Calculation of Phase Diagrams for Aqueous Protein Solutions

In recent publications, phase diagrams have been generated from simple models of globular proteins interacting via anisotropic interactions. In these models, protein solubility is determined from the favorable energetic interactions due to the formation of protein−protein contacts in the crystal that overcome the unfavorable loss in entropy from constraining a protein molecule upon crystallization. In this work, we develop a statistical mechanical description for protein crystallization of which a key component is the quantitative calculation of this entropy loss. We calculate the entropic term from experimental crystallographic data for lysozyme and show that the empirical correlation of the osmotic second virial coefficient with lysozyme solubility corresponds to 6−8 contacts per protein molecule in the crystal. In addition, our model predicts that the two-body potential of mean force between lysozyme molecules is highly anisotropic. This has important implications for determining the position of a fluid−fluid critical point metastable to the fluid−solid equilibrium. That position is important because, as shown previously, crystallization kinetics are maximized at temperatures slightly exceeding the fluid−fluid critical temperature.