Chemical Kinetics and Mass Action in Coexisting Phases

Entering the Next Phase: Predicting Biological Effects of Biomolecular Condensates

Biomolecular condensates are increasingly recognized as important drivers of cellular function; their dysregulation leads to pathology and disease. We discuss three questions in terms of the impending utility of data-driven techniques to predict condensate-driven biological outcomes, i.e., the impact of cellular state changes on condensates, the effect of condensates on biochemical processes within, and condensate properties that result in cellular dysregulation and disease.

Competition between Self-Assembly and Phase Separation Governs High-Temperature Condensation of a DNA Liquid

In many biopolymer solutions, attractive interactions that stabilize finite-sized clusters at low concentrations also promote phase separation at high concentrations. Here we study a model biopolymer system that exhibits the opposite behavior, whereby self-assembly of DNA oligonucleotides into finite-sized, stoichiometric clusters tends to inhibit phase separation. We first use microfluidics-based experiments to map a novel phase transition in which the oligonucleotides condense as the temperature increases at high concentrations of divalent cations. We then show that a theoretical model of competition between self-assembly and phase separation quantitatively predicts changes in experimental phase diagrams arising from DNA sequence perturbations. Our results point to a general mechanism by which self-assembly shapes phase boundaries in complex biopolymer solutions.

Local environment in biomolecular condensates modulates enzymatic activity across length scales

The mechanisms that underlie the regulation of enzymatic reactions by biomolecular condensates and how they scale with compartment size remain poorly understood. Here we use intrinsically disordered domains as building blocks to generate programmable enzymatic condensates of NADH-oxidase (NOX) with different sizes spanning from nanometers to microns. These disordered domains, derived from three distinct RNA-binding proteins, each possessing different net charge, result in the formation of condensates characterized by a comparable high local concentration of the enzyme yet within distinct environments. We show that only condensates with the highest recruitment of substrate and cofactor exhibit an increase in enzymatic activity. Notably, we observe an enhancement in enzymatic rate across a wide range of condensate sizes, from nanometers to microns, indicating that emergent properties of condensates can arise within assemblies as small as nanometers. Furthermore, we show a larger rate enhancement in smaller condensates. Our findings demonstrate the ability of condensates to modulate enzymatic reactions by creating distinct effective solvent environments compared to the surrounding solution, with implications for the design of protein-based heterogeneous biocatalysts.

A solid beta-sheet structure is formed at the surface of FUS droplets during aging

Phase transitions are important to understand cell dynamics, and the maturation of liquid droplets is relevant to neurodegenerative disorders. We combined NMR and Raman spectroscopies with microscopy to follow, over a period of days to months, droplet maturation of the protein fused in sarcoma (FUS). Our study reveals that the surface of the droplets plays a critical role in this process, while RNA binding prevents it. The maturation kinetics are faster in an agarose-stabilized biphasic sample compared with a monophasic condensed sample, owing to the larger surface-to-volume ratio. In addition, Raman spectroscopy reports structural differences upon maturation between the inside and the surface of droplets, which is comprised of β-sheet content, as revealed by solid-state NMR. In agreement with these observations, a solid crust-like shell is observed at the surface using microaspiration. Ultimately, matured droplets were converted into fibrils involving the prion-like domain as well as the first RGG motif.

Compartmental exchange regulates steady states and stochastic switching of a phosphorylation network

The phosphoregulation of proteins with multiple phosphorylation sites is governed by biochemical reaction networks that can exhibit multistable behavior. However, the behavior of such networks is typically studied in a single reaction volume, while cells are spatially organized into compartments that can exchange proteins. In this work, we use stochastic simulations to study the impact of compartmentalization on a two-site phosphorylation network. We characterize steady states and fluctuation-driven transitions between them as a function of the rate of protein exchange between two compartments. Surprisingly, the average time spent in a state before stochastically switching to another depends nonmonotonically on the protein exchange rate, with the most frequent switching occurring at intermediate exchange rates. At sufficiently small exchange rates, the state of the system and mean switching time are controlled largely by fluctuations in the balance of enzymes in each compartment. This leads to negatively correlated states in the compartments. For large exchange rates, the two compartments behave as a single effective compartment. However, when the compartmental volumes are unequal, the behavior differs from a single compartment with the same total volume. These results demonstrate that exchange of proteins between distinct compartments can regulate the emergent behavior of a common signaling motif.

Segregation disrupts the Arrhenius behavior of an isomerization reaction

Coexistence of segregation and interconversion or isomerization reaction among molecular species leads to fascinating structure formation in the biological and chemical worlds. Using Monte Carlo simulations of the prototype Ising model, we explore the chemical kinetics of such a system consisting of a binary mixture of isomers. Our results reveal that even though the two concerned processes are individually Arrhenius in nature, the Arrhenius behavior of the isomerization reaction gets significantly disrupted due to an interplay of the nonconserved dynamics of the reaction and the conserved diffusive dynamics of segregation. The approach used here can be potentially adapted to understand reaction kinetics of more complex reactions.

