Langmuir 1991, 7, 1900-1908
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Entropy-Driven Tension in Vesicle Membranes and Unbinding of Adherent Vesicles Evan Evans Pathology and Physics, University of British Columbia, Vancouver, British Columbia, Canada V6T 1 W5 Submitted to Symposium Chairman October 8, 1990. Received November 15,1990. I n Final Form: April 22, 1991 In recent years, it has become apparent that condensed-fluid membranes behave similar to linearflexible polymers. Thermal motions act to randomize surface conformations; thus, constraints posed by closed capsule volumes or binding to stiff substrates lead to entropy-driven steric forces. With micromechanical methods, entropy-driventension (and thereby curvature elasticity) in vesicle membranes and properties of vesicle-vesicle "unbinding" in the weak adhesion regime have been measured. Although thermal fluctuations only become visible when bilayer tensions fall below 10-3 dyn/cm, entropy effects significantly "soften" surface expansion and adhesion properties at levels of tension and binding energy that are orders of magnitude higher. Thus, a self-consistentfield approximation has been developed to capture the essential features of the continuous unbinding transition and to provide a useful method to predict the renormalization of underlying long-range interaction.
Introduction Molecularly thin membranes are of widespread interest in science. In physics and chemistry, membranes represent low-dimensional condensed states of matter where the surface to volume can reach enormous proportions and the material exhibits a rich set of liquid and solid structures. In biology, membranes are the central design employed by Nature to construct higher cellular organisms and subcellular organelli. The conventional view presents thin membranes as anisotropic-continuous materials characterized by surface elastic and viscous properties.'V2 Further, as "macrocolloidal" structures, membranes interact with one another-and with other condensed materials-via the classical forces involved in the stability and coagulation of colloidal dispersions, i.e. van der Waals attraction and electric double-layer repulsion at long-range with close approach ultimately opposed by solvent and surface structure forcesa3t4Complementary to the "engineering materials" view, developments over the past decade have brought to light unexpected features of membranes. Because of the exceptional flexibility, fluid membranes are "soft" surfaces where thermal fluctuations course through a wide range of continuous shapes and the configurational entropy associated with these forms becomes a significant part of the free energy in many situations. Thus, entropy-driven forces arise when fluctuations are restricted. The "bare" elastic properties of the membrane become coupled to produce more compliant response to displacement force^;^^^ also, the direct interactions between rigid-plane surfaces are transformed to As will be extend repulsion and diminish (1)Evans, E.;Skalak,R. Mechanics and Thermodynamics of Biomembranes; CRC Press: Boca Ratan, FL, 1980; pp 1-254. (2)Evans, E.;Needham, D. J. Phys. Chem. 1987,91,4219. (3)Rand, R. P.; Parsegian, V. A. Biochim. Biophys. Acta 1989,988, 351-376. (4)Israelachvili, J. Intermolecular and Surface Forces; Academic Press: London, 1985;pp 1-296. (5)Helfrich, W.; Servuss,R.-M. Nuouo Cimento SOC.Ital. Fis, D 1984, 03,137. (6)Evans, E.; Rawicz, W. Phys. Reu. Lett. 1990,64, 2094. (7) Helfrich, W. 2.Naturforsch., A: Phys., Phys. Chem.,Kosmophys. 1978,33A,305. (8)Evans, E.; Parsegian, V. A. Proc. Natl. Acad. Sci. U.S.A. 1986,83, 7132. (9)Lipowsky, R.; Leibler, S. Phys. Reu. Lett. 1986,56,2541.
0743-7463/91/2407-1900$02.50/0
demonstrated here, effects of entropy confinement can be significant when single condensed-fluid membranes form closed-vesiclecapsules and when vesicles bind (adhere) to other surfaces by colloidal attraction.
