X-ray scattering by partially disordered membrane systems

A method of analysing the X-ray diagrams of imperfect membrane lattices with degrees of stacking disorder between 2 and 6% is presented. The method is, however, generally applicable to partially disordered lattices of centrosymmetric membranes. This can also be extended to the case of asymmetric membranes occurring in one orientation only, or in pairs, back-to-back. The procedure allows the determination of the statistical quantities characteristic of the partially disordered lattices and the separation of the diffuse scattering component. As a direct consequence, the refinement of membrane electron density projections becomes feasible and an example is presented for erythrocyte membrane lattices. A one-dimensional model of the refined electron density profile of the erythrocyte membrane is used to calculate numerically the X-ray scattering for a partially disordered lattice of N membrane units. A residual of 15% is obtained with this model and the difference between the observed and calculated values can be minimized further with the proposed refinement procedure.