INTRODUCTION

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Quantitative determinations of intermolecular and surface forces are of primary importance in phenomena such as vesicle-vesicle interaction, adhesion, and membrane fusion. Because these processes occur mainly in biological solutions and in the presence of buffers and various types of solutes, it is important to determine bilayer interactions in the presence of model hydrosoluble solutes. Sugar units of molecular or macromolecular size are the major constituent of the soluble parts of glycolipids and glycoproteins and play a major role in the dynamical properties of the membrane and in recognition processes.

Over a wide range of concentrations and temperatures, model biological membranes made of the synthetic phospholipid DMPC (1,2-dimyristoyl-sn-glycero-3-phosphocholine) form neutral lyotropic lamellar phases. The biologically relevant phase is the L, which has been the most studied, pure, in excess water, or in the presence of various aqueous solutes, polymers, or proteins.

The identification of the dominant interactions in biphasic samples involving a lamellar phase in coexistence with a reservoir requires the knowledge of the exact content of each of the two microphases in equilibrium. In most binary systems, the knowledge of the average composition combined with scattering experiments is sufficient to describe the samples in terms of structure and composition of the coexisting phases. In ternary systems, scattering experiments combined with an analysis of the third component's concentration to determine its osmotic pressure is the most suitable way to proceed. For example, when large polyelectrolytes coexist with concentrated clay dispersions, the complete separation of the two phases allows the thermodynamics to be understood (Morvan et al., 1994). However, such samples often have the appearance of gels that are very difficult to separate in two "pure" phases unless ultracentrifugation is used. Such samples are supposed to be studied at thermodynamic equilibrium (although in principle the pressure applied by centrifugation could be quantified as well). Alternative strategies rely on delicate determination of Bragg-reflection shapes (Salditt et al. 1998; Salditt, 1999), adsorption in a surface force apparatus, and pipette aspiration (Parsegian and Rand, 1995). However, bilayer adsorption quenches all modes of interaction related to fluctuations to create systems irrelevant to the equation of state in bulk.

Lyotropic lamellar phases prepared in an excess of water and in the presence of a host molecule represent a general case where the host can be either a soluble molecule or a confined polymer (Demé et al., 1996, 1997), a cosurfactant, a polymer confined in the membranes (Radlinska et al., 1995). In the case of soluble molecules, their osmotic pressure can be considered in the force balance. Assuming additivity of molecular and entropic forces (low fluctuations), the osmotic pressure of the excess solution _s can be written:

(1)

in which _hyd., _vdw, and _und. refer to the distance dependant hydration, van der Waals, and entropic contributions to membrane interactions. '_s is the added osmotic pressure due to the presence of sugar confined between the membranes. At maximal swelling, the difference between the osmotic pressure of the coexisting phases is zero. If one of the phases is pure or almost pure water (solution of lipid at the CMC), then the total osmotic pressure in the lyotropic domains is zero as well, resulting from the balance between dispersion forces and short range hydration forces (Lis et al., 1982).

Finally, in the case of a coexistence between inner and external sugar solution in excess, and when equilibrium via molecular diffusion of the sugar has been completed, we have to consider the concentration in the midplane and the concentration in the reservoir. These two concentrations are likely to be equal (Demé et al. 2000). Then, the two osmotic terms related to the sugar compensate and Eq. 1 simplifies to:

(2)

The well-known case of osmotic compression by polymer solutions corresponds to:

(3)

in which _p is the osmotic pressure of the external polymer solution. Exclusion of the polymer from the water layers results in a zero repulsive contribution in the force balance of the lamellar phase.

However, according to Diamant (submitted manuscript), in the case of multilamellar domains dispersed in an excess of solution, and if the sum of the pressures is low (of the order of 100-1000 Pa), the contact energy between the two macroscopic phases coexisting in the sample cannot be neglected. The repulsion between bilayers may be compensated by the macroscopic surface tension between the lamellar domains and the sugar solution in excess. Eq. 2 becomes:

(4)

in which  is the macroscopic surface tension between lamellar domains and the reservoir solution. A and V are the variations associated to contact area and volume of the lamellar domains, approximated in the form of a Laplace relation in which R is the mean radius of the domains. Eq. 4 shows that a significant contribution can result from a nonzero surface tension combined to small lamellar domains (MLVs (multilamellar vesicles)). This tension stabilizes onions against unbinding (Diamant and Cates, 2001).

