Long Range Interactions beyond first neighbour

Intermolecular forces organizing complex fluids …Laboratory experiments for challenging predictive theories.

•  4-The equation of state of lipids in the multi-lamellar vesicle state in the presence of additives

..charged lipids.. ,plus salts and non-electrolytes

1 thomas.zemb@icsm.fr

With free counter-ion :Charged lipids

Measuring EOS is a way to test the validity of colloidal electrostatics

•  B. Demé (2002) : Giant Collective Fluctuations of Charged Membranes at the Lamellar-to-Vesicle Unbinding Transition 2

•  1,2-Dioleoyl-sn-Glycero-3-Phospho-L-serine-N-sodium salt

•  Formula:

•  Molar Mass = 810

•  Structural charge = 1e/molecule

With free counter-ion :Charged lipids

Measuring EOS is a way to test the validity of colloidal electrostatics

•  B. Demé (2002) : Giant Collective Fluctuations of Charged Membranes at the Lamellar-to-Vesicle Unbinding Transition 3

•  1,2-Dioleoyl-sn-Glycero-3-Phospho-L-serine-N-sodium salt

•  Formula:

•  Molar Mass = 810

•  Structural charge = 1e/molecule

€

π = k.T. ρ+ − ρ−( )E= 0 − 2.ρS[ ]

Without added salt

With added salt (« buffer » ) : e-kdw

dw

D*= dw+2t

2t

What theory says : counter-ion entropy inducethe osmotic pressure

B. Demé, Langmuir, Part II, 18, 2002, 1005-1013

Mg Cl2 P/P0=33%

Mg NO3

P/P0=53%

Na Cl

P/P0=75%

K Cl

P/P0=80%

Ba Cl

P/P0=85% K2SO4

P/P0=95%

10

B. Demé, Langmuir Part I:, 18, 2002, 997-1004

Evolution of SAXS pattern versus dilution

Form factor of a single DOPS bilayer (SAXS)

B. Demé, M. Dubois, Th. Gulik-Krzywicki and Th. Zemb, Langmuir Part I:, 18, 2002, 997-1004

B. DeméLangmuir Part I:, 18, 2002, 997-1004

Extract teh structure factor (powder average) X-rays Neutron

5

DOPS 30%

DOPS 14%

DOPS 5 %

6 « Diluted state »: spontaneous vesicles (inside/outside counter- ion distribution difference)*

*= M. Dubois et al. Langmuir (1991)

B. Demé, M. Dubois, Th. Gulik-Krzywicki and Th. Zemb, Langmuir Part I:, 18, 2002, 997-1004

kc≈ 0.06 dw/Lb => ξ= t.ekc=200nm

d=30 nm; s=80nm;2t=4nm ld > 100nm; lG-C = 1nm; Lb = 0.7nm

« OYSTER » STATE CHARACTERISTICS:

B. Demé, , Langmuir Part I:, 18, 2002, 997-1004

9 « MICROSTARUCTURES » WHILE DECREASING OSMOTIC PRESSURE

B. Demé, Langmuir, Part II, 18, 2002, 997-1004 B. Demé, Langmuir, Part II, 18, 2002, 1005-1013

Vapor pressure

Data for DPPG from Cowley et al, 1978

Osmotic stress using PEG 110

Theevidentnonlinearitydemonstrates self-consistentlythat no salt (background or impurity) induces a measur-able Debye screening length. Also, no exponential en-hancement by uncorrelated fluctuations23 is observed. Inthepast, screeningby residual charged specieshas limitedinvestigations of charged lipid bilayers in the absence ofsalt, as reported in the case of the synthetic cationicsurfactant DDABr.24

In the present case, electrostatic interactions aredominant and long-range order is shownby the sharpnessof quasi-Bragg peaks. However, undulations lead to aprogressive broadening until the structure factor disap-pears. While lowering the imposed osmotic pressures, anasymptotic behavior toward a swelling of 700 Å is shownin Figure 6.

In previous studies, the swelling of DMPS has beendescribed in the presence of variable concentrations ofmonovalent salt by Hauser and co-workers.25,26 Theynoticed that the maximum swelling, that is, the distancewhere the osmotic pressure is expected to vanish, isdependent on the nature of the added salt, but in theabsence of salt the swelling is limited to 105 Å. Again, in

the case ofDMPSbut in the samedomain of concentrationand ionic strength, Cevc et al.27 and Copeland andAndersen28 have measured and explained the effect ofdilutionandpH on the lamellar phasewithmolten chains(LR). Chain melting is shifted from 35 to 50 °C when thenet charge per head ofDOPS is zero due to neutralizationof the negative groups. In our case (DOPS, no added salt),the observedmaximumswelling ismuch larger (!6) thanin these previous studies (Figure 3).

The power-law behavior is shown in Figure 6 wheredata ofFigure 5 are shown in log-log representation. TheLangmuir equation, predicting a dw

-2 decay in the so-called high charge limit, is the universal relation whichconsiders the electrostatic repulsionbetween two chargedplanes facingeachother.8Theequationof stateestablishedexperimentally for DOPS is in good agreement with thisrelation for 100 Å< dw < 500 Å (Figure 6). This behaviorresults from the unscreened electrostatic interaction dueto the absence of residual salt in the case of a chargedlipid with only sodium counterions.

