Enzyme-Enriched Condensates Show Self-Propulsion, Positioning, and Coexistence

Nonequilibrium thermodynamics of non-ideal reaction-diffusion systems: Implications for active self-organization

We develop a framework describing the dynamics and thermodynamics of open non-ideal reaction-diffusion systems, which embodies Flory-Huggins theories of mixtures and chemical reaction network theories. Our theory elucidates the mechanisms underpinning the emergence of self-organized dissipative structures in these systems. It evaluates the dissipation needed to sustain and control them, discriminating the contributions from each reaction and diffusion process with spatial resolution. It also reveals the role of the reaction network in powering and shaping these structures. We identify particular classes of networks in which diffusion processes always equilibrate within the structures, while dissipation occurs solely due to chemical reactions. The spatial configurations resulting from these processes can be derived by minimizing a kinetic potential, contrasting with the minimization of the thermodynamic free energy in passive systems. This framework opens the way to investigating the energetic cost of phenomena, such as liquid-liquid phase separation, coacervation, and the formation of biomolecular condensates.

Active RNA synthesis patterns nuclear condensates

Biomolecular condensates are membraneless compartments that organize biochemical processes in cells. In contrast to well-understood mechanisms describing how condensates form and dissolve, the principles underlying condensate patterning - including their size, number and spacing in the cell - remain largely unknown. We hypothesized that RNA, a key regulator of condensate formation and dissolution, influences condensate patterning. Using nucleolar fibrillar centers (FCs) as a model condensate, we found that inhibiting ribosomal RNA synthesis significantly alters the patterning of FCs. Physical theory and experimental observations support a model whereby active RNA synthesis generates a non-equilibrium state that arrests condensate coarsening and thus contributes to condensate patterning. Altering FC condensate patterning by expression of the FC component TCOF1 impairs ribosomal RNA processing, linking condensate patterning to biological function. These results reveal how non-equilibrium states driven by active chemical processes regulate condensate patterning, which is important for cellular biochemistry and function.

Diffusiophoresis promotes phase separation and transport of biomolecular condensates

The internal microenvironment of a living cell is heterogeneous and comprises a multitude of organelles with distinct biochemistry. Amongst them are biomolecular condensates, which are membrane-less, phase-separated compartments enriched in system-specific proteins and nucleic acids. The heterogeneity of the cell engenders the presence of multiple spatiotemporal gradients in chemistry, charge, concentration, temperature, and pressure. Such thermodynamic gradients can lead to non-equilibrium driving forces for the formation and transport of biomolecular condensates. Here, we report how ion gradients impact the transport processes of biomolecular condensates on the mesoscale and biomolecules on the microscale. Utilizing a microfluidic platform, we demonstrate that the presence of ion concentration gradients can accelerate the transport of biomolecules, including nucleic acids and proteins, via diffusiophoresis. This hydrodynamic transport process allows localized enrichment of biomolecules, thereby promoting the location-specific formation of biomolecular condensates via phase separation. The ion gradients further impart directional motility of condensates, allowing them to exhibit enhanced diffusion along the gradient. Coupled with a reentrant phase behavior, the gradient-induced enhanced motility leads to a dynamical redistribution of condensates that ultimately extends their lifetime. Together, our results demonstrate diffusiophoresis as a non-equilibrium thermodynamic force that governs the formation and transport of biomolecular condensates.

Delayed Excitations Induce Polymer Looping and Coherent Motion

We consider inhomogeneous polymers driven by energy-consuming active processes which encode temporal patterns of athermal kicks. We find that such temporal excitation programs, propagated by tension along the polymer, can effectively couple distinct polymer loci. Consequently, distant loci exhibit correlated motions that fold the polymer into specific conformations, as set by the local actions of the active processes and their distribution along the polymer. Interestingly, active kicks that are canceled out by a time-delayed echo can induce strong compaction of the active polymer.

Reaction-Driven Diffusiophoresis of Liquid Condensates: Potential Mechanisms for Intracellular Organization

The cellular environment, characterized by its intricate composition and spatial organization, hosts a variety of organelles, ranging from membrane-bound ones to membraneless structures that are formed through liquid-liquid phase separation. Cells show precise control over the position of such condensates. We demonstrate that organelle movement in external concentration gradients, diffusiophoresis, is distinct from the one of colloids because fluxes can remain finite inside the liquid-phase droplets and movement of the latter arises from incompressibility. Within cellular domains diffusiophoresis naturally arises from biochemical reactions that are driven by a chemical fuel and produce waste. Simulations and analytical arguments within a minimal model of reaction-driven phase separation reveal that the directed movement stems from two contributions: Fuel and waste are refilled or extracted at the boundary, resulting in concentration gradients, which (i) induce product fluxes via incompressibility and (ii) result in an asymmetric forward reaction in the droplet's surroundings (as well as asymmetric backward reaction inside the droplet), thereby shifting the droplet's position. We show that the former contribution dominates and sets the direction of the movement, toward or away from fuel source and waste sink, depending on the product molecules' affinity toward fuel and waste, respectively. The mechanism thus provides a simple means to organize condensates with different composition. Particle-based simulations and systems with more complex reaction cycles corroborate the robustness and universality of this mechanism.

