Distinguishing near- versus off-critical phase behaviors of intrinsically disordered proteins.

Intrinsically disordered prion-like low complexity domains (PLCDs) drive phase transitions that underlie the biogenesis of many biomolecular condensates. Here, we report results from large-scale Monte Carlo simulations on lattices aided by computations of Binder cumulants and rigorous finite-size scaling. These approaches enable accurate mapping of the critical regime and computations of the full binodal of an archetypal PLCD. This weakly associating polymer undergoes phase separation coupled to percolation. Between the lowest temperature and the critical point, the concentrations along the left arm of the binodal vary by four orders of magnitude. The overlap line intersects the left arm of the binodal well below the critical point. This, taken together with the intersection of the percolation line and the left arm of the binodal, leads to demarcation of the binodal into three regimes. Regime I is farthest from the critical point. Here, the coexisting dilute phase is akin to a gas of dispersed polymers. The dilute arm of the binodal lies above the overlap line in Regimes II and III. Here, the semidilute nature of dilute phases enables clustering of polymers that is enhanced by intermolecular associations. The coexisting dense phases form confined percolated networks in Regimes I and II. In Regime III, which is closest to the critical point, the dense phase becomes unconfined and fragmented, and the system is defined by two interconnected, system-spanning networks. In addition to mapping the critical point accurately, we evaluated methods for identifying the theta temperature. We find that scaling approaches based on assumptions from two-parameter theories for homopolymers yield erroneous estimates of the theta temperature of an archetypal PLCD. Accurate estimation of the theta temperature requires direct calculation of the temperature dependence of the two-body interaction coefficient. We discuss implications for inferring solvent quality from scaling analysis of segmental distances of disordered proteins.