Formation of Condensed-Fluid Bilayer Vesicles and the Conventional Mechanics of Membranes Diacyl lipids are commonly chosen as constituents of membranes because, in certain conditions, they spontaneously produce stacks of condensed-fluid bilayers when initially hydrated from anhydrous powders. Further hydration of these stacks leads to eruption of vesicular envelopes with no detectable solubility in the adjacent aqueous environment. When the umbilical attachment to a "maternal" lamellar domain is severed, a closed bilayer capsule is formed from the membrane envelope. This vesicle can then be transferred into a lipid-free buffer without dissolving (as such, the upper limit to solubility appears to be 10-13-10-14M). The surface of an isolated bilayer capsule appears not to exchange lipid monomers and exists tension-free when the hydrostatic pressures of the adjacent aqueous regions are made equal. If subjected to mechanical or osmotic stress, the vesicle becomes pressurized and the membrane tension is increased; tension values up to several dyn/cm are possible above which rupture will occur.2 For the macroscopic-sizevesicles ( 20 pm) used in micromechanical experiments, inside-outside pressure differences remain small ( 1,some contact can be formed initially without vesicle tension; to make further contact, the surface must increase and the membrane will be stressed. For very weak adhesion where bending stiffness enlarges the contour at the periphery of the contact, the dimensionless contact parameter x , represents the “flattening” of the vesicle shape caused by contact with the substrate. The actual dimension of the contact region must be derived from the continuity of the bending-dominated contour with the exterior spherical CY N
wa N &,/(l-K,) (9) Energies of cohesion between neutral-lipid bilayers are usually not large (X0.3 erg/cm2). The tensions induced in vesicle membranes by adhesion will be of similar magnitude; hence, tension is expected to increase exponentially with expansion as predicted by eq 5. For lipid bilayer membranes, the tension exhibits a very rapid rise since 8 ~ k , / k TN 600! Thus, the practical experimental approach is to establish the vesicle area at a measurable level of tension ;O (20.1 dyn/cm) by micropipet aspiration (cf. Figure 4). Then, the appropriate tension for the projected area required to form the adherent shape can be predicted from this experimentally accessiblereference state by
-T = -~~e-E*k,(ao-a)/kT
(10)
Consequently, observation of the actual contact dimension in conjunction with the vesicle area and volume at the reference tension provide unique specification of the “average” shape of the adherent vesicle and the level of tension in the surface. With this procedure, it is possible to examine adhesion energies in the “weak” adhesion regime (10-6-10-3erg/cm2) where pressures inside vesicles fall below the limit (10-6atm) of regulation by pipet suction.
Parallel Restriction of Fluctuations a n d Entropy-Driven Unbinding of Adherent Membranes In the conventional analysis of membrane adhesion and disjoining by colloidal forces, it is expected that van der Waals attraction Va should lead to a stable energy minimum even for charged surfaces in electrolyte solutions if the magnitude of the energy reduction exceeds kT, i.e. A,(V, + V,) + kT < 0. The inverse-power law attraction dominates over the exponentially decaying repulsion at large distances. Consequently, neutral surfactant membranes-and moderately charged membranes ( I 1charge per lipid) in 0.1 M levels of electrolyte-are predicted to adhere when contact areas are of macroscopic size. What is observed, however, is that charged vesicles in 0.1 M electrolyte exhibit rapidly weakening adhesion and finally no vesicle-vesicle attraction at much lower charge densities (-0.07 charge/lipid). Further, when the surface charge density nears the level required to prevent adhesion, vesicles exhibit visible fluctuations indicative of extremely low membrane tensions. In this “weak”regime of adhesion, the contact area is progressively reduced (cf. Figure 2) with small additions of surface charge which demonstrates “unbinding” of the bilayers. Adhesion energies for