Interfacial chemical reactivity enhancement

Interfacial enhancements of chemical reaction equilibria and rates in liquid droplets are predicted using a combined theoretical and experimental analysis strategy. Self-consistent solutions of reaction and adsorption equilibria indicate that interfacial reactivity enhancement is driven primarily by the adsorption free energy of the product (or activated complex). Reactant surface activity has a smaller indirect influence on reactivity due to compensating reactant interfacial concentration and adsorption free energy changes, as well as adsorption-induced depletion of the droplet core. Experimental air-water interfacial adsorption free energies and critical micelle concentration correlations provide quantitative surface activity estimates as a function of molecular structure, predicting an increase in interfacial reactivity with increasing product size and decreasing product polarity, aromaticity, and charge (but less so for anions than cations). Reactions with small, neutral, or charged products are predicted to have little reactivity enhancement at an air-water interface unless the product is rendered sufficiently surface active by, for example, interactions with interfacial water dangling OH groups, charge transfer, or voltage fluctuations.

Nonequilibrium Wet-Dry Cycling Acts as a Catalyst for Chemical Reactions

Recent experimental studies suggest that wet-dry cycles and coexisting phases can each strongly alter chemical processes. The mechanisms of why and to what degree chemical processes are altered when subjected to evaporation and condensation are unclear. To close this gap, we developed a theoretical framework for nondilute chemical reactions subject to nonequilibrium conditions of evaporation and condensation. We find that such conditions can change the half-time of the product's yield by more than an order of magnitude, depending on the substrate-solvent interaction. We show that the cycle frequency strongly affects the chemical turnover when the system is maintained out of equilibrium by wet-dry cycles. There exists a resonance behavior in the cycle frequency where the turnover is maximal. This resonance behavior enables wet-dry cycles to select specific chemical reactions, suggesting a potential mechanism for chemical evolution in prebiotic soups at early Earth.

Fluctuations and Shape Dependence of Microphase Separation in Systems with Long-Range Interactions

The combination of phase separation and long-ranged, effective, Coulomb interactions results in microphase separation. We predict the sizes and shapes of such microdomains and uniquely their dependence on the macroscopic sample shape which also affects the effective interfacial tension of fluctuations of the lamellar phase. These are applied to equilibrium salt solutions and block copolymers. Nonequilibrium phase separation in the presence of chemical reactions (e.g., cellular condensates) is mapped to the Coulomb theory to which our predictions apply. In some cases, the effective interfacial tension can be ultralow.

Interplay between self-assembly and phase separation in a polymer-complex model

We present a theoretical model for predicting the phase behavior of polymer solutions in which phase separation competes with oligomerization. Specifically, we consider scenarios in which the assembly of polymer chains into stoichiometric complexes prevents the chains from phase-separating via attractive polymer-polymer interactions. Combining statistical associating fluid theory with a two-state description of self-assembly, we find that this model exhibits rich phase behavior, including reentrance, and we show how system-specific phase diagrams can be derived graphically. Importantly, we discuss why these phase diagrams can resemble-and yet are qualitatively distinct from-phase diagrams of polymer solutions with lower critical solution temperatures.

Dynamical control enables the formation of demixed biomolecular condensates

Cellular matter can be organized into compositionally distinct biomolecular condensates. For example, in Ashbya gossypii, the RNA-binding protein Whi3 forms distinct condensates with different RNA molecules. Using criteria derived from a physical framework for explaining how compositionally distinct condensates can form spontaneously via thermodynamic considerations, we find that condensates in vitro form mainly via heterotypic interactions in binary mixtures of Whi3 and RNA. However, within these condensates, RNA molecules become dynamically arrested. As a result, in ternary systems, simultaneous additions of Whi3 and pairs of distinct RNA molecules lead to well-mixed condensates, whereas delayed addition of an RNA component results in compositional distinctness. Therefore, compositional identities of condensates can be achieved via dynamical control, being driven, at least partially, by the dynamical arrest of RNA molecules. Finally, we show that synchronizing the production of different RNAs leads to more well-mixed, as opposed to compositionally distinct condensates in vivo.

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.

Synthetic Gene Circuits Combining CRISPR Interference and CRISPR Activation in E. coli: Importance of Equal Guide RNA Binding Affinities to Avoid Context-Dependent Effects

Gene expression control based on clustered regularly interspaced short palindromic repeats (CRISPR) has emerged as a powerful approach for constructing synthetic gene circuits. While the use of CRISPR interference (CRISPRi) is already well-established in prokaryotic circuits, CRISPR activation (CRISPRa) is less mature, and a combination of the two in the same circuits is only just emerging. Here, we report that combining CRISPRi with SoxS-based CRISPRa in Escherichia coli can lead to context-dependent effects due to different affinities in the formation of CRISPRa and CRISPRi complexes, resulting in loss of predictable behavior. We show that this effect can be avoided by using the same scaffold guide RNA structure for both complexes.

