Structure determination of asymmetric membrane profiles using an iterative Fourier method

An iterative Fourier method is applied to solving and refining the electron density profile projected into the line perpendicular to a membrane surface. Solutions to the continuous X-ray scattering pattern derived from swelling of multilayer systems or from membrane dispersions can be obtained by this technique. The method deals directly with the observed structure factors and does not rely on deconvolution of the Patterson function. We used this method previously to derive the electron density profile for acetylcholine receptor membranes (Ross et al., 1977). The present paper is an analysis of the theoretical basis for the procedure. In addition, the technique is tested on artificially generated continuous-scattering data, on the data for frog sciatic nerve myelin derived from swelling experiments by Worthington and McIntosh (1974), and on the data for purple membrane (Blaurock and Stoeckenius, 1971). Although the method applies to asymmetric membranes, the special case of centrosymmetric profiles is also shown to be solvable by the same technique. The limitations of the method and the boundary conditions that limit the degeneracy of the solution are analyzed.