagonal lattices; and 5), rotationally and laterally coupled domain movement before domain border contact. All patterns proved to be specific for the SMase-driven system since they could not be observed with Cer-enriched domains generated by defined mixtures of SM/Cer in enzyme-free monolayers at the same surface pressure ( = 10 mN/m). Following the theories of lateral shape transitions, dipolar electrostatic interactions of lipid domains, and direct determinations of the monolayer dipole potential, our data show that SMase induces a domain-specific packing and orientation of the molecular dipole moments perpendicular to the air/water interface. In consequence, protein-driven generation of specific out-of-equilibrium states, an accepted concept for maintenance of transmembrane lipid asymmetry, must also be considered on the lateral level. Lateral enzyme-specific out-of-equilibrium organization of lipid domains represents a new level of signal transduction from local (nm) to long-range (µm) scales. The cross-talk between lateral domain structures and dipolar electrostatic fields adds new perspectives to the mechanisms of SMase-mediated signal transduction in biological membranes.

	INTRODUCTION

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS AND DISCUSSION CONCLUSIONS APPENDIX: DEFINITIONS SUPPLEMENTARY MATERIAL ACKNOWLEDGEMENTS REFERENCES

 
Phospholipases are a heterogeneous group of metabolic proteins that transduce lipid-specific signals at the membrane level (Wakelam et al., 1993; Exton, 1994; Krönke, 1999). Despite their structural and functional diversity, the activity of each lipolytic enzyme depends only on a few generic surface parameters. Lateral surface pressure, lipid composition and packing, phase coexistence, and surface electrostatics regulate enzymatic activities within narrow ranges (Jain and Berg, 1989; Honger et al., 1997; Muderhwa and Brockman, 1992; Maggio, 1966; Basañez et al., 1996). Due to the extreme sensitivity of their catalytic activity on subtle changes of the physicochemical conditions of the lipid interface, the precise molecular regulation of these enzymes can only be studied in systems with a rigorous control of the substrate organization (Bianco et al., 1989, 1990; Maggio, 1999; Grainger et al., 1990; Ransac et al., 1991; Honger et al., 1997; Fanani and Maggio, 1997; Jungner et al., 1997; Liu and Chong, 1999).

Many studies have shown that the activity of lipolytic enzymes is favored by membrane defects that can be introduced by changes of lipid composition, anisotropically organized lipid substrates, phase coexistence, connectivity of the lipid phase domains (percoregulation), and tensions along the interfacial plane (Jain and Berg, 1989; Honger et al., 1997; Muderhwa and Brockman, 1992; Maggio, 1966; Basañez et al., 1996; Roberts, 1996; Heinz et al., 1998; Gatt, 1999). In this context, the regulation of the activity of PLA₂ (Liu and Chong, 1999) and cholesterol oxidase (Wang et al., 2004) has been related to several critical amounts of cholesterol that induce specific regular superlattice structures over ranges that exceed the local molecular interactions in lipid surfaces (Somerharju et al., 1985, 1999; Chong, 1994; Virtanen et al., 1988, 1995; Chong and Sugár, 2002). PLA₂ activity has also been reported to be altered by Cer-induced defects in phosphatidylcholine interfaces (Huang et al., 1999; Fanani and Maggio, 1997). For sphingomyelinase (SMase)-driven conversion of sphingomyelin (SM) to ceramide (Cer) we could show that SMase not only sculptured the surface topography but also that the variations of the latter affected the time course of the reaction (Fanani et al., 2002). Since phospholipases generate second messengers that are involved in cascades of membrane-mediated signaling, the surface modulation of the activity of phospholipases represents a convergent point for biochemical and structural information exchange. In this context, local enzymatic alterations of chemical lipid structures are transduced to the intermolecular level through defined lipid interactions, leading to variations of membrane properties which, in turn, regulate activity and affect cross-communication between different phospholipase pathways (Fanani and Maggio, 1998). Lipid mixing-demixing processes and the concomitant structuring of segregated domains with different lipid composition or phase state profoundly influences precatalytic and catalytic steps of the phosphohydrolytic reactions (Bianco et al., 1991; Grainger et al., 1990; Fanani and Maggio, 2000; Fanani et al., 2002; Ruiz-Arguello et al., 2002).

Fundamental cellular processes like proliferation, differentiation, and cell death are triggered by the locally and temporally stimulated activation of different SMases that hydrolyze SM to phosphocholine and Cer (Levade and Jaffrézou, 1999; Hannun and Luberto, 2000; Szabo et al., 2004). Cer functions as a key pivotal compound that links the metabolism of phospho-, sphingo-, and glycosphingo-lipids, all of which can control phospholipase activity and membrane topology (Bianco et al., 1991; Basañez et al., 1996; Saéz-Cirión et al., 2000; Maggio, 1994; Maggio et al., 2004). Besides the conception of Cer as an important second messenger (Kolesnick et al., 2000), several authors have reported direct structural consequences of SMase-driven SMCer conversion in biological membranes. Primary structural consequences involve the formation of lateral Cer-enriched lipid domains (Holopainen et al., 1997, 2001) and the dilution of SM-enriched membrane rafts (Gulbins et al., 2004). Secondary structural consequences of lateral lipid reorganization concern physical membrane parameters like permeability (Ruiz-Arguello et al., 1996) as well as three-dimensional sculpturing of membrane vesicles (Holopainen et al., 2000), or the formation of apoptotic bodies (Tepper et al., 2000). Finally, structural reorganization has been reported to couple back to cellular signaling through the agglomeration of CD-95 and different ion channels in Cer-enriched membrane domains (Szabo et al., 2004; Gulbins et al., 2004).

Several studies have reported lateral phase segregation of Cer-enriched domains in model membrane systems (Holopainen et al., 1997, 1998; Huang et al., 1999; Carrer and Maggio, 1999; Carrer et al., 2003; Ruiz-Arguello et al., 2002). We provided the first direct visual evidence in real-time for SMase-induced formation of Cer-enriched domains in SM monolayers under precise control of the surface intermolecular packing (Fanani et al., 2002). The results revealed a bidirectional communication between effects taking place at the local catalytic level and the supramolecular surface organization. The present work employs improved time-resolved epifluorescence microscopy of the SMase-driven reaction and of predefined enzyme-free mixtures of SM/Cer in combination with advanced image processing routines. We disclose a series of morphologic transitions, a defined hexagonal surface organization (super-structures), and the generation of long-range topographic pattern (super-super-structures) of the evolving SMase-generated Cer-enriched domains and apply theories of lateral shape transitions (McConnell, 1990; Vanderlick and Möhwald, 1990) and dipolar electrostatic interactions between lipid domains (McConnell, 1991, 1993; Nassoy et al., 1996) to reveal the underlying physical properties that lead to the SMase-driven regulation of surface architecture.