However,wekeep inmind that sodium ionsare stronglycoupled to the bilayers. The Gouy-Chapman length ! isthe distance required to gain/lose 1 kT in free energy forone given counterion. Numerically, the Gouy-Chapmanlength is given by ! ) "/(2#Lb), where Lb is the Bjerrumlength (7.2 Å in water). The area per molecule " ) 62 Å2

is given by the molecular volume of DOPS3 (1350 Å3) andthe known thickness of the membrane 44 Å (see part 1).TheGouy-Chapman length is then 1.4Å forDOPS. Mostcounterions are thus condensed in the first nanometer,that is, a thickness largelybelowthewater layer thickness.The distribution of remaining counterions presents nogradient between bilayers. The midplane theorem8 iden-tifies the osmoticpressurewith the activity of counterionsat dw/2. We are here in a typical range of millimoles. Inthat regime, dw . ! and a prediction by Attard et al. isavailable:2

We compare this prediction to our experimental datain Figure 6. At the swelling cutoff which appears as adeviation from the Langmuir equation, data are closer tothe Gouy-Chapman regime given by eq 2, but the slopeof the experimental decay is significantly different fromthis prediction.

In the dilute regime limit, this prediction has beenrecalculated by Lukatsky and Safran29 with slightlydifferent numerical constants. It is markedly differentfromthepower-lawdecay (dw

-3/2) calculatedas theperfect-gas limit.30 This would give a different slope too, incom-patible with our experimental results.

deVries,31usinga theorydevelopedbyOdijk,32 considersthe case of large undulations occurring at high charge inthe condition !d > 10. In the case of DOPS, we have !-1

" 100 nm, dmax ) 70 nm. We are in a regime where deVriespredictsno fluctuationenhancing of the electrostaticterm and no damping either. Considering the pressure-distance relation, the asymptotic swelling appears as a

(23) de Vries, R. Phys. Rev. E 1997, 56, 1879-1886.(24) Dubois, M.; Zemb, Th. Langmuir 1991, 7, 1352-1360.(25) Hauser, H.; Shipley, G. G. Biochemistry 1983, 22, 2171-2178.(26) Hauser, H.; Paltauf, F.; Shipley, G. G. Biochemistry 1982, 21,

1061-1067.

(27) Cevc, G.; Watts, A.; Marsh, D. Biochemistry 1981, 20, 4955-4965.

(28) Copeland, B. R.; Andersen, H. C. Biochemistry 1982, 21, 2811-2820.

(29) Lukatsky, D. B.; Safran, S. A. Phys. Rev. E 1999, 60, 5848-5857.

(30) Pincus, P. A.; Safran, S. A. Europhys. Lett. 1998, 42, 103-108.(31) de Vries, R. J. Phys. II France 1994, 4, 1541-1555.(32) Odijk, T. Langmuir 1992, 8, 1690-1691.

Figure6. Log-log representationof thepressure!vsdistancecurve (same data as Figure 5). The dashed line is calculatedaccording to the Langmuir equation (eq 1), and the solid lineis the relation proposed by Attard et al. (ref 2) (eq 2). Thisrepresentation evidences the dominant electrostatic repulsionin the case of counterions only. At pressures exceeding 107 Pa,steric terms come into play and the pressure is higher thanpure electrostatics. In the regime where the electrostaticrepulsion is the dominant interaction, the Langmuir equationholds. At 103 Pa (arrow), the pressure drops sharply towardcomplete unbinding. The same symbols as inFigure 5 are used.

! =kbT

dw3 [2 + #

2ln(dw

! )] (2)

1010 Langmuir, Vol. 18, No. 4, 2002 Deme et al.

Langmuir (1937) … Ninham B, Attard P , Safran (1998)

DDAB DOPS

In cationic lipids, thory overestimates the osmotic pressure, ??? 14

M. Dubois, Th. Zemb , Current Opinion in Coll. and Interf. Sci. 5, 2000, 27-37

Charged layers in the presence of added salts

•  D. Andelmann (1995) «Electrostatic properties of membranes » 17

The two first are obesrved experimentally

€

Π = 64.kT.cs ' .γ2.e−κ .dw

κ = Zi2ci

M. Dubois. « Osmotic pressures in lamellar phases in the presence of added salt » (1992)

What theory says at saturation plus added salt :

Addition of small solutes: DMPC + SUGAR ? 2 cases: -excess water: zero pressure - in the linear swelling regime

Lipids with sugar in the « interlayer » water

10-3

10-2

10-1

100

101

102

103

104

I(q)

cm

-1

2 4 6 80.01

2 4 6 80.1

2 4

q Å-1

150

100

50

0

√I(q

) c

m-1

/2

1.00.80.60.40.20.0

ΦD2O

« Where » is the sugar gone ?

B. Demé, J. Applied Cryst. (2000 ) 33, 569-573

Sugar adsortion equilibria : partial release of bound water

Demé, B: Hydration forces between bilayers in the presence of dissolved or surface-linked sugars (2011)

20% DMPC with added glucose and fructose

minimum at a sugar concentration !s " 0.22 and a maximum of theweakening of the van der Waals attraction at that concentration (LeNeveuet al., 1977). To account for the presence of the sugar in the aqueous layersof the lamellar phase, we have calculated !s for the different sugarconcentrations !s considering the partition of the sugar between lamellardomains and the excess solution (Deme and Zemb, 2000). From !s " 0 to0.22, the van der Waals attraction is progressively weakened, and therelative strength of repulsive contributions increases, leading to theobserved swelling. Above !s " 0.22, van der Waals forces are rein-forced leading to a stronger attractive contribution and an expecteddeswelling. In the presence sugar, we use the double film model, whichgives a good approximation of the triple film model (see Fig. 4) and forwhich the dependence of the Hamaker constant is known (LeNeveu etal., 1977).

