We present a minimal model to study the effects of pH on liquid phase separation of macromolecules. Our model describes a mixture composed of water and macromolecules that exist in three different charge states and have a tendency to phase separate. This phase separation is affected by pH via a set of chemical reactions describing protonation and deprotonation of macromolecules, as well as self-ionization of water. We consider the simple case in which interactions are captured by Flory-Huggins interaction parameters corresponding to Debye screening lengths shorter than a nanometer, which is relevant to proteins inside biological cells under physiological conditions. We identify the conjugate thermodynamic variables at chemical equilibrium and discuss the effective free energy at fixed pH. First, we study phase diagrams as a function of macromolecule concentration and temperature at the isoelectric point of the macromolecules. We find a rich variety of phase diagram topologies, including multiple critical points, triple points, and first-order transition points. Second, we change the pH relative to the isoelectric point of the macromolecules and study how phase diagrams depend on pH. We find that these phase diagrams as a function of pH strongly depend on whether oppositely charged macromolecules or neutral macromolecules have a stronger tendency to phase separate. One key finding is that we predict the existence of a reentrant behavior as a function of pH. In addition, our model predicts that the region of phase separation is typically broader at the isoelectric point. This model could account for both in vitro phase separation of proteins as a function of pH and protein phase separation in yeast cells for pH values close to the isoelectric point of many cytosolic proteins.

中文翻译：

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由pH控制的液相分离

我们提出了一个最小模型来研究 pH 值对大分子液相分离的影响。我们的模型描述了一种由水和大分子组成的混合物，这些大分子以三种不同的电荷状态存在，并具有相分离的趋势。这种相分离通过一系列描述大分子质子化和去质子化以及水的自电离的化学反应受到 pH 值的影响。我们考虑一个简单的情况，其中相互作用被 Flory-Huggins 相互作用参数捕获，对应于比纳米短的德拜筛选长度，这与生理条件下生物细胞内的蛋白质有关。我们确定了化学平衡时的共轭热力学变量，并讨论了固定 pH 值下的有效自由能。第一的，我们研究相图作为大分子浓度和大分子等电点温度的函数。我们发现了丰富多样的相图拓扑，包括多个临界点、三相点和一阶转变点。其次，我们相对于大分子的等电点改变 pH 值，并研究相图如何依赖于 pH 值。我们发现这些作为 pH 值函数的相图很大程度上取决于带相反电荷的大分子或中性大分子是否具有更强的相分离趋势。一个关键发现是我们预测了作为 pH 值函数的可重入行为的存在。此外，我们的模型预测相分离区域通常在等电点更宽。