	MATERIALS AND METHODS

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS AND DISCUSSION CONCLUSIONS APPENDIX: DEFINITIONS SUPPLEMENTARY MATERIAL ACKNOWLEDGEMENTS REFERENCES

 
Chemicals
Bovine brain sphingomyelin (SM) and ceramide (Cer) were purchased from Avanti Polar Lipids (Alabaster, AL). Bacillus cereus sphingomyelinase (SMase) was obtained from Sigma-Aldrich (Lot No. 48H4058, St. Louis, MO). The lipophilic fluorescent probe 1,1'-didodecyl-3,3,3',3'- tetramethylindocarbocyanine perchlorate (DiIC₁₂) was purchased from Molecular Probes (Eugene, OR). NaCl was roasted at 500°C for 4 h.

Solvents and chemicals were of the highest commercial purity available. Surface-active impurities in the solvents and buffers were checked as described in Fanani and Maggio (1997).

Lipid monolayers and epifluorescence microscopy
All experiments were carried out at room temperature. Isotherms of surface pressure and surface (dipole) potential as a function of the mean molecular area of SM, Cer, and their defined mixtures at different molar concentrations were determined at 25°C (Fanani and Maggio, 1998; Fanani et al., 2002). The values of mean molecular areas, surface potential per unit of molecular surface density (V/n), and resultant dipole moment density perpendicular to the water surface (µ) were calculated directly from the compression isotherms (Maggio, 1999). SM/DiIC₁₂ and SM/Cer/DiIC₁₂ monolayers (0.5 mol % of DiIC₁₂) were obtained by spreading 20 µl of lipid solution in chloroform-methanol (2:1) over a subphase of 10 mM Tris-HCl, 125 mM NaCl, and 3 mM MgCl₂, pH 8, until reaching a surface pressure of 0.5 mN/m (Fanani and Maggio, 1997). After solvent evaporation (10 min), the monolayer was compressed slowly to the desired surface pressure ( = 10 mN/m) and equilibrated for 15 min. As previously reported, SM and Cer show low lateral miscibility (<12%) and form Cer-enriched domains (Fanani et al., 2002). Epifluorescence microscopy (Zeiss Axioplan, Carl Zeiss, Oberkochen, Germany) was carried out at 25°C with a mercury lamp (HBO 50), a 20x objective, a rhodamine filter set, and an all-Teflon zero-order trough (Kibron µ-Trough S; Kibron, Helsinki, Finland) mounted on the microscope stage. Monolayer flow was restricted with an open-end Teflon mask with a vertical slit covering the objective and extending through the film into the subphase. Images (exposure times 0.1–0.3 s) were registered with a software-controlled (Metamorph 3.0, Universal Imaging, Union City, CA), charge-coupled device (CCD) camera (Micromax, Princeton Instruments, Downingtown, PA).

Determination of enzymatic activity
As previously reported, the determination of enzymatic activity is based upon the different cross-sectional areas of SM (84 Ų) and Cer (51 Ų) in lipid monolayers at 10 mN/m (Fanani and Maggio, 1997; Fanani et al., 2002). The enzymatic reaction was followed in real-time after injection of a diluted solution of SMase into the subphase of the reaction compartment (2 ml; 3.14 cm²), reaching a final bulk concentration of 228 pmol/ml. The reaction compartment consists of a circular trough with an adjacent reservoir compartment whose surfaces are connected through a narrow and shallow slit. The time course of the SMase-driven SMCer conversion was determined by recording the reduction of the total monolayer surface area at a constant surface pressure of = 10 mN/m. The constant surface pressure was maintained automatically by the film barriers of the surface balance which replenished a film of pure SM from the reservoir compartment (Fanani and Maggio, 1998). A detailed analysis of the two-dimensional kinetics was previously published and the rate constants of the different steps of the reaction were identified and determined (Fanani and Maggio, 2000). It was shown that the reaction lag time was due to a slow bimolecular surface activation of the enzyme, followed by a pseudo zero-order kinetic regime in which the reaction proceeded with a constant rate at a constant enzyme concentration (irreversibly adsorbed to the interface; see Fanani and Maggio, 2000). During this period the reaction rate is independent of the surface concentration of SM. The substrate is in excess with respect to the enzyme until the accumulation of the Cer causes a slowdown of the rate and progressive halting of the reaction (see Fig. 1 a, inset). We also performed experiments of film-transfer to enzyme-free subphases which showed that the steady-state, pseudo zero-order rate was unaltered. This demonstrated that the reaction was truly two-dimensional and carried out by the tiny catalytic amounts of enzyme, adsorbed irreversibly to the interface. In addition, experiments with iodinated radioactive enzyme indicated that the formation of Cer did not cause enzyme desorption that could lead to the slowing down of the reaction after the steady-state period. The determination of the amount of adsorbed enzyme yielded a substrate/enzyme ratio between 1.2 and 2.4 10⁴, which represents an excess substrate of 2000 times the value of the two-dimensional K_M (Fanani and Maggio, 2000). Additionally, the variation of the amount of adsorbed enzyme changes the metabolic rate proportionally, as long as the surface concentration of SM remains at least 10 times above K_M. Although the substrate is continuously replenished from the adjacent reservoir to the reaction compartment (Fanani and Maggio, 1998), Cer-enriched domains accumulate until 80% of the original surface concentration of SM in the reaction compartment is metabolized and the reaction halts (Fig. 1, this article; see also Fanani et al., 2002). This observation also supports the interpretation of the film-transfer experiment: SMase adsorbs irreversibly to the SM interface and increasing proportions of Cer do not impair the interfacial enzyme adsorption (Fanani and Maggio, 2000). Due to the accumulation of Cer-enriched domains, the rate eventually decreases and the reaction cannot be defined as a true zero-order kinetics, as in other hydrolytic reactions where soluble products desorb immediately from the interface (e.g., PLA₂ or PLC; Bianco et al., 1989, 1990); in these cases an indefinitely constant rate under true zero-order conditions is achieved as long as the substrate is replenished continuously from the adjacent monolayer reservoir. To point out this important difference, we denominate the SMase-catalyzed reaction as pseudo zero-order during the linear period of the catalysis.

