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 g(ij)(r) are approximated by their zero-density limit (i.e., the Boltzmann factor), we propose a more accurate representation of g(ij)(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 particularly 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 beta-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.