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 $\sigma ,$ as well as the traditional osmotic pressure $P,$ both as functions of the lamellar repeat spacing $D$ and the aqueous separation $a.\mathrm{}$ 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 ${\lambda }_{\mathrm{fl}}$ 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 $1.9-2.0\hspace{0.5em}\mathrm{\AA };$ the Hamaker parameter for the van der Waals interaction is about $5\times {10}^{-14}\hspace{0.5em}\mathrm{erg}$ if the bending moduli $K_c$ are chosen to be different for the three lipids and in the range $(0.5\mathrm{}-0.8)\times {10}^{-12}\hspace{0.5em}\mathrm{erg}.$