Lipid bilayer repulsive forces

When membranes fuse, the so-called stalk hypothesis suggests that the intermediate hemifusion state (Fig. 6.4c) comprises a structure in which proximal monolayers layers are connected by a bent stalk and the distal layers are pulled towards each other, thus forming a dimple (see also Fig. 6.5) The stalk model has been supported by theoretical and experimental observations. The fusion of model membranes appears to occur via the same series of fusion intermediates as those in vivo, although the approach of membranes is not Rab/SNARE mediated but is driven by reduced bilayer repulsion forces arising from hydration, electrostatic interactions, thermal fluctuations (Helfrich interaction) or osmotic stress. Membrane fusion is also promoted by defects introduced into the membrane by lateral phase separation (for example of lipid rafts, see above), high spontaneous membrane curvature, or addition of macromolecules or proteins into the membrane. 

In a lipid/water system, the thickness of the bilayers is constant, and the unbinding transition can occur, in principle, by varying the Hamaker constant or temperature.22 For lyotropic lamellar liquid crystals, hyperswelling in a liquid of one kind might also occur if the lamellae of the other kind are thin enough and hence unbound. However, thin lamellae might lead to a positive contribution to the free energy (since the repulsive forces overcome at short distances the van der Waals attraction), and hence the lamellar phase can become unstable. 

For neutral bilayers, there are no long-range doublelayer forces which, coupled with the van der Waals attraction, could explain the stability of the lamellar structure. At small separations, the required repulsion is provided by the hydration force, which was investigated both experimentally6-8 and theoretically.9,10 However, it was experimentally observed that the lipid bilayers could be swollen in water up to very large interlayer distances,11 where the short-range exponential hydration repulsion becomes negligible. 

In the case of a linear interaction between neighboring lipid bilayers, Helfrich has demonstrated that the repulsive free energy due to confinement is inversely proportional to (7b2. While this result is strictly valid for a harmonic interaction potential (linear force), we assume that it can be extended to any interaction. We will examine later under what conditions this approximation is accurate. 

The dependence of the interaction force between two undulating phospholipid bilayers and of the root-mean-square fluctuation of their separation distances on the average separation can be determined once the distribution of the intermembrane separation is known as a function of the applied pressure. However, most of the present theories for interacting membranes start by assuming that the distance distribution is symmetric, a hypothesis invalidated by Monte Carlo simulations. Here we present an approach to calculate the distribution of the intermembrane separation for any arbitrary interaction potential and applied pressure. The procedure is applied to a realistic interaction potential between neutral lipid bilayers in water, involving the hydration repulsion and van der Waals attraction. A comparison with existing experiments is provided. 

When the surfaces were not rigid, as in the case of lipid bilayers, the oscillations of the force were smoothed out and the interactions became monotonic. The short-range repulsion between neutral7 or weakly charged8 bilayers, often called hydration force, was exhaustively investigated experimentally and was found to have an exponential decay, with a decay length between 1.5 and 3 A, while the preexponential factor varied by more than an order of magnitude. 

Another mechanism for the hydration repulsion between lipid bilayers was more recently proposed by Marcelja.22 It is based on the fact that in water the ions are hydrated and hence occupy a larger volume. The volume exclusion effects ofthe ions are important corrections to the Poisson— Boltzmann equation and modify substantially the doublelayer interaction at low separation distances. The same conclusion was reached earlier by Ruckenstein and Schiby,28 and there is little doubt that the hydration of individual ions modifies the double-layer interaction, providing an excess repulsion force.28 However, while the hydration of ions affects the double-layer interactions, the hydration repulsion is strong even in the absence of an electrolyte, or double-layer repulsion. 

It is well-known that free films of water stabilized by surfactants can exist as somewhat thicker primary films, or common black films, and thinner secondary films, or Newton black films. The thickness of the former decreases sharply upon addition of electrolyte, and for this reason its stability was attributed to the balance between the electrostatic double-layer repulsion and the van der Waals attraction. A decrease in its stability leads either to film rupture or to an abrupt thinning to a Newton black film, which consists of two surfactant monolayers separated by a very thin layer ofwater. The thickness of the Newton black film is almost independent of the concentration of electrolyte this suggests that another repulsive force than the double layer is involved in its stability. This repulsion is the result of the structuring of water in the vicinity of the surface. Extensive experimental measurements of the separation distance between neutral lipid bilayers in water as a function of applied pressure1 indicated that the hydration force has an exponential behavior, with a decay length between 1.5 and 3 A, and a preexponential factor that varies in a rather large range. 

