Reconstruction of three-dimensional electron density models from small angle X-ray scattering data for macromolecules. A space averaging approach

Solution small-angle X-ray scattering (SAXS) is an established experimental technique for the study of structural parameters of large biomolecules and composite structures. Synchrotron radiation sources have enhanced the power of the technique in many different respects, more notably in permitting the study of the time evolution of complex structures. One of the SAXS benefits is that it provides low resolution information about protein without the need to crystallize it.; Recently a number of algorithms have been developed to reconstruct low-resolution 3-dimensional electron density maps from 1-dimensional small angle X-ray scattering (SAXS) data from bio-molecules. I found that algorithms for generating low resolution electron 3D density maps from SAXS data suffer from an intrinsic instability associated with the insufficient number of scattering beads (or "dummy atoms") used for modeling.; I argue that this results from the lack of enforcement of the continuity of electron density inside the model and present a space averaging procedure which can be used to calculate a stable and unbiased SAXS profile of the model.; The proposed theory allows to resolve 25 years old problem of SAXS information content. Introducing concept of model noise and spatial resolution, I explain how reliability of particular low resolution 3D model may be determined and therefore justify success of the existing 3D reconstruction algorithms.; I also prove that much better reconstruction results may be achieved if space averaging is used, opening wider horizons for the method application.; As a separate part of the thesis I discuss problem of uniqueness of the reconstructed model and present classes of structural partners for several common shapes. Tables of structural partners facilitate the reconstructed model interpretation and may be very important in case of complicated or highly symmetrical structures.