RESULTS

Scattering curves

Fig. 1 shows a selection of two-dimensional SAXS patternsillustrating the effect of adding glucose to the DMPC la-mellar phase. Two sharp quasi-Bragg reflections character-istic of the lamellar structure are clearly visible. The effectof adding sugar is already visible at 5%: the reflectionsbroaden and the second order disappears around #$s% "0.20 by weight of sugar in the aqueous phase. On radiallyaveraged data (Fig. 2, in I(q)&q2 versus q representation),

FIGURE 1 Selection of two-dimensional SAXS patterns of DMPC/glucose suspensions prepared with increasing concentrations of glucose (from left toright: $s " 0, 0.05, 0.10, and 0.20). The volume fraction of the lipid #$L% relative to the “water ' sugar volume” is 0.20.

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 glucoseor 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 of Lecithin Lamellar Phases 219

Biophysical Journal 82(1) 215–225

20% DMPC with added glucose and fructose

one can verify that despite the important disorder, the sam-ples are still lamellar at high sugar concentration. In bothcases (glucose and saccharose), the monotonic swelling andthe simultaneous softening are evidenced by a shift of thepeaks toward low angles and by the progressive broadeningof the quasi-Bragg reflections. Because the indexing is keptfor any sugar content explored, the shift of the peak to smallangles corresponds to a monotonic increase of the interla-mellar spacing. In binary suspensions (DMPC ! water), themembrane thickness is known to vary only in the monopha-sic L! domain where no excess of water is present (Janiaket al., 1976) and at the L"-P"" and P""-L! transitions due todifferent chain tilt angles or melting of the chains. In ternarymixtures with saccharose (Stumpel et al., 1985) small de-viations can be attributed to an untilting of the chains butnever lead to a swelling increase of several tens of ang-stroms as observed here. The change in periodicity of thelamellar phase is due to an increase of the water layerthickness.

Swelling versus sugar concentration

The effect of mono- and disaccharides on the periodicityof the lamellar phase is shown on Fig. 3. Data obtainedwith egg lecithin (two lower curves) are the results fromLeNeveu et al. (1977) obtained with glucose and saccha-rose, whereas data obtained with DMPC (two upper

curves) correspond to the spacings calculated from thescattering curves shown in Fig. 2 with glucose and fruc-tose. Here, we have plotted the periodicity change #dinstead of the periodicity d to account for the differencein periodicity between DMPC (60.4 Å) and egg lecithin(63 Å) in the absence of sugar. The difference is due tothe chain composition of DMPC (two C14 chains) and egglecithin (mixture of various chain lengths). DMPC andegg-lecithin have bending rigidities of the order of $10kT (Sackmann, 1995). Small differences in thickness dueto different chain lengths may affect the van der Waalscontribution (Eqs. 7 and 10) but not significantly inregard to the deviations of several tens of Angstromsobserved here.

Fig. 3 shows the monotonic swelling observed uponaddition of sugar in the range of studied concentrations(solid lines are guides to the eyes). It emphasizes the globaleffect of adding small hydrosoluble molecules such as glu-cose or fructose: favoring repulsive interactions leading to amonotonic swelling. The same trend is observed for themono- and the disaccharide with a more pronounced swell-ing excess with the disaccharide, as previously reportedwith other disaccharides like lactose (Deme et al., 1996) orsaccharose (Ricoul et al., 1997). There is a large differencebetween our data and older results (LeNeveu et al., 1977;Stumpel et al., 1985) and an opposite trend at high sugarconcentration. In a previous study (Deme, 1995; Deme etal., 1996), we already observed a swelling-deswelling se-quence induced by the addition of oligosaccharides. But thiswas observed when samples were equilibrated only a fewdays. In such a case, nonequilibrium of the sample results inan excess of sugar in the reservoir leading to an osmoticcompression of the lamellar phase analogous to the oneobserved with polysaccharides. Osmotic pressures of con-centrated sugar solutions can be that high that an uncom-pleted diffusion can result in opposite effects to those ob-served at equilibrium.

Force balance in pure water

We have calculated the van der Waals force according tothree different models: the double film model with the headgroups either in or out of the aqueous layers and the triplefilm model with Hamaker constants for the chains/headsinterface, the head/water interface, and the cross-term. Weused the following Hamaker constants: A1 % 3 & 10'21 J,A2 % 10'22 J, and A3 % 10'21 J (Ricoul, 1997). The threepressure-distance curves are shown in Fig. 4 A. We havecalculated the total pressure-distance curve in the threecases considered here (Fig. 4 B). The two series of curvesshow that the triple film model (solid line) is best approx-imated by the double film model when the head group layeris included in the membrane (dashes) rather than in theaqueous phase (dots). This is due to the fact that dielectricproperties of the layer of hydrated headgroups are closer to

FIGURE 3 Change of the periodicity of the lamellar domains versussugar concentration in the aqueous phase as measured by SAXS. Ourresults obtained with DMPC ! glucose (E) and fructose (!) are comparedwith those of LeNeveu et al. (1977) obtained with egg lecithin ! glucose(R) and saccharose (v). Plotting #d instead of d accounts for the mem-brane thickness difference between the two phospholipids. Data obtainedwith DMPC are calculated from curves of Figs. 1 and 2. The error on d isof the order of (0.5 Å ((1 Å on #d). The solid lines are guides to the eye.

220 Deme et al.

Biophysical Journal 82(1) 215–225

Swelling AND peak broadening the stack is observed at eqiilibrium

compared with the resolution function of the cameradetermined experimentally with an attenuated transmittedbeam (FWHM ! 8.8 " 10#3 Å#1). This comparisonshows that the effect of softening increases with theamount of sugar and that it is strong enough to beobserved with a setup not particularly optimized forhigh-resolution experiments.

