Thermodynamic study of protein phases formation and clustering in model water-protein-salt solutions

Thermodynamic analysis of the water-protein-salt system, based on the description of the spinodal curve, has been carried out in various coordinate systems: (water chemical potential, protein concentration m2); (protein “solubility” log S, salt concentration m3); (effective temperature, critical composition of the system m2/m3). Such presentations explain the existence of diagrams with normal and retrograde protein solubility as a result of straightforward effect of ions present in solution as well as some features of the widely used phase diagram in coordinates (temperature, protein concentration). Analytic expressions for coefficients K and b of the salting out equation log S = −K·m3 + b as functions of protein charge and protein adsorbed ions have been obtained and identified with the spinodal characteristic points reflecting quasi-equilibrium between protein-lean phase and dense protein-rich phase. Liquid-liquid, liquid-solid phase transitions, dynamic protein clusters and second virial coefficient that characterize interaction between solution components have been thus interrelated. The results of our thermodynamic analysis have been compared with the data reported for lysozyme .