Ambiguity assessment of small‐angle scattering curves from monodisperse systems. (1st May 2015) - Petoukhov, Maxim V.; Svergun, Dmitri I.
<x xml:space="preserve">Abstract</x> A novel approach is presented for an a priori assessment of the ambiguity associated with spherically averaged single‐particle scattering. The approach is of broad interest to the structural biology community, allowing the rapid and model‐independent assessment of the inherent non‐uniqueness of three‐dimensional shape reconstruction from scattering experiments on solutions of biological macromolecules. One‐dimensional scattering curves recorded from monodisperse systems are nowadays routinely utilized to generate low‐resolution particle shapes, but the potential ambiguity of such reconstructions remains a major issue. At present, the (non)uniqueness can only be assessed by a posteriori comparison and averaging of repetitive Monte Carlo‐based shape‐determination runs. The new a priori ambiguity measure is based on the number of distinct shape categories compatible with a given data set. For this purpose, a comprehensive library of over 14 000 shape topologies has been generated containing up to seven beads closely packed on a hexagonal grid. The computed scattering curves rescaled to keep only the shape topology rather than the overall size information provide a `scattering map' of this set of shapes. For a given scattering data set, one rapidly obtains the number of neighbours in the map and the associated shape topologies such that in addition to providing a quantitative ambiguity measure the algorithm may also serve as an alternative shape‐analysis tool. The approach has been validated in model calculations on geometrical bodies and its usefulness is further demonstrated on a number of experimental X‐ray scattering data sets from proteins in solution. A quantitative ambiguity score (a‐score) is introduced to provide immediate and convenient guidance to the user on the uniqueness of the ab initio shape reconstruction from the given data set.