It is known that added compounds can drastically modifythe bending rigidity of phospholipid membranes, either inthe direction of a stiffening or in that of a softening (Sack-mann, 1995). However, we are not aware of any evidence ofa membrane softening by nonlipophilic or nonamphiphilicmolecules. The general underlying mechanism of mem-brane softening by small carbohydrate molecules is notunderstood, although the data clearly show the combinationof a swelling and a softening. McDaniel et al. (1983) haveproposed a mechanism in the case of a softening induced byanother small carbohydrate (glycerol). Surface tension mea-surements on water-glycerol mixtures show that glycerolreduces the surface tension of water. Using Gibbs’ equationand for 50% glycerol, 90% of the surface is occupied byglycerol. Thus, lateral repulsions and the area per moleculecould be increased and this could favor a softening of thebilayer by thinning of the apolar layer. But there is no directevidence of such mechanism in the ternary system. Thereason why disaccharides induce more swelling thanmonosaccharides is also not completely clear, although arelation with the solute size has already been reported(Deme et al., 1996) and may seem straightforward.

The change of dielectric properties of the water layersinduces deviations of the order of a few Angstroms. TheHamaker constant is calculated for every interbilayersugar concentration (!s) and by taking into account theknown optical properties of the solution. Without sugarA ! 1.24 kT, at the optical match point A ! Av!0 ! 0.71kT, 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 hy-dration, van der Waals, and entropic contributions havebeen added and where the only variable is the bendingrigidity constant of the membranes kc. The calculationwas done in the absence of sugar (6A) and at the matchpoint of the frequency-dependent van der Waals contri-bution where Av$0 ! 0 (!s ! 0.22). In this approach, wedo not introduce tension release but incorporate all soft-ening effects into an effective bending constant and ex-tract the equilibrium distance versus kc. For any value ofkc it is given by the intercept of the pressure-distancecurve with the x axis, where attractive and repulsiveterms counterbalance. Fig. 7 shows the full set of equi-librium distances versus kc resulting from the simulationcompared with experimental equilibrium distances ob-tained without sugar, with glucose or fructose. As shownon Fig. 6, A and B, below a certain value of kc the curvesdo not go through an attractive regime anymore, and thepressure-distance curve becomes purely repulsive. Thispredicts an unbinding transition and yields both the equi-

FIGURE 5 Peak shapes (E) in normalized representation (I/Io versus q-qo), and experimental instrument resolution function of the SAXS camera (F),showing the broadening of quasi-Bragg reflections upon addition of glucose and fructose to the lamellar suspensions. Results are shown for sugarconcentrations ranging from 0 to 0.20 w/w of glucose (left) and fructose (right). The FWHM of the resolution function is 8.8 " 10#3 Å#1.

222 Deme et al.

Biophysical Journal 82(1) 215–225

Demé, B (2002) : Swelling of lecithin lamellar phases in the presence of small carbohydrates

Demé, B (2002) : Swelling of lecithin lamellar phases in the presence of small carbohydrates

Force balance in the presence of solute at 20% lecithin

librium distance of the membranes in lamellar domainsbefore unbinding and the value of kc at which unbinding

should occur. As shown on Fig. 6 B in the presence ofsugar, the prediction is not in agreement with the exper-imental result, unbinding being predicted for distancesbelow those observed experimentally. In the absence ofsugar the entropic term is less pronounced and the valueof kc that yields the experimental distance is 20 ! 5 kT.

In the presence of sugar, we observe experimentally anincrease of 22 Å (glucose) and 28 Å (fructose), which wouldbe due to fluctuation of membranes directly or indirectly as-sociated to bilayer softening or tension release. Note thatwithin this simple additive model, ignoring the effect of sur-face tension release, an unbinding at 72 Å for a kc " 4.5 kT,associated to the Helfrich force dominating van der Waals, ispredicted. If we consider the increase in maximal periodicityobserved here without unbinding, we have to conclude thatrepulsion forces are increased monotonically in the presence ofsugar. Depletion due to undulation also adds an attractivepotential that prevents unbinding. Because we have the com-bination of two effects and nonlinearity of the interactions,numerical simulations of pressure-distance curves are doneusing an effective bending constant. In principle, one couldsimulate these curves and extract the equilibrium periodicityby keeping kc constant and varying !, according to Seifert’sexpression (Seifert, 1995).

The presence of fluctuations due to membrane softeningand/or release of surface tension is consistent with theobserved evolution of the shape of the quasi-Bragg peaks(Fig. 5). Without added sugar, the central part of the peak isdominated by the resolution of the Germanium monochro-

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 thevan 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.

FIGURE 7 Comparison of simulated periodicities to those observed exper-imentally. Simulated values of d are extracted from pressure-distance curves asthose shown in Fig. 6 in absence of added sugar (f) and in the presence ofsugar at #s " 0.22 (!). Experimental values are represented as dotted lineswithout sugar (61.4 Å) and at the point of maximal screening of the van derWaals contribution in the case of glucose and fructose (respectively dmax " 82and 88 Å). Both series of simulations suggest an unbinding transition for avalue of d well below the experimental values.

Swelling of Lecithin Lamellar Phases 223

Biophysical Journal 82(1) 215–225

and water (A1(. . . )), aliphatic chains and head groups (A3(. . . )), and across-term (A2(. . . )). This latter term is one order of magnitude below thetwo others and is usually neglected (Evans and Needham, 1987).

