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 different biomolecular condensates. The mapping of critical points is essential for generating quantitative assessments of driving forces and for distinguishing phase behaviors in the critical versus off-critical regimes. Computations play an important role in connecting the molecular-scale interactions to mesoscale phase behaviors of PLCDs and other intrinsically disordered proteins. We report results from accurate mapping of the critical regime for an archetypal PLCD. This is achieved by combining large-scale simulations with computations of Binder cumulants and the use of rigorous finite-size scaling approaches. The computed binodal, defined by knowledge of the critical point and intersection of the left arm of the binodal by the overlap and percolation lines, can be demarcated into three distinct regimes. Regime I is farthest from the critical point, with the coexisting dilute phase being akin to a gas of dispersed polymers. Regime II lies above the intersection of the overlap line and the dilute arm of the binodal. Here, coexisting dilute phases are characterized by heterogeneous cluster-size distributions with heavy tails. In Regimes I and II, dense phases are confined percolated networks. Regime III is closest to the critical point. Here, the dense phase becomes unconfined and the percolated network swells to become system-spanning. Thus, Regime III comprises two interconnected, system-spanning networks. In addition to accurately mapping the critical point, we also evaluated methods for identifying the theta temperature. We find that conventional scaling approaches lead to erroneously low estimates of the theta temperature. Instead, accurate estimation of the theta temperature requires direct calculation of the temperature dependence of the two-body interaction coefficient. We discuss the broader implications of these findings for inferring solvent quality from scaling analyses.