Theory of the structure factor of lipid bilayers

Abstract

The goal of this research is to obtain the structure of lipid bilayers using low-angle scattering with the q vector perpendicular to the bilayers. This requires obtaining the form factor F(h) for the bilayer, which in turn requires correcting the intensity I(h) of the hth order peak by the structure factor S(q), which is a nontrivial function for bilayers in noncrystalline arrays. In this paper the classical theory of smectic liquid crystal scattering is first used to calculate detailed structure factors for unoriented, powder averaged samples. These calculations suggest that the form factors used in conventional biophysical determinations of electron densities require very large corrections. We then show that the classical correlation function in turn requires correction. Our modified correlation function yields much smaller corrections to the form factors. We also modify the standard finite-size factor that is required to fit the peaks. This second modification changes the detailed shape of the peaks while retaining nearly the same form factor corrections and the classical power law tails.