Method for obtaining structure and interactions from oriented lipid bilayers

Precise calculations are made of the scattering intensity $I\left(\mathbf{q}\right)$ from an oriented stack of lipid bilayers using a realistic model of fluctuations. The quantities of interest include the bilayer bending modulus $K_c,$ the interbilayer interaction modulus B, and bilayer structure through the form factor ${F(q}_z).\mathrm{}$ It is shown how $K_c$ and B may be obtained from data at large $q_z$ where fluctuations dominate. Good estimates of ${F(q}_z)$ can be made over wide ranges of $q_z$ by using $I\left(\mathbf{q}\right)$ in $\mathbf{q}$ regions away from the peaks and for $q_r\ne 0$ where details of the scattering domains play little role. Rough estimates of domain sizes can also be made from smaller $q_z$ data. Results are presented for data taken on fully hydrated, oriented DOPC bilayers in the $L_{\alpha }$ phase. These results illustrate the advantages of oriented samples compared to powder samples.