Akram Sk Ashif, Chattaraj Aniruddha, Salava Terry, Ditlev Jonathon, Loew Leslie M, Schmit Jeremy D
Department of Physics, Kansas State University, Manhattan, KS 66506, USA.
R. D. Berlin Center for Cell Analysis and Modeling, University of Connecticut School of Medicine, Farmington, CT 06030.
bioRxiv. 2025 Aug 29:2025.08.27.672390. doi: 10.1101/2025.08.27.672390.
The solubility product is a rigorous description of the phase boundary for salt precipitation and has also been used to qualitatively describe the condensation of biomolecules. Here we present a derivation of the solubility product showing that the solubility product is also a robust description of biomolecules phase boundaries if care is taken to account for soluble oligomers and variable composition within the dense phase. Our calculation describes equilibrium between unbound monomers, the dense phase, and an ensemble of oligomer complexes with significant finite-size contributions to their free energy. The biomolecule phase boundary very nearly resembles the power law predicted by the solubility product when plotted as a function of the monomer concentrations. However, this simple form is confounded by the presence of oligomers in the dilute phase. Accounting for the oligomer ensemble introduces complexities to the power law phase boundary including re-entrant behavior and large shifts for stoichiometrically matched molecules. We show that allowing variable stoichiometry in the dense phase expands the two phase region, which appears as curvature of the phase boundary on a double-logarithmic plot. Furthermore, this curvature can be used to predict variations in the dense phase composition at different points along the phase boundary.
溶度积是对盐沉淀相边界的严格描述，也被用于定性描述生物分子的凝聚。在此，我们给出溶度积的推导，表明如果注意考虑可溶性低聚物和致密相内的可变组成，溶度积也是生物分子相边界的可靠描述。我们的计算描述了未结合单体、致密相以及对其自由能有显著有限尺寸贡献的低聚物复合物集合之间的平衡。当绘制为单体浓度的函数时，生物分子相边界非常接近溶度积预测的幂律。然而，这种简单形式因稀相中存在低聚物而变得复杂。考虑低聚物集合会给幂律相边界带来复杂性，包括折返行为和化学计量匹配分子的大位移。我们表明，允许致密相中有可变化学计量会扩大两相区域，这在双对数图上表现为相边界的曲率。此外，这种曲率可用于预测沿相边界不同点处致密相组成的变化。
