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, but independent of concentration and the requirements of a compact, folded particle. We show that V-c defines a ratio, Q(R), that determines the molecular mass of proteins or RNA ranging from 10 to 1,000 kilodaltons. Furthermore, we propose a statistically robust method for assessing model-data agreements (chi(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, Q(R), chi(2)(free) and R-SAS) provide analytical tools for unbiased and accurate macromolecular structural characterizations in solution.