Theory of the nucleation of protein macromolecular ions

Protein molecules are amphoteric and exist in aqueous solution as macromolecular ions that carry a charge which depends upon temperature and pH. Despite the repulsive Coulomb forces acting between them, protein macromolecular ions can form crystals in pH buffered solutions of strong electrolytes. It is proposed that the first step in the mechanism of crystallization is the formation of crystal nuclei made from partially discharged macromolecular ions that have exchanged H+ with the buffer. We suggest that the strength of the bare Coulomb repulsive force is weakened by the Debye-Huckel plasma screening provided by the inert electrolyte. This screening causes the rate of nucleus formation to increase with increasing ionic strength. Extending classic nucleation theory to account for these various charge effects, the results are applied to the case of lysozyme and a calculation is made of the dependence of the steady state nucleation rate upon temperature, pH, ionic strength, and protein supersaturation. It is found that the nucleation rate increases with increasing temperature and increasing ionic strength. Under condition of fixed temperature, supersaturation, and inionic strength, the nucleation rate has local maxima at low pH, where individual lysozyme macro ions are highly charged, and at pH similar or equal to 11, where they have zero average net charge. At both pH values, the nucleus that determines the rate has minimum size. In contrast to standard nucleation theory, which ignores charge, it is found that the size of the nucleus that controls the rate is different from the size of the nucleus that has the lowest concentration. All other conditions being the same, it is predicted that lysozyme crystals should nucleate most rapidly near pH = 2 and near pH = 11.