Protein solutions close to liquid-liquid phase separation exhibit a universal osmotic equation of state and dynamical behavior

Liquid-liquid phase separation (LLPS) of protein solutions is governed by highly complex protein-protein interactions. Nevertheless, it has been suggested that based on the extended law of corresponding states (ELCS), as proposed for colloids with short-range attractions, one can rationalize not only the thermodynamics, but also the structure and dynamics of such systems. This claim is systematically and comprehensively tested here by static and dynamic light scattering experiments. Spinodal lines, the isothermal osmotic compressibility $\kappa_\text{T}$ and the relaxation rate of concentration fluctuations $\Gamma$ are determined for protein solutions in the vicinity of LLPS. All these quantities are found to exhibit a corresponding-states behavior. This means that, for different solution conditions, these quantities are essentially the same if considered at similar reduced temperature or second virial coefficient. For moderately concentrated solutions, the volume fraction $\phi$ dependence of $\kappa_\text{T}$ and $\Gamma$ can be consistently described by Baxter's model of adhesive hard spheres. The off-critical, asymptotic $T$ behavior of $\kappa_\text{T}$ and $\Gamma$ close to LLPS is consistent with the scaling laws predicted by mean-field theory. Thus, the present work aims at a comprehensive experimental test of the applicability of the ELCS to structural and dynamical properties of concentrated protein solutions.