Direct calculation of unambiguous electron-density distributions of Langmuir-Blodgett films normal to the membrane plane

In regard to X-ray diffraction, Langmuir-Blodgett (LB) films consisting of lipid bilayers represent a 'one-dimensional crystal' with a very small number of unit cells in the direction of stacking. Such bounded systems yield X-ray diffraction diagrams which, in certain respects, contain more information than those of the conventional effectively infinite single crystals. This additional information consists of the profiles of the broadened reflections and their dislocation from the reciprocal-lattice points. These profiles are specific for each different structure and hence enable the direct calculation of unambiguous electron-density distributions from a single set of intensity data. At first, the Q function (the generalized Patterson function), i.e. the distance statistics of the structure sought after is calculated from the intensity data. Thereafter, the unambiguous convolution square root of the Q function must be determined, which is identical to the unknown electron-density distribution. For this purpose two mathematically completely different methods were established and compared. They are applied to diffraction patterns of Langmuir-Blodgett films of simple synthetic lipids with characteristic molecular subunits and showed identical results within the experimental resolution. This verifies the structures and the methods to calculate them. Furthermore, all features of the simple structures were compatible with the expectations. All one-dimensional electron-density distributions showed the common features of lipid bilayers. The characteristic molecular subunits can be recognised and reveal some interesting details. In general, they yield information about orientation, conformation and localization of molecular subunits and membrane components.