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Life is chemical intelligence. What is the source of intelligent behavior in molecular systems? Here we illustrate how, in contrast to the common belief that energy use in non-equilibrium reactions is essential, the detailed balance equilibrium properties of multicomponent liquid interactions are sufficient for sophisticated information processing. Our approach derives from the classical Boltzmann machine model for probabilistic neural networks, inheriting key principles such as representing probability distributions via quadratic energy functions, clamping input variables to infer conditional probability distributions, accommodating omnidirectional computation, and learning energy parameters via a wake phase / sleep phase algorithm that performs gradient descent on the relative entropy with respect to the target distribution. While the cubic lattice model of multicomponent liquids is standard, the behaviors exhibited by the trained molecules capture both previously-observed phenomena such as core-shell condensate architectures as well as novel phenomena such as an analog of Hopfield associative memories that perform recall by contact with a patterned surface. Our final example demonstrates equilibrium classification of MNIST digits. Experimental implementation using DNA nanostar liquids is conceptually straightforward. 

Abstract Condensation by phase separation has recently emerged as a mechanism underlying many nuclear compartments essential for cellular functions. Nuclear condensates enrich nucleic acids and proteins, localize to specific genomic regions, and often promote gene expression. How diverse properties of nuclear condensates are shaped by gene organization and activity is poorly understood. Here, we develop a physics-based model to interrogate how spatially-varying transcription activity impacts condensate properties and dynamics. Our model predicts that spatial clustering of active genes can enable precise localization and de novo nucleation of condensates. Strong clustering and high activity results in aspherical condensate morphologies. Condensates can flow towards distant gene clusters and competition between multiple clusters lead to stretched morphologies and activity-dependent repositioning. Overall, our model predicts and recapitulates morphological and dynamical features of diverse nuclear condensates and offers a unified mechanistic framework to study the interplay between non-equilibrium processes, spatially-varying transcription, and multicomponent condensates in cell biology. 

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. 

A hallmark of biological systems is that particular functions and outcomes are realized in specific contexts, such as when particular signals are received. One mechanism for mediating specificity is described by Fisher’s “lock and key” metaphor, exemplified by enzymes that bind selectively to a particular substrate via specific finely tuned interactions. Another mechanism, more prevalent in multicellular organisms, relies on multivalent weak cooperative interactions. Its importance has recently been illustrated by the recognition that liquid-liquid phase transitions underlie the formation of membraneless condensates that perform specific cellular functions. Based on computer simulations of an evolutionary model, we report that the latter mechanism likely became evolutionarily prominent when a large number of tasks had to be performed specifically for organisms to function properly. We find that the emergence of weak cooperative interactions for mediating specificity results in organisms that can evolve to accomplish new tasks with fewer, and likely less lethal, mutations. We argue that this makes the system more capable of undergoing evolutionary changes robustly, and thus this mechanism has been repeatedly positively selected in increasingly complex organisms. Specificity mediated by weak cooperative interactions results in some useful cross-reactivity for related tasks, but at the same time increases susceptibility to misregulation that might lead to pathologies. 

The nucleus contains diverse phase-separated condensates that compartmentalize and concentrate biomolecules with distinct physicochemical properties. Here, we investigated whether condensates concentrate small-molecule cancer therapeutics such that their pharmacodynamic properties are altered. We found that antineoplastic drugs become concentrated in specific protein condensates in vitro and that this occurs through physicochemical properties independent of the drug target. This behavior was also observed in tumor cells, where drug partitioning influenced drug activity. Altering the properties of the condensate was found to affect the concentration and activity of drugs. These results suggest that selective partitioning and concentration of small molecules within condensates contributes to drug pharmacodynamics and that further understanding of this phenomenon may facilitate advances in disease therapy.