Hydration forces

This exponential interaction dominating all other contributions at shortdistances (!25 Å) has been largely studied in a number of systems and hasbeen reviewed (Rand and Parsegian, 1989). The hydration pressure isknown for DMPC from previous osmotic stress measurements using pul-lulan solutions (Deme et al., 1996). It is characterized by an exponentialdecay length of 1.91 Å and an extrapolated pressure at zero separation of4.5 " 109 N/m2 yielding the distance-dependent contribution:

#hyd.$dw% ! 4.5 " 109e&dw/1.91 (11)

The decay length is close to the value of 1.93 Å reported for egg lecithin(LeNeveu et al., 1976) but slightly below the 2.2 Å reported for DMPC (Liset al., 1982).

In the following, we will consider that confined sugar molecules do notinterfere with the polar head layer and do not modify the hydration force.This assumption is supported by a recent small angle neutron scatteringstudy where contrast variation was used to determine the partition of sugarsbetween lamellar domains and excess solution (Deme et al., 2000). It wasshown that sugar molecules are partially depleted from the confined region.The absence of interaction between glucose monomers and phosphocholineheadgroups was also shown by neutron reflectivity on DMPC monolayersspread on glucose and pullulan solutions (Deme and Lee, 1997). Finally, inthe range of periodicities observed in the presence of sugar it vanishes andcan be considered negligible at high sugar concentration.

Entropic forces

The entropic contribution (Helfrich, 1978) that originates in excluded-volume interactions is usually neglected in the force balance of lipidsforming stiff membrane stacks. Effectively, considering a membrane bend-ing rigidity kc of the order of 10 kT for pure DMPC in water (Sackmann,1995) and introducing a repulsive term of entropic origin in the forcebalance increases the equilibrium distance of the membranes by less than1 Å. The effect is minor in the binary system, but it has importantconsequences in the ternary system (when the lamellar phase is swollenand the van der Waals contribution in the balance weaker). We will takethis contribution into account by using the relation (Helfrich, 1994):

#und.$dw% !3#2

64$kT%2

dm3.kc

! '

1 $ '"3

(12)

in which ' is the volume fraction of the lipid in the lamellar domainsdeduced from the measured lamellar spacing and from the known mem-brane thickness dm (35.5 Å).

Forces associated with sugar exclusion frommultilayer vesicles

If the multilayer vesicle, on the time scale considered, is permeable to thesmall solute, the activity of molecules inside and outside is the same andthere is no osmotic term due to sugar exclusion from the MLVs. Anotherview of the same effect is to consider that the first hydration layer is notavailable for the solute (Lyle and Tiddy, 1986; Deme and Zemb, 2000).Thus, the concentration of solute in the mid-plane between bilayers is thesame as in the bulk and hence, no compression due to osmotic stressinduced via depletion has to be considered. The case of uncharged mole-cules has been recently considered in detail (Bonnet-Gonnet et al., 2001).

However, we have to consider the general mechanism proposed recently(Diamant, 2001) where the partial exclusion of solute from the bilayersallows the release of surface tension and thus minimizes the free energy. Inthe presence of this mechanism implying depletion of sugar, the LaplaceEq. 4 has to be corrected according to:

(#i$dw% ! po % 2&/RMLV (13)

in which the osmotic stress is difficult to evaluate. This extra osmoticcompression due to this new type of depletion cannot be evaluated quan-titatively. There is only a higher bound for it, considering the concentrationdifference inside and outside. If the solution is equivalent to a perfect gas,this upper limit is given by:

po ' $)*s $ )s%kT (14)

if )s is expressed as a number density (m&3).The mechanism proposed by Diamant is analogous to a depletion

mechanism. However, it is not a depletion due to sterical incompatibility asin the case of polymers, but the concentration inside and outside aredifferent because of the nonvanishing surface tension of the bilayers in agiven crystallite of smectic phase, i.e., one multilayer vesicle (or onion)versus external medium. Thus, to minimize the bilayer free energy, deple-tion of the nonadsorbing solute can be associated to the undulations of thebilayer without intrinsic local softening of the bilayer.

Force balance and additivity

A long standing problem is the validity of adding entropic forces tomolecular interactions. This was reviewed recently (Lipowsky, 1995b).The general difficulty is that fluctuations enhance any exponentially de-creasing interaction. Analytical solutions to these problems are not avail-able, and treatments using renormalization theory only indicate trends.Because additivity of molecular forces with entropic contributions cannotbe supposed a priori, we only indicate qualitative trends for the “effectivestiffness” of the membrane, either directly induced by the presence of thesolute or via the tension release suggested by Diamant.

Partition of sugars between lamellar phase andexcess solution

Using small-angle neutron scattering and solvent contrast variation withdeuterated sugars, we have determined the sugar partition coefficient inmicroseparated samples (Deme and Zemb, 2000). In the system presentedhere, detailed knowledge of the composition of the two coexisting phasesallows a quantitative reinterpretation of the equation of state (pressureversus distance). At equilibrium, in samples prepared with a mean sugarvolume fraction !'s+ , 0.115 the sugar concentration in the interbilayerwater layers is lower by -one-third than in the excess solution (respec-tively )s , 0.095 and )s* , 0.155). This corresponds to a partialexclusion of 18% of sugar molecules from the water layers relative to themean sample concentration !'s+, leading to )s* + )s. We take thiseffect into account by considering the exact sugar concentration betweenbilayers ()s) to calculate the extent of screening of the dispersion force.

Force balance in the presence of sugar

Addition of sugar to water increases the index of refraction of the aqueouslayers and as a consequence decreases the difference in polarizabilities (Eq.7). This reduces the contribution of visible frequencies to the total van derWaals interaction. At a sufficiently high interbilayer sugar concentration()s), the aqueous polarizability begins to exceed that of the hydrocarbonand polar head layers and the total interaction increases with added sugar.Thus, the Hamaker constant is modified but not monotonically with a

218 Deme et al.

Biophysical Journal 82(1) 215–225

and water (A1(. . . )), aliphatic chains and head groups (A3(. . . )), and across-term (A2(. . . )). This latter term is one order of magnitude below thetwo others and is usually neglected (Evans and Needham, 1987).