View larger version (87K): [in this window] [in a new window]   FIGURE 1  Time course of SMase-driven SMCer conversion and simultaneous formation of Cer-enriched lipid domains at a constant surface pressure ( = 10 mN/m). Dark-shaded regions in b–e represent the formation of Cer-enriched lipid phases with unfavorable partition conditions for the lipophilic fluorescent dye DiIC12. (a) Number (open circles) and mean size (open triangles) of DiIC12-depleted domains as derived by segmentation of Cer-enriched lipid domains from the digital picture series (x,y-dimension = 450 x 354 µm). Symbols are connected by ß-splines. Number and mean area of DiIC12-depleted domains were calculated by image-processed epifluorescence microscopy (see Materials and Methods). Error bars were calculated until t4 (beginning of domain border contact) and defined the SD for the corresponding populations (N for counting experiments). (Inset) Time-dependent reduction of the total film area by the surface barrier movement of the barostat at constant surface pressure ( = 10 mN/m). (b–e) Representative microscopic CCD images (x,y-dimension 450 x 354 µm) of DiIC12 fluorescence in SM monolayers (high dye concentration/bright fluorescence) and in Cer-enriched domains (low dye concentration/fluorescence). The images visualize discrete stages at selected times t of the enzymatic reaction (b, t t2; c, t = t3; d, t = t4; and e, t t5. Compare to shaded vertical lines in a).

View larger version (106K): [in this window] [in a new window]   FIGURE 2  Shape transitions of Cer-enriched domains during the time course of SMase-driven SMCer conversion. (a) Mean values of the morphologic parameters: P2/A (open circles), the curvature of the border trajectory normalized by the length of border trajectory (i.e., curvature/perimeter; solid squares), and the number of saddle points of the border trajectories (open triangles) are connected by ß-spline curves. All parameters were derived by image-processed epifluorescence microscopy, as described in Materials and Methods. At t3, the rate of spontaneous domain formation falls abruptly and Cer-enriched domains start to grow in a linear manner until the percolation of the domains at t = t4 (compare to Fig. 1). Error bars define SD for P2/A and the normalized curvature. For the population intrinsic variation of the number of saddle points of the border trajectories, we show a representative normalized frequency distribution of a total of 725 Cer-enriched domains at t = t3''' (d). (b–f) Representative microscopic picture series (51.3 x 51.3 µm) of DiIC12-depleted Cer-enriched domains in SM monolayers visualize morphologically discrete stages at different times of the enzymatic reaction. (b, t3'; c, t3''; d, t3'''; e, t4; and f, t5 correspond to vertical shaded lines in a, this figure, and in Fig. 1 a. Domain borders in the upper row are highlighted by open edges. As the morphologic parameters in a suggest, the Cer-enriched domains start to grow in a circular manner, until successive branching is detected. To outline the transition from first-order to second-order branching, branches were sketched manually into the domains in d and e (upper row).

View larger version (72K): [in this window] [in a new window]   FIGURE 3  Formation of hexagonal Cer-enriched domain lattices as observed during the time course of SMase-driven SMCer conversion. (a) Lattice formation of Cer-enriched domains is monitored by different parameters. The mean values and the corresponding SD of the nearest domain distances between Cer-enriched domains are plotted for the center and border distances (solid and open circles, respectively). The mean values of the parameter of highest gap distance (hgd) are plotted as open triangles. The population intrinsic variation of this parameter can be estimated from d and g and c and f, (also see i, l, o in Fig. 4). Data points are connected by ß-spline curves. The figure insets (x,y-dimension = 94 x 72 µm) visualize the hexagonal lipid domain distribution at t3X and t3XX. (b–g) The parameter hgd is compared for randomly seeded domain centers (b and e) with the experimental situation established by SMase-driven SMCer conversion (c and f) at the beginning of the spontaneous domain formation (t3) (b and c) and before the percolation of the Cer-enriched domains (t4) (e and f). In the model systems (b and e), the number of the seeded domain centers reflects the conditions of the corresponding SMase-driven experiments (c and f). The areas b, c, e, and f represent x,y-dimensions of 450 x 354 µm. The histograms (d and g) plot the hgd-frequency distribution for randomly seeded domain centers (open columns) and the enzymatically generated domain centers (solid columns). The domain centers are connected with the first (b and c) and the first six nearest domain centers (e and f), reflecting the preferential-lattices formation in the SMase-driven system (c and f). In f, the hexagonal lattices are light-shaded to indicate the non-uniform distribution into a superlattice.

View larger version (96K): [in this window] [in a new window]   FIGURE 4  Comparative formation of Cer-enriched domain lattices as observed in defined mixtures of SM/Cer (left column) and during the time course of SMase-driven SMCer conversion (center column). The surface pressure in both systems is = 10 mN/m. Picture frames in the left and the center columns present x,y-dimensions of 450 x 354 µm. Amplified insets in j, k, m, and n have x,y-dimensions of 112.5 x 88.5 µm. The histograms (right column) present the parameter of highest gap distance for the defined mixtures of SM/Cer (shaded columns) and for the SMase-driven SMCer conversion (solid columns). The fraction of Cer increases from 2 mol % (a–c); 5 mol % (d–f); 20 mol % (g–i); 30 mol % (j–l); to 50 mol % (m–o).

View larger version (51K): [in this window] [in a new window]   FIGURE 6  Repulsive electrostatic interdomain energies between Cer-enriched domains generated during the time course of SMase-driven SMCer conversion. (a) Mean values of the interdomain energy are connected by ß-spline curves. Interdomain energies were calculated for each Cer-enriched domain with respect to the next-nearest-neighbor domain. Error bars define SD. The inset shows dipole moment densities µSM/Cer as calculated from the surface potential V measured in pure monolayers and in defined mixtures of SM/Cer at = 10 mN/m. The difference of the dipole moment densities between the Cer-enriched domains in the SM monolayer were calculated by µ = µCer – µSM = 6.14 · 10–3 D/Å2 (see text and Materials and Methods). The striped region marks energies below the thermal energy W(T) = 4.08 · 10–21 J (T = 295 K). (b) Frequency distribution of the repulsive electrostatic domain energies at t = t3 (open columns) and t = t3X (shaded columns) of the SMase-driven enzymatic reaction. For each domain, the energy was calculated with respect to the first six nearest-neighbor domains. The arrow points out the thermal energy at T = 295 K. (c) Color-coded presentation of the repulsive dipolar domain energies between lipid domains at t = t3X of the SMase-driven enzymatic reaction (x,y-dimension = 450 x 176 µm). Energies between 1 · 10–21 J and 6 · 10–20 J are logarithmically scaled by the color bar. For each domain, the energy was calculated pixelwise with respect to the six nearest-neighbor domains.

