(Dis-)appearance of liquid-liquid phase transitions in a heterogeneous activated patchy particle model and experiment

The ion-activated patchy particle model is an important theoretical framework to investigate the phase behavior of globular proteins in the presence of multivalent ions. In this study, we examine and highlight the influence of patch heterogeneity on the extension, appearance, and disappearance of the liquid-liquid coexistence region of the phase diagram. We demonstrate that within this model the binding energy between salt ions and patches of different types is a key factor in determining the phase behavior. Specifically, we show under which conditions liquid-liquid phase separation (LLPS) in these systems can appear or disappear for varying binding energy and ion-mediated attraction energy between ion-occupied and unoccupied patches. In particular, we address the influence of the patch type dependence of these energies on the (dis)appearance of LLPS. These results rationalize our new results on ion-dependent liquid-liquid phase separation in solutions of bovine serum albumin with trivalent cations. In comparison with models with non-activated patches, where the gas-liquid transition disappears when the number of patches approaches two, we find the complementary mechanism that ions may shift the attractions from stronger to weaker patches (with an accompanying disappearance of the transition) if their binding energy to the patches changes. The results have implications for the understanding of charge-driven LLPS in biological systems and its suppression.