<p>Small-angle X-ray scattering (SAXS) is a biophysical technique that allows one to study the statistical conformation of a biopolymer in solution. The two-dimensional data obtained from SAXS is a low-resolution probe of the statistical conformation- it is a population weighted orientational average of all conformers within a conformational ensemble. Traditional biological SAXS experiments seek to describe an "average" structure of a protein, or enumerate a "minimal ensemble" of a protein at the atomic resolution scale. However, for highly flexible proteins, an average structure or minimal ensemble may be insufficient for enumeration of conformational space, and may be an over-parameterized model of the statistical conformation. This work describes a SAXS analysis of highly flexible proteins and presents a protocol for describing the statistical conformation based on minimally parameterized polymer physics models and judicious use of ensemble modeling. This protocol is applied to the structural characterization of S. aureus protein A - a crucial virulence factor - and Fibronectin III domains 1-2 - an important structural protein.</p> / Dissertation