such a transition are plotted in Figure 6 as a function of the energy-densityprefactor for electric double-layerrepulsion (ergs/cm2). Here adhesion tests were carried-out with vesicles made from neutral phosphatidylcholine lipids plus small amounts of negatively charged phosphatidylserine (0 to 7 charges per 100 lipids). The solid triangle symbols are direct measurements derived from micropipet control of vesicle tensions; the open triangle symbols are values of adhesion energy derived from the constitutive relation for entropy-driven tension (eq 10) and contact geometry (described in the previous section). The dashed curve is the classical adhesion energy predicted by superposition of electric double-layer repulsion and the attractive potential derived from the adhesion energy for the neutrallipid bilayers. Nonclassical “unbinding” appears clearly
Entropy-Driven Tension in Vesicle Membranes
Langmuir, Vol. 7, No.9, 1991 1905 function Q and the probability density function Pimplicit in the ensemble-average (...) are defined by the meanfield. Since the elastic energies for membrane excitations (shape fluctuations) are the same in both Hamiltonians, eq 11 can be expressed as
neutroltchorged lipid in 0.1 NaCl
IO+ \
classical double- layer disjoining
Wa
(ergs/cd)
4 Io
F/A I-kT/A In 8 + ( V - P)
'\
u
-~ IO+
lo-'
I
IO
sq = 0
"e s (ergs/cm2) Figure6. Adhesion energies (measuredwith neutral plus charged lipid vesicles) plotted as a functionof the prefactor V , for electric double-layer repulsion in 0.1 M NaCl. Solid triangles are direct measurementsof adheaion energyderived from micropipet control of vesicle tensions; open triangles are values of adhesion energy derived with the elastic relation for entropy-driventension (eq 10) and contact geometries. The solid curve is the prediction obtained with the SCMF method described in the text.
aa a precipitous departure from the conventional colloid treatment. This departure is consistent with the anticipated "softening" and expansion of intermembrane repulsion by entropy confinement as will be described in the next section. Interactions Renormalized by Thermal Undulations: SCMF Approximation Thermodynamic analyses of membrane shape fluctuations are formulated on the basis that all geometric conformations are accessible. The likelihood of occurrence of a particular shape is proportional to a Boltzmann probability derived from the elastic energy required to displace the contour from its equilibrium shape. Consequently, large numbers of time-dependent shapes make up the ensemble of membrane configurations. The free energy is derived from a partition function that is the sum (integral) over all of the configuration probabilities. Cumulation over all surface conformations leads to a functional integral that, without further simplification and approximation, is extremely difficult to analyze in most situations. Rigorous approaches have involved recursive perturbation schemes (renormalization group methods) or random-walk (Monte Carlo) computer simulations, neither of which is easily implemented. Thus, similar to the practical (and successful) approach developed in polymer thermodynamics, a self-consistent mean-field (SCMF) approximation has been developed to provide a tractable method for estimation of free energies and forces.16 The self-consistent field method is based on an extremum principle developed by Peierls and articulated by Feynman as the following bound to the free energy" FI-kTlnQ+ (H-fi)
(12) where V and P are the direct potential and mean-field interaction, respectively. (Note: for a membrane held against a substrate by osmotic pressure, a term pZ must be added to the direct potential.) The upper bound to the free energy establishes a variational principle which is used to obtain an "optimized" mean-field through
(11)
where R is a mean-field Hamiltonian (energy) chosen to approximate the true Hamiltonian (H)in the partition function for a particular configuration; the partition (16) Evans, E.; Ipsen, J.; Parsegian,V. A. Manuscript in preparation. (17) Peierls,R. E.Phys.Reu. 1938,54,918. Feynman,R. P.Statistical Mechanics: A Set of Lectures; Frontiers in Physics; Benjamin/Cummings: Reading, MA, 1972.
