Structure Determination from Disordered Ensembles of Identical Particles

X-ray scattering techniques have long ranked among the most important methods for studying amorphous materials and other highly disordered targets. Well-established X-ray scattering methods often consist of recording time-averaged scattered intensity maps which, under the Born approximation, straightforwardly reveal information about ensemble-averaged, two-point, electron density correlations within the target. In the case of isotropic targets that consist of disordered ensembles of randomly oriented particles, scattering data are typically reduced to a histogram of electron pair distances (the "pair distribution function," or PDF). While the information contained in the one-dimensional PDF is limited, a rich set of structural properties can often be determined straightforwardly (e.g., radius of gyration, surface area, short-range correlation length scales, fractal dimension). One of the well-known pinnacles of the methodology is the application of small-angle X-ray scattering (SAXS) to solutions of identical biological macromolecules [1-3], which is now routinely used to rapidly determine ab initio low-resolution (>1 nm) protein structures [4].