The interest in lipid bilayers is due to their relevance to biological membranes [1], They exhibit a richness of structures due to the interplay between many different inter- and intrabilayer forces. Among all the multilamellar bilayer structures, probably the most pertinent to biological membranes are the lamellar ones. Their equilibrium spacing is considered to be the result of a balance between attractive and repulsive forces. While the former forces are just the usual van der Waals interactions, the latter are composed of double layer forces (for charged bilayers) [2], hydration forces (due to the structuring of water near interfaces) [3] and repulsive forces generated by the thermal undulation of the membranes [4]. 

The forth issue is the increase in the repulsion between bilayers at short distances. In Fig. 1, the osmotic pressure is plotted as a function of separation distance (data from Ref. [13]) for no added salt, for l M KC1 and for 1 M KBr. They reveal an increase in repulsion at short separation distances upon addition of salt. While the relatively small difference between 1 M KC1 and 1 M KBr can be attributed to the charging of the neutral lipid bilayers by the binding of Br (but not C.1-) [14], the relatively large difference between no salt and 1 M KCl is more difficult to explain. Even a zero value for the Hamaker constant (continuous line (2) in Fig. 1), in the 1 M KCl case, is not enough to explain the increase in repulsion, determined experimentally. The screening of the van der Waals interaction, at distances of the order of three Debye-Hiickel lengths (about 10 A) should lead, according to Petrache et al. calculations, to a decrease of only about 30% of the Hamaker constant (from 1.2kT to about 0.8kT, see Fig. 5C of Ref. [14]). Therefore, an additional mechanism to increase the hydration repulsion or the undulation force (or both) upon addition of salt should exist to explain the experiments. 

The force between neutral surfaces (with a surface dipole density) depends on the electrolyte concentrations, as shown in Fig. 3b, particularly at large separations. However, at small separations, the interaction appears to be well described by an exponential with a decay length AH. For neutral lipid bilayers, the equilibrium is reached at a distance of about 20 A, at which the attractive van der Waals interaction balances the repulsive hydration and thermal undulation interactions [43], The experiments regarding the forces between neutral lipid bilayers [11] sample the interactions at separations smaller than 20 A, for which the dependence on ionic strength is much weaker. By adding to the total pressure a typical van der Waals disjoining pressure [12] ... 

The repulsion of the polar heads does. If there are two hydrocarbon chains per polar head group, the nonpolar volume per head group is twice that of an amphiphilic lipid with one hydrocarbon chain. The greater repulsive force in the latter prevents the lipid molecules from coming too close and thus keeps the micellar size small. The weaker repulsive force and larger hydrocarbon volume in the former allow very much larger structures to form namely, bilayers and vesicles. 

Fig. 9. Force-distance relationships for lipid bilayers. Data for repulsion between dilau-roylphosphatidylcholine bilayers at 25°C. At high pressures (0) the bilayers bave been forced into a frozen-chain gel phase, a response that shows the structural importance of forces exerted by osmotic stress. The exponential part of the melted liquid-crystalline samples ( ) is best fit by an exponential decay constant of 2.6 A. From Parsegian et al. (1986).

Another aspect of current interest associated with the lipid-water system is the hydration force problem.i -20 When certain lipid bilayers are brought closer than 20-30 A in water or other dipolar solvents, they experience large repulsive forces. This force is called solvation pressure and when the solvent is water, it is called hydration pressure. Experimentally, hydration forces are measured in an osmotic stress (OS) apparatus or surface force apparatus (SFA)2o at different hydration levels. In OS, the water in a multilamellar system is brought to thermodynamic equilibrium with water in a polymer solution of known osmotic pressure. The chemical potential of water in the polymer solution with which the water in the interlamellar water is equilibrated gives the net repulsive pressure between the bilayers. In the SEA, one measures the force between two crossed cylinders of mica coated with lipid bilayers and immersed in solvent. 

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