Statistical mechanics of protein solutions

We study theoretically thermodynamic properties of spherical globular proteins in aqueous solution with added monovalent salt. We show how one can determine an effective interaction potential between the proteins from experimental data as a function of salt concentration and we apply this to the protein lysozyme at a solution pH of 7.5 and ionic strengths between 0.05 M and 2 M. It turns out that apart from steric and electrostatic repulsions, there is also an attractive interaction between the proteins. We then develop a method, which we name the optimized Baxter model (OBM), to determine thermodynamic properties of the protein solution, also at large volume fractions of proteins. We apply this method to predict the osmotic compressibility of the protein solution as a function of protein concentration and we show that the predictions compare fairly well with experimental data of lysozyme at several salt concentrations. Since both the OBM and the effective interaction between the proteins are only approximate, we use the OBM to predict thermodynamic properties of a model system with known interaction potential, and we compare these predictions with results from computer simulations to see how accurate the OBM actually is. We also look at the phase equilibrium between a protein solution and protein crystals. We use the OBM to determine the osmotic pressure and the chemical potential of the solution and we show that one can explain the ionic-strength dependence of the chemical potential with a simple model for the crystal. We apply the same method to crystals of silicotungstate in equilibrium with the solution phase. Finally, we predict the first-order correction in the density of the collective diffusion coefficient and we compare the predictions to experimental results on lysozyme