A founding paper of biological membrane physics (LeNeveu et al., 1977) proposed a qualitative explanation of the observed maximal swelling of neutral phospholipid membranes in the presence of small carbohydrate molecules. From the measurement of the maximal swelling versus sugar concentration, it has been inferred that the primary effect of sugar addition was to shield the frequency-dependent contribution of the dispersion force by matching the permitivity of the layers, thus producing a minimum in the attractive dispersion force. The associated maximal swelling observed when sugar is added to zwitterionic lecithin/water dispersions has been explicitly calculated and has been shown to be consistent with the experimental observation made at that time: a swelling till 0.22 sugar weight fraction followed by a deswelling at higher concentration. The explanation of the unexpected nonmonotonic effect led to similar works (McDaniel et al., 1983; Stümpel et al., 1985) in which qualitatively analogous results were observed. In the latter reference a similar trend was reported, although much less pronounced and in the L' phase (5°C).

In earlier work (Demé et al., 1996), we reported monotonic swelling of the DMPC lamellar phase induced by added mono- or disaccharides. It was also shown that in samples containing oligosaccharides where molecular diffusion was not completed, compression due to residual excess of sugar in the reservoir (equivalent to a deswelling of the lamellar phase) could be observed as in the case of osmotic compression by polysaccharides. The oligosaccharides were from the series of glucose oligomers ranging from n = 2 (maltose) to n = 5 (maltopentaose). It was shown that for a given incubation time the osmotic stress was a function of the sugar size. Thus, the excess of sugar in the coexisting solution is higher when the molecular weight is increased until the extreme case of the polysaccharide (pullulan) where complete exclusion of the chains takes place. In this case, the applied osmotic pressure is known from separate measurements on the polymer solution.

DMPC binary phase diagrams are given in Janiak et al. (1976, 1979) and Smith et al. (1988) for DMPC. We reconsider here the case of DMPC in the presence of large amounts of added sugar (mono- or disaccharide) and propose a new interpretation of our recent results (Demé and Zemb, 2000). These contradict older work but confirm those of our previous studies (Demé, 1995; Demé et al., 1996; Ricoul, 1997).

	MATERIALS AND METHODS

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Materials

Chemicals

X-ray camera

Methods

Particular care was taken in sample preparation to ensure thermodynamic equilibrium. There are several possible strategies: either by relying on diffusion of solute in water and through defects in bilayers or by starting from nearly molecularly dispersed dry powder obtained by freeze drying very dilute ternary solutions. We have noticed in previous work that the material obtained by freeze drying from the dilute mixture allows rapid reswelling equivalent to what is obtained after several weeks of molecular diffusion (Demé et al., 1996). This rapid reswelling is a critical step, particularly when the "solvent" is a polymer solution (Demé et al., 1997). In the partition equilibrium of a small solute, it is crucial that the samples are studied at equilibrium of the chemical potentials of all entities, because any difference between the coexisting phases may have dramatic effects. In the present case of high sugar concentrations, a residual osmotic stress can be strong and lead to important modifications of the equilibrium distance between membranes. However, diffusion coefficients of small sugars are such that the equilibrium time remains within the range of 1 to 2 weeks, i.e., reasonable time compared with the quasi infinite time required for polymers to diffuse in confined water layers and compatible with the chemical stability of the compounds at incubation temperature.

Samples were incubated for 2 weeks at 30°C with regular vortexing. SAXS experiments were performed at 30°C as well. This is well above the chain melting temperature of pure DMPC, corresponding to the P'-L transition (23°C) and still above the transition in the presence of sugar (Stümpel et al., 1985). SAXS experiments are performed directly on the biphasic mixtures. The ternary samples are microseparated with the lamellar phase at "maximal swelling" in equilibrium with excess sugar solution. Large multilayer vesicles are formed on a mesoscopic scale, i.e., they are too small to be easily separated from the pure coexisting solvent but large enough to produce sharp and perfectly isotropic Debye-Sherrer rings whose profile is not limited by the number of layers but by the interlayer fluctuations (Dubois and Zemb, 1991). Lamellar domains appear in the form of onions or MLVs producing Maltese crosses under polarizing microscope and hence contain several thousands of membranes and some macroscopic surface tension (Diamant, 2001), which may quench fluctuations (Seifert, 1995). Unfortunately, the value of the tension and how it changes in the presence of sugar are not known.