Chemotactic Interactions Drive Migration of Membraneless Active Droplets

In nature, chemotactic interactions are ubiquitous and play a critical role in driving the collective behavior of living organisms. Reproducing these interactions in vitro is still a paramount challenge due to the complexity of mimicking and controlling cellular features, such as tangled metabolic networks, cytosolic macromolecular crowding, and cellular migration, on a microorganism size scale. Here, we generate enzymatically active cell-sized droplets able to move freely, and by following a chemical gradient, able to interact with the surrounding droplets in a collective manner. The enzyme within the droplets generates a pH gradient that extends outside the edge of the droplets. We discovered that the external pH gradient triggers droplet migration and controls its directionality, which is selectively toward the neighboring droplets. Hence, by changing the enzyme activity inside the droplet, we tuned the droplet migration speed. Furthermore, we showed that these cellular-like features can facilitate the reconstitution of a simple and linear protometabolic pathway and increase the final reaction product generation. Our work suggests that simple and stable membraneless droplets can reproduce complex biological phenomena, opening new perspectives as bioinspired materials and synthetic biology tools.

Exploring the Synthesis of Self-Organization and Active Motion

Proteins, genetic material, and membranes are fundamental to all known organisms, yet these components alone do not constitute life. Life emerges from the dynamic processes of self-organization, assembly, and active motion, suggesting the existence of similar artificial systems. Against this backdrop, our Perspective explores a variety of chemical phenomena illustrating how nonequilibrium self-organization and micromotors contribute to life-like behavior and functionalities. After explaining key terms, we discuss specific examples including enzymatic motion, diffusiophoretic and bubble-driven self-propulsion, pattern-forming reaction-diffusion systems, self-assembling inorganic aggregates, and hierarchically emergent phenomena. We also provide a roadmap for combining self-organization and active motion and discuss possible outcomes through biological analogs. We suggest that this research direction, deeply rooted in physical chemistry, offers opportunities for further development with broad impacts on related sciences and technologies.

Nucleic acid liquids

The confluence of recent discoveries of the roles of biomolecular liquids in living systems and modern abilities to precisely synthesize and modify nucleic acids (NAs) has led to a surge of interest in liquid phases of NAs. These phases can be formed primarily from NAs, as driven by base-pairing interactions, or from the electrostatic combination (coacervation) of negatively charged NAs and positively charged molecules. Generally, the use of sequence-engineered NAs provides the means to tune microsopic particle properties, and thus imbue specific, customizable behaviors into the resulting liquids. In this way, researchers have used NA liquids to tackle fundamental problems in the physics of finite valence soft materials, and to create liquids with novel structured and/or multi-functional properties. Here, we review this growing field, discussing the theoretical background of NA liquid phase separation, quantitative understanding of liquid material properties, and the broad and growing array of functional demonstrations in these materials. We close with a few comments discussing remaining open questions and challenges in the field.

Enabling High Activation of Glucose-6-Phosphate Dehydrogenase Activity Through Liquid Condensate Formation and Compression

Droplet formation via liquid-liquid phase separation is thought to be involved in the regulation of various biological processes, including enzymatic reactions. We investigated a glycolytic enzymatic reaction, the conversion of glucose-6-phosphate to 6-phospho-D-glucono-1,5-lactone with concomitant reduction of NADP+ to NADPH both in the absence and presence of dynamically controlled liquid droplet formation. Here, the nucleotide serves as substrate as well as the scaffold required for the formation of liquid droplets. To further expand the process parameter space, temperature and pressure dependent measurements were performed. Incorporation of the reactants in the liquid droplet phase led to a boost in enzymatic activity, which was most pronounced at medium-high pressures. The crowded environment of the droplet phase induced a marked increase of the affinity of the enzyme and substrate. An increase in turnover number in the droplet phase at high pressure contributed to a further strong increase in catalytic efficiency. Enzyme systems that are dynamically coupled to liquid condensate formation may be the key to deciphering many biochemical reactions. Expanding the process parameter space by adjusting temperature and pressure conditions can be a means to further increase the efficiency of industrial enzyme utilization and help uncover regulatory mechanisms adopted by extremophiles.

