DSPC domains studied by Brewster angle microscopy

Chemistry and Physics of Lipids 133 (2005) 165–179

Temperature and pressure dependent growth and morphology of DMPC/DSPC domains studied by Brewster angle microscopy Alexandre Arnold, Isabelle Cloutier, Anna M. Ritcey, Mich`ele Auger∗ Department of Chemistry, Centre de Recherche en Sciences et Ing´enierie des Macromol´ecules, Universit´e Laval, Qu´ebec city (Qu´ebec), Canada G1K 7P4 Received 16 July 2004; received in revised form 30 September 2004; accepted 30 September 2004 Available online 11 November 2004

Abstract In this work, the temperature and pressure dependent growth of domains in DMPC/DSPC monolayers at various molar ratios was studied by Brewster angle microscopy. Upon compression, roughly discoidal domains with some branching are formed. Further compression leads to an increase in both the number and the average size of the domains, which range between ca. 5 and 20 ␮m. The isobaric heating of the monolayers results in a gradual decrease of the domain size until their disappearance. The size and morphology of the domains depend not only on equilibrium parameters such as temperature, pressure and composition, but appear to be also strongly dependent on non-equilibrium parameters such as the rate of perturbation. The comparison between our results and those previously published for bilayers allows us to infer that the growth behaviour in monolayers can be qualitatively but not quantitatively extrapolated to bilayers. © 2004 Elsevier Ireland Ltd. All rights reserved. Keywords: Brewster angle microscopy; Lipid monolayers; Domains; DMPC; DSPC; Nucleation theory

1. Introduction The lateral heterogeneity of biological membranes is now a well-established property (Vereb et al., 2003). It is believed to play a key role in important biological processes such as membrane protein binding, insertion and function (Brown and London, 2000; Mouritsen ∗ Corresponding author. Tel.: +1 418 656 3393; fax: +1 418 656 7916. E-mail address: [email protected] (M. Auger).

and Jørgensen, 1997; Simons and Ikonen, 1997), membrane permeability (Mouritsen and Jørgensen, 1995), and in plane molecular reactions (Edidin, 1997). In order to understand the physical processes which rule the existence, size and shapes of these domains, a series of model lipid mixtures have been studied by several techniques such as for example, atomic force microscopy (AFM) (Kaasgaard et al., 2001; Ratto and Longo, 2002; Sanchez and Badia, 2003), two-photon fluorescence spectroscopy (Bagatolli and Gratton, 2000b; Baumgart et al., 2003) and Monte Carlo simulations

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(Jørgensen and Mouritsen, 1995; Sug´ar et al., 1999). Among these model membranes, the binary mixture of dimyristoylphosphatidylcholine (DMPC) and distearoylphosphatidylcholine (DSPC) stands out as one of the most studied (Leidy et al., 2001; Morrow et al., 1991; Sankaram et al., 1992; Sug´ar et al., 1999; Vaz et al., 1989). The temperature-composition phase diagram of this system displays a broad biphasic region in which gel and liquid crystalline domains coexist (Foster and Yguerabide, 1979; Knoll et al., 1981; Shimshick and McConnell, 1973). The lateral structure of this system in supported or non-supported bilayers has recently been observed by AFM (Giocondi and Le Grimellec, 2004; Giocondi et al., 2001; Kaasgaard et al., 2003; Leidy et al., 2002) and two-photon fluorescence microscopy (Bagatolli and Gratton, 2000a). Monolayers at the air–water interface are extremely valuable model membranes (McConnell, 1991; M¨ohwald, 1990; M¨ohwald et al., 1995; Vollhardt, 2002). Experiments in which molecular area, surface pressure, temperature and chemical nature of the subphase are varied can easily be performed and by this means, a broad set of thermodynamic parameters, which characterize the monolayer can be accurately determined (Adamson, 1982; Gaines, 1966). Although transmembrane processes cannot be studied in monolayers, this system is very well suited to study processes at the membrane surface (Brezesinski and M¨ohwald, 2002). In addition to their role as model membranes, the monolayer is the biological state of pulmonary surfactants, which coat the alveolar air spaces in lungs (Discher et al., 1999; Veldhuizen and Haagsman, 2000). Since its initial development, Brewster angle microscopy (BAM) (H´enon and Meunier, 1991; H¨onig and M¨obius, 1991) has established itself as a simple and non-perturbing technique to characterize the lateral structure of monolayers on the ␮m length scale. Its non-perturbing character makes it an ideal technique to study phenomena in which nucleation processes are of major importance, such as domain formation. In the present study, we have used BAM to monitor domain formation in DMPC/DSPC monolayers at the air–water interface. Experiments in which the monolayers were compressed or heated were performed at different DMPC/DSPC molar ratios. We have also determined the importance of the history of the sample in terms of the conditions of deposition and rate of pertur-

bation and provided a qualitative and semi-quantitative explanation of these effects in the context of classical nucleation theory. In order to determine to what point and in which conditions the growth behaviour in monolayers can be extrapolated to bilayers, a strong emphasis is put on determining the similarities and differences between these two model membranes. It should be noted that BAM images of the same system have recently been published (Kubo et al., 2001). In that work however, a single temperature was probed at the extreme low end of the phase coexistence region. In the present study, we provide results at variable surface pressures at a temperature, which is well within the biphasic region as well as results of variable temperature experiments, both of which are necessary to discuss the relationship with bilayers.

2. Experimental The lipids dimyristoylphosphatidylcholine and distearoylphosphatidylcholine were purchased from Avanti Polar Lipids (Alabaster, AL) and used without further purification. Solutions with different DMPC/DSPC molar ratios in chloroform were prepared at a fixed concentration of 1 mg ml−1 . For all the experiments, the solutions were spread on distilled water purified with a Millipore Milli-Q filtering system with a resistivity of ≥ 18.1 M
cm. In all cases, the pH of the subphase was 5.5 and the chloroform was left to evaporate for 30 min before the beginning of the experiments. The experimental setup consisted of a commercial computerized Langmuir trough (NIMA technology, Coventry, England) upon which was mounted a BAM 2 plus Brewster angle microscope manufactured by Nanofilm Technologie (G¨ottingen, Germany). The isothermal experiments were carried out by setting the subphase at the desired temperature prior to the deposition of the lipid solution and subsequent compression. For the isobaric experiments, the solutions were spread at 20 ◦ C, the monolayer compressed to the target surface pressure, and the Langmuir trough controller set to the isobaric mode. Surface pressures were measured using a filter paper Wilhelmy plate. The Langmuir trough and the Brewster angle microscope being in a closed environment, no significant evaporation of the subphase was observed during the experiments.