View larger version (48K): [in this window] [in a new window]   FIGURE 7  Synopsis of multiple stages in the lipid domain organization induced by SMase-driven SMCer conversion. The timescale in the upper part of the diagram covers the entire period of the pseudo zero-order kinetics of the enzymatic conversion, which starts directly after the lag time (t2) and lasts until the constant SMCer conversions cease at t > t5. The total area covered by growing Cer-enriched domains is plotted in percent of the total monolayer area. Representative examples depict domain morphologies at three different stages of the enzymatic reaction. On top of the timescale, solid arrows indicate Cer concentrations used to compare defined mixtures of SM/Cer to the SMase-driven system (Figs. 4 and 5). Below the timescale, shaded arrows mark the entire set of SMase-induced transitions, which are listed in the lower bar charts: the first horizontal bar chart summarizes morphologic transitions of the Cer-enriched domains (Figs. 1 and 2); the second chart focuses on the domain lattice organization (Figs. 3 and 4); the third chart indicates changes of the interdomain energy (Fig. 6); the fourth chart marks the transition of uncoupled domain movement to directly coupled domain movement; and the fifth, lower dark-shaded chart shows the different kinetic steps of the enzymatic reaction as determined by the surface barrier movement (Fig. 1 a, inset).

View larger version (30K): [in this window] [in a new window]   FIGURE 5  Comparative formation of Cer-enriched domains as observed during the time course of the SMase-driven SMCer conversion (solid lines and symbols) and in defined mixtures of SM/Cer (shaded lines and symbols). (a) Nearest domain border distances between the Cer-enriched domains. (b) Mean size of the DiIC12-depleted Cer-enriched domains. The striped regions mark domain sizes which are below the theoretical critical areas for domain instabilities for the SMase-driven system (Ac 11 µm2, solid) and for the mixtures of SM/Cer (Ac 33 µm2, shaded) (see Results And Discussion). (c) Mean number of perimeter saddle points. Error bars define SD for the corresponding domain populations. Parameters were calculated for Cer concentrations of 2, 5, 20, 30, and 50 mol % in analogy to the representative picture frames in Fig. 4. For the SMase-driven SMCer conversion, data points for Cer concentrations of 10 mol % were added for better interpolation of the corresponding ß-spline curves.

The number of unconnected Cer-enriched domains per image frame; the connectivity of object domains in the binary object masks was defined with a four-neighbor algorithm. After that, unconnected objects were numbered and counted automatically in the corresponding image frames.

The area (A) of the lipid domains was calculated from the number of pixels in the segmented binary object masks and the known pixel size (0.684 x 0.685 µm²).

The object border trajectories enclosing the Cer-enriched lipid domains were parameterized by the Freeman chain code (Freeman, 1970). The calculation of the length of the border trajectories or perimeter P was accomplished as described before (Härtel et al., 2003).

The curvature of the object trajectories and the number of saddle points was also derived from the presentation of the object border trajectories in the Freeman chain code.

The zoom-invariant shape-sensitive parameter circularity (P²/A) was determined by the division of the square of the perimeter of a domain by its respective area.

For the calculation of the domain centers of the irregularly shaped Cer-enriched lipid domains, we used the calculation of the translation-, rotation-, and zoom-invariant moments according to Castleman (1996). In the course of their calculation, the centers of gravity [x',y'] are derived from the first- and zero-order order moments: x' = M₁₀/M₀₀ and y' = M₀₁/M₀₀.

For every segmented domain, two parameters were calculated to characterize the nearest domain distance. First, the minimum border distance (r_b) calculates the minimal distance from the border of each domain to the border of the closed domain neighbor. The minimum center distance (r_c) does the same with respect to the domain centers. Note that the nearest-neighbor with respect to the border distances is not necessarily the same nearest-neighbor with respect to the center distance.

The parameter highest-gap distance (hgd) is calculated as follows: 1), for each segmented Cer-enriched domain in an image frame, the domain centers are calculated as described above; 2), for each center, the Euclidean distances to the 10 most proximate domain centers are determined; and 3), distances are sorted by size into a vector, and the ranking position (1–10) of the distance with the highest gap to the following distance is defined as the hgd (for an hexagonal lattice structure the hgd-value will be 6; for a pentagonal lattice structure the hgd-value will be 5; etc.).

The electrostatic field E generated at a distance r_d from a unit domain area (one pixel: xy = 0.684 x 0.685 µm²) was calculated by In this equation, µ is the difference of the dipole moment densities of the lipid domains composed of pure Cer or SM (µ = µ_Cer – µ_SM, see Fig. 6), ₀ = 8.85 10^–12 [CV^–1 m^–1] is the dielectric constant in vacuum, and is the effective dielectric constant at the air/water interface (for the calculation of electric fields of lipid domains, 7 yielded good agreement with experimental results based on solvatochromic measurements in sphingolipid interfaces (Montich et al., 1985) and from the determination of the velocities of electrically charged microspheres (Nassoy et al. 1996). Following the latter authors, the energy W(r_d) acquired by a dipolar probe is given by the scalar product between the dipole µ' and E(r_d). For one unit lipid domain area, µ' is calculated by µ' = µ · xy, and the energy between two unit domain areas results in The sum over all pixel combinations of two domains A and B, (Eq. 1), finally yields the total interdomain energy between the respective domains. This procedure can be expanded successively to calculate the interdomain energies between a higher numbers of domains.

