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

TL;DR

This study demonstrates that protein solutions near liquid-liquid phase separation follow a universal osmotic equation of state and exhibit behavior consistent with the extended law of corresponding states, linking thermodynamics, structure, and dynamics.

Contribution

It provides comprehensive experimental validation that the extended law of corresponding states applies to the thermodynamics, structure, and dynamics of concentrated protein solutions near LLPS.

Findings

Quantitative agreement with the extended law of corresponding states.

Baxter's model describes concentration fluctuations well.

Scaling laws near LLPS are consistent with mean-field theory.

Abstract

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.