z Next, the pressure is found by Obviously, the important task is to determine the optimum mean-field. For membrane-membrane interactions, derivation of the mean-field is guided by developments in the statistical mechanics of polymer solutions and the "polymer-membrane" analogy outlined previously. Several ingredients are involved in the SCMF method for membranes. First, conformations z(3)of the membrane are assumed to be composed of random, uncorrelated harmonic excitations about a mean position 2 where (UO, uq) are the amplitudes of the displacement modes with wave vectors in the range ?r2/S,12 < q2 < $/a$. The microscopic cutoff "ao" represents the length scale where membrane bending stiffness increases precipitously and h. The displacement uo eliminates undulations, a0 describes fluctuations in position of a statistically independent piece of the membrane with an area S1l2. The benefit of this assumption is to reduce the unnormalized probability for a configuration to a product of Gaussianlike functions X Boltzmann factors for the expectation of occurrence of particular shapes in the potential field subject to external forces. The variance uq2of each Gaussian factor is derived from the bending energy of each internal mode of excitation
-
For an isolated membrane (where the potential field and pressure are negligible), displacements of the surface relative to the mean position will be described by completely Gaussian statistics and the lateral correlation length A. becomes the full-size of the membrane, i.e. Ell2 When confined in a potential field V(z) (which includes the action of external osmotic pressure,pz), the Gaussianlike probabilities for bending excitations become strongly attenuated as the energies of configurations within a membrane piece rise above kT. Excursions of the membrane that approach these limiting separations are repelled back to more favorable locations in the potential field. As a consequence, the lateral correlation lengths of undulations are reduced ("screened"). In general, there is a distribution of lateral correlation lengths; but for the SCMF approximation, it is assumed that on the average the surface breaks up into N statistically separate regions with the size given by an "effective" correlation length 511 (i.e. N = A/,&2). Therefore, the next step in the SCMF method is to determine the mean field that governs the distributions of fluctuations in membrane position for a region of size .&2. The mean field is expressed in two parts:
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1906 Langmuir, Vol. 7, No. 9,1991
the first is a barrier function &z) which represents the energetic limit for closest approach to the substrate allowed by the repulsive field. The explicit cutoff 2 for extreme configurations depends on both the gradient of the potential and the size [112 of a region. The second is the mean field within the cutoff restriction. Definition of this part follows naturally from the concept that the confining potential strongly regulates the position of membrane segments with sizes 2[112but has little effect on the internal bending modes of excitation. Thus, the mean field that is “felt” by a membrane region is the average of the direct potential over the internal modes of excitation within the region
Evans
excitation within the independent section, i.e.
Thus, the mean-square fluctuation bo2) in average separation and the mean-square fluctuation (uc2)for the internal bending excitations both increase at a rate proportional to the size of the region until lateral tension begins to suppress undulations. Consequently, the prob[ ~ ~PC(zluo,[ll2) ~) spread-out as ability densities P o ( u o ~ and the correlation length increases until the repulsive portion (16) of the mean field and the steric cutoff begin to confine the distributions. Stationary distributions are found when the free energy (eq 12) is minimum. where P,(zlu~,[l,~) is the joint probability distribution for By rescaling integration variables in the expression for fluctuations within a membrane region located at + UO. Consequently, the probability distribution P o ( u o ~ for [ ~ ~ ~ ) entropy of an isolated membrane, the entropy contributions for undulation modes within a “fluctuating pillow” fluctuations uo in average position of membrane regions of size [112 cancel out directly, which demonstrates the is given by the Boltzmann relation underlying assumption that these degrees of freedom are little affected by the confining potential. Longer wave(17) length excitations are “squashed”, which reduces the correlation length and thereby restricts the entropy. As such, the following expression for free energy density is obtained from eq 12 in the limit of large membrane area The