H. Chandola, T. Williamson, B.A. Craig, A.M. Friedman, and C. Bailey-Kellogg, "Stoichiometries and affinities of interacting proteins from concentration series of solution scattering data: Decomposition by least squares and quadratic optimization", J. Appl. Cryst., 2014, 47:899-914.

In studying interacting proteins, complementary insights are provided by analyzing the association model (the stoichiometry and affinity constants of the intermediate and final complexes) and the quaternary structure of the resulting complexes. Many current methods for analyzing protein interactions give either a binary answer to the question of association or at best provide only part of the complete picture. We present here a method to extract both types of information from x-ray or neutron scattering data for a series of solutions containing the complex components in different concentrations. Our method determines the association pathway and constants, along with the scattering curves of the individual members of the mixture, so as to best explain the scattering data for the set of mixtures. The derived curves then enable reconstruction of the intermediate and final complexes. Using a new analytic method, we also extend our approach to evaluate the association models and scattering curves in the presence of contaminants, testing both a non-participating monomer and a large homo-oligomeric aggregate. Using simulated solution scattering data for four hetero-oligomeric complexes with different structures, molecular weights, and association models, we demonstrate that our method accurately determines the simulated association model and monomer scattering profiles. We also demonstrate that the method is robust to both random noise and systematic noise from such contaminants, and is applicable over a large range of weak association constants typical of transient protein-protein complexes.