Critical regimes of two-phase systems formed by intrinsically disordered proteins

Phase separation of polymer solutions is defined by the presence of mean-field and critical regimes that are delineated by a crossover regime. Intrinsically disordered proteins (IDPs), especially those of low net charge and small fractions of ionizable residues, are exemplars of finite-sized heteropolymers that have been described using the formalism of associative polymers or pseudo homopolymers. The critical regime is characterized by large conformational and concentration fluctuations. This makes it difficult to map critical points and characterize the critical regime. Most analyses of simulated phase behaviors presume that the two-phase regime can be mapped onto the universality class of a 3D Ising model without regard to the crossover regime. Here, we investigate the phase transitions of different IDPs and compare their phase behaviors to equivalent, finite-sized homopolymers. We introduce and adapt order parameters to show clear evidence for a crossover from the mean-field to fluctuation-dominated regimes. The relevant order parameters include the interface width between coexisting phases analyzed as a function of temperature. Direct identification of the crossover regime allows for rigorous estimation of different critical points, aided by the Binder cumulant analysis, finite-size scaling, and advanced sampling techniques. We compare our results to experimental data and prescribe a ready-to-implement protocol for the analysis of phase behaviors of IDPs near the critical regime.