Vapor-liquid coexistence of patchy models: relevance to protein phase behavior

The vapor-liquid coexistence boundaries of fluids composed of particles interacting with highly directional patchy interactions, in addition to an isotropic square well potential, are evaluated using grand canonical Monte Carlo simulations combined with the histogram reweighting and finite size scaling methods. We are motivated to study this more complicated model for two reasons. First, it is established that the reduced widths of the metastable vapor-liquid coexistence curve predicted by a model with only isotropic interparticle interactions are much too narrow when compared to the experimental phase behavior of protein solutions. Second, interprotein interactions are well known to be "patchy." Our results show that at a constant total areal density of patches, the critical temperature and the critical density increase monotonically with an increasing number of uniformly spaced patches. The vapor-liquid coexistence curves plotted in reduced coordinates (i.e., the temperature and the density scaled by their respective critical values) are found to be effectively independent of the number of patches, but are much broader than those found for the isotropic models. Our findings for the reduced width of the coexistence curve are almost in quantitative agreement with the available experimental data for protein solutions, stressing the importance of patchiness in this context.