	RESULTS AND DISCUSSION

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS AND DISCUSSION CONCLUSIONS APPENDIX: DEFINITIONS SUPPLEMENTARY MATERIAL ACKNOWLEDGEMENTS REFERENCES

 
As reported previously (Fanani and Maggio, 1998), the SMase-driven SMCer conversion in SM monolayers was determined by following the reduction of the surface area on the reaction compartment at a constant surface pressure = 10 mN/m (Fig. 1 a, inset). The molecular kinetics underlying the different precatalytic and catalytic steps responsible for the shape of the reaction curve has been discussed in detail before (Fanani and Maggio, 2000):

1. SMase is injected into the subphase of the SM monolayer (first vertical shaded line in the inset of Fig. 1).
   
2. SMase partitions rapidly to the substrate film through a diffusion-limited process.
   
3. A lag-time period is due to a slow, precatalytic, bimolecular enzyme activation step at the interface.
   
4. SMase-driven SMCer conversion reaches a transient steady-state rate (pseudo zero-order kinetics).
   
5. The SMCer conversion is halted due to the surface enrichment in Cer which limits substrate availability (Fanani and Maggio, 2000; Fanani et al., 2002).
   

SMase-generated Cer-enriched domains undergo morphologic transitions
In Fig. 1 a, the SMase-driven formation of Cer-enriched domains in SM monolayers is characterized by the number and the mean area of the segmented DiIC₁₂-depleted areas in the digital picture series taken during the catalytic reaction (Fig. 1, b–e). The first shaded vertical line (t1 in Fig. 1 a) marks the injection of SMase into the subphase of the reaction compartment and t2 (Fig. 1, a and b) marks the beginning of detectable SMCer conversion by the reduction of the total film area. During a time period of 40 s (t2–t3), Cer-enriched domains form spontaneously at an approximately linear rate (12 s^–1). At t3 (Fig. 1, a and c), the rate of spontaneous domain formation abruptly decreases and the areas of Cer-enriched domains start to grow linearly until the domain borders cannot be separated any longer on the chosen microscopic scale (t > t4). That period correlates with the catalytic reaction entering, and remaining, in the pseudo zero-order steady state of the SMCer conversion (Fig. 1, a and d). At t > t5, Cer-enriched domains finally form a single connected phase whereas SMCer conversion persists at a slow rate until 80% of the total SM has been converted to Cer. At this point, only traces of the LE phase of the SM monolayer remain encapsulated between the Cer-enriched domains (Fig. 1, a and e).

During the linear growth of the mean areas of the Cer-enriched domains simultaneous to the steady-state reaction (t3–t4), several morphologic parameters reveal successive shape transitions which mark discrete shape instabilities of the two-dimensional domains (Fig. 2). Right after the spontaneous domain formation (t3) the mean number of saddle points of the domain border trajectories remains constant, until the parameter starts to grow steadily at t > t3'. In 1990, Vanderlick and Möhwald introduced the discrete mode (m [0, 1, 2, ...]) and the relative amplitude of undulation ( [0–1]) for the description of shape transitions from circular to regularly undulated lipid domains. With m and , the domain shape can be parameterized by the border trajectory R() = (1 + · cos(m · )) (Eq. 2), using polar coordinates ( [0, 2]) and the mean radius of the lipid domain . It should be emphasized that the number of saddle points of a border trajectory of a closed lipid domain (n) can only adopt even numbers n [0, 2, 4, ...] which are directly correlated to m by a factor of 2 (n = 2 · m). In Fig. 2, we derived n from all domain border trajectories segmented in the CCD-images without prior mode selection. In this manner, defects or impurities in the lipid phase which possess high numbers of border trajectory perturbations (see Fig. 1, b and c, and Fig. 2 c) are included in the plotted mean values. A closer look at the population statistics reveals that 85% of all segmented domains correspond to the group of freshly nucleated Cer-enriched domains that do not present any border trajectory undulations during the initial part of the SMase-driven Cer formation (t < t3', data not shown). Right after the spontaneous formation of Cer-enriched domains (t3), the circular population is characterized by a mean domain area (A) of A(t3) = 6 ± 3.2 (standard deviation, i.e., SD) µm². The domain areas continue to grow in a circular manner until first-domain border undulations can be detected at t3'. At this time, the domains have almost doubled their area to A(t3') = 11 ± 4.5 µm² (Fig. 2, b and c). At t > t3' the number of perimeter saddle points (n) grows steadily into an average number of 18 (corresponding to m = 9 border undulations), before the domain borders start to touch at t4 (Fig. 2, d–f). At this time, the kinetics enters the end of the pseudo zero-order steady-state catalysis and the reaction rate falls (Fig. 1, inset).

Based on the theoretical treatment of harmonic shape transitions from circular domains to shapes with a higher rotation symmetry (McConnell, 1990) or on computer simulations (Vanderlick and Möhwald, 1990), the critical radius r_m at which a circular domain becomes unstable with respect to a shape with a m-fold rotation symmetry (or border undulation) is given by r_m = d · e^Zm · e/µ²/4 (Eq. 3). In this equation, is the line tension at the domain boundary, µ is the difference in the dipole moment density between the segregated lipid domains and its surrounding lipid phase, d is the molecular distance between neighboring dipoles, and Z_m are shape transition exponents defined by the geometrical rotation symmetry m. We can determine r_m directly from the critical area of the domains at the point of the shape transition (t3'): r_m(t3') = (A(t3')/)^0.5 = 1.87 ± 0.35 µm. The frequency of the modes m for the Cer enriched domains after the first shape transition (t3') can be derived directly from the number of saddle points: m = n/2. The inset of Fig. 2 a shows a normalized histogram for a total of 725 Cer-enriched domains at t3''' whose frequency values follow a Gaussian-like distribution which centers between n = 12 and 14, corresponding to m = 6 and 7, respectively. Using Z_m=6 = 12.88/3 according to Vanderlick and Möhwald (1990) and calculating d = 9.2 Å from the mean distance between adjacent Cer molecules (d_Cer = 2 · r_Cer = 2 · (51 Ų/)^0.5 = 8.1 Å) and SM molecules (d_SM = 2 · r_SM = 2 · (84 Ų/)^0.5 = 10.3 Å), we derive the dimensionless number _{SMase, t3'} = µ²/ = 1/ln[4 · r_m/(d · e^4.29)] = 0.212 ± 0.008. The value relates the energy of the repulsive electrostatic interactions (µ²) to the energy of the border-minimizing line tension (), which are the determinant factors for equilibrium shapes of two-dimensional lipid domains. With _SMase and Z_m=0 = 3 for circular lipid domains in equilibrium, Eq. 3 opens a direct access to the theoretical equilibrium size (A_eq): A_eq = · (d · e³ · e^1//4)² = 8.84 ± 2.24 µm². In conclusion, SMase-generated, Cer-enriched domains are characterized by an equilibrium size A_eq 8.8 µm² which lies just between the size after the spontaneous domain formation A(t3) 6 µm² and the critical domain size for the first shape transition A(t3') 11 µm².

