  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.
