Interbilayer interactions from high-resolution x-ray scattering

The fundamental issue of interactions between lipid bilayers is addressed experimentally and theoretically. We report high-resolution x-ray scattering data for bilayers composed of three different kinds of phosphatidylcholine lipids. These data yield the interbilayer water spacing fluctuation a, as well as the traditional osmotic pressure P, both as functions of the lamellar repeat spacing D and the aqueous separation a. We show theoretically how to obtain the functional form of the fluctuational free energy from the sigma data, which is then determined to within a factor that depends upon the bending modulus, K-c. The resulting functional form determined from experimental data has an exponential decay rather than the power law decay that applies for hard confinement in the large a regime, thereby showing that a theory of soft confinement is necessary. However, the existing theory of soft confinement predicts an exponential decay, but with a smaller decay length lambda(fl) than we obtain. We then use these results to analyze the osmotic pressure data in terms of the bending modulus K-c and the interbilayer interactions consisting of van der Waals and hydration interactions. For all three chemically different lipids we find that the decay length lambda of the hydration pressure is 1.9 -2.0 Angstrom; the Hamaker parameter for the van der Waals interaction is about 5 x 10(-14) erg if the bending moduli K-c are chosen to be different for the three lipids and in the range (0.5-0.8) x 10(-12) erg.