Force balance

The three major contributions we consider are the van der Waals, the hydration, and the entropic forces (Eq. 1). The membranes composing the lamellar stack of alternated water and lipid layers are described by a simple model consisting of an aliphatic core of melted chains surrounded by hydrated polar heads. The membrane thickness d_m, is defined by:

(5)

in which d_h is the thickness of the hydrocarbon core and d_p that of the polar head layer. The measured periodicity is the sum of the membrane and water layer thicknesses:

(6)

van der Waals forces

Double film model

(7)

(8)

34

1

(9)

Triple film model

(10)

Hydration forces

(11)

Entropic forces

(12)

Forces associated with sugar exclusion from multilayer vesicles

(13)

(14)

3

Force balance and additivity

Partition of sugars between lamellar phase and excess solution

Force balance in the presence of sugar

	RESULTS

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Scattering curves

Fig. 1 shows a selection of two-dimensional SAXS patterns illustrating the effect of adding glucose to the DMPC lamellar phase. Two sharp quasi-Bragg reflections characteristic of the lamellar structure are clearly visible. The effect of adding sugar is already visible at 5%: the reflections broaden and the second order disappears around <_s> = 0.20 by weight of sugar in the aqueous phase. On radially averaged data (Fig. 2, in I(q)×q² versus q representation), one can verify that despite the important disorder, the samples are still lamellar at high sugar concentration. In both cases (glucose and saccharose), the monotonic swelling and the simultaneous softening are evidenced by a shift of the peaks toward low angles and by the progressive broadening of the quasi-Bragg reflections. Because the indexing is kept for any sugar content explored, the shift of the peak to small angles corresponds to a monotonic increase of the interlamellar spacing. In binary suspensions (DMPC + water), the membrane thickness is known to vary only in the monophasic L domain where no excess of water is present (Janiak et al., 1976) and at the L-P' and P'-L transitions due to different chain tilt angles or melting of the chains. In ternary mixtures with saccharose (Stümpel et al., 1985) small deviations can be attributed to an untilting of the chains but never lead to a swelling increase of several tens of angstroms as observed here. The change in periodicity of the lamellar phase is due to an increase of the water layer thickness.

View larger version (46K): [in this window] [in a new window]   FIGURE 1   Selection of two-dimensional SAXS patterns of DMPC/glucose suspensions prepared with increasing concentrations of glucose (from left to right: s = 0, 0.05, 0.10, and 0.20). The volume fraction of the lipid <L> relative to the "water + sugar volume" is 0.20.

View larger version (20K): [in this window] [in a new window]   FIGURE 2   Radially averaged SAXS curves (I(q).q2 versus q plots) showing the swelling and the softening of the lamellar phase upon addition of glucose or fructose to DMPC suspensions. (Left) DMPC (<L> = 0.20) + glucose from s = 0 to 0.50 by weight in water. (Right) DMPC (<L> = 0.20) + fructose from s = 0 to 0.40 by weight in water.

Swelling versus sugar concentration

The effect of mono- and disaccharides on the periodicity of the lamellar phase is shown on Fig. 3. Data obtained with egg lecithin (two lower curves) are the results from LeNeveu et al. (1977) obtained with glucose and saccharose, whereas data obtained with DMPC (two upper curves) correspond to the spacings calculated from the scattering curves shown in Fig. 2 with glucose and fructose. Here, we have plotted the periodicity change d instead of the periodicity d to account for the difference in periodicity between DMPC (60.4 Å) and egg lecithin (63 Å) in the absence of sugar. The difference is due to the chain composition of DMPC (two C₁₄ chains) and egg lecithin (mixture of various chain lengths). DMPC and egg-lecithin have bending rigidities of the order of ~10 kT (Sackmann, 1995). Small differences in thickness due to different chain lengths may affect the van der Waals contribution (Eqs. 7 and 10) but not significantly in regard to the deviations of several tens of Angstroms observed here.