ensemble average of the mean field is identical with F / A N ( V )+ kT/2[,2 (20) the direct-geometric average of the underlying potential which ensures self-consistency, This self-consistency Here a quadratic approximation has been introduced which relation based on the concept that the confining potential reveals the role of the direct potential as well as entropy strong& regulates the location of membrane segments with confinement sizes 2[112 but has little effect on the excitations of the internal undulation modes, i.e. the “polymer-membrane” -kT In [Q0/(27ra,2)’/2] z ( V)tIl2- kT/2 analogy. In the absence of long-range repulsion, the total meanThe full probability density function P(zl[l12)is the square fluctuation (tL2= uo2+ uc2)is bounded only by convolution of the probability density Po(u01[11~)for membrane separation. The fluctuations “grow” to reach positions (Z UO) of membrane regions and the joint an equilibrium value determined by tL2= cZ2, where c cv probability density Pc(zlu~,[l12) for bending excitations 0.1. This geometric (steric) restriction establishes the within a region, both of which depend on the size of the relation between separation distance and correlation length membrane section. For the internal modes, a Gaussian as specified by eqs 19. Consequently, the general features distribution exists initially when is very small but of steric repulsion are found directly by substitution of til2 becomes progressively modulated by the cutoff restriction = f ( Z 2 ) into the free energy expression eq 20. Hence, two as increases. As a random process, evolution of the regimes are predicted for steric energy differentiated by unnormalized distribution followsfrom convolution of the membrane tension (represented by the length scale AT2 = distribution with the microscopic Gaussian-like source of 4 ~ k , / ; ~ ) .For weak tension, the square of the correlation probability (characterized by the increment in meanlength is directly proportional to the square of the Keeping terms to first square fluctuation Auc2 separation distance which yields the classic 1/Z2repulsive order in A[112, expansion of the integral representation leads law established by Helfrich’ many years ago to a “diffusion”equation for the unnormalized distribution (analogous to a polymer random walk)
+
-
This “diffusion” equation is solved to obtain continuous functions for the joint probability distribution subject to the boundary conditions stipulated by the barrier function S(z), i.e. Pc = 0 at z = 2. The width of the distribution g, is governed by the dependence of the total mean-square fluctuation uc2(for bending excitations) on the correlation length, calculated from eq 15. Evolution of the probability density Po(u0l[ll2) for positions of independent regions is determined directly by the mean field defined in eq 16plus the self-consistent requirement that fluctuations uo in average position should “grow”at the same rate as the longest wavelength bending
However,when separations exceed 2 > (kT/41rc;)’/~,then the form of the repulsion crosses over to more rapid exponential decay approximated by (22)
As recognized originally by Helfrich: this cross over is very important because it allows weak power-lawattraction to overcome steric repulsion at large distances when the membrane is under tension. This raises an important but subtle issue in regard to adhesion of flaccid vesicles (fluctuating at extremely low tension levels) to attractive substrates. A t first glance, it appears that the steric force at “zero” tension should prevaiI at long range to prevent
Entropy-Driven Tension in Vesicle Membranes
Langmuir, Vol. 7, No. 9, 1991 1907
0.10
coefficient (also scaled by&), On the basis of the theory18 for van der Waals interactions between discrete layers, the attraction follows an inverse power law form which ranges between 2Hh2/12rZ2> Ipal> &(dBlh)'/2?rZ4
X/t
A H E AH/EH 0.05
0
0
500 AH
1000
/E"
Figure 7. Predictions for continuous unbinding of multimembranes as functions of _theunderlying-exponentialrepulsion power-law attraction AH, and bilayer thickness d B l / X (see text for definitions of the dimensionless variables). Equilibrium separations 2 are scaled by the decay length X of the repulsive field.
vr,
adhesion; but this "unbound" state may be metastable. If adherent states exist under tension, then the level of tension required to produce a lower energy adhesive state may be achieved by extension of the membrane due to the area/volume constraint. In other words, the fixed area and volume always imply a possible tension and if the free energy required to reach this tension is less than the free energy reduction produced by adhesion, then a bound state will eventually be the equilibrium configuration.
