Langmuir 1994,lO, 3369-3370
Strength of van der Waals Attraction between Lipid Bilayers+ A theoretical calculation of the Hamaker constants for the van der Waals interaction between phospholipid bilayers in water was recently presented by Parsegian,’ a calculation that also appears to demonstrate that the Hamaker constants (or coefficients)for bilayers supported on mica A, are 2-5 times higher than for free bilayers At,. Unfortunately, the approximate equations for calculating the forces and the optical and structural parameters used to model phospholipid bilayers were unrealistic. Thus, the approximate equations (eqs 1 and 2 in ref 1) used for computing the Hamaker coefficients depend on certain combining relations2that do not apply when there is a large zero-frequencycontribution to the net interaction as occurs for bilayers in water (ref 2, p 201). Second, through a model of the phospholipid bilayer as a pure liquid alkane film with no polar head its optical properties were set unrealistically close to those for water. This procedure-known as “refractive index matchingmakes the adsorbed layers effectively “invisible” in the medium2 so that the net interaction becomes dominated by the properties of the supporting substrate irrespective of the thickness of the adsorbed layer. Both of these procedures produced an artificially small “theoretical” value for At, of less than 4 x J and a correspondingly large value for the ratio AmI&even at bilayer separations as small as 10-20 A. If the appropriate optical properties for lipid bilayers are used, for example, using the measured refractive index (1.46- 1.49) of free egg-PC bilayers* or similar values obtained for adsorbed PC bilayers5 rather than the value (1.41-1.42) for a nonpolar hydrocarbon J is liquid,’,3 a Hamaker constant of Ab (7-9) x obtained.2 Concerning the data in question, the experimentally quoted values for A for adsorbed lipid bilayers of PC and J for DLPC, DMPC, PE in water are5 (7 f 1) x DPPC, and DPPE in both the gel and fluid states, and similar values of (7.5 f 1.5) x were measured between the uncharged sugar lipids MGDG and DGDG.6 In comparison, the reported values for free lipid bilayers deduced from osmotic pressure data a t similar temperatures are7 4.9, 7.9, 6.1, 8.2, and 32.5 x J for the phospholipids DLPC, DMPC, DPPC, egg-PC, and eggPE, respectively, and (31-76) x J for uncharged sphingolipids.s In a later reanalysis of the osmotic pressure data, Evans and Parsegiang argued that these values should be increased by a factor of about 1.5, for example, from 8.2 to 11 x J for egg-PC. Thus, free bilayers appear to have a very large range of Hamaker + Abbreviations: PC, phosphatidylcholine; PE, phosphatidylethanolamine; DLPC, dilauroyl-PC; DMPC, dimyristoyl-PC; DPPC, dipalmitoyl-PC;DSPC, di&~yl-PC;DPPE, dipalmibyl-PE; MGDG, monogalactosyl diglyceride; DGDG, digalactosyl diglyceride. (1)Parsegian, V. A. Langmuir 1993,9,3625-3628. (2)Israelachvili, J.N. Intermolecular and Surface Forces; Academic Press: London, 1991. (3)Parsegian, V.A.; Ninham, B. W. Biophys. J . 1970,10,664-674. (4)Cherry, R.J.;Chapman, D. J. Mol. Bwl. 1969,40,19-32. (5)Marra, J.; Israelachvili, J. Biochemistry 1988,24,4608-4618. (6)Marra, J. J . Colloid Interface Sci. 1988,107,446-458. (7)Lis, L. J.;McAlister,M.; Fuller, N.; Rand, R. P.; Parsegian, V. A. Biophys. J . 1982,37, 657-666. (8)Tamura-Lis, W.; Lis, L. J.; Collins, J. M. J . Colloid Interface Sci. 1986,114,214-219. (9)Evans, E.;Parsegian, V. A. Proc. Natl. Acad. Sci. U S A . 1986, 83,7132-7136. (10)Israelachvili, J. N.; Wennerstrtim,H. J . Phys. Chem. 1992,96, 520-531. (11)McIntosh, T.J.; Simon, S. A. Biochemistry 1993,32, 83748384. (12)Wiener, M. C.; White, S. H. Biophys. J . 1992,61,434-447.
