We suggest structure characterization of macromolecular assemblies by combining assembly shape determined by electron cyromicroscopy with information about subunit proximity determined by affinity purification. To achieve this aim, structure characterization is expressed as a problem in satisfaction of spatial restraints that (1) represents subunits as spheres, (2) encodes information about the subunit excluded volume, assembly shape, and pulldowns in a scoring function, and (3) finds subunit configurations that satisfy the input restraints by an optimization of the scoring function. Testing of the approach with model systems suggests its feasibility.