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Prior to imaging the monolayer, the incident 532 nm wavelength Nd:YAG laser and the CCD camera were set at the Brewster angle (i.e. the angle at which no reflection on pure water could be detected). The BAM image size is 220 ␮m × 275 ␮m and the lateral resolution is 1 ␮m. As the objects at the air–water interface were highly mobile, single snapshots in which only the central region is in-focus were recorded. The necessary geometrical corrections and the evaluation of domain sizes were performed with the Nanofilm Technologie software provided with the microscope.

3. Results 3.1. Growth and morphology as a function of lateral pressure 3.1.1. Isotherms We have first performed a series of isothermal compressions at 30 ◦ C for different DMPC/DSPC molar ratios. The isotherms, which are presented in Fig. 1, show that for pure DMPC the surface pressure starts ˚2 to increase smoothly at a molecular area of 120 A −1 molecule . As the available surface area is further decreased, the slope of the isotherm increases gradually indicating that the monolayer is increasingly rigid. This behaviour can be described as the gradual compression of a liquid expanded phase (LE). The isotherm of pure DSPC is almost flat down to a molecular area of

Fig. 1. Surface–pressure isotherms at 30 ± 1 ◦ C for DMPC/DSPC monolayers at different molar ratios.

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˚ 2 molecule−1 where the surface pressure abruptly 50 A increases, the steep slope of the isotherm being characteristic of a considerably rigid condensed film. These isotherms are in good agreement with those found in the literature (see Mingotaud et al., 1993 and references therein). The isotherms of the binary mixtures lie in between the isotherms of the pure lipids, the film becoming more expanded as the DMPC/DSPC molar ratio is increased, but do not follow the additivity rule, Am = x1 A1 + x2 A2 , describing the behaviour of an ideal mixture (Adamson, 1982). The deviation from this rule was positive in all cases, the mean molecular areas of the monolayer being systematically higher than the sum of the molecular areas of the two pure components, but decreased as the monolayers were compressed. A maximum positive deviation to the ideal behaviour was measured for the equimolar mixture and a surface pressure of 5 mN m−1 . No horizontal plateau was observed in any of the isotherms but a kink, or a change in slope, could be detected for the (25:75) mixture. The collapse pressures which varied between 50 and 62 mN m−1 were relatively constant, possibly indicating a low miscibility (Sanchez and Badia, 2003). 3.1.2. Brewster angle microscopy BAM images of the monolayers during the isothermal compression process are shown in Fig. 2. Initially, no domains can be observed for the pure DMPC monolayer but the image becomes progressively brighter as the monolayer is compressed, indicating an increase of monolayer surface density. Small bright domains (≤ 5 ␮m) become visible at ≈ 15 mN m−1 for the (75:25) mixture. Upon further compression, the total number of domains increases while their sizes remain approximately constant. Note that in order to distinguish between an increase in the number of domains from a decrease of the interdomain distance, the total number of domains was obtained by multiplying the number of domains in the field of view by the available surface area. In Brewster angle microscopy, condensed phases are bright and expanded phases dark (H´enon and Meunier, 1991; H¨onig and M¨obius, 1991) due to differences in surface density and/or monolayer thickness. The observed phenomenon is therefore the growth of a condensed lipid phase in an expanded phase. The case of the (50:50) mixture is somewhat more complex. At

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Fig. 2. Effect of surface pressure on DMPC/DSPC systems at different molar ratios, T = 30 ± 1 ◦ C.

≈ 10 mN m−1 (not shown), larger domains then for the (75:25) ratio appear (between 5 and 10 ␮m, the longest distance within the flower-like domain is taken as the characteristic size). As the monolayer is compressed, the number of domains very slowly increases and their mean size increases from 10 to approximately 15 ␮m. At the lower DMPC/DSPC ratio of (25:75), domains with sizes ca. 10 ␮m and irregular shapes start to appear at ≈ 5 mN m−1 . With increasing surface pressure, whereas the number of domains remains nearly constant, their size gradually increases up to an average of 20 ␮m. At a surface pressure of 30 mN m−1 , the flowerlike domains start to join, leaving large areas of the monolayer occupied by the expanded phase. Finally, the pure DSPC monolayer appears as a bright surface from 5 mN m−1 to the collapse pressure. The phospholipid film has a uniform aspect except at 5 mN m−1 ,

where some texture might indicate the presence of heterogeneities. Observing the BAM images in Fig. 2 for a given surface pressure is equivalent to examining a cross section of the system temperature composition phase diagram at 30 ◦ C. According to the phase diagram (Foster and Yguerabide, 1979; Knoll et al., 1981; Shimshick and McConnell, 1973), the fluid and gel phases coexist between DSPC mole fractions of ca. 0.1 and 0.75 and the relative amount of gel phase increases with the DSPC mole fraction. In the case of the monolayer, the surface covered by bright liquid condensed areas also becomes larger, due to an increase of the average size of the domains. It is interesting to note that the monolayer of the (75:25) mixture is composed of a much higher number of domains then the two other compositions studied, which both contain a similar number of domains.

A. Arnold et al. / Chemistry and Physics of Lipids 133 (2005) 165–179

A brief comment can be made on the morphology of the observed domains. Above a certain size of approximately 10 ␮m, the domains have a branching tendency and therefore have a flower-like shape. The equilibrium shapes of lipid domains have been described theoretically as resulting from the competition between the line tension at the edges of the domains and longrange dipole–dipole repulsions between the lipids (for a review see McConnell, 1991). Within this theoretical framework, a high line tension will favour compact shapes whereas a high electrostatic repulsion will favour elongated shapes. In certain cases however, dendritic or fractal domains have been observed resulting from non-equilibrium conditions, for example the fast compression of the monolayer (see M¨ohwald et al., 1995 and references therein). We have therefore evaluated the effect of compression speed and the results are shown in Fig. 3. As the compression becomes faster, the number of domains increases and their average size decreases. The effect on the branching of the domains is however negligible or below the resolution of the technique. As demonstrated by Li et al. (1998), the concentration of the spreading solution is an additional param-

