Modeling phase transitions in mixtures of β-γ lens crystallins

We analyze the experimentally determined phase diagram of a gamma D-beta B1 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-cloud versus packing fraction eta measurements for a pure (x(2) = 0) gamma D 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 x(2) vs. eta 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 beta B1 crystallin protein and to calculate; (ii) complete equilibrium surface (T-cloud-x(2)-eta) 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 gamma D and beta B1 proteins. This interesting result may be related to the fact that gamma D has a more than nine times smaller quadrupole moment than its partner in the mixture.