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

Abstract

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, Vc, 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 Vc defines a ratio, QR, 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 (χ2free) akin to cross-validation. Our approach prevents over-fitting of the SAS data and can be used with a newly defined metric, RSAS, for quantitative evaluation of resolution. Together, these metrics (Vc, QR, χ2free and RSAS) provide analytical tools for unbiased and accurate macromolecular structural characterizations in solution. Small-angle scattering of X-rays or neutrons is more readily applied to macromolecular complexes than is X-ray crystallography, and is particularly useful for protein complexes with high flexibility; here new quantitative metrics are presented that will allow solution-derived structures to be validated and assessed for mass, resolution and accuracy. Small-angle scattering (SAS) of X-rays or neutrons is more readily applied to macromolecular complexes than is X-ray crystallography, and is particularly useful for proteins and complexes with high flexibility. John Tainer and Robert Rambo have developed a new series of quantitative metrics that allow the accuracy of such solution-derived structures to be validated. This refinement strengthens the intrinsic capabilities of SAS for high-throughput analyses and should expand its application to studying flexible macromolecules and nanoparticles in solution.