The formation of biomolecular condensates inside cells often involve intrinsically disordered proteins (IDPs), and several of these IDPs are also capable of forming dropletlike dense assemblies on their own, through liquid-liquid phase separation. When modeling 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.

中文翻译：

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蛋白质液滴形成的有限尺度缩放分析

细胞内生物分子缩合物的形成通常涉及内在无序的蛋白质（IDP），并且这些IDP中的一些还能够通过液-液相分离自行形成液滴状致密的装配体。在对热力学相变建模时，众所周知的是，有限尺寸缩放分析可能是一种有价值的工具。然而，据我们所知，这种方法以前尚未应用于建模依赖序列的生物分子相分离的计算难题。在这里，我们实现了有限大小的缩放方法，以研究连续的疏水性极性蛋白质模型中两个10珠序列的相行为。结合这些序列的可逆显式蒙特卡罗模拟，有限大小的缩放分析既可行又有益，尽管依赖于渐近大型系统的理论结果。尽管两个序列在​​低温下均形成密集的簇，但该分析表明它们中只有一个经历了液-液相分离。此外，观察到液滴形成的转变温度随系统尺寸逐渐收敛，因此，即使对于我们最大的系统，转变也偏移了8％。使用有限大小的缩放分析，可以估计并纠正此偏移。这样，即使对于我们最大的系统，转换也可以偏移8％。使用有限大小的缩放分析，可以估计并纠正此偏移。这样，即使对于我们最大的系统，转换也可以偏移8％。使用有限大小的缩放分析，可以估计并纠正此偏移。