Further morphologic information is provided by the time course of the mean curvature of the border trajectories which are normalized by the perimeter (P) (Fig. 2 a). Right after the spontaneous domain formation (t3), the P-normalized curvature drops rapidly and passes over to its final constant level at t3''. A close observation of the domain morphology in the picture series (Fig. 2, d–f) reveals that the Cer-enriched domains maintain the P-normalized curvature through a combination of effects:

1. Cer-enriched domains perform consecutive shape transitions to higher modes m.
   
2. The relative amplitude of mode undulation increases successively from 0.25 at t3' to 0.5 at t4 (estimated values for the domain shapes).
   
3. The apexes of existing modes m undergo successive branching or bifurcation.
   

The evolution of the morphology of Cer-enriched domains by SMase activity can also be characterized in terms of thermodynamic first- and second-order phase transitions (McConnell, 1991). Apart from the spontaneous domain nucleation that fulfills the criteria for a first-order phase transition, the conversion from circular shapes to shapes of higher harmonics as well as the fractal-like branching belong in the category of continuous second-order phase transitions; these shapes are topologically equivalent since they do not include discontinuities during the transitions (Peitgen et al., 1998). Since the shape transition at t3''' occurs approximately in the middle of the pseudo zero-order kinetic regime (see Fig. 7), the domain shape and their two-dimensional organization (see below) appear to represent an optimal structural code, signaling the maintenance of efficient steady-state catalysis. On the other hand, the appearance of secondary-order branching between t3''' and t4 precedes the deviation of the reaction from pseudo zero-order kinetics, signaling a marked decrease of the reaction rate, and the gradual halting of SMCer conversion (Fig. 7).

SMase-generated Cer-enriched domains adopt hexagonal lattice formations
Complementing information about discrete stages in the organization of Cer-enriched lipid domains is provided by the nearest domain distances (Fig. 3 a). This parameter was calculated either with respect to the domain centers (r_c) (solid circles) or the domain borders (r_b) (open circles with the corresponding SDs). During the spontaneous formation of Cer-enriched domains (t < t3), both distances drop rapidly to 10 µm. After that, the nearest border distance drops at a rate of 0.012 µm/s to 7 µm whereas the nearest center distance increases up to a maximum value of 13 µm at t3^X. During this interval, the SD of the nearest border distance diminishes by a factor of 4. The increasing center distance and the diminishing SD of the border distances indicate specific interdomain interactions that organize the Cer-enriched domains directly after their spontaneous formation (t3). Without specific interactions, lipid domains are primarily subjected to random Brownian motion, which should not affect the average distribution of the domain distances (McConnell, 1991, 1993). Although the decreasing r_b could be explained by the growth of the domains, the reduction of the corresponding SD and the increase of r_c cannot. Lipid domain interactions are primarily governed by dipolar repulsion which exerts an ordering effect on the domain topology as soon as the repulsion energy competes with the thermal energy of magnitude k_bT (this point will be discussed in combination with Fig. 6 below). After t3^X, the decrease of the nearest border distance accelerates to a rate of 0.026 µm/s, reducing the nearest border distance to 3 µm at t3^XX. During this time interval, the nearest center distance drops only slightly down to 12 µm. At t > t3^XX, the decrease of the nearest border distance slows down to 0.008 µm/s until the apparent percolation of the domains at t4. At this time, the nearest center distance has only been reduced to 11 µm.

The visual perception of the organization of Cer-enriched domains during the SMase-driven SMCer conversion suggests the formation of a primarily hexagonal domain lattice (Figs. 1–3) which is also referred to as supercrystal or superstructure phases (McConnell, 1991). A perfect lattice formation with well-defined angular alignments cannot be expected in our experimental system, since size and shapes of the generated Cer-enriched domains are subjected to variations within their population. With the purpose of quantifying somewhat irregular domain lattices, we introduce the parameter of highest-gap distance (hgd) which indicates the type of lattice by reporting the frequencies of the number of closest nearest-neighbors to a domain in the lattice. To validate that hgd is an adequate descriptor for our system, we compared the frequency distributions of the hgd in stochastically originated model systems (Fig. 3, b and e) to hgd-frequency distributions derived from the SMase-driven experiment at two different stages of the enzymatic reaction (Fig. 3, c and f). The hgd-frequency distribution confirms that the domain centers are randomly distributed at the end of the spontaneous domain formation (t3, Fig. 3, a–d). At t4 instead, the value with the highest hgd-frequency proves that the SMase-driven system predominantly forms a hexagonal lattice (Fig. 3, f and g). Apart from this important quantitative conclusion, the direct visualization of the connected domain centers highlights similarities between the random system and the SMase-driven experiment at t3 (Fig. 3, b and c). Here, each domain center is connected to its nearest-neighbor, in accordance to the highest hgd-frequency (Fig. 3 d). At t4 instead (Fig. 3, e and f), each domain center is connected to its six nearest-neighbors, according to the highest hgd-frequency (Fig. 3 g). At this stage of the reaction (end of the pseudo zero-order, steady-state kinetics), a clear difference can be observed between the random model system and the SMase-driven experiment (Fig. 3, e and f).

The time course of the hgd-values during the SMase-driven SMCer-conversion depicts a surprisingly rapid organization of Cer-enriched domains from random distribution to a predominantly hexagonal domain lattice. Right after the spontaneous domain formation (t3), the mean values of the hgd (Fig. 3 a), the histogram (Fig. 3 d), and the CCD-image (Fig. 3 c) congruently support a random distribution of the Cer-enriched domains. At t > t3, the mean values of the hgd rise steeply, confirming that dipolar repulsion instantly exerts an ordering effect on the domain organization (see discussion of Fig. 6). During this period, the number of saddle points (border undulations) increase steadily, indicating the predominance of repulsive dipolar energy over the border line-tension. At t3^X, the Cer-enriched domains have already adopted a predominantly hexagonal lattice formation. At this time, the transition between first- and second-order branching takes place (Fig. 2, a–d, and Fig. 7) and the enzymatic reaction enters the pseudo zero-order regime (Fig. 1 a, inset, and Fig.7). The predominantly hexagonal lattice formation is maintained until first domain borders start to touch at t > t4 (Fig. 3 f). Non-uniform clustering of the more regular hexagonal lattice units formed by the domain centers is clearly noticeable in Fig. 3 f, indicating an even higher level of superlattice structuring. The latter also shows a self-similar organization in the long-range with a fractal dimension of 1.83–1.86. In contrast, the random distribution with the same number of domain centers does not form self-similar structures (Fig. 3 e) and has a fractal dimension between 1.97 and 1.99 indicating no self-similarity (indistinguishable from the Euclidean dimension of 2 for a nonfractal surface).

