Small-Angle X-ray Crystallography on Single-Crystal Regions of Inverse Bicontinuous Cubic Phases: Lipid Bilayer Structures and Gaussian Curvature-Dependent Fluctuations.

I report for the first time an X-ray crystallographic study on single-crystal regions of cubic phases of a lyotropic liquid crystal. The single-crystal regions of three inverse bicontinuous cubic phases of a lipid, monoolein, diffracted X-ray only in small-angle regions, but amplitudes of structure factors were determined from the small-angle X-ray diffraction data with high accuracy. Structure factors from lipid bilayer models with constant thickness were optimized to amplitudes obtained from the X-ray data. By using amplitudes of the structure factors from X-ray data and phases from the models, electron density maps of three cubic phases were reconstructed. Lipid bilayer membranes, consisting of high density head regions and low density tail regions, were clearly distinguished in the electron density maps. Water regions had slightly lower density than that of the lipid head regions and were clearly visible for two of the cubic phases. Centers of bilayer membranes were located on the corresponding triply periodic minimal surfaces in the maps. Electron density data indicated Gaussian curvature-dependent fluctuations of bilayer membranes: the smaller the Gaussian curvature is, the larger the fluctuation becomes. The technique described in this report is expected to bring new knowledge in the structural research of lyotropic liquid crystals.