Phase-separated droplets swim to their dissolution

Biological macromolecules can condense into liquid domains. In cells, these condensates form membraneless organelles that can organize chemical reactions. However, little is known about the physical consequences of chemical activity in and around condensates. Working with model bovine serum albumin (BSA) condensates, we show that droplets swim along chemical gradients. Active BSA droplets loaded with urease swim toward each other. Passive BSA droplets show diverse responses to externally applied gradients of the enzyme's substrate and products. In all these cases, droplets swim toward solvent conditions that favor their dissolution. We call this behavior "dialytaxis", and expect it to be generic, as conditions which favor dissolution typically reduce interfacial tension, whose gradients are well-known to drive droplet motion through the Marangoni effect. These results could potentially suggest alternative physical mechanisms for active transport in living cells, and may enable the design of fluid micro-robots.

Diffusiophoresis promotes phase separation and transport of biomolecular condensates

The internal microenvironment of a living cell is heterogeneous and comprises a multitude of organelles with distinct biochemistry. Amongst them are biomolecular condensates, which are membrane-less, phase-separated compartments enriched in system-specific proteins and nucleic acids. The heterogeneity of the cell engenders the presence of multiple spatiotemporal gradients in chemistry, charge, concentration, temperature, and pressure. Such thermodynamic gradients can lead to non-equilibrium driving forces for the formation and transport of biomolecular condensates. Here, we report how ion gradients impact the transport processes of biomolecular condensates on the mesoscale and biomolecules on the microscale. Utilizing a microfluidic platform, we demonstrate that the presence of ion concentration gradients can accelerate the transport of biomolecules, including nucleic acids and proteins, via diffusiophoresis. This hydrodynamic transport process allows localized enrichment of biomolecules, thereby promoting the location-specific formation of biomolecular condensates via phase separation. The ion gradients further impart active motility of condensates, allowing them to exhibit enhanced diffusion along the gradient. Coupled with a reentrant phase behavior, the gradient-induced active motility leads to a dynamical redistribution of condensates that ultimately extends their lifetime. Together, our results demonstrate diffusiophoresis as a non-equilibrium thermodynamic force that governs the formation and transport of biomolecular condensates.

Irreversible Mesoscale Fluctuations Herald the Emergence of Dynamical Phases

We study fluctuating field models with spontaneously emerging dynamical phases. We consider two typical transition scenarios associated with parity-time symmetry breaking: oscillatory instabilities and critical exceptional points. An analytical investigation of the low-noise regime reveals a drastic increase of the mesoscopic entropy production toward the transitions. For an illustrative model of two nonreciprocally coupled Cahn-Hilliard fields, we find physical interpretations in terms of actively propelled interfaces and a coupling of eigenmodes of the linearized dynamics near the critical exceptional point.

Entropy production in the nonreciprocal Cahn-Hilliard model

We study the nonreciprocal Cahn-Hilliard model with thermal noise as a prototypical example of a generic class of non-Hermitian stochastic field theories, analyzed in two companion papers [Suchanek, Kroy, and Loos, Phys. Rev. Lett. 131, 258302 (2023)10.1103/PhysRevLett.131.258302; Phys. Rev. E 108, 064123 (2023)10.1103/PhysRevE.108.064123]. Due to the nonreciprocal coupling between two field components, the model is inherently out of equilibrium and can be regarded as an active field theory. Beyond the conventional homogeneous and static-demixed phases, it exhibits a traveling-wave phase, which can be entered via either an oscillatory instability or a critical exceptional point. By means of a Fourier decomposition of the entropy production rate, we quantify the associated scale-resolved time-reversal symmetry breaking, in all phases and across the transitions, in the low-noise regime. Our perturbative calculation reveals its dependence on the strength of the nonreciprocal coupling. Surging entropy production near the static-dynamic transitions can be attributed to entropy-generating fluctuations in the longest wavelength Fourier mode and heralds the emerging traveling wave. Its translational dynamics can be mapped on the dissipative ballistic motion of an active (quasi)particle.

Nonequilibrium interfacial properties of chemically driven fluids

Chemically driven fluids can demix to form condensed droplets that exhibit phase behaviors not observed at equilibrium. In particular, nonequilibrium interfacial properties can emerge when the chemical reactions are driven differentially between the interior and exterior of the phase-separated droplets. Here, we use a minimal model to study changes in the interfacial tension between coexisting phases away from equilibrium. Simulations of both droplet nucleation and interface roughness indicate that the nonequilibrium interfacial tension can either be increased or decreased relative to its equilibrium value, depending on whether the driven chemical reactions are accelerated or decelerated within the droplets. Finally, we show that these observations can be understood using a predictive theory based on an effective thermodynamic equilibrium.