Hydration forces

This exponential interaction dominating all other contributions at shortdistances (!25 Å) has been largely studied in a number of systems and hasbeen reviewed (Rand and Parsegian, 1989). The hydration pressure isknown for DMPC from previous osmotic stress measurements using pul-lulan solutions (Deme et al., 1996). It is characterized by an exponentialdecay length of 1.91 Å and an extrapolated pressure at zero separation of4.5 " 109 N/m2 yielding the distance-dependent contribution:

#hyd.$dw% ! 4.5 " 109e&dw/1.91 (11)

The decay length is close to the value of 1.93 Å reported for egg lecithin(LeNeveu et al., 1976) but slightly below the 2.2 Å reported for DMPC (Liset al., 1982).

In the following, we will consider that confined sugar molecules do notinterfere with the polar head layer and do not modify the hydration force.This assumption is supported by a recent small angle neutron scatteringstudy where contrast variation was used to determine the partition of sugarsbetween lamellar domains and excess solution (Deme et al., 2000). It wasshown that sugar molecules are partially depleted from the confined region.The absence of interaction between glucose monomers and phosphocholineheadgroups was also shown by neutron reflectivity on DMPC monolayersspread on glucose and pullulan solutions (Deme and Lee, 1997). Finally, inthe range of periodicities observed in the presence of sugar it vanishes andcan be considered negligible at high sugar concentration.

Entropic forces

The entropic contribution (Helfrich, 1978) that originates in excluded-volume interactions is usually neglected in the force balance of lipidsforming stiff membrane stacks. Effectively, considering a membrane bend-ing rigidity kc of the order of 10 kT for pure DMPC in water (Sackmann,1995) and introducing a repulsive term of entropic origin in the forcebalance increases the equilibrium distance of the membranes by less than1 Å. The effect is minor in the binary system, but it has importantconsequences in the ternary system (when the lamellar phase is swollenand the van der Waals contribution in the balance weaker). We will takethis contribution into account by using the relation (Helfrich, 1994):

#und.$dw% !3#2

64$kT%2

dm3.kc

! '

1 $ '"3

(12)

in which ' is the volume fraction of the lipid in the lamellar domainsdeduced from the measured lamellar spacing and from the known mem-brane thickness dm (35.5 Å).

Forces associated with sugar exclusion frommultilayer vesicles

If the multilayer vesicle, on the time scale considered, is permeable to thesmall solute, the activity of molecules inside and outside is the same andthere is no osmotic term due to sugar exclusion from the MLVs. Anotherview of the same effect is to consider that the first hydration layer is notavailable for the solute (Lyle and Tiddy, 1986; Deme and Zemb, 2000).Thus, the concentration of solute in the mid-plane between bilayers is thesame as in the bulk and hence, no compression due to osmotic stressinduced via depletion has to be considered. The case of uncharged mole-cules has been recently considered in detail (Bonnet-Gonnet et al., 2001).

However, we have to consider the general mechanism proposed recently(Diamant, 2001) where the partial exclusion of solute from the bilayersallows the release of surface tension and thus minimizes the free energy. Inthe presence of this mechanism implying depletion of sugar, the LaplaceEq. 4 has to be corrected according to:

(#i$dw% ! po % 2&/RMLV (13)

in which the osmotic stress is difficult to evaluate. This extra osmoticcompression due to this new type of depletion cannot be evaluated quan-titatively. There is only a higher bound for it, considering the concentrationdifference inside and outside. If the solution is equivalent to a perfect gas,this upper limit is given by:

po ' $)*s $ )s%kT (14)

if )s is expressed as a number density (m&3).The mechanism proposed by Diamant is analogous to a depletion

mechanism. However, it is not a depletion due to sterical incompatibility asin the case of polymers, but the concentration inside and outside aredifferent because of the nonvanishing surface tension of the bilayers in agiven crystallite of smectic phase, i.e., one multilayer vesicle (or onion)versus external medium. Thus, to minimize the bilayer free energy, deple-tion of the nonadsorbing solute can be associated to the undulations of thebilayer without intrinsic local softening of the bilayer.

Force balance and additivity

A long standing problem is the validity of adding entropic forces tomolecular interactions. This was reviewed recently (Lipowsky, 1995b).The general difficulty is that fluctuations enhance any exponentially de-creasing interaction. Analytical solutions to these problems are not avail-able, and treatments using renormalization theory only indicate trends.Because additivity of molecular forces with entropic contributions cannotbe supposed a priori, we only indicate qualitative trends for the “effectivestiffness” of the membrane, either directly induced by the presence of thesolute or via the tension release suggested by Diamant.

Partition of sugars between lamellar phase andexcess solution

Using small-angle neutron scattering and solvent contrast variation withdeuterated sugars, we have determined the sugar partition coefficient inmicroseparated samples (Deme and Zemb, 2000). In the system presentedhere, detailed knowledge of the composition of the two coexisting phasesallows a quantitative reinterpretation of the equation of state (pressureversus distance). At equilibrium, in samples prepared with a mean sugarvolume fraction !'s+ , 0.115 the sugar concentration in the interbilayerwater layers is lower by -one-third than in the excess solution (respec-tively )s , 0.095 and )s* , 0.155). This corresponds to a partialexclusion of 18% of sugar molecules from the water layers relative to themean sample concentration !'s+, leading to )s* + )s. We take thiseffect into account by considering the exact sugar concentration betweenbilayers ()s) to calculate the extent of screening of the dispersion force.