View larger version (20K): [in this window] [in a new window]   FIGURE 3   Change of the periodicity of the lamellar domains versus sugar concentration in the aqueous phase as measured by SAXS. Our results obtained with DMPC + glucose () and fructose () are compared with those of LeNeveu et al. (1977) obtained with egg lecithin + glucose () and saccharose (). Plotting d instead of d accounts for the membrane thickness difference between the two phospholipids. Data obtained with DMPC are calculated from curves of Figs. 1 and 2. The error on d is of the order of ±0.5 Å (±1 Å on d). The solid lines are guides to the eye.

Fig. 3 shows the monotonic swelling observed upon addition of sugar in the range of studied concentrations (solid lines are guides to the eyes). It emphasizes the global effect of adding small hydrosoluble molecules such as glucose or fructose: favoring repulsive interactions leading to a monotonic swelling. The same trend is observed for the mono- and the disaccharide with a more pronounced swelling excess with the disaccharide, as previously reported with other disaccharides like lactose (Demé et al., 1996) or saccharose (Ricoul et al., 1997). There is a large difference between our data and older results (LeNeveu et al., 1977; Stümpel et al., 1985) and an opposite trend at high sugar concentration. In a previous study (Demé, 1995; Demé et al., 1996), we already observed a swelling-deswelling sequence induced by the addition of oligosaccharides. But this was observed when samples were equilibrated only a few days. In such a case, nonequilibrium of the sample results in an excess of sugar in the reservoir leading to an osmotic compression of the lamellar phase analogous to the one observed with polysaccharides. Osmotic pressures of concentrated sugar solutions can be that high that an uncompleted diffusion can result in opposite effects to those observed at equilibrium.

Force balance in pure water

We have calculated the van der Waals force according to three different models: the double film model with the head groups either in or out of the aqueous layers and the triple film model with Hamaker constants for the chains/heads interface, the head/water interface, and the cross-term. We used the following Hamaker constants: A₁ = 3 × 10²¹ J, A₂ = 10²² J, and A₃ = 10²¹ J (Ricoul, 1997). The three pressure-distance curves are shown in Fig. 4 A. We have calculated the total pressure-distance curve in the three cases considered here (Fig. 4 B). The two series of curves show that the triple film model (solid line) is best approximated by the double film model when the head group layer is included in the membrane (dashes) rather than in the aqueous phase (dots). This is due to the fact that dielectric properties of the layer of hydrated headgroups are closer to those of the hydrophobic chain layer than those of pure water. As expected when headgroups are considered as part of the aqueous layer, the van der Waals pressure diverges at the chain-head interface (d_w = d_p), whereas divergence occurs at the head-solvent interface (d_w = 0) for the two other models. Note that periodicities calculated by adding the water and membrane thicknesses (d_w + d_b) differ by only 1.2 Å between the two models: 60 Å (d_w = 24.5 Å) for the triple film model and 61.2 Å (d_w = 25.7 Å) for the double film model with d_a = d_w. In regard to these small differences between the measured periodicity (60.4 Å by SAXS) and calculated ones, the zero of the van der Waals attraction can be adjusted to fit exactly the experimental equilibrium distance. It yields (vdw) = 0.4 Å for the triple film model and (vdw) = 0.8 Å for the double film model. This value defines the position where the contribution diverges and is used in the following calculation in the presence of sugar.

View larger version (12K): [in this window] [in a new window]   FIGURE 4   van der Waals pressure as calculated according to the three models described in text (left) and total pressure-distance curves resulting from the sum of van der Waals, hydration, and entropic contributions in the frame of the additivity approximation (right). The zero on the x axis corresponds to the head-solvent interface. The zero on the y axis corresponds to the equilibrium pressure (lamellar domains in equilibrium with excess water or sugar solution). The osmotic pressure of the sugar solution is equilibrated by the sugar confined between the membranes and producing the same pressure (equilibrium condition). (Dotted lines) Double film model with da = dw + 2dp; (dashed lines) double film model with da = dw; (full lines) triple film model. Calculated equilibrium distances corresponding to the three models are: 30.2 Å (double film model, da = dw + 2dp), 25.7 Å (double film model, da = dw), and 24.5 Å (triple film model). When the polar head layer is incorporated in the aqueous phase (da = dw + 2dp) divergence occurs for dw = dp instead of dw = 0 for the two other models.

