A new approach for structure analysis of two-dimensional membrane protein crystals using X-ray powder diffraction data.

The application of powder diffraction methods to problems in structural biology is generally regarded as intractable because of the large number of unresolved, overlapping X-ray reflections. Here, we use information about unit cell lattice parameters, space group transformations, and chemical composition as a priori information in a bootstrap process that resolves the ambiguities associated with overlapping reflections. The measured ratios of reflections that can be resolved experimentally are used to refine the position, the shape, and the orientation of low-resolution molecular structures within the unit cell, in leading to the resolution of the overlapping reflections. The molecular model is then made progressively more sophisticated as additional diffraction information is included in the analysis. We apply our method to the recovery of the structure of the bacteriorhodopsin molecule (bR) to a resolution of 7 Å using experimental data obtained from two-dimensional purple membrane crystals. The approach can be used to determine the structure factors directly or to provide reliable low-resolution phase information that can be refined further by the conventional methods of protein crystallography.

Diffractive imaging using partially coherent x rays.

The measured spatial coherence characteristics of the illumination used in a diffractive imaging experiment are incorporated in an algorithm that reconstructs the complex transmission function of an object from experimental x-ray diffraction data using 1.4 keV x rays. Conventional coherent diffractive imaging, which assumes full spatial coherence, is a limiting case of our approach. Even in cases in which the deviation from full spatial coherence is small, we demonstrate a significant improvement in the quality of wave field reconstructions. Our formulation is applicable to x-ray and electron diffraction imaging techniques provided that the spatial coherence properties of the illumination are known or can be measured.