Cer-enriched lipid domains generated by SMase activity or mixtures of SM/Cer adopt different morphologic properties and lattice organization
As we have shown in a previous publication (Fanani et al., 2002), mixtures of SM/Cer form a high number of Cer-enriched domains which cover a higher percentage of the total lipid monolayer area than the SMase-driven system at equal Cer concentrations. Finally, percolation of the domains occurs at lower Cer concentrations in the enzyme-free SM/Cer-mixtures. Figs. 4 and 5 reveal substantial differences in the lateral organization and in the morphology of Cer-enriched domains. The lattice organization of Cer-enriched domains generated by SMase activity is compared to domains generated by defined mixtures of SM/Cer at concentrations of 2, 5, 20, 30, and 50 mol % Cer in Fig. 4. At Cer-concentrations of 2 mol %, the hgd-frequency distribution indicates randomly distributed lipid domains in both systems (compare Fig. 4 c to Fig. 3, b–d). At Cer-concentrations of 5 mol %, the hgd-frequency distribution shifts to the right, indicating first repulsive interactions between the domains in both experimental systems (Fig. 4, d–f). At Cer-concentrations of 20 mol % (Fig. 4, g and h), the hgd-frequency distribution has strongly shifted to the right (Fig. 4 i). For the SMase-driven system, the distribution provides a sharp maximum at an hgd of six neighbors. The domains formed by the mixtures of SM/Cer also differ from randomly distributed lipid domains, but 1), the frequency distribution is significantly broader in comparison to the SMase-driven system; and 2), the most frequently formed lattice structure includes five, instead of six, nearest-neighbors. At Cer-concentrations of 30 mol %, the hgd-frequency distribution does not indicate any further increase in the order of the SMase-driven system (Fig. 4 f). For the domains formed by the SM/Cer-mixture instead, the order increases slightly, but the most frequent lattice structure still includes only five instead of six nearest-neighbors and has a broader distribution. At Cer-concentrations of 50 mol %, the hgd-frequency distributions shift slightly to the left for both experimental systems which is probably due to advanced percolation of the Cer-enriched domains (Fig. 4 m), and due to first touching domain borders (Fig. 4 n). In summary, Cer-enriched domains generated by mixtures of SM/Cer do not spontaneously form hexagonal domain lattices. Instead, hexagonal lattice formation is a defined feature of Cer-enriched domains generated by the SMase-driven SMCer conversion.

In addition to the system-specific lattice organization of Cer-enriched domains (Fig. 4), Fig. 5 contrasts further domain properties in both experimental setups. First, Fig. 5 a parameterizes the packing of the lipid domains by the nearest distance between adjacent domain borders. Cer-enriched domains of the SMase-driven system (solid triangles) are packed more closely than domains generated by defined mixtures of SM/Cer (shaded triangles). At low Cer concentrations (2–5 mol %), the differences are more pronounced than at higher Cer concentration (20–50 mol %). These differences can also be perceived visually in the corresponding picture frames (Fig. 4). Second, the domain size (Fig. 5 b) and shape (Fig. 5 c) differ in both experimental systems. For the SMase-driven monolayer, the domain size (solid circles) and the number of domain border saddle points (solid squares) rise with increasing Cer concentration. For the defined mixtures of SM/Cer instead, both parameters decrease up to Cer concentrations of 20 and 30 mol % before they increase again up to Cer concentrations of 50 mol % (shaded circles and squares). At 20 and 30 mol %, the vast majority of these domains adopt circular shapes (compare to Fig. 4, g and j) with mean domain areas of A_20mol% = 14.9 ± 10.6 µm² and A_30mol% = 19.1 ± 14.9 µm². Since Cer-enriched domains formed freely in the SM/Cer monolayer, Eq. 3 (see Supplementary Material) offers a direct access to : _{SM/Cer,20mol%} = µ²/ = 1/ln[4 · r₀/(d · e³)] yields 0.163 ± 0.007, respecting Z₀ = 3 for circular Cer-enriched domains (McConnell, 1990, 1991) with an equilibrium radius of r₀ = 2.18 ± 0.67 µm, and d = 9.4 Å as calculated above. In the same manner, we calculated _{SM/Cer,30mol %} = 0.159 ± 0.007 for a Cer-concentration of 30 mol %. The determination of _SM/Cer from the equilibrium condition allows us in this case to calculate the critical domain area (A_c) which defines when the circular domain shapes become unstable and adopt higher modes m (McConnell, 1990; Vanderlick and Möhwald, 1990). In accordance to the theory of shape transition, circular shapes can only be stable for A < A_c (A_c = · (d · e^10/3 · e^1//4)²), which yields 27.8 ± 11.04 or 37.9 ± 15.6 µm² for 20 or 30 mol % Cer, or a mean critical area of A_c 33 µm², respectively (see Fig. 5 b). For the SM/Cer-mixture, we can actually observe enhanced formation of undulated shapes for domain areas A > A_c (compare Fig. 4, a, d, and m; and Fig. 5 b).

As shown, _SM/Cer is much smaller than _SMase,t3' = 0.212 calculated for the SMase-driven system during the first shape transition (see above). Using the experimental values for µ (determinant parameter for lattice organization and domain size/shape, see Fig. 6 a and discussion below), we can calculate the line tension = µ²/ (the second determinant parameter for domain size/shape). The ratio _SMase/_SM/Cer = ((6.14 · 10^–3 D/Ų)² / _SMase) / ((1.27 · 10^–3 D/Ų)²/_SM/Cer) yields 16.5 or 17.5 for Cer-concentrations of 20–30 mol %, indicating much stronger line tension for the SMase-driven system. On the other hand, the ratio reveals that for the SMase-driven system the repulsive dipolar interaction energies are even more significant. The theory of shape transition allowed us to calculate the critical domain area A_c from the determination of the equilibrium area A_eq of the Cer-enriched domains generated by the SM/Cer-mixture. On the other hand, we could calculate the equilibrium domain area A_eq from the determination of the critical area A_c at the first shape transition in the SMase-driven system. The value A_eq in the SMase-driven system resulted to be approximately twice as high, and A_C even three times as high (see Fig. 5 b) as the values determined for the SM/Cer-mixture. According to these values, we can observe that SMase-generated Cer-enriched domains expose higher modes than the corresponding domains of the SM/Cer-mixture (Fig. 4, g, j, and m).

