Mechanism of polymer molecular weight-dependent suppression and promotion of liquid–liquid phase separation of a protein solution by the addition of polymer

Polyethylene glycol (PEG) is a widely used precipitant to concentrate proteins. The effect of PEG is generally understood to be an entropic attraction between proteins due to the depletion effect of PEG around proteins. However, measurements by Bloustine et al. [Phys. Rev. Lett. 96, 087803 (2006)] of the liquid-liquid phase separation (LLPS) temperature have shown that a lysozyme solution is stabilized and destabilized by the addition of low and high molecular-weight PEG, respectively. They also presented a theoretical model of the LLPS temperature as a virial expansion of the free energy and concluded that, in addition to the depletion effect, the attractive interaction between protein and PEG is necessary to explain the experiments. In the present study, theoretical calculations based on liquid-state density functional theory utilizing coarse-grained models are conducted to demonstrate that the protein-PEG effective attraction is responsible for the suppression and promotion of LLPS upon the addition of low- and high-weight PEG, respectively. In contrast, if the interactions between the protein and the PEG are solely due to the excluded volume effect, PEG of any molecular weight destabilizes the solution. These results suggest the necessity to reconsider the conventional understanding of the effects of polymer addition, which have been historically attributed to solely the depletion force.