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Universal effective interactions of globular proteins close to liquid-liquid phase separation: corresponding-states behavior reflected in the structure factor

Intermolecular interactions in protein solutions in general contain many contributions. If short-range attractions dominate, the state diagram exhibits liquid-liquid phase separation (LLPS) that is metastable with respect to crystallization. In this case, the extended law of corresponding states (ELCS) suggests that thermodynamic properties are insensitive to details of the underlying interaction potential. Using lysozyme solutions, we investigate the applicability of the ELCS to the static structure factor and in how far effective colloidal interaction models can help to rationalize the phase behavior and interactions of protein solutions in the vicinity of the LLPS binodal. The (effective) structure factor has been determined by small-angle X-ray scattering (SAXS). It can be described by Baxter's adhesive hard-sphere model, which implies a single fit parameter from which the normalized second virial coefficient $b_2$ is inferred and found to quantitatively agree with previous results from static light scattering. The $b_2$ values are independent of protein concentration, but systematically vary with temperature and solution composition, i.e. salt and additive content. If plotted as a function of temperature normalized by the critical temperature, the values of $b_2$ follow a universal behaviour. These findings validate the applicability of the ELCS to globular protein solutions and indicate that the ELCS can also be reflected in the structure factor.