NSF-Simons Center for Mathematical & Statistical Analysis of Biology, Harvard University, Cambridge, MA 02138;
School of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138.
Proc Natl Acad Sci U S A. 2021 Nov 9;118(45). doi: 10.1073/pnas.2108551118.
Fluids in natural systems, like the cytoplasm of a cell, often contain thousands of molecular species that are organized into multiple coexisting phases that enable diverse and specific functions. How interactions between numerous molecular species encode for various emergent phases is not well understood. Here, we leverage approaches from random-matrix theory and statistical physics to describe the emergent phase behavior of fluid mixtures with many species whose interactions are drawn randomly from an underlying distribution. Through numerical simulation and stability analyses, we show that these mixtures exhibit staged phase-separation kinetics and are characterized by multiple coexisting phases at steady state with distinct compositions. Random-matrix theory predicts the number of coexisting phases, validated by simulations with diverse component numbers and interaction parameters. Surprisingly, this model predicts an upper bound on the number of phases, derived from dynamical considerations, that is much lower than the limit from the Gibbs phase rule, which is obtained from equilibrium thermodynamic constraints. We design ensembles that encode either linear or nonmonotonic scaling relationships between the number of components and coexisting phases, which we validate through simulation and theory. Finally, inspired by parallels in biological systems, we show that including nonequilibrium turnover of components through chemical reactions can tunably modulate the number of coexisting phases at steady state without changing overall fluid composition. Together, our study provides a model framework that describes the emergent dynamical and steady-state phase behavior of liquid-like mixtures with many interacting constituents.
自然系统中的流体，如细胞质，通常包含数千种分子物种，这些分子物种组织成多种共存相，从而实现多样化和特定的功能。大量分子物种之间的相互作用如何编码各种涌现相尚不清楚。在这里，我们利用随机矩阵理论和统计物理的方法来描述具有许多物种的流体混合物的涌现相行为，这些物种的相互作用是从基础分布中随机抽取的。通过数值模拟和稳定性分析，我们表明这些混合物表现出阶段性的相分离动力学，并在稳态下具有不同组成的多个共存相的特征。随机矩阵理论预测了共存相的数量，通过具有不同组分数量和相互作用参数的模拟得到了验证。令人惊讶的是，该模型预测了一个由动力学考虑得出的上限，该上限远低于由平衡热力学约束得出的吉布斯相律所得到的上限。我们设计了包含组分数量和共存相之间线性或非单调缩放关系的集合，通过模拟和理论验证了这些集合。最后，受生物系统相似性的启发，我们表明通过化学反应引入组分的非平衡周转率可以在不改变整体流体组成的情况下，可调和地调节稳态时共存相的数量。总之，我们的研究提供了一个模型框架，描述了具有许多相互作用成分的类液相混合物的涌现动力学和稳态相行为。
