*Biophys. J.*, 2008, 94:4906-4923. [paper]

We describe a method by which a single experiment can reveal both association model (pathway and constants) and low-resolution structures of a self-associating system. Small angle scattering data are collected from solutions at a range of concentrations. These scattering curves are mass-weighted linear combinations of the scattering from each oligomer. Singular value decomposition of the data yields a set of basis vectors, from which the scattering curve for each oligomer is reconstructed using coefficients that depend on the association model. A search identifies the association pathway and constants that provide the best agreement between reconstructed and observed data. Using simulated data with realistic noise, our method finds the correct pathway and association constants. Depending on the simulation parameters reconstructed curves for each oligomer differ from the ideal by 0.05-0.99% in median absolute relative deviation. The reconstructed scattering curves are fundamental to further analysis, including interatomic distance distribution calculation and low-resolution ab initio shape reconstruction of each oligomer in solution. This method can be applied to x-ray or neutron scattering data from small angles to modest (or higher) resolution. Data can be taken under physiological conditions or particular conditions (e.g. temperature) can be varied to extract fundamental association parameters (ΔH_{ass}, ΔS_{ass}).