Continuous Unbinding and Disjoining by Electric Double-Layer Forces Continuous "unbinding" of an adherent membrane (driven by temperature or direct repulsion) has been a significant prediction from renormalization group analy ~ e s .The ~ transition was shown to be second order with no coexistence between bound (adherent) and unbound (completely separate) states. The conclusion is very important since it predicts that no energy barrier opposes approach of a membrane to an adherent configuration. Similarly, results from the self-consistent mean-field (SCMF) approximation demonstrate continuous "unbinding" as a function of temperature and repulsive potential. Even though mean-field approximations are not expected to yield correct exponents for unbinding near the critical point (where fluctuations become extremely large), the SCMF approach yields useful values of adhesion ("binding'') energy for weakly bound states accessible to physical measurements. In Figure 7, SCMF predictions for disjoining of multimembranes are plotted for 3 orders of magnitude of the underlying expcnential repulsion (characterized by a scaled prefactor Vr) given by p e-z/x
vr
f
vrh2/EH
E, E ( k T ) 2 / 1 6 ~ 2 k c ~ where A is the characteristic decay length for repulsion and EHis the "Helfrich" energy scale specified by the prefactor for pure steric repulsion in eq 21. Continuous unbinding in Figure 7 is shown by the uniform decrease in reciprocal of equilibrium separation (scaled by decay length) as a function of reduction in the attraction
where the crossover in power-law behavior depends on the ratio d ~ l / Xof bilayer thickness to decay length for repulsion. This ratio strongly affects the predictions for unbinding as shown in Figure 7. The nonclassical effect of entropy confinement in Figure 7 appears as a deflection of the curves to nonzero values (or "critical" values) for the attraction coefficient at infinite separation. The power-law feature and quantitative form for the Helfrich steric repulsion have been confirmed for multilamellar arrays above the critical point ("unbound").1*20 However, the transition from bound-to-unbound state for a single membrane has not been examined in relation to theoretical predictions. The data in Figure 6 provide a test for the predictions in Figure 7. To make the comparison, it is necessary to know the membrane bending stiffness k, and the characteristics A H , V,, and h of the underlying interaction. For the phospholipid vesicles used in these adhesion tests, the bending modulus has been erg).6 Thus, the Helmeasured to be about 24kT (erg) frich energy scale is set at about 0.0027kT (1.1 X for a single bilayer at a temperature of -23 OC. Next, based on osmotic dehydration properties of multilamellar arrays (see Appendix), a decay length h of about 1.6 A and energy prefactor VJ2 of order 10-13 erg are derived for neutral phosphatidylcholine lipids in the gel state. These values yield lo3for the scaled value Vp Since the bilayer thickness is about 35 A, the critical value of the van der Waals coefficient AH*for cohesion of these neutral multierg. (Note: the critical bilayers is predicted to be 1 X value of attraction coefficient for unbinding is a factor of 2-3 larger when d ~ l / N h 10, which agrees well with results from renormalization group and Monte Carlo calculations.91~~) Also, a van der Waals coefficient AH equal to erg is sufficient to correlate the small value -5-6 X measured for the adhesion energy erg/cm2). On the basis of the direct interaction alone (without renormalization by entropy confinement), the bilayer would be 6-7 A closer to the stiff membrane substrate and the adhesion erg/ energy would be about 4-fold greater ( - 5 X cmz). This prediction is consistent with the experimental measurements of adhesion energy for these neutral phospholipids immobilized on rigid, mica sheets where equilibrium separations were lower and adhesion energies were erg/cm2 (somewhat larger found to be higher, 8-10 X than expected because attraction was augmented by the highly refractive mica sheets).= Accepting a van der Waals coefficient of 5-6 X 10-14 erg ( A H 500), multilamellar arrays of these neutral bilayers appear to exist well-above the critical point. So, how can small additions of electrically charged lipids to neutral bilayers (in 0.1 M electrolyte) cause unbinding as shown in Figure 2 and represented by the data in Figure 6? On the basis of the charge density required to achieve complete unbinding (and a decay length of about 10 A),
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(18)Ninham,B. W.; Parsegian, V. A. J. Chem. Phys. 1970,543398. (19) Evans, E. Electrochim. Acta, in press. (20)Rous, D.; Sdinya, C. R. J. Phys. (Paris) 1988,49,307. Safiiya, C. R.; Sirota, E.B.; Row, D.; Smith, G. S. Phys. Reu. Lett. 1989,62,1134. (21) Richetti, P.; Kekicheff, P.; Parker, J. L.; Ninham, B. W. Nature 1990, 346, 252. (22) Lipowski, R.; Seifert U. Mol. Cryst. Liq. Cryst., in prese. (23) Marra, J.; Israelachvili, J. Biochemistry 1985, 24, 4608.
