Atomic-resolution structural information from scattering experiments on macromolecules in solution.

The pair-distance distribution function (PDDF) contains all structural information probed in an elastic scattering experiment of macromolecular solutions. However, in small-angle x-ray scattering (SAXS) or small-angle neutron scattering (SANS) experiments only their Fourier transform is measured over a restricted range of scattering angles. We therefore developed a mathematically simple and computationally efficient method to calculate the PDDFs as well as accurate scattering intensities from molecular dynamics simulations. The calculated solution scattering intensities are in excellent agreement with SAXS and wide-angle x-ray scattering (WAXS) experiments for a series of proteins. The corresponding PDDFs are remarkably rich in features reporting on the detailed protein structure. Using an inverse Fourier transform method, most of these features can be recovered if scattering intensities are measured up to a momentum transfer of q≈2-3Å(-1). Our results establish that high-precision solution scattering experiments utilizing x-ray free-electron lasers and third generation synchrotron sources can resolve subnanometer structural detail, well beyond size, shape, and fold.