Fig. 3. Effect of compression speed on the 50:50 DMPC/DSPC system at 30 ± 1 ◦ C and P = 35 mN m−1 . The barrier speeds are (A) ˚ 2 molecule−1 min−1 ; (B) 0.37 A ˚ 2 molecule−1 min−1 ; (C) 0.12 A ˚ 2 molecule−1 min−1 and (D) 0.96 A ˚ 2 molecule−1 min−1 . 0.73 A

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eter, which can influence both the size and the morphology of phospholipid monolayer domains. BAM images of monolayers spread from solutions with different concentrations are presented in Fig. 4. Clearly, as the deposition concentration is increased, the size of the domains increases whereas their number decreases. These two tendencies are in good qualitative agreement with previously published work in which the authors related the number and size of the domains to the presence of impurities in the solvent, which increases in absolute number with increasing deposition volume (decreasing deposition concentration) (Li et al., 1998). Interestingly, the branching of the domains increases with domain size. This effect of the spreading concentration should be kept in mind when comparing our results with those obtained by other techniques. 3.2. Growth and morphology as a function of temperature The behaviour of bilayers is more commonly studied at constant pressure as a function of temperature. In analogy with these studies, we have performed a series of experiments in which the monolayer is heated and the surface area is adjusted in order to keep the lateral pressure constant. BAM images were recorded for a fixed surface pressure (35 mM m−1 ) and varying DMPC/DSPC molar ratios (Fig. 5) and for a 50:50 mixture at different surface pressures (Fig. 6). As can be observed in Fig. 5, at constant surface pressure, the pure lipids remain in a liquid expanded (DMPC) and liquid condensed phase (DSPC) throughout the heating process. The melting of DSPC should take place at a higher temperature not accessible with our setup. The monolayers composed of mixed lipids in DMPC/DSPC molar ratios of (75:25) and (50:50) appear as composed of bright compact domains within

Fig. 4. Effect of the concentration of the deposition solution on the 50:50 DMPC/DSPC system at 30 ± 1 ◦ C and P = 35 mN m−1 .

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Fig. 5. Effect of temperature on DMPC/DSPC systems at different molar ratios for a surface pressure of 35 mN m−1 .

a continuous dark background. The most easily described melting process is the one observed for the (75:25) mixture. As the temperature is initially increased, the number of domains remains almost constant with only slight fluctuations and the average size of the domains slowly decreases from a characteristic size of approximately 8 ␮m. At 35 ◦ C, their characteristic size has dropped to 5 ␮m on average, although the distribution of sizes becomes more heterogeneous. The number of domains starts to decrease as domains disappear or their sizes fall below the resolution of BAM. Finally at 45 ◦ C, the surface is dark and homogeneous. The equimolar system behaves somewhat similarly, although the size distribution is now much less homogeneous, roughly bimodal, with domains of ≈ 8 ␮m coexisting with smaller ones of approximately 5 ␮m. The

domains are systematically smaller than those composing the (75:25) monolayer. Some domains merge at the lower temperatures. At the higher temperatures, some domains are deformed from a circular to a more elongated shape. With increasing temperature, the number of domains is globally constant but the proportion of smaller domains increases. At 45 ◦ C, only a small number of domains remain and these finally disappear upon further heating. The (25:75) mixture is difficult to characterize with the available resolution. At 21 ◦ C, the film seems to be composed of a bright matrix in which some dark pores with radii ca. 3 ␮m can be seen. The bright film appears to be composed of merged bright clusters. Further heating of the monolayer seems to induce an increase in the number of pores and the clusters become more distinct. These domains however did

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Fig. 6. Effect of temperature on the 50:50 DMPC/DSPC system at different surface pressures.

not detach from one another at the probed temperatures. It is interesting to note in the results presented in Fig. 5 that, in contrast to the variable pressure experiments, no fingering was observed for the bright domains obtained in the variable temperature experiments. The domains are mostly circular and a very small fingering tendency, yielding irregular shapes, was only observed for the (75:25) mixture. On the other hand, a clear trend can be noticed by examining the BAM images at constant temperature before the domains start to disappear (at 21 and 30 ◦ C, rows 1 and 2 of Fig. 5 for example). More specifically, the system seems to accommodate an increasing liquid condensed/liquid expanded ratio by forming a greater number of smaller domains.

In order to better understand the interrelationship between temperature and surface pressure and eventually determine if a characteristic pressure exists at which domain morphology in monolayers can be compared to the one in bilayers, we performed a set of experiments in which the temperature was varied at four different surface pressures. The images obtained (Fig. 6), show a common melting behaviour at all surface pressures. At low temperatures, the monolayer is composed of a rather heterogeneous size distribution of circular bright domains and as the temperature is increased, the domain sizes start to decrease until they finally disappear. Interestingly, the melting completion temperatures, which are shown in Table 1, increase linearly with surface pressure. Differences between the heating and cooling processes were addressed by letting the completely melted

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Table 1 Melting completion temperatures obtained from the monolayer experiments (Tmmono ) and comparison with the melting completion temperatures in bilayers (Tmbil ) (adapted from Knoll et al., 1981) DMPC/DSPC molar ratio 50:50

100:0 75:25 50:50 25:75 0:100

Surface pressure (mN m−1 )

Tmmono (◦ C)

5 15 25 35

32 37 40 46 < 21 39 46 > 47 > 47

35

monolayers cool down to 25 ◦ C at constant pressure. Examples of images obtained before and after this process are shown in Fig. 7. The size of the domains appears more homogeneous after the thermal treatment and the average sizes are greater. The average domain sizes before heating and after cooling are 7 and 8 ␮m at 25 mN m−1 , 6 and 10 ␮m at 15 mN m−1 , and 5 and 12 ␮m at 5 mN m−1 . The heating–cooling process therefore seems to alter the size of the domains more strongly at lower surface pressures.

