Interaction of proteins in solution from small angle scattering: a perturbative approach

In this work an improved methodology for studying interactions of proteins in solution by small-angle scattering is presented. Unlike the most common approach, where the protein-protein correlation functions gij(r) are approximated by their zero-density limit (i.e., the Boltzmann factor), we propose a more accurate representation of gij(r) that takes into account terms up to the first order in the density expansion of the mean-force potential. This improvement is expected to be particulary effective in the case of strong protein-protein interactions at intermediate concentrations. The method is applied to analyze small-angle x-ray scattering data obtained as a function of the ionic strength (from 7 to 507 mM) from acidic solutions of β-lactoglobulin at the fixed concentration of 10 gl-1. The results are compared with those obtained using the zero-density approximation and show significant improvement, particularly in the more demanding case of low ionic strength.