Title: Understanding the Salt Effects on the Liquid-Liquid Phase Separation of Proteins

Abstract: Protein aggregation via liquid-liquid phase separation (LLPS) is ubiquitous in nature and intimately connects to many human diseases. Although it is widely known that the addition of salt has crucial impacts on the LLPS of protein, full understanding of the salt effect remains an outstanding challenge. Here, we develop a molecular theory which systematically incorporates the self-consistent field theory for charged macromolecules into the solution thermodynamics. The electrostatic interaction, hydrophobicity, ion solvation and translational entropy are included in a unified framework. Our theory fully captures the long-standing puzzles of the non-monotonic salt concentration dependence and the specific ion effect. We find that proteins show salting-out at low salt concentrations due to ionic screening. The solubility follows the inverse Hofmeister series. In the high salt concentration regime, protein remains salting-out for small ions but turns to salting-in for larger ions, accompanied by the reversal of the Hofmeister series. We reveal that the solubility at high salt concentrations is determined by the competition between the solvation energy and translational entropy of ion. Furthermore, we derive an analytical criterion for determining the boundary between the salting-in and salting-out regimes. The theoretical prediction is in quantitative agreement with experimental results for various proteins and salt ions without any fitting parameters.