4. Discussion 4.1. Isothermal compression 4.1.1. Identification of the phases and phase transitions In the case of monolayers composed of a single molecule, transitions between expanded and condensed phases can usually be determined by changes in the monolayer compressibility, readily observed on the slope of the π–A isotherms. In particular, a first-order phase transition should be accompanied by a horizontal plateau in the π–A isotherm. According to the phase rule, this is not the case for a two-component mixture. The observation by BAM of two phases however proves the existence of at least one first order phase transition. A more accurate characterization of the phases present in phospholipid monolayers, mainly obtained by X-ray diffraction and BAM studies, has lead to the identification of a considerable number of phases depending on the 2D translational order of the molecules, their orientation, and the conformational order of the chains (Andelman et al., 1994; Kaganer et al., 1999). For in-

Tmbil (◦ C) –

23 37 47 52 55

stance, differences of BAM contrast within a domain are associated with changes in chain orientation. In the present study, however, no internal contrast could be observed due to the small size of the domains. The presence of bright domains in a dark background therefore only allows us to describe the phases in presence as condensed and expanded, respectively. 4.1.2. Influence of nucleation on domain formation and growth Nucleation theory can be used to describe the formation of a new phase. In classical nucleation theory, the number and sizes of the new phase seeds is governed by their free energy G = −nµ + 2πrλ (see Adamson, 1982; Landau and Lifshitz, 1980). In this expression, n is the number of molecules in the seed, µ is the chemical potential difference between the two phases (which

Fig. 7. BAM images of the 50:50 DMPC/DSPC system at 25 ± 1 ◦ C and different surface pressures, upon isobaric heating (top row) and isobaric cooling after complete melting (bottom row).

A. Arnold et al. / Chemistry and Physics of Lipids 133 (2005) 165–179

depends on how far the system is from equilibrium), r is the radius of the circular nucleation seed and λ is the line tension between the two phases. This expression shows that droplets of the new phase, formed by fluctuations, will only be stable above a certain critical radius which depends on the relative magnitudes of line tension and chemical potential difference, a lower line tension will favour the formation of a greater number of small domains. With increasing DSPC mole fraction, the number of domains clearly decreases whereas their sizes increase. According to the classical interpretation of phase diagrams, at a given surface pressure and for all molar ratios, the two phases have the same compositions and only differ in their relative proportions. The difference in nucleation can therefore not be attributed to differences in line tension but would rather depend on the non-equilibrium conditions in which the system is placed. With increasing DSPC content, the nucleation process seems to take place closer to equilibrium, therefore yielding a smaller number of larger domains. In this experiment, the extent of deviation from equilibrium can be measured by a disequilibrium parameter, equal to the difference between the applied surface pressure and the surface pressure at which the system enters the biphasic region. Unfortunately, this particular pressure is difficult to determine since the first seeds, which appear upon entering the coexistence region are likely to be below the resolution of BAM. The rate of nucleation will have a second consequence. More specifically, as nucleation becomes less favourable, the increasing total amount of condensed phase imposed by thermodynamics upon compression will be accommodated by the growth of the domains (McConnell, 1991). This trend is indeed observed in the DMPC/DSPC monolayers: whereas at the lower DSPC content, nucleation carries on during compression and almost no growth of the domains is observed, as the DSPC content increases, the number of domains tends to become stable and their growth upon compression increases. An additional factor may influence domain growth: if the domains are close enough, the equilibrium theory of McConnell predicts an increase of domain size due to inter-domain electrostatic repulsions (McConnell, 1991). It appears from this that the history of the sample will be of great importance since, as shown by the results presented in Figs. 3 and 4, domain size and number depend on both compression

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speed and deposition conditions. A greater concentration of lipids in the deposition solution or a slower compression speed will lead to a smaller number of larger domains. 4.1.3. Have the domains attained their equilibrium shapes? According to the domain shape theory developed by the group of McConnell (McConnell, 1991; McConnell and Moy, 1988), in which the free energy of the system is a sum of electrostatic and line tension contributions, the equilibrium shape of an isolated domain is circular when line tension prevails on dipolar repulsions. On the other hand, a great variety of shapes, which result from non-equilibrium growth conditions, have been observed experimentally and predicted theoretically (Ben-Jacob and Garik, 1990; Gehlert and Vollhardt, 1997; Gliozzi et al., 1994; Indiveri et al., 1996; Mayer and Vanderlick, 1997; Miller et al., 1986). The developed growth models depend on dipolar repulsions and line tension, as is the case for the equilibrium models, and an additional competition between growth due to a disequilibrium parameter and rearrangement due to temperature (Gliozzi et al., 1994). If growth happens close to equilibrium, the domains formed are close to their equilibrium shapes and are therefore circular, ellipsoidal or cardioid. As the deviation from equilibration is increased, the shapes become more irregular, branched, dendritic and finally fractal (Gehlert and Vollhardt, 1997; M¨ohwald et al., 1995). Interestingly, the interplay between the different growth parameters has an important consequence, which is observed in our results: as long as the cluster is small, compact shapes are favoured whereas above a certain size, branching starts (Gliozzi et al., 1994). The type of shapes observed for the (50:50) and the (25:75) mixtures is usually associated with intermediate disequilibrium parameters (compression speeds) or a low line tension with respect to electrostatic repulsions (Ben-Jacob and Garik, 1990; Mayer and Vanderlick, 1997). Since the morphology is not much altered when the compression speed is changed (Fig. 3), we believe that the shape of the domains is mainly due to a low line tension. It should also be noted that the exper˚2 imental compression speed used in this work (0.73 A −1 −1 molecule min ) is considered as a slow compression rate in single component monolayer studies and therefore associated to a low disequilibrium parameter

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(see for example Jyoti et al. (1996) or Gehlert and Vollhardt (1997)). In addition, the fact that the shape of the domains did not change after waiting periods of the order of hours also supports the hypothesis of a low line tension. Considering these results, and the differences in the shape of the domains formed upon compression (Fig. 2) and after the heating and cooling process (Fig. 7), the morphology of the domains seems to be a consequence of the growth process. More specifically, the domains would then be in a metastable-branched shape, which does not relax to a smooth shape due to low line tension. Interestingly, FRAP (Almeida et al., 1992) and combined AFM and FRAP (Ratto and Longo, 2002) studies of similar phospholipid systems have provided evidence for the existence of a diffuse interface between surrounding gel domains in supported bilayers. The presence of such a diffuse interface, composed of more ordered fluid lipids, could contribute to a lowering of line tension. It should be noted that although the shapes of the domains might be metastable, this does not imply that the total system is not at thermodynamic equilibrium. More specifically, the total amount of condensed phase follows the phase rule, which seems to be the case at least qualitatively. 4.2. Isobaric melting As the temperature is increased, one can expect two phenomena to take place: on the one hand the condensed phase domains will melt into an expanded phase and on the other hand the line tension will decrease (Muller and Gallet, 1991). For all compositions, the melting process is readily observed: the size of the domains decreases until the domains completely disappear. For all compositions and a surface pressure of 35 mN m−1 (Fig. 5), the temperatures at which no condensed domains remain are very close to the gel–liquid crystalline melting completion temperatures in DMPC/DSPC bilayers (Knoll et al., 1981; Shimshick and McConnell, 1973) (see Table 1 for comparison). The reduction in line tension can be responsible for the occasional domain deformation at higher temperatures. Clearly, in this series of experiments, the number and sizes of the domains is fixed and depend on the nucleation process at the deposition temperature, i.e. at the lowest temperature. At this initial temperature, as the DSPC content increases, a greater total condensed surface is formed which is composed of a greater num-

