SAS profile correlations reveal SAS hierarchical nature and information content

In structural biology, Small-Angle Scattering experiments (SAS) are unique, because although they provide low resolution data, they can be performed in closer-to-native conditions than those arising in X-Ray crystallography. A number of questions on SAS, however, remain unsolved, particularly in the light of modelling ensembles of conformers in solution. In this article, we study the ensemble average and covariance of SAS profiles analytically. Using this ensemble covariance, we demonstrate the hierarchical nature of SAS profiles. Furthermore, we show that the information content is not uniform and reaches its maximum in the intermediate q range. The arguments are generalized using microsecond-scale molecular dynamics trajectories of the lysozyme and on an ensemble of the intrinsically disordered protein p15PAF. We show that for highly flexible systems, the SAS profile is a representation of the ensemble of conformers in solution, and not that of one conformer in particular.