Why forces between proteins follow different Hofmeister series for pH above and below pI

Abstract

The relative effectiveness of different anions in crystallizing proteins follows a reversed Hofmeister sequence for pH < pI and a direct Hofmeister sequence for pH > pI. The phenomenon has been known almost since Hofmeister's original work but it has not been understood. It is here given a theoretical explanation. Classical electrolyte and double layer theory deals only with electrostatic forces acting between ions and proteins. Hydration and hydration interactions are dealt with usually only in terms of assumed hard core models. But there are, at and above biological salt concentrations, other non-electrostatic (NES) ion-specific forces acting that are ignored in such modeling. Such electrodynamic fluctuation forces are also responsible for ion-specific hydration. These missing forces are variously comprehended under familiar but generally unquantified terms, typically, hydration, hydrogen bonding, π-electron–cation interactions, dipole–dipole, dipole-induced dipole and induced dipole-induced dipole forces and so on. The many important body electrodynamic fluctuation force contributions are accessible from extensions of Lifshitz theory from which, with relevant dielectric susceptibility data on solutions as a function of frequency, the forces can be extracted quantitatively, at least in principle. The classical theories of colloid science that miss such contributions do not account for a whole variety of ion-specific phenomena. Numerical results that include these non-electrostatic forces are given here for model calculations of the force between two model charge-regulated hen-egg-white protein surfaces. The surfaces are chosen to carry the same charge groups and charge density as the protein. What emerges is that for pH < pI (where the anions are counter-ions) the repulsive double layer forces increase in the order NaSCN < NaI < NaCl, while at higher pH > pI (where anions are co-ions) the forces increase in the order NaCl < NaI < NaSCN. This is in excellent agreement with both solubility experiments and experiments using SAXS. The results are also consistent with cation effects observed in protein solutions. Our results may provide some insights into a long-standing problem in solution chemistry and biology.