Following numerous simplifying assumptions, thermodynamic calculation of the phase diagram is based on perturbation theory where the reference system is (but need not be) an assembly of hard spheres. To calculate the perturbation term, we need a potential of mean force for describing protein-protein interactions. It is the potential of mean force that provides the key for a successful calculation.
Using one perturbation theory for a simple fluid and another for a simple solid, pressures and chemical potentials are readily calculated leading to construction of the phase diagram. At a fixed temperature, the two equations of equilibrium (both phases are at the same pressure and chemical potential) yield the densities of the two equilibrated phases.
For these calculations we need to know the solution's pH and the protein's size, electric charge and, perhaps, dipole moment. Further, we need to know the concentration of added electrolyte (salt) and, as emphasized in recent work, the nature of the salt.
The primary effect of the salt is to screen repulsive electrostatic protein-protein interactions. Thus, addition of salt encourages protein precipitation, an important separation step in biotechnology. However, for protein precipitation, some salts are much more efficient than others, as discovered by Hofmeister over 100 years ago. Recent quantitative work indicates that the Hofmeister effect is due, at least in part, to ion-ion and ion-protein dispersion forces.
Some information on the potential of mean force can be obtained from experimental data for the osmotic second virial coefficient of the protein solution at fixed pH and salt concentration.
For illustration, calculated phase diagrams are shown for aqueous lysozyme with sodium chloride, sodium iodide or sodium isocyanate, all at the same pH and salt concentration. These three phase diagrams are significantly different due to the nature of the salt.