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constants which, if anything, are higher than for adsorbed bilayers (possible reasons for this are discussed below), and none of the measured values agrees with the -4 x lod2’J calculated by Parsegian.’ From the above theoretical analysis and experimental data, one may conclude that the best current estimate for the Hamaker coefficients of lipid bilayers in water is A = (7.5 f 1.5) x J. We may further note that in salt or physiological salinesolutions lower Hamaker constants, closer to A ES: 3 x J, have been measured between adsorbed DGDG bilayers,‘jwhich is theoretically expected due to the electrostatic screening of the zero-frequency J by electrolyte i o n ~ . ~No J~ contribution of -3 x such effects have been observed between uncoated mica surfaces in solutions of different ionic strengths, which is a further indication that the mica substrates have a negligible effect on the van der Waals forces between supported bilayers at separations less than a few nanometers. Concerning the larger adhesion forces measured between adsorbed bilayers than between free bilayers, Parsegian’ attributes this to the additional attraction comingfrom the supporting substrate surfaces. However, this effect could be due to an increased repulsion between free bilayers, rather than to an increased attraction between supported bilayers. Given that the measured Hamaker constants actually appear to be larger between free bilayers, we must consider this alternative possibility. It is now well-established both theoreticallylo and experimentally’’ that free bilayers have an additional repulsion arising from the thermal fluctuationsundulations and protrusions of the bilayers and lipid molecules-which extends their surfaces and head groups well beyond the “unhydrated bilayer surfaces.12 This structural characteristic of fluid bilayers must be taken into account in any analysis of van der Waals forces and Hamaker constants from experimental data.5 The “experimental” values quoted by Parsegian’ and cow o r k e r ~ ~were ~ ~ -calculated, ~ assuming that no such undulations or protrusions exist, which effectively overestimates the water ap thickness (bilayer separation) by as much as 10-15 .5J0-12 This could account for why Hamaker constants estimated from osmotic pressure data are too variable and too high, often up to an order of magnitude larger than theoretical expectations and directly measured values (see above). The diffise nature of fluid bilayer-water interfaces also makes it difficult to unambiguously define a plane of origin for the van der Waals force or assign a unique Hamaker coefficient. Marra and I~raelachvili~ defined an efjrectiue “VDW plane” for fluid bilayers as the plane from which the VDW force “appears” to originate-a definition that is expected to apply a t surface separations larger than the thicknesses of the diffuse layers. Direct force measurements between supported bilayers of DPPC,S DPPE,5 and DGDG6showed that this definition works well down to bilayer separations of -20 A,and that the effective VDW plane for these bilayers is about 5 A out from the “unhydrated” interfaces (ref 5, Figures 3 and 13; ref 6, Figure 10). The compositional nonuniformities of bilayers presents yet another problem for the calculation of van der Waals forces and Hamaker constants. Marra and I~raelachvili~ obtained slightly higher average refractive index values for DLPC than for DMPC and DPPC bilayers arising from the larger relative contribution of the polar head groups
1
(13)Mahanty, J.;Ninham, B. W. Dispersion Forces; Academic Press: London, 1976.
0743-7463/94/2410-3369$04.50/00 1994 American Chemical Society
3370 Langmuir, VoE. 10, No. 9, 1994 for the shorter-chained lipid. Since the more polarizable head groups are located in the interfacial region rather than inside the bilayers, their presence would increase the van der Waals attraction even more than that assuming a uniform refractive index across the bilayer. In conclusion, interpreting the results of force measurements can be theoretically difficult due to the structural complexitiesof lipid bilayers. This is especially true for free bilayers in the fluid state where undulation, protrusion, and steric-hydration forces can significantly enhance the short-range repulsion yet push out the effective VDW plane. In the case supported lipid bilayers, direct force measurements show that (i>the Hamaker coefficients generally fall within the range A = (7.5 f 1.5)
Comments x J in water, decreasing to about half this value in physiological salt solution, (ii)the effectiveVDW plane is about 5 A from the "unhydrated" surfaces, and (iii) supporting mica (or similar) substrates have a minor effect on the van der Waals forces at separations less than a few nanometers. This work was supported by NSF Grant CTS90-05868.
J. N. Israelachvili Department of Chemical Engineering, University of California, Santa Barbara, California 93106 Received February 2, 1994 In Final Form: May 6, 1994