ber of smaller domains, indicating that the domains are formed further from equilibrium with increasing DSPC concentration. Indeed, as determined in the isobaric experiments, the systems enter the biphasic domains at decreasing surface pressures with increasing DSPC content. Comparing Figs. 5 and 6, it can be determined that the nucleation process depends on the DMPC/DSPC molar ratio but not significantly on the surface pressure since similar numbers and sizes of domains are observed at all surface pressures for the (50:50) mixture (Fig. 6). The dependence of the monolayer structure on initial nucleation is also confirmed by the experiment presented in Fig. 7. The nucleation process upon cooling yields results different from those obtained by monolayer compression at low temperature. The domains are more homogeneous in size, indicating that under these conditions, phase separation possibly occurs closer to quasi-equilibrium and the monolayer is now composed of larger domains as the surface pressure is reduced. This phenomenon can also be interpreted in terms of classical nucleation theory. Since the melting completion temperature increases with surface pressure (see Fig. 6), at 25 ◦ C, the higher the surface pressure, the further the monolayer will be from equilibrium. Nucleation is therefore favoured and a higher number of smaller domains are formed. 4.3. Monolayers and bilayers 4.3.1. Similarities and differences in the lateral structure of monolayers and bilayers It is not always clear to what point phenomena observed in monolayers can be extrapolated to bilayers, the real state of biological membranes. The comparison between monolayers and bilayers has been extensively studied but crucial questions still remain unanswered (Marsh, 1996). For instance, the surface pressure at which a monolayer should be compressed to compare it to a bilayer is not unambiguously determined. The approach usually followed to find this equivalence pressure is to determine in what conditions both systems have identical characteristics such as, for example, molecular packing and thermal expansion (Hui et al., 1975), absolute areas and area changes upon transitions (Blume, 1979), or the two latter and transition enthalpies (K¨oberl et al., 1997). Marsh provides theoretical and experimental support for an equivalence

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surface pressure equal to the opposing free energy density, which is ca. 30–35 mN m−1 (Marsh, 1996). Moreover, the identification of the gel and liquid crystalline phases in bilayers with the liquid expanded and liquidcondensed phases in monolayers is not trivial. By using external reflection Fourier transform spectroscopy, (Mitchell and Dluhy, 1988) have however shown that for phospholipids such as DPPC, the LE-LC transition involves a conformational change in the hydrocarbon chains. The LE phase is associated with conformational disorder, as is the case for the liquid crystalline phase in lipid bilayers, whereas in the LC phase, the chains are all in the trans configuration as is the case for the bilayer gel phase. Although this is not a sufficient proof that the corresponding phases are identical, it shows that they are at least strongly correlated. More specifically, within the context of this work, the differences in miscibility and lateral structure in the case of mixtures are unknown. By comparing our results with the classic temperature-composition phase diagram and recent AFM (Giocondi et al., 2001) and two-photon fluorescence microscopy (Bagatolli and Gratton, 2000a) studies on DMPC/DSPC bilayers, a series of similarities and differences can be discussed. Considering the melting completion temperatures, Figs. 5 and 6 and Table 1 show that these are close to the ones of DMPC/DSPC bilayers when a surface pressure of 35 mN m−1 is applied. At this surface pressure, the areas per lipid molecule in the pure monolayers are similar, considering the experimental error, to ˚ 2 molecule−1 versus the ones reported for bilayers (34 A 2 −1 2 ˚ ˚2 ˚ 45 A molecule and 71 A molecule−1 versus 65 A −1 molecule for DSPC and DMPC monolayers and bilayers, respectively) (Marsh, 1990). There are however two striking differences between the lateral structure seen on the BAM images and the one which can be seen or deduced from other techniques (Bagatolli and Gratton, 2000a; Giocondi et al., 2001; Sug´ar et al., 1999; Vaz et al., 1989). The first difference concerns the topology. Whereas, FRAP (Vaz et al., 1989) and Monte Carlo simulations (Michonova-Alexova and Sug´ar, 2002; Sug´ar et al., 1999) predict that the fluid phase becomes discontinuous at some point within the two-phase coexistence region, the monolayers observed by BAM were composed of condensed domains separated by an expanded phase, except for the (25:75) mixture in which the domains joined although their merging was not observed. The discontinuous nature

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of the fluid phase was also observed in single bilayers deposited on mica by AFM (Giocondi et al., 2001) but is not mentioned in the two-photon fluorescence microscopy work (Bagatolli and Gratton, 2000a). The second difference concerns the size of the domains. Whereas AFM studies have provided evidence for submicron sized domains (Giocondi et al., 2001; Kaasgaard et al., 2003; Leidy et al., 2002), as expected from indirect techniques (Arnold et al., 2004; Gliss et al., 1998; Sankaram et al., 1992) and Monte Carlo simulations (Michonova-Alexova and Sug´ar, 2001; Sug´ar et al., 1999), domains with sizes between 5 and 20 ␮m were observed in this work, a size which is close to the ones imaged by two-photon fluorescence microscopy (Bagatolli and Gratton, 2000a). 4.3.2. Electrostatic effects Following the reasoning of Marsh (1996), if the equivalence pressure is attained, the remaining difference between monolayers and bilayers is the electrostatic interaction between the two monolayers. Although this interaction is certainly weak, and most authors have considered bilayers as composed of two independent monolayers, Smorodin and Melo (2001) have shown theoretically that the electrostatic interactions between two domains spanning the bilayer can explain the differences in sizes between monolayers and bilayers. It should be noted that as shown in the present study, both the size and shapes of monolayer domains are strongly dependent on deposition and compression conditions. In particular, the dependence of domain size on the concentration of the deposition aliquots suggests that other solvents might give different results. Despite this fact, since the experiments in which the monolayer is cooled from a homogeneous liquid expanded phase yield domains with similar sizes (Fig. 7), we believe that the discrepancies in domain sizes between mono and bilayers are at least not solely due to the deposition conditions. The question of the topological difference between monolayers and bilayers has to our knowledge not yet been addressed. A possible explanation for this effect could be the existence of an energy barrier due to electrostatic repulsion between condensed domains, which would prevent the domains from getting close enough to merge. A greater line tension in monolayer domains could also be responsible for this difference but the possibility that the coalescence of the domains might require the compression

