Interbilayer interactions from high-resolution x-ray scattering

Abstract

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 $\ensuremath{\sigma},$ 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 $\ensuremath{\sigma}$ 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 ${\ensuremath{\lambda}}_{\mathrm{fl}}$ 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 $\ensuremath{\lambda}$ of the hydration pressure is $1.9\ensuremath{-}2.0 \mathrm{\AA{}};$ the Hamaker parameter for the van der Waals interaction is about $5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}14} \mathrm{erg}$ if the bending moduli ${K}_{c}$ are chosen to be different for the three lipids and in the range $(0.5\ensuremath{-}0.8)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}12} \mathrm{erg}.$