We analyze the experimentally determined phase diagram of a γD–βB1 crystallin mixture. Proteins are described as dumbbells decorated with attractive sites to allow inter-particle interaction. We use thermodynamic perturbation theory to calculate the free energy of such mixtures and, by applying equilibrium conditions, also the compositions and concentrations of the co-existing phases. Initially we fit the T_cloudversus packing fraction η measurements for a pure (x₂ = 0) γD solution in 0.1 M phosphate buffer at pH = 7.0. Another piece of experimental data, used to fix the model parameters, is the isotherm x₂vs. η at T = 268.5 K, at the same pH and salt content. We use the conventional Lorentz–Berthelot mixing rules to describe cross interactions. This enables us to determine: (i) model parameters for pure βB1 crystallin protein and to calculate; (ii) complete equilibrium surface (T_cloud–x₂–η) for the crystallin mixtures. (iii) We present the results for several isotherms, including the tie-lines, as also the temperature-packing fraction curves. Good agreement with the available experimental data is obtained. An interesting result of these calculations is evidence of the coexistence of three phases. This domain appears for the region of temperatures just out of the experimental range studied so far. The input parameters, leading good description of experimental data, revealed a large difference between the numbers of the attractive sites for γD and βB1 proteins. This interesting result may be related to the fact that γD has a more than nine times smaller quadrupole moment than its partner in the mixture.

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.

Disordered porous materials filled with liquid or solution may be considered as partly-quenched, i.e., as systems in which some of the degrees of freedom are quenched and others annealed. In such cases, the statistical-mechanical averages used to calculate the system's thermodynamical properties become double ensemble averages: first over the annealed degrees of freedom and then over all possible values of the quenched variables. In this respect, the quenched-annealed systems differ from regular mixtures. The multi-faceted applications of the partly-quenched systems to a kaleidoscope of technological and biological processes make the understanding of these systems important and of interest. Present contribution reviews recent developments in theory and simulation of partly-quenched systems containing charges. Specifically, two different models of such systems are discussed: (a) the model in which the nanoporous system (matrix subsystem) formed by charged obstacles is electroneutral, and (b) the model, where the subsystem of obstacles has some net charge. The latter model resembles, for example, the situation in ion exchange resins etc. Various theoretical methods are applied to investigate structural and dynamical peculiarities of such systems. One is the replica Ornstein-Zernike theory, especially adapted for charged systems, and the other is the Monte Carlo computer simulation method. These two approaches are well suited to study thermodynamical parameters, such as the mean activity coefficient of the annealed electrolyte or Donnan's exclusion parameter. Highly relevant issue of dynamics of ions in partly-quenched systems is also addressed. For this purpose, the Brownian dynamic method is used: the self-diffusion coefficients of ions are calculated for various model parameters and discussed in light of the experimental data. These results, together with the thermodynamical data mentioned above, provide additional evidence that properties of the adsorbed fluid substantially differ from those of its bulk counterpart.