Phase separation in fluids with many interacting components

Abstract

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.

The intertwined physics of active chemical reactions and phase separation

“…These equations possess many parameters leading to immense complexity. Solution strategies range from numerical evolution for specific examples [28,42,43] to full analytical treatment, e.g., via linear stability analysis [44]. We will pursue both approaches for specific examples highlighting the rich behavior.…”

“…In fact, even ternary mixtures can display surprisingly complex phase diagram [34,69,70,76] and this trend continuous for increasing component counts [28,77]. We can now simulate systems of a few tens of components [42,43] and analyze large systems in particular cases using random matrix theory [42,[78][79][80] and scaling analysis [81]. However, such random, unstructured interactions might not represent biological examples very well.…”

Learning without neurons in physical systems

“…Similar ideas of learning in multi-component phase separation (59,60), e,g., based on DNA nanostars (49), are likely to be realized in the coming years. All of these works suggest that inevitable physical processes ( 46) such as self-assembly, phase separation and nucleation can enable learning and perform pattern recognition, despite not being set up to mimic a neural network element by element (57) as in circuit approaches.…”

Catalysis-Induced Phase Separation and Autoregulation of Enzymatic Activity

“…While effective interactions mediated by self-generated chemical gradients have been previously described in the context of phoretic active colloids or chemotactic microorganisms [21][22][23][24][25], these were based on a microscopic and hydrodynamic description of individual colloid-colloid interactions. The theoretical framework presented here takes a complementary approach based on non-equilibrium thermodynamics and Flory-Huggins theory of suspensions, to manifestly connect the phenomenology to the existing studies on intracellular phase separation [3][4][5][6][7][8][9][10]. We find that this catalysis-induced phase separation (CIPS) can be described by a mapping to an effective free energy, and thus shows equilibrium features such as the existence of binodal and spinodal lines which meet at a critical point.…”

“…It is generally believed that the main drivers of phase separation in such systems are the attractive equilibrium interactions between the different soluble components, which are needed to overcome the entropic costs associated with phase separation [3,4]. The emergence of condensates that are enriched or depleted in specific molecules can be designed by tuning these interactions [5][6][7][8]. On the other hand, it is clear that intracellular environments are far from being at thermodynamic equilibrium, and that the possible effects of non-equilibrium activity on phase separation need to be taken into consideration [9][10][11][12][13][14][15].…”