Variable-Resolution Scattering Reveals Ensemble Properties

Abstract

SAXS/SANS determine the size and structure of particles and macromolecules in solution. However, the conventional low-angle determination of the radius of gyration, Rg, cannot separately resolve its scattering-weighted mean and the width of its distribution. Because the apparent Rg includes a contribution from ensemble variance, the distribution width is required even to recover the mean Rg. Here, we introduce TENOR-SAXS, a method for estimating the scattering-weighted width of an Rg distribution by applying two anisotropic digital smearings to a single 2D scattering image. Comparing the smeared images provides curvature information unavailable from the conventional radial profile. The resulting observables require no explicit model of the native instrumental point-spread function and show only weak sensitivity over the range of native resolutions typical of SAXS measurements examined here. Analytical expressions are derived in the low-angle and narrow-distribution limits for ensembles described by a known or independently constrained single-particle form factor. For verification, we simulated scattering by particles with several form factors and ensembles with different size distributions, all agree well with the analytical theory. To leading order, the principal observable depends on the scattering-weighted mean and variance rather than on the distribution's functional form or higher moments. For simulated data corresponding to feasible synchrotron exposure times for biological samples, the distribution width and, expressed as a fraction of its mean, was recovered with a typical discrepancy of ~0.1, while the scattering-weighted mean Rg was recovered with ~2% relative discrepancy. TENOR-SAXS thus provides a framework for estimating ensemble width from existing 2D scattering data without explicit instrumental desmearing and for correcting the variance contribution to the apparent radius