Minimum Mean Squared Error Estimation of the Radius of Gyration in Small-Angle X-Ray Scattering Experiments

ABSTRACTSmall-angle X-ray scattering (SAXS) is a technique that yields low-resolution structural information of biological macromoleculesby exposing a large ensemble of molecules in solution to a powerful X-ray beam. The beam interacts with the molecules and the intensity of the scattered beam is recorded on a detector plate. The radiusof gyrationfor a molecule, which is a measure of the spread of its mass, can be estimated from the lowest scattering angles of SAXS data. This estimation method requires specification of a window of scattering angles. Under a local polynomial model with autoregressive errors, we develop methodology and supporting asymptotic theory for selection of an optimal window, minimum mean square errorestimation of the radiusof gyration, and estimation of its variance. Simulation studies confirm the quality of our asymptotic approximations and the superior performance of the proposed methodology relative to the accepted standard. Our semi-automated methodology makes it feasible t...