Multicompartment calcium alginate microreactors to reduce substrate inhibition in enzyme cascade reactions

The formation of macromolecularly enriched condensates through associative or segregative liquid-liquid phase separation phenomena is known to play a central role in controlling various cellular functions in nature. The potential to spatially and temporally modulate multistep chemical reactions and pathways has inspired the use of phase-separated systems for the development of various synthetic colloidal micro- and nanoreactor systems. Here, we report a rational and synthetically minimal design strategy to emulate intended spatiotemporal functions in morphologically intricate and structurally defined calcium alginate hydrogel microreactors possessing multicompartmentalized internal architectures. Specifically, we implement a thermal phase separation protocol to achieve fine-control over liquid-liquid phase separation inside complex aqueous emulsion droplet templates that are loaded with hydrophilic polymer mixtures. Subsequent gelation of alginate-containing droplet templates using a novel freeze-thaw approach that can be applied to both scalable batch production or more precise microfluidic methods yields particle replicas, in which subcompartmentalized architectures can be retained. Larger active components can be enriched in the internal compartments due to their preferential solubility, and we show that selective sequestration of enzymes serves to create desired microenvironments to control and tune the reaction kinetics of a multistep enzyme cascade by reducing their mutual interference. This demonstration of mitigating substrate inhibition that is based primarily on optimizing the multicompartmentalized hydrogel particle morphology offers new opportunities for the simple and synthetically-minimal batch generation of hydrogel-based synthesis microreactors.

Theoretical and Data-Driven Approaches for Biomolecular Condensates

Biomolecular condensation processes are increasingly recognized as a fundamental mechanism that living cells use to organize biomolecules in time and space. These processes can lead to the formation of membraneless organelles that enable cells to perform distinct biochemical processes in controlled local environments, thereby supplying them with an additional degree of spatial control relative to that achieved by membrane-bound organelles. This fundamental importance of biomolecular condensation has motivated a quest to discover and understand the molecular mechanisms and determinants that drive and control this process. Within this molecular viewpoint, computational methods can provide a unique angle to studying biomolecular condensation processes by contributing the resolution and scale that are challenging to reach with experimental techniques alone. In this Review, we focus on three types of dry-lab approaches: theoretical methods, physics-driven simulations and data-driven machine learning methods. We review recent progress in using these tools for probing biomolecular condensation across all three fields and outline the key advantages and limitations of each of the approaches. We further discuss some of the key outstanding challenges that we foresee the community addressing next in order to develop a more complete picture of the molecular driving forces behind biomolecular condensation processes and their biological roles in health and disease.

Dynamical control enables the formation of demixed biomolecular condensates

Macromolecular phase separation underlies the regulated formation and dissolution of biomolecular condensates. What is unclear is how condensates of distinct and shared macromolecular compositions form and coexist within cellular milieus. Here, we use theory and computation to establish thermodynamic criteria that must be satisfied to achieve compositionally distinct condensates. We applied these criteria to an archetypal ribonucleoprotein condensate and discovered that demixing into distinct protein-RNA condensates cannot be the result of purely thermodynamic considerations. Instead, demixed, compositionally distinct condensates arise due to asynchronies in timescales that emerge from differences in long-lived protein-RNA and RNA-RNA crosslinks. This type of dynamical control is also found to be active in live cells whereby asynchronous production of molecules is required for realizing demixed protein-RNA condensates. We find that interactions that exert dynamical control provide a versatile and generalizable way to influence the compositions of coexisting condensates in live cells.

Dynamical control enables the formation of demixed biomolecular condensates

Macromolecular phase separation underlies the regulated formation and dissolution of biomolecular condensates. What is unclear is how condensates of distinct and shared macromolecular compositions form and coexist within cellular milieus. Here, we use theory and computation to establish thermodynamic criteria that must be satisfied to achieve compositionally distinct condensates. We applied these criteria to an archetypal ribonucleoprotein condensate and discovered that demixing into distinct protein-RNA condensates cannot be the result of purely thermodynamic considerations. Instead, demixed, compositionally distinct condensates arise due to asynchronies in timescales that emerge from differences in long-lived protein-RNA and RNA-RNA crosslinks. This type of dynamical control is also found to be active in live cells whereby asynchronous production of molecules is required for realizing demixed protein-RNA condensates. We find that interactions that exert dynamical control provide a versatile and generalizable way to influence the compositions of coexisting condensates in live cells.