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Finite-size scaling analysis of protein droplet formation

The formation of biomolecular condensates inside cells often involve intrinsically disordered proteins (IDPs), and several of these IDPs are also capable of forming droplet-like dense assemblies on their own, through liquid-liquid phase separation. When modelings thermodynamic phase changes, it is well-known that finite-size scaling analysis can be a valuable tool. However, to our knowledge, this approach has not been applied before to the computationally challenging problem of modeling sequence-dependent biomolecular phase separation. Here, we implement finite-size scaling methods to investigate the phase behavior of two 10-bead sequences in a continuous hydrophobic/polar protein model. Combined with reversible explicit-chain Monte Carlo simulations of these sequences, finite-size scaling analysis turns out to be both feasible and rewarding, despite relying on theoretical results for asymptotically large systems. While both sequences form dense clusters at low temperature, this analysis shows that only one of them undergoes liquid-liquid phase separation. Furthermore, the transition temperature at which droplet formation sets in, is observed to converge slowly with system size, so that even for our largest systems the transition is shifted by about 8%. Using finite-size scaling analysis, this shift can be estimated and corrected for.