Force balance in the presence of sugar

Addition of sugar to water increases the index of refraction of the aqueouslayers and as a consequence decreases the difference in polarizabilities (Eq.7). This reduces the contribution of visible frequencies to the total van derWaals interaction. At a sufficiently high interbilayer sugar concentration()s), the aqueous polarizability begins to exceed that of the hydrocarbonand polar head layers and the total interaction increases with added sugar.Thus, the Hamaker constant is modified but not monotonically with a

218 Deme et al.

Biophysical Journal 82(1) 215–225

after several weeks of molecular diffusion (Deme et al., 1996). Thisrapid reswelling is a critical step, particularly when the “solvent” is apolymer solution (Deme et al., 1997). In the partition equilibrium of asmall solute, it is crucial that the samples are studied at equilibrium ofthe chemical potentials of all entities, because any difference betweenthe coexisting phases may have dramatic effects. In the present case ofhigh sugar concentrations, a residual osmotic stress can be strong andlead to important modifications of the equilibrium distance betweenmembranes. However, diffusion coefficients of small sugars are suchthat the equilibrium time remains within the range of 1 to 2 weeks, i.e.,reasonable time compared with the quasi infinite time required forpolymers to diffuse in confined water layers and compatible with thechemical 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 thechain melting temperature of pure DMPC, corresponding to the P!!-L"

transition (23°C) and still above the transition in the presence of sugar(Stumpel et al., 1985). SAXS experiments are performed directly on thebiphasic mixtures. The ternary samples are microseparated with the lamel-lar phase at “maximal swelling” in equilibrium with excess sugar solution.Large multilayer vesicles are formed on a mesoscopic scale, i.e., they aretoo small to be easily separated from the pure coexisting solvent but largeenough to produce sharp and perfectly isotropic Debye-Sherrer ringswhose profile is not limited by the number of layers but by the interlayerfluctuations (Dubois and Zemb, 1991). Lamellar domains appear in theform of onions or MLVs producing Maltese crosses under polarizingmicroscope and hence contain several thousands of membranes and somemacroscopic surface tension (Diamant, 2001), which may quench fluctu-ations (Seifert, 1995). Unfortunately, the value of the tension and how itchanges in the presence of sugar are not known.

Force balance

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

dm # dh $ 2dp (5)

in which dh is the thickness of the hydrocarbon core and dp

that of the polar head layer. The measured periodicity is thesum of the membrane and water layer thicknesses:

d # dm $ dw (6)

van der Waals forces

In the following calculations only the force between first neighbors isconsidered (Israelachvili, 1991). The thickness of the membrane inexcess water is considered constant. It is known to be concentrationdependent in the monophasic L" domain and to vary at phase transitionswhere chain-packing rearrangements take place (Janiak et al., 1979).Regarding retardation effects that affect the frequency-dependent con-tribution of the Hamaker constant (Ninham and Parsegian, 1970), wehave neglected them because of the membrane separations, which donot exceed 50 Å.

Double film model

The relation used to calculate the van der Waals pressure considers, in thecase of the double film model, a thickness da that corresponds to the

thickness of the aqueous region separating the hydrophobic layers. Thecontribution of the van der Waals attraction to the total pressure of thesample can be calculated according to Ninham and Parsegian (1970):

"vdw#dw$ # %A

6& ! 1da

3 %2

#da $ dh$3 $

1#da $ 2dh$

3"(7)

in which A is the nonretarded Hamaker constant calculated for the sym-metric case of two identical apolar phases interacting across water. It canbe decomposed into a zero frequency contribution (Av%0) and a frequency-dependent contribution (Av&0) (Israelachvili, 1991):

A # Av%0 $ Av&o #34 kT#'1 % '2

'1 $ '2$2

$3hve

16%2

#n12 % n2

2$2

#n12 % n2

2$3/2

(8)

in which subscripts 1 and 2 refer to the apolar phase and to the water,respectively. h is the Planck constant % 6.63 ' 10(34 J's, '1 and '2 thedielectric constants, n1 and n2 the refractive indexes, and ve the absorptionfrequency. Taking '1 % 2, '2 % 80, n1 % 1.464, n2 % 1.333, and a singleabsorption frequency in the ultraviolet ve % 3 ' 1015 s(1 one obtains:

A # Av%0 $ Av&0

# 2.9 ( 10(21 $ 2.2 ( 10(21

# 5.1 ( 10(21J #1.2 kTroom$ (9)

Triple film model

It has been shown (Attard and Mitchell, 1987; Attard et al., 1988) thatthe shape of experimental pressure-distance curves was better repro-duced when a more detailed triple film model was considered todescribe the membrane as a well-defined medium composed of distincthydrophobic and polar regions with distinct dielectric properties (Nin-ham and Parsegian, 1970; Evans and Needham, 1987). In this case, thetriple film model describes the van der Waals pressure, according to therelation (Ninham and Parsegian, 1970):

"vdw#dw$ # %A1

6&! 1dw

3

%2

#dw $ 2dp $ dh$3 $

1#dw $ 4dp $ 2dh$

3"%

A2

6&! 1#dw $ dp$

3 %1

#dw $ dp $ dh$3

%1

#dw $ 3dp $ dh$3 $

1#dw $ 3dp $ 2dh$

3"%

A3

6&! 1#dw $ dp$

3 %1

#dw $ 2dp $ d)3

$1

#dw $ 3dp $ 2dh$3" (10)

which accounts for a Hamaker constant related to correlations of differ-ences in polarizability between adjacent layers, integrated over the elec-tromagnetic spectrum. It is the sum of three terms related to polar heads

Swelling of Lecithin Lamellar Phases 217

Biophysical Journal 82(1) 215–225

Equation of state when the solvent is a glucose solution

DMPC/glucose/dextran/H2O quaternary samples in excess sugar solution

zwitterionic bilayers [11]. This simulation suggests a larger concen-tration of trehalose near the interface, suggesting preferential bindingat the lipid bilayer [12,13]. Adsorption of sugar should profoundlymodify the intensity of the hydration force.