In summary, our results demonstrate that neither morphologic properties nor hexagonal lattice formation of Cer-enriched domains generated by SMase activity can be reproduced by enzyme-free mixtures of SM/Cer. The differences in A_eq, A_C, , µ², and are not only valuable descriptors for the observed domains, they further indicate a different molecular organization of the Cer/SM lipids within the respective Cer-enriched domains. The dipole moment density µ of lipid layers results from the hydrocarbon interior (mainly the terminal C-H bonds of the acyl chains), the headgroups, and the first few water layers adjacent to the interface (Brockman, 1994; Langner and Kubica, 1999). Since Cer-enriched domains are more compact (Fanani et al., 2002), ordered, and less fluid than SM layers (Holopainen et al., 1997, 1998), the resultant alignment of the terminal C-H bonds of the acyl chains between adjacent lipids increase the dipole moment density in Cer-enriched domains in comparison to SM-enriched regions (Fanani, 2001). Additionally, the ratio indicates that the Cer-enriched domains formed by the SMase-driven system are either packed with a higher order, or exclude a higher proportion of remaining SM, than the Cer-enriched domains of the SM/Cer-mixture. Our previous data (Fanani et al., 2002) supports the latter explanation, inasmuch as the total area covered by Cer-enriched domains of the SM/Cer-mixture was significantly larger than the total area covered by SMase-generated, Cer-enriched domains at the same Cer concentration.

Although the surface pattern of the SMase-driven system could not be reproduced by defined mixtures of SM/Cer, similar features have been observed in other lipid systems: nucleation of circular domains, circular growth, and successive second-order shape transitions toward higher modes have also been reported in gel phases in the fluid-gel coexistence regions of phospholipids during compression along pressure-area isotherms (Vanderlick and Möhwald, 1990; McConnell, 1991). Additionally, flower-like Cer-enriched domains with modes between 6 and 7 are formed by Cer_24:1:DMPC monolayers at surface pressures of 30 and 40 mN/m and at a molar ratio of 20:80 (Holopainen et al., 2001). At a molar ratio of 70:30, the same components formed fractal-like domains at surface pressures between 5 and 40 mN/m. Unfortunately, the authors did not discuss nor provide a quantitative evaluation of the lateral domain organization.

Reciprocal action among interdomain energy, morphologic transitions, and lateral organization of Cer-enriched domains
Repulsive interactions at the molecular (lipid) or the supramolecular (domain) level in combination with two-dimensional phase immiscibility can provide important driving forces for surface organization. One example at the molecular level is the regular distribution of sterols in phospholipid bilayers on the basis of the lipid superlattice model (Somerharju et al., 1985; Virtanen et al., 1988, 1995). According to this model, lipid components with a different cross-sectional area than the surrounding lipids introduce lateral tensions that are minimized when the components adopt a regular distribution inside the matrix (Somerharju et al., 1999). Among other effects, regular lipid distributions have been proposed to control membrane lipid composition and asymmetry through the regulation of membrane-active enzymes. In this context, molecular superlattices formed by cholesterol have shown to regulate the metabolic activity for phosphohydrolytic enzymes like PLA₂ (Chong and Sugár, 2002; Liu and Chong, 1999). In further studies, PLA₂-activity has been affected by SMase-generated Cer in a surface pressure-dependent and molecular packing-dependent manner (Fanani and Maggio, 1997, 1998). Despite the identical hydrocarbon moieties of SM and Cer used in this study, SM and Cer are practically immiscible at a surface pressure of = 10 mN/m, and SM adopts a liquid-expanded state whereas Cer forms a very condensed monolayer (Fanani et al., 2002). Under these conditions, the mean molecular area of SM is 84 Ų whereas Cer occupies 51 Ų and resembles a molecular geometry of an inverted cone due to the small size of its polar headgroup. These geometrical features lead to lateral tensions that induce changes of the interfacial curvature or topology (Kolesnick et al., 2000) and have even been found to induce asymmetrical bilayer budding in SM liposomes on a micrometer scale (Holopainen et al., 2000). Nevertheless, regular, lattice-like Cer distributions in lipid membranes have not yet been observed and all available publications hint at the formation of segregated Cer-enriched lateral domains (Holopainen et al., 1997, 1998; Szabo et al., 2004) or Cer-enriched membrane platforms (Gulbins et al., 2004). Our own findings that SM and Cer are mutually immiscible (Fanani et al., 2002) also contradict a possible regular Cer distribution. As shown in Figs. 3 and 4, SMase-generated, Cer-enriched domains form superlattices that are not equivalent to the molecular superlattices discussed above. But, following the concepts of entropy, regular patterns intrinsically possess a higher content of information than irregular patterns, and can convey information between different scales via the underlying lattice forces. Although molecular superlattices close the communication gap between single lipid headgroup distances (nanometer scale) up to a few lipid headgroup distances of <10 nm (Somerharju et al., 1999), domain superlattices actually reach the 10-µm scale via repulsive interdomain energies resulting from the intrinsic dipole moment density µ (Fig. 3 a and Fig. 6).

Under certain assumptions, the dipole moment density µ_X of a lipid class X in a monolayer perpendicular to the air-water interface can be calculated from the surface dipole potential V (Brockman, 1994; Cseh and Benz, 1999). We determined V in pure monolayers of SM and Cer, and in defined mixtures of SM/Cer at = 10 mN/m (Fanani, 2001). We obtained V = 270, 285, 300, 318, 336, 357, 419, and 500 mV (maximum mean plus SE, ±30 mV) at 0, 10, 20, 30, 40, 50, 75, and 100 mol % [Cer]. Since SM and Cer are practically immiscible, these experimental values are within 10% of the values calculated for fully immiscible monolayers. From these values and the corresponding mean molecular areas, we calculated the dipole moment densities µ_SM/Cer: 7.16 · 10^–3, 7.55 · 10^–3, 7.97 · 10^–3, 8.43 · 10^–3, 8.93 · 10^–3, 9.47 · 10^–3, 11.1 · 10^–3, and 13.3 · 10^–3 D/&