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Living organisms rely on molecular networks, such as gene circuits and signaling pathways, for information processing and robust decision-making in crowded, noisy environments. Recent advances show that interacting biomolecules self-organize by phase transitions into coexisting spatial compartments called condensates, often on cellular surfaces such as chromatin and membranes. In this paper, we demonstrate that multicomponent fluids can be designed to recruit distinct condensates to surfaces with differing compositions, performing a form of surface classification by condensation. We draw an analogy to multidimensional classification in machine learning and explore how hidden species, analogous to hidden nodes, expand the expressivity and capacity of these interacting ensembles to facilitate complex decision boundaries. By simply changing levels of individual species, we find that the same molecular repertoire can be reprogrammed to solve new tasks. Together, our findings suggest that the physical processes underlying biomolecular condensates can encode and drive adaptive information processing beyond compartmentalization. 

Biomolecular condensates mediate diverse and essential cellular functions by compartmentalizing biochemical pathways. Many condensates have internal subdomains with distinct compositional identities. A major challenge lies in dissecting the multicomponent logic that relates biomolecular features to emergent condensate organization. Nuclear paraspeckles are paradigmatic examples of multidomain condensates, comprising core and shell layers with distinct compositions that are scaffolded by the lncRNA NEAT1, which spans both layers. A prevailing model of paraspeckle assembly proposes that core proteins bind directly and specifically to core-associated NEAT1 domains. Combining informatics and biochemistry, we unexpectedly find that the essential core proteins FUS and NONO bind and condense preferentially with shell-associated NEAT1 domains. The shell protein TDP-43 exhibits similar NEAT1 domain preferences on its own but forms surfactant-like shell layers around core protein-driven condensates when both are present. Together, experiments and physics-based simulations suggest that competitive RNA binding and immiscibility between core and shell proteins order paraspeckle layers. More generally, we propose that subcondensate organization can spontaneously arise from a balance of collaborative and competitive protein binding to the same domains of a lncRNA. 

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.