Accurate assessment of mass, models and resolution by small-angle scattering

Modern small angle scattering (SAS) experiments with X-rays or neutrons provide a comprehensive, resolution-limited observation of the thermodynamic state. However, methods for evaluating mass and validating SAS based models and resolution have been inadequate. Here, we define the volume-of-correlation, V(c): a SAS invariant derived from the scattered intensities that is specific to the structural state of the particle, yet independent of concentration and the requirements of a compact, folded particle. We show V(c) defines a ratio, Qr, that determines the molecular mass of proteins or RNA ranging from 10 to 1,000 kDa. Furthermore, we propose a statistically robust method for assessing model-data agreements (X(2)(free)) akin to cross-validation. Our approach prevents over-fitting of the SAS data and can be used with a newly defined metric, R(sas), for quantitative evaluation of resolution. Together, these metrics (V(c), Qr, X(2)(free), and R(sas)) provide analytical tools for unbiased and accurate macromolecular structural characterizations in solution.