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of the monolayer to higher surface pressures cannot be ruled out. An additional difference between bilayers and monolayers is the fact that a ripple phase cannot form in monolayers. Recently, the important role that might play the presence of the ripple phase in the growth and morphology of lipid domains has been evidenced (Kaasgaard et al., 2003; Leidy et al., 2002) and additional differences can therefore be expected between domains in monolayers and bilayers if they are composed of ripple phase forming lipids. 4.3.3. Are the growth behaviours in monolayers and bilayers comparable? Despite these differences, it is interesting to examine to what point the growth behaviour in monolayers can be extrapolated to bilayers. As is illustrated throughout this work, the lateral structure in the examined monolayers is strongly dependent on the nucleation process and therefore on the history of the sample, and, in certain cases, the monolayer can remain in a metastable state. In addition, the possible existence of an energetic barrier preventing the coalescence of domains even at high surface pressures might be of great importance. This must be kept in mind when comparing our results with the ones obtained by other techniques such as AFM in which the binary system is usually brought into the biphasic domain by heating the sample (Giocondi et al., 2001; Kaasgaard et al., 2003; Leidy et al., 2002). In contrast, the compression of the monolayer is analogous to a cooling of the sample and, even in the case of the variable temperature experiments, the monolayer has to be compressed prior to the heating process. Giocondi et al. (2001) have studied single DMPC/DSPC equimolar bilayers by AFM. Upon heating of their sample, small fluid domains with diameters between 0.05 and 0.30 ␮m appeared. Further increase of the temperature resulted in an increase of the number and sizes of the fluid domains. The gel phase finally became discontinuous at 37.5 ◦ C. These results are difficult to compare with ours since the starting point in the heating of the monolayers was a discontinuous condensed phase and the heating of the monolayer results in a simple decrease of these domain sizes. Although a different system was studied, consisting of two lipids DLPC and DSPC with hydrocarbon chains differing by six carbons, the results of Ratto and Longo (2002) might be easier to compare to ours. These authors prepared a series of mica-supported bilayers by quenching

unilamellar vesicles at high temperature in the homogeneous fluid phase onto the cold substrate. We believe this procedure to be in closer analogy to the compression of a monolayer. By this quenching technique, they obtained circular gel phase domains with diameters of ca. 0.12 ␮m. Increasing the quenching temperature difference resulted in a higher number of smaller domains, similarly to what is obtained upon faster compression of the monolayer in our case. Increasing the DSPC content increased the number of gel domains, the size of these domains being constant. The DMPC/DSPC monolayers follow a similar trend except for the unusual behaviour of the (50:50) mixture. Finally, the gel domains in this study merged, disconnecting the fluid phase, when the total area covered by the gel phase attained 70% of the surface. It is noteworthy that similarly to the monolayer case, the shape of the circular gel domains in the supported bilayer was not altered until they merged. DMPC/DSPC bilayers have also been studied by Monte Carlo simulations (Jørgensen and Mouritsen, 1995; Michonova-Alexova and Sug´ar, 2001, 2002; Sug´ar et al., 1999). In all these studies, domains between tens and hundreds of nanometers were obtained. In some cases, the small nanometer scale domains were found to coexist with a large micrometer scale domain (Michonova-Alexova and Sug´ar, 2001, 2002; Sug´ar et al., 1999). When a large domain was found, it was seen to decrease in size as the temperature was increased (Michonova-Alexova and Sug´ar, 2001) as is observed for monolayers in the present work. The number of domains is also found to be variable, the number of gel domains decreasing with increasing temperature (Sug´ar et al., 1999, 2001). One of these Monte Carlo studies focused on the non-equilibrium behaviour of the binary mixture (Jørgensen and Mouritsen, 1995). In this work, after a temperature quench from the fluid to the gel–fluid domain, a large number of gel clusters are formed which slowly grow in time. This is analogous to the increase in size of the liquid condensed domains upon compression. Interestingly, the results of these calculations clearly demonstrate the differences in composition between the interfaces and the bulk of the domains. This results in a decrease of line tension, which can stabilize non-equilibrium domains (Jørgensen and Mouritsen, 1995) and affect the average size of the domains, as discussed in the present study.

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5. Summary and conclusions In this work, the temperature and pressure dependent growth of liquid condensed domains in DMPC/DSPC monolayers was studied by BAM. The isothermal experiments show that at a high DMPC/DSPC ratio, nucleation is favoured and increasing numbers of small domains ca. 5 ␮m are formed upon compression. As the DSPC content increases, a smaller number of larger branched domains are formed which grow until sizes ca. 20 ␮m with increasing surface pressure. In these isothermal experiments, with decreasing DMPC/DSPC content, a higher total condensed phase is obtained due to a lower number of larger domains. At all the DMPC/DSPC ratios and surface pressures, isobaric heating of the monolayers induces a decrease of the size of the domains until they disappear. In these experiments, at a given surface pressure and temperature, a greater total condensed surface area is also found for the DSPC rich monolayers. It is however in this case always due to a greater number of domains. Both the domain sizes and morphologies, as well as their evolutions upon perturbation, show that the nucleation process is very important in determining the lateral structure of the monolayer. The dimensions and shape of the domains therefore strongly depend not only on the thermodynamic parameters, temperature, pressure and composition, but also on deposition conditions and perturbation speed. From the comparison between our results and those obtained in bilayers, one can infer that monolayers provide a qualitative but not quantitative description of domain growth in biological membranes. We believe, in agreement with previously published theoretical work (Smorodin and Melo, 2001), that the differences in domain size between bilayers and monolayers are most likely due to electrostatic interactions between the two bilayer leaflets.

Acknowledgments The authors wish to thank Fr´ed´eric Dechamplain for his technical assistance and helpful discussions and Isabelle Marcotte for her critical reading of the manuscript. This work was supported by the Natural Science and Engineering Research Council (NSERC) of Canada, by the Fonds Qu´eb´ecois de la Recherche sur

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la Nature et les Technologies (FQRNT) and by the Centre de Recherche en Sciences et Ing´enierie des Macromol´ecules (CERSIM).

