Shannon sampling based approach for the structural solution of nano-objects by laboratory and synchrotron SAXS data

We propose a Shannon sampling based approach for the analysis of laboratory and synchrotron small-angle X-ray scattering (SAXS) data. This method avoids calculation of the pair distance distribution function P(r), which is typically used as an alternative to the model-dependent fitting of SAXS data for determining the size and shape of the scattering object. Using this new approach it is also possible to skip any model-dependent fit of the SAXS data. The method has been tested on SAXS data collected from Polysorbate 20, d--tocopheryl polyethylene glycol 1000 succinate spheroidal core–shell micelles and relevant well known proteins (lysozyme, apoferritin, carbonic anhydrase 2) of different molecular weights. The results confirm the potential of the approach, even for laboratory scattering data and in the presence of polydispersity. The method allows the reliable derivation of maximum size, mass, volume, polar/equatorial asymmetry, hydration fraction, shell thickness and core/shell electron-density differences for core–shell structures, directly in the q domain, working on SAXS data measured from dilute samples for which interparticle structure factors are negligible.