A model-free method for extracting interaction potential between protein molecules using small-angle X-ray

A small-angle X-ray scattering has been used to probe protein–protein interaction in solution. Conventional methods need to input modeled potentials with variable/invariable parameters to reproduce the experimental structure factor. In the present study, a model-free method for extracting the excess part of effective interaction potential between protein molecules in solutions over an introduced hard-sphere potential by using experimental data of small-angle X-ray scattering is presented on the basis of liquid-state integral equation theory. The reliability of the model-free method is tested by the application to experimentally derived structure factors for dense lysozyme solutions with different solution conditions [Javid et al., Phys. Rev. Lett. 99, 028101 (2007), Schroer et al., Phys. Rev. Lett. 106, 178102 (2011)]. The structure factors calculated from the model-free method agree well with the experimental ones. The model-free method provides the following picture of the lysozyme solution: these are the stabilization of contact-pair configurations, large activation barrier against their formations, and screened Coulomb repulsion between the charged proteins. In addition, the model-free method will be useful to verify whether or not a model for colloidal system is acceptable to describing protein–protein interaction.