References Adamson, A.W., 1982. Physical Chemistry of Surfaces. Wiley, New York. Almeida, P.F.F., Vaz, W.L.C., Thompson, T.E., 1992. Lateral diffusion and percolation in two-phase, two-component lipid bilayers. Topology of the solid-phase domains in-plane and across the lipid bilayer. Biochemistry 31, 7198–7210. Andelman, D., Brochard, F., Knobler, C., Rondelez, F., 1994. Structures and phase transitions in Langmuir monolayers. In: Gelbart, W.M., Ben-Shaul, A., Roux, D. (Eds.), Micelles, Membranes, Microemulsions and Monolayers. Springer, New York, pp. 559–602. Arnold, A., Paris, M., Auger, M., 2004. Anomalous diffusion in a gel–fluid lipid environment: a combined solid-state NMR and obstructed random-walk perspective. Biophys. J. 87, 2456–2469. Bagatolli, L.A., Gratton, E., 2000a. A correlation between lipid domain shape and binary phospholipid mixture composition in free standing bilayers: a two-photon fluorescence microscopy study. Biophys. J. 79, 434–447. Bagatolli, L.A., Gratton, E., 2000b. Two photon fluorescence microscopy of coexisting lipid domains in giant unilamellar vesicles of binary phospholipid mixtures. Biophys. J. 78, 290–305. Baumgart, T., Hess, S.T., Webb, W.W., 2003. Imaging coexisting fluid domains in biomembrane models coupling curvature and line tension. Nature 425, 821–824. Ben-Jacob, E., Garik, P., 1990. The formation of patterns in nonequilibrium growth. Nature 343, 523–530. Blume, A., 1979. A comparative study of the phase transitions of phospholipid bilayers and monolayers. Biochim. Biophys. Acta 557, 32–44. Brezesinski, G., M¨ohwald, H., 2002. Langmuir monolayers to study interactions at model membrane surfaces. Adv. Colloid Interface Sci. 100–102, 563–584. Brown, D.A., London, E., 2000. Structure and function of sphingolipid- and cholesterol-rich membrane rafts. J. Biol. Chem. 275, 17221–17224. Discher, B.M., Schief, W.R., Vogel, V., Hall, S.B., 1999. Phase separation in monolayers of pulmonary surfactant phospholipids at the air–water interface: composition and structure. Biophys. J. 77, 2051–2061. Edidin, M., 1997. Lipid microdomains in cell surface membranes. Curr. Opin. Struct. Biol. 7, 528–532. Foster, M.C., Yguerabide, J., 1979. Partition of a fluorescent molecule between liquid–crystalline and crystalline regions of membranes. J. Membr. Biol. 45, 125–146. Gaines, G.L., 1966. Insoluble Monolayers at Liquid–Gas Interfaces. Wiley, New York. Gehlert, U., Vollhardt, D., 1997. Nonequilibrium structures in 1-monopalmitoyl-rac-glycerol monolayers. Langmuir 13, 277–282.

178

A. Arnold et al. / Chemistry and Physics of Lipids 133 (2005) 165–179

Giocondi, M., Le Grimellec, C., 2004. Temperature dependence of the surface topography in dimyristoylphosphatidylcholine/distearoylphosphatidylcholine multibilayers. Biophys. J. 86, 2218–2230. Giocondi, M., Pacheco, L., Milhiet, P.E., Le Grimellec, C., 2001. Temperature dependence of the topology of supported dimyristoyl–distearoyl phosphatidylcholine bilayers. Ultramicroscopy 86, 151–157. Gliozzi, A., Levi, A.C., Menessini, M., Scalas, E., 1994. Temperature and disequilibrium dependence of cluster growth. Physica A 203, 347–358. Gliss, C., Clausen-Schaumann, H., Gunther, R., Odenbach, S., Randl, O., Bayerl, T.M., 1998. Direct detection of domains in phospholipid bilayers by grazing incidence diffraction of neutrons and atomic force microscopy. Biophys. J. 74, 2443–2450. H´enon, S., Meunier, J., 1991. Microscope at the Brewster angle: direct observation of first-order phase transitions in monolayers. Rev. Sci. Instrum. 62, 936–939. H¨onig, D., M¨obius, D., 1991. Direct visualization of monolayers at the air–water interface by Brewster Angle Microscopy. J. Phys. Chem. 95, 4590–4592. Hui, S.W., Cowden, M., Papahadjopoulos, D., Parsons, D.F., 1975. Electron diffraction study of hydrated phospholipid single bilayers. Effects of temperature, hydration and surface pressure of the “precursor” monolayer. Biochim. Biophys. Acta 382, 265– 275. Indiveri, G., Levi, A.C., Gliozzi, A., Scalas, E., M¨ohwald, H., 1996. Cluster growth with long-range interactions. Thin Solid Films 284–285, 106–109. Jørgensen, K., Mouritsen, O.G., 1995. Phase separation dynamics and lateral organization of two-component lipid membranes. Biophys. J. 69, 942–954. Jyoti, A., Prokop, R.M., Li, J., Vollhardt, D., Kwok, D.Y., Miller, R., M¨ohwald, H., Neumann, A.W., 1996. An investigation of the compression rate dependence on the surface pressure-surface area isotherm for a dipalmitoylphosphatidylcholine monolayer at the air/water interface. Colloids Surf. A 116, 173–180. Kaasgaard, T., Leidy, C., Crowe, J.H., Mouritsen, O.G., Jørgensen, K., 2003. Temperature-controlled structure and kinetics of ripple phases in one- and two-component supported lipid bilayers. Biophys. J. 85, 350–360. Kaasgaard, T., Leidy, C., Ipsen, J.H., Mouritsen, O.G., Jørgensen, K., 2001. In situ atomic force microscope imaging of supported lipid bilayers. Single Mol. 2, 105–108. Kaganer, V.M., M¨ohwald, H., Dutta, P., 1999. Structure and phase transitions in Langmuir monolayers. Rev. Mod. Phys. 71, 779–819. Knoll, W., Ibel, K., Sackmann, E., 1981. Small-angle neutron scattering study of lipid phase diagrams by the contrast variation method. Biochemistry 20, 6379–6383. K¨oberl, M., Hinz, H.-J., Rapp, G., 1997. Enthalpy is a proper criterion for comparability of monolayer and bilayer studies: isobaric temperature scanning measurements on glycolipid monolayers. Chem. Phys. Lipids 85, 23–43. Kubo, I., Adachi, S., Maeda, H., Seki, A., 2001. Phosphatidylcholine monolayers observed with Brewster angle microscopy and π–A isotherms. Thin Solid Films 393, 80–85.