Evans
1908 Langmuir, Vol. 7,No. 9, 1991
vw
the scaled prefactor for the added electric doublelayer repulsion is calculated to be only 102 for a single bilayer, significantly less than the value for hydration repulsion. This shows that although the neutral bilayer exists as a bound state, it can be easily disjoined by weak double-layer repulsion. The reason for this sensitive feature is the pronounced shift in crossover of the powerlaw behavior for attraction which accompaniesthe increase in decay length X for repulsion, i.e. from 1.6 to 9.7 8, (the Debye screening length in 0.1 M NaC1). Thus, the ratio of bilayer thickness to decay length is reduced from about 25 to 3. As shown in Figure 7, the qualitative effect is to shift the unbinding transition to larger values of the attraction coefficient. The full prediction for disjoining of bilayers by the electric double-layer field (in 0.1 M electrolyte) is plotted as the solid curve in Figure 6 and appears to give good correlation with the results from the adhesion tests.
Acknowledgment. This work was supported by Medical Research Council of Canada Grant MT7477 and US. National Institutes of Health Grant HL45099. The author gratefully acknowledges the expert technical assistance of V. Rawicz who performed the vesicle adhesion tests. Appendix The underlying, direct interaction between phosphatidylcholine bilayers can be estimated from osmotic dehydration properties of multibilayer arrays of these lipids in the gel state. As described in ref 3,correlation of X-ray diffraction (lamellar repeat spacing) with gravimetric (weight ratio of 1ipid:water) data provide a measure of average water separation between bilayers as a function of osmotic stress. Because of the elastic compressibility of the fluid-lipid bilayer (or lack of compressibility in the gel state), the calculation of average water separation requires a small (but important) correction for the increase in bilayer thickness which accompanies dehydration. On the basis of published data3*24 for dipalmitoylphosphatidylcholine (DPPC) lipids in water, Figure 8 shows the major difference between osmotic dehydration properties of these multibilayers above-and below-the acyl chain (24) McIntosh, T.J.; Simon, S. A. Biochemistry 1986,25,4058.
9 \
a LOG,,
0: DPPC (25 "0
pr
(dyn/cm2)
\
\\
d:
\
7
6
5 0
IO
20
30
40
2
(1, Figure 8. Osmotic pressure P, versus bilayer separation
Z
(average aqueous space) computed from X-ray diffraction and gravimetric data for multibilayer arraysof dipalmitoylphosphatidylcholine (DPPC)lipids in the gel state (25 "C) and liquid state (50 "C). (Data are replotted from ref 3 and corrected for bilayer elastic compressibility.) The dashed curve is the superposition of exponentiallydecayingrepulsionand van der Waals attraction taken as the "direct" potential. The solid curve is the renormalized prediction calculated from the direct potential with SCMF method.
crystallizationtemperature (-41 "C). The principaleffect is an increase in decay length of the hydration repulsion upon melting (from X 1.6 8,in the gel state to X 2.2 A in the fluid state). Also, in the gel state, there is clear evidence of a strongly bound state (at -16-18 A separation) driven by van der Waals attraction. However, in the liquid state, the cohesion is much weaker and thestressfree equilibrium expands to separations of about 31 A. Taking the gel state properties as the underlying interaction, the dashed curve in Figure 8 was calculated by direct superposition of a repulsive potential (V, = 380 ergs/cm2, h = 1.6 A) and van der Waals attraction (AH = 5-6 X 10-14erg). Next, the solid curve in Figure 8 was predicted from the direct potential with the SCMF approach; the result gives good correlation with data for the bilayer liquid state at 50 "C.
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