Model for a mixture of macroions, counterions, and co-ions in a waterlike fluid

Protein Association in Solution: Statistical Mechanical Modeling

Protein molecules associate in solution, often in clusters beyond pairwise, leading to liquid phase separations and high viscosities. It is often impractical to study these multi-protein systems by atomistic computer simulations, particularly in multi-component solvents. Instead, their forces and states can be studied by liquid state statistical mechanics. However, past such approaches, such as the Derjaguin-Landau-Verwey-Overbeek (DLVO) theory, were limited to modeling proteins as spheres, and contained no microscopic structure-property relations. Recently, this limitation has been partly overcome by bringing the powerful Wertheim theory of associating molecules to bear on protein association equilibria. Here, we review these developments.

Calorimetric studies of interactions between low molecular weight salts and bovine serum albumin in water at pH values below and above the isoionic point

Isothermal titration calorimetry was used to determine the temperature and salt concentration dependence of the enthalpy of mixing, Δ_mix H, of bovine serum albumin (BSA) in aqueous buffer solutions with several low molecular weight salts. Three buffers were used: acetate (pH = 4.0), MOPS (7.2), and borate (9.2). Since the isoionic point of BSA is at pI ≈ 4.7, the net charge of BSA in acetate buffer was positive (≈ +20), while in the other two buffer solutions it was negative (≈ -15 in MOPS and ≈ -25 in borate). The majority of the recorded heat effects were exothermic, while only at pH = 9.2 a weak endothermic effect upon mixing BSA with LiCl, NaCl, and KCl was observed. For all buffer solutions the absolute values of Δ_mix H of sodium salts followed the order: NaCl < NaBr < NaNO₃ < NaI < NaSCN, which is the reverse Hofmeister series for anions. The magnitude of the effects was the largest in acetate buffer and decreased with an increasing pH value of the solution. While the effect of varying the anion of the added salts was strongly pronounced at all pH values, the effect of the cation (LiCl, NaCl, KCl, RbCl and CsCl salts) was weak. The most interesting feature of the results obtained for pH > pI was the fact that Δ_mix H were considerably more sensitive to the anion (co-ion to the net BSA charge) than to the cation species. This indicated that anions interacted quite strongly with the BSA even at pH values where the net charge of the protein was negative. We showed that Δ_mix H at high addition of salts correlated well with the enthalpy of hydration of the corresponding salt anion. This finding suggested, consistently with some previous studies, that a part of the exothermic contribution to Δ_mix H originated from the hydration changes upon the protein-salt interaction. Theoretical analysis, based on the primitive model of highly asymmetric electrolyte solutions solved within the mean spherical approximation, was used to estimate Coulomb effects upon mixing.

Explicit-water theory for the salt-specific effects and Hofmeister series in protein solutions

Effects of addition of salts on stability of aqueous protein solutions are studied theoretically and the results are compared with experimental data. In our approach, all the interacting species, proteins, ions, and water molecules, are accounted for explicitly. Water molecules are modeled as hard spheres with four off-center attractive square-well sites. These sites serve to bind either another water or to solvate the ions or protein charges. The ions are represented as charged hard spheres, and decorated by attractive sites to allow solvation. Spherical proteins simultaneously possess positive and negative groups, represented by charged hard spheres, attached to the surface of the protein. The attractive square-well sites, mimicking the protein-protein van der Waals interaction, are located on the surface of the protein. To obtain numerical results, we utilized the energy route of Wertheim's associative mean spherical approximation. From measurable properties, we choose to calculate the second virial coefficient B2, which is closely related to the tendency of proteins to aggregate and eventually crystalize. Calculations are in agreement with experimental trends: (i) For low concentration of added salt, the alkali halide salts follow the inverse Hofmeister series. (ii) At higher concentration of added salt, the trend is reversed. (iii) When cations are varied, the salts follow the direct Hofmeister series. (iv) In contrast to the colloidal theories, our approach correctly predicts the non-monotonic behavior of B2 upon addition of salts. (v) With respect to anions, the theory predicts for the B2 values to follow different sequences below and above the iso-ionic point, as also confirmed experimentally. (vi) A semi-quantitative agreement between measured and calculated values for the second virial coefficient, as functions of pH of solution and added salt type and concentration, is obtained.