Landau, L.D., Lifshitz, E.M., 1980. Statistical Physics (Part 1). Pergamon Press, Oxford. Leidy, C., Kaasgaard, T., Crowe, J.H., Mouritsen, O.G., Jørgensen, K., 2002. Ripples and the formation of anisotropic lipid domains: imaging two-component supported double bilayers by atomic force microscopy. Biophys. J. 83, 2625–2633. Leidy, C., Wolkers, W.F., Jørgensen, K., Mouritsen, O.G., Crowe, J.H., 2001. Lateral organization and domain formation in a twocomponent lipid membrane system. Biophys. J. 80, 1819–1828. Li, J.B., Miller, R., Vollhardt, D., M¨ohwald, H., 1998. Spreading concentration effect on the morphology of phospholipid monolayers. Thin Solid Films 327–329, 84–86. Marsh, D., 1990. CRC Handbook of Lipid Bilayers. CRC Press Inc., Boca Raton. Marsh, D., 1996. Lateral pressure in membranes. Biochim. Biophys. Acta 1286, 183–223. Mayer, M.A., Vanderlick, T.K., 1997. Monte Carlo simulations of the shapes of domains in phospholipid monolayers. Phys. Rev. E 55, 1106–1119. McConnell, H.M., 1991. Structures and transitions in lipid monolayers at the air–water interface. Annu. Rev. Phys. Chem. 42, 171–195. McConnell, H.M., Moy, V.T., 1988. Shapes of finite two-dimensional lipid domains. J. Phys. Chem. 92, 4520–4525. Michonova-Alexova, E.I., Sug´ar, I.P., 2001. Size distribution of gel and fluid clusters in DMPC/DSPC lipid bilayers. A Monte Carlo simulation study. J. Phys. Chem. B 105, 10076–10083. Michonova-Alexova, E.I., Sug´ar, I.P., 2002. Component and state separation in DMPC/DSPC lipid bilayers: a Monte Carlo simulation study. Biophys. J. 83, 1820–1833. Miller, A., Knoll, W., M¨ohwald, H., 1986. Fractal growth of crystalline phospholipid domains in monomolecular layers. Phys. Rev. Lett. 56, 2633–2636. Mingotaud, A., Mingotaud, C., Patterson, L.K., 1993. Handbook of Monolayers. Academic Press, San Diego. Mitchell, M.L., Dluhy, R.A., 1988. In situ FT-IR investigation of phospholipid monolayer phase transitions at the air–water interface. J. Am. Chem. Soc. 110, 712–718. M¨ohwald, H., 1990. Phospholipid and phospholipid–protein monolayers at the air/water interface. Annu. Rev. Phys. Chem. 41, 441–476. M¨ohwald, H., Dietrich, A., B¨ohm, C., Brezesinski, G., Thoma, M., 1995. Domain formation in monolayers. Mol. Membr. Biol. 12, 29–38. Morrow, M.R., Srinivasan, R., Grandal, N., 1991. The phase diagram of dimyristoylphosphatidylcholine and chain-perdeuterated distearoylphosphatidylcholine: a deuterium NMR spectral difference study. Chem. Phys. Lipids 58, 63–72. Mouritsen, O.G., Jørgensen, K., 1995. Micro-, nano- and meso-scale heterogeneity of lipid bilayers and its influence on macroscopic membrane properties. Mol. Membr. Biol. 12, 15–20. Mouritsen, O.G., Jørgensen, K., 1997. Small-scale lipid–membrane structure: simulation versus experiment. Curr. Opin. Struct. Biol. 7, 518–527. Muller, P., Gallet, F., 1991. First measurement of the liquid–solid line energy in a Langmuir monolayer. Phys. Rev. Lett. 67, 1106– 1109.

A. Arnold et al. / Chemistry and Physics of Lipids 133 (2005) 165–179 Ratto, T.V., Longo, M.J., 2002. Obstructed diffusion in phaseseparated supported lipid bilayers: a combined atomic force microscopy and fluorescence recovery after photobleaching approach. Biophys. J. 83, 3380–3392. Sanchez, J., Badia, A., 2003. Atomic force microscopy studies of lateral phase separation in mixed monolayers of dipalmitoylphosphatidylcholine and dilauroylphosphatidylcholine. Thin Solid Films 440, 223–239. Sankaram, M.B., Marsh, D., Thompson, T.E., 1992. Determination of fluid and gel domain sizes in two-component, two-phase lipid bilayers. An electron spin resonance spin label study. Biophys. J. 63, 340–349. Shimshick, E.J., McConnell, H.M., 1973. Lateral phase separation in phospholipid membranes. Biochemistry 12, 2351– 2359. Simons, K., Ikonen, E., 1997. Functional rafts in cell membranes. Nature 387, 569–572. Smorodin, V., Melo, E., 2001. Shape and dimensions of gel-domains in phospholipid bilayers: a theoretical study. J. Phys. Chem. B 105, 6010–6016.

179

Sug´ar, I.P., Michonova-Alexova, E.I., Chong, P.L.-G., 2001. Geometrical properties of gel and fluid clusters in DMPC/DSPC bilayers: Monte Carlo simulation approach using a two-state model. Biophys. J. 81, 2425–2441. Sug´ar, I.P., Thompson, T.E., Biltonen, R.L., 1999. Monte Carlo simulation of two-component bilayers: DMPC/DSPC mixtures. Biophys. J. 76, 2099–2110. Vaz, W.L.C., Melo, E.C.C., Thompson, T.E., 1989. Translational diffusion and fluid domain connectivity in a two-component, twophase phospholipid bilayer. Biophys. J. 56, 869–876. Veldhuizen, E.J.A., Haagsman, H.P., 2000. Role of pulmonary surfactant components in surface film formation and dynamics. Biochim. Biophys. Acta 1467, 255–270. Vereb, G., Szollosi, J., Matk´o, J., Nagy, P., Farkas, T., V´ıgh, L., M´atyus, L., Waldmann, T.A., Damjanovich, S., 2003. Dynamic, yet structured: the cell membrane three decades after the Singer–Nicolson model. Proc. Natl. Acad. Sci. U.S.A. 100, 8053–8058. Vollhardt, D., 2002. Supramolecular organisation in monolayers at the air/water interface. Mat. Sci. Eng. C 22, 121–127.