Model for Concentration-Dependent Effects of Charge Regulation on Protein Solution Thermodynamics and Liquid-liquid Phase Separation

We study, theoretically, the effects of charge regulation of an eye lens protein, bovine gammaB-crystallin, on its thermodynamic properties. In a recent analysis we found that near neutral pH, because of continual exchange of protons with the solvent, approximately 400 charge patterns of this protein occur often enough to affect protein-protein interactions. We build a free energy model that incorporates orientation-dependent short-range protein-protein interactions and accommodates specific pairs of protonation patterns. The effective potential includes simplified, screened electrostatic interactions between pattern pairs, hard-core interactions, and dispersion forces. We apply conditions for multiple chemical equilibria and for multicomponent phase separation of proteins that are taken to have fixed patterns. The first-order concentration-dependent effect is that pattern probabilities increase with increasing concentration for members of those pairs of patterns that have more net protein-protein attraction. The model gives a way to study relationships between phase boundaries and chemical equilibria, because the intersection of the chemical equilibrium curve with the multicomponent phase boundaries yields the binary liquid-liquid phase boundary.