An approach combining small-angle X-ray solution scattering (SAXS) data with coarse-grained (CG) simulations is developed to characterize the assembly states of Hck, a member of the Src-family kinases, under various conditions in solution. First, a basis set comprising a small number of assembly states is generated from extensive CG simulations. Second, a theoretical SAXS profile for each state in the basis set is computed by using the Fast-SAXS method. Finally, the relative population of the different assembly states is determined via a Bayesian-based Monte Carlo procedure seeking to optimize the theoretical scattering profiles against experimental SAXS data. The study establishes the concept of basis-set supported SAXS (BSS-SAXS) reconstruction combining computational and experimental techniques. Here, BSS-SAXS reconstruction is used to reveal the structural organization of Hck in solution and the different shifts in the equilibrium population of assembly states upon the binding of different signaling peptides.