(308f) The Crystallization Thresholds Determined by the Residual Entropy Rule for the Two-Term Yukawa Potential as a Model for Protein Solutions

It has recently been recognized that protein-protein interactions in solutions can be modeled by a two-term Yukawa potential (a short-ranged attraction plus a long-ranged repulsion). Neutron scattering experiments on protein solutions (such as lysozyme) have shown that prior to crystallization, proteins form a ?cluster phase?. Interestingly, the peculiar structure factors S(q) of the clusters can be captured by the simple 2-Yukawa potentials. We show that this 2-Yukawa potential is closely related to the Derjaguin-Landau-Verwey-Overbeek (DLVO) interaction in colloidal chemistry. We apply two theoretical approaches to determine the crystallization limits for this 2-Yukawa potential: (i) a self-consistent integral equation theory based on the zero-separation closure (ZSEP) to the Ornstein-Zernike equation; and (ii) the one-phase residual entropy rule proposed by Giaquinta-Giunta (1992). Since the ZSEP theory is self-consistent, it gives accurate structures S(q) and thermodynamic properties, as well as accurate entropy values. These ingredients enabled us to calculate the residual entropy, ÄSn, and consequently determine the conditions where the fluid phase enters the solid phase.

Five combinations of parameters (K1, Z1, and Z2) are investigated. Theoretical calculations are checked with Monte Carlo simulations, and are shown to have exceptional credence. We found that the single-phase crystallization rule of Giaquinta and Giunta is useful in determining the crystallization limits. Etiological factors are clarified that shed lights on the quantitative cause-and-effect relations for protein crystallization.