	DISCUSSION

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Force balance versus sugar concentration

Our goal was to investigate in detail the swelling of DMPC lamellar dispersions in equilibrium with excess solutions of glucose and fructose. We have proposed to reconsider the force balance of the ternary system by taking into account the full balance of forces including the modification of the dielectric properties in the aqueous layers and entropic interactions induced by the softening of the membranes upon addition of sugar molecules. To determine the key role of the confined solute in the force balance, we had developed a neutron contrast variation method to determine the exact amount of sugar in the lamellar domains and in the coexisting excess solution (Demé and Zemb, 2000). This method is the most suited when macroscopic separation of the lamellar domains from the excess aqueous solution is not possible by means that do not modify the equilibrium between the phases in coexistence. We applied it using deuterated sugars so that the delicate step of macroscopic separation of the two coexisting phases was avoided.

The origin of excess swelling (from 0 to ~30 Å) results from an increase of the water layer thickness. A swelling of 30 Å cannot result from a change of membrane thickness due to a rearrangement of the chains and/or of the heads, although a small contribution to the observed swelling cannot be rejected (Stümpel et al., 1985). Appearance of fluctuations is also supported by SAXS data (Figs. 1 and 2). The shape of the first reflection is shown Fig. 5 for several sugar concentrations. It is compared with the resolution function of the camera determined experimentally with an attenuated transmitted beam (FWHM = 8.8 × 10³ Ź). This comparison shows that the effect of softening increases with the amount of sugar and that it is strong enough to be observed with a setup not particularly optimized for high-resolution experiments.

View larger version (15K): [in this window] [in a new window]   FIGURE 5   Peak shapes () in normalized representation (I/Io versus q-qo), and experimental instrument resolution function of the SAXS camera (), showing the broadening of quasi-Bragg reflections upon addition of glucose and fructose to the lamellar suspensions. Results are shown for sugar concentrations ranging from 0 to 0.20 w/w of glucose (left) and fructose (right). The FWHM of the resolution function is 8.8 × 103 Å1.

It is known that added compounds can drastically modify the bending rigidity of phospholipid membranes, either in the direction of a stiffening or in that of a softening (Sackmann, 1995). However, we are not aware of any evidence of a membrane softening by nonlipophilic or nonamphiphilic molecules. The general underlying mechanism of membrane softening by small carbohydrate molecules is not understood, although the data clearly show the combination of a swelling and a softening. McDaniel et al. (1983) have proposed a mechanism in the case of a softening induced by another small carbohydrate (glycerol). Surface tension measurements on water-glycerol mixtures show that glycerol reduces the surface tension of water. Using Gibbs' equation and for 50% glycerol, 90% of the surface is occupied by glycerol. Thus, lateral repulsions and the area per molecule could be increased and this could favor a softening of the bilayer by thinning of the apolar layer. But there is no direct evidence of such mechanism in the ternary system. The reason why disaccharides induce more swelling than monosaccharides is also not completely clear, although a relation with the solute size has already been reported (Demé et al., 1996) and may seem straightforward.

The change of dielectric properties of the water layers induces deviations of the order of a few Angstroms. The Hamaker constant is calculated for every interbilayer sugar concentration (_s) and by taking into account the known optical properties of the solution. Without sugar A = 1.24 kT, at the optical match point A = A_v=0 = 0.71 kT, and for the largest concentration investigated A = 0.84 kT.