In a seminal paper, Lyle and Tiddy [14] demonstrated theequivalence of the hydration force as measured via osmotic stressand the speciation of free/boundwater partition asmeasured by NMR.If one considers as “free” all water molecules that rotate fast, with anet free energy of interaction with the bilayer of less than 1 kT, and as“bound” all water molecules with slow motion, large NMR protonrelaxation due to free energy higher than 1 kT, one can derive anexponential value of the hydration force. This force is seen as aderivative of the free energy versus spacing from NMR and vice-versain the whole domain of existence of lamellar phases of neutral linearsurfactants containing polyoxyethylene head-groups. These experi-ments have been a direct proof of the dehydration with constantdecay lengthwhen varying temperature. In binary systems containinghydrated uncharged head-groups, the “molecular force balance” is thesimplest known, since hydration forces compensate attractive van derWaals forces. One considers only the interplay between two majormechanisms when analysing experimental results obtained via directthermodynamic methods, implying some control or measurement ofthe water activity, including via relative vapour pressure.

From a thermodynamical point of view, forces between water–oilinterfaces in the presence of sugar can be quantified from surfacetension data only, since partial exclusion or adsorption from a solute ona liquid–liquid interface must be considered. In this thermodynamicalapproach, sucrose and glucose are seen as repelled from the water–airinterface, while glycerol is “neutral” towards the same interface, i.e. it isneither depleted nor adsorbed (a situation largely exploited in freezefracture electronmicroscopy techniques). The situation at the air–waterinterface is linked to the water penetration “into” the phospholipidlayer [15].

The situation is totally different for glycolipids, i.e. when thecarbohydrates made from one up to seven sugar rings are bound tothe bilayer via covalent binding. In this case the dominating repulsionoriginates from the water molecules bound to the sugar headgroupsexposed to the solvent. Glycolipid binary phase diagrams indeedresemble phase diagrams in the presence of chaotropic ions [16] orhydrotropes [17].

However, osmotic pressures of zwitterionic lipids below andbeyond chain melting temperature have not been demonstrated to bequalitatively different. In the frozen-chain form, protruding head-groups are bound to a crystalline plane. To our knowledge, dynamicalprotrusion mechanism has not been detected experimentally asdominant for a short range primary hydration force [18,19].

In the case of grafted head-groups, i.e. the case of glycolipids, anexponential repulsive primary hydration is expected, albeit withlarger contact pressure. This is the case for neutral glycolipids, whilethe presence of charged glycolipids, e.g. those containing sialic acidfunctions, are expected to be also affected by secondary hydrationforces [7,20,21]. In the latter case, the surface layer can even bedepleted from the surface. In this review, the hydration forces will beconsidered separately for the two cases.

Since the introduction of the SFA [22] and of the more reliable“colloidal probe method” based on the AFM combined to a small glassbead [23], a dominating “long range” attractive interaction hassometimes been reported. The sugar hydration layer has a lowerdielectric constant thanpurewater sincewaterdipoles are “immobilised”by the semi-rigid sugar ring. Therefore, the van der Waals attractionconsidered in the so-called triple film approximation is amplified [24]. Inthe force balance, this enhanced van der Waals interaction coulddominate all repulsive hydration mechanisms. We do not consider thisphenomenon in the present review, since it is an effect of the presence ofsugar on the van derWaals attractionwhich is always present [25–28]. Atypical example where short range hydration with 0.2 nm decay can bedistinguished from electrostatic repulsion due to low ionic strength isshown in Fig. 2 [28]. In this case of a membranemade of GM1 andDDPC,the attraction mechanism is linked to the intermediary range locatedbetween the two exponential decays. Close to 40 nm, a damping of theforce is measured. However, when osmotic stress at equilibrium is used,all molecular mechanisms including lateral fluctuations and in-planemiscibility effects are participating and combine together [8]. This is notthe case in AFM or SFA indirect experiments since hysteresis effects arestrong. Hysteresis effects due to lateral segregation have also beenobservedusing agemini glycolipidmixedwithDPPC [29]. In this case, thehydration force could not be determined quantitatively since bilayers

Fig. 1. MD simulation snapshot of DPPC bilayers in the presence of trehalose (taken from[11]); copyright Taylor and Francis 2006.

Fig. 2. Forces between GM1/DPPC (25/75) coated mica surfaces in water. The long rangeelectrostatic force is fitted assuming a surface potential of 30 mV. Three compressions areshown (T=20 °C, pH 5.6). Taken from [28]; copyright Elsevier 1993.

585B. Demé, T. Zemb / Current Opinion in Colloid & Interface Science 16 (2011) 584–591

Hydration force and undulation increase ?

What we have learnt for non-electrolytes :

Measuring EOS is a way to test force balance for bilayers van der Waals, hydration, electrostatic, depletion +

steric entropic… (.. But lateral equation of state is needed in anisotropic systems…) Water soluble additives:

-are either dissolved or adsorbed (steric) -always change the van der Waals forces -may induce softening and undulations - change the hydration force ?

•  B. Demé (2011) Hydration forces bewteen bilayers in the presence of dissolved or surface-linked sugars 27