On Fig. 6 we show a few characteristic pressure-distance curves from a series of simulations where hydration, van der Waals, and entropic contributions have been added and where the only variable is the bending rigidity constant of the membranes k_c. The calculation was done in the absence of sugar (6A) and at the match point of the frequency-dependent van der Waals contribution where A_v>0 = 0 (_s = 0.22). In this approach, we do not introduce tension release but incorporate all softening effects into an effective bending constant and extract the equilibrium distance versus k_c. For any value of k_c it is given by the intercept of the pressure-distance curve with the x axis, where attractive and repulsive terms counterbalance. Fig. 7 shows the full set of equilibrium distances versus k_c resulting from the simulation compared with experimental equilibrium distances obtained without sugar, with glucose or fructose. As shown on Fig. 6, A and B, below a certain value of k_c the curves do not go through an attractive regime anymore, and the pressure-distance curve becomes purely repulsive. This predicts an unbinding transition and yields both the equilibrium distance of the membranes in lamellar domains before unbinding and the value of k_c at which unbinding should occur. As shown on Fig. 6 B in the presence of sugar, the prediction is not in agreement with the experimental result, unbinding being predicted for distances below those observed experimentally. In the absence of sugar the entropic term is less pronounced and the value of k_c that yields the experimental distance is 20 ± 5 kT.

View larger version (15K): [in this window] [in a new window]   FIGURE 6   Simulated pressure-distance curves versus kc obtained by summing intermolecular forces and an entropic contribution according to Eq. 11. (A) In the absence of sugar and (B) at a sugar concentration s = 0.22 corresponding to the match point of the frequency-dependant contribution of the van der Waals attraction (Av>0 = 0). (A) From bottom to top kc = 20, 5, 3, 2.55 (unbinding), and 2 kT. (B) From bottom to top kc = 20, 10, 6, 4.55 (unbinding), and 4 kT.

View larger version (16K): [in this window] [in a new window]   FIGURE 7   Comparison of simulated periodicities to those observed experimentally. Simulated values of d are extracted from pressure-distance curves as those shown in Fig. 6 in absence of added sugar () and in the presence of sugar at s = 0.22 (). Experimental values are represented as dotted lines without sugar (61.4 Å) and at the point of maximal screening of the van der Waals contribution in the case of glucose and fructose (respectively dmax = 82 and 88 Å). Both series of simulations suggest an unbinding transition for a value of d well below the experimental values.

In the presence of sugar, we observe experimentally an increase of 22 Å (glucose) and 28 Å (fructose), which would be due to fluctuation of membranes directly or indirectly associated to bilayer softening or tension release. Note that within this simple additive model, ignoring the effect of surface tension release, an unbinding at 72 Å for a k_c = 4.5 kT, associated to the Helfrich force dominating van der Waals, is predicted. If we consider the increase in maximal periodicity observed here without unbinding, we have to conclude that repulsion forces are increased monotonically in the presence of sugar. Depletion due to undulation also adds an attractive potential that prevents unbinding. Because we have the combination of two effects and nonlinearity of the interactions, numerical simulations of pressure-distance curves are done using an effective bending constant. In principle, one could simulate these curves and extract the equilibrium periodicity by keeping k_c constant and varying , according to Seifert's expression (Seifert, 1995).

The presence of fluctuations due to membrane softening and/or release of surface tension is consistent with the observed evolution of the shape of the quasi-Bragg peaks (Fig. 5). Without added sugar, the central part of the peak is dominated by the resolution of the Germanium monochromator (full circles). Large wings are easily detected but with a significant diffuse scattering, which disables a quantitative determination of the bilayer stiffness using a Caillé-type approach. The Caillé parameter can only be fitted on one peak and not on several orders using the same parameter (Salditt et al., 1998) and the approach is only consistent using three detectable orders when one is far from the phase boundary, i.e., far from maximal swelling, unlike here. Moreover, broadening of the quasi-Bragg peaks can be induced either by a strengthening of the Helfrich force or by partial exclusion due to tension release mediated by the mechanism proposed by Diamant. The two mechanisms may coexist and be of similar magnitude. This coexistence disables the possibility of full calculation of the effect until the complete pressure-distance relation is measured for several sugar concentrations. The full relation (experimental equation of state) of lecithin bilayers in the presence of small solutes is not known and will be considered in the near future by using the osmotic stress induced by polymers in the presence of sugar. The case of sugar addition discussed here, where partial exclusion of sugar occurs together with excess swelling, generalizes the concept of Donnan exclusion, long known in the case of added salt, to nonpolar solutes.