Breakdown of the law of rectilinear diameter and related surprises in the liquid-vapor coexistence in systems of patchy particles

Dissipative Self-Assembly of Patchy Particles under Nonequilibrium Drive: A Computational Study

Inspired by biology and implemented using nanotechnology, the self-assembly of patchy particles has emerged as a pivotal mechanism for constructing complex structures that mimic natural systems with diverse functionalities. Here, we explore the dissipative self-assembly of patchy particles under nonequilibrium conditions, with the aim of overcoming the constraints imposed by equilibrium assembly. Utilizing extensive Monte Carlo (MC) and Molecular Dynamics (MD) simulations, we provide insight into the effects of external forces that mirror natural and chemical processes on the assembly rates and the stability of the resulting assemblies comprising 8, 10, and 13 patchy particles. Implemented by a favorable bond-promoting drive in MC or a pulsed square wave potential in MD, our simulations reveal the role these external drives play in accelerating assembly kinetics and enhancing structural stability, evidenced by a decrease in the time to first assembly and an increase in the duration the system remains in an assembled state. Through the analysis of an order parameter, entropy production, bond dynamics, and interparticle forces, we unravel the underlying mechanisms driving these advancements. We also validated our key findings by simulating a larger system of 100 patchy particles. Our comprehensive results not only shed light on the impact of external stimuli on self-assembly processes but also open a promising pathway for expanding the application by leveraging patchy particles for novel nanostructures.

Driven Self-Assembly of Patchy Particles Overcoming Equilibrium Limitations

Bridging biological complexity and synthetic material design, we investigate dissipative self-assembly in patchy particle systems. Utilizing Monte Carlo and Molecular Dynamics simulations, we demonstrate how external driving forces mitigate equilibrium trade-offs between assembly time and structural stability, traditionally encountered in self-assembly processes. Our findings also extend to biological-mimicking environments, where we explore the dynamics of patchy particles under crowded conditions. This comprehensive analysis offers insights into advanced material design, opening avenues for innovations in nanotechnology applications.

Interfacial exchange dynamics of biomolecular condensates are highly sensitive to client interactions

Phase separation of biomolecules can facilitate their spatiotemporally regulated self-assembly within living cells. Due to the selective yet dynamic exchange of biomolecules across condensate interfaces, condensates can function as reactive hubs by concentrating enzymatic components for faster kinetics. The principles governing this dynamic exchange between condensate phases, however, are poorly understood. In this work, we systematically investigate the influence of client-sticker interactions on the exchange dynamics of protein molecules across condensate interfaces. We show that increasing affinity between a model protein scaffold and its client molecules causes the exchange of protein chains between the dilute and dense phases to slow down and that beyond a threshold interaction strength, this slowdown in exchange becomes substantial. Investigating the impact of interaction symmetry, we found that chain exchange dynamics are also considerably slower when client molecules interact equally with different sticky residues in the protein. The slowdown of exchange is due to a sequestration effect, by which there are fewer unbound stickers available at the interface to which dilute phase chains may attach. These findings highlight the fundamental connection between client-scaffold interaction networks and condensate exchange dynamics.

Liquid-Vapor Coexistence and Spontaneous Evaporation at Atmospheric Pressure of Common Rigid Three-Point Water Models in Molecular Simulations

Molecular dynamics (MD) simulations are widely used to investigate molecular systems at atomic resolution including biomolecular structures, drug-receptor interactions, and novel materials. Frequently, MD simulations are performed in an aqueous solution with explicit models of water molecules. Commonly, such models are parameterized to reproduce the liquid phase of water under ambient conditions. However, often, simulations at significantly higher temperatures are also of interest. Hence, it is important to investigate the equilibrium of the liquid and vapor phases of molecular models of water at elevated temperatures. Here, we evaluate the behavior of 11 common rigid three-point water models over a wide range of temperatures. From liquid-vapor coexistence simulations, we estimated the critical points and studied the spontaneous evaporation of these water models. Moreover, we investigated the influence of the system size, choice of the pressure-coupling algorithm, and rate of heating on the process and compared them with the experimental data. We found that modern rigid three-point water models reproduce the critical point surprisingly well. Furthermore, we discovered that the critical temperature correlates with the quadrupole moment of the respective water model. This indicates that the spatial arrangement of the partial charges is important for reproducing the liquid-vapor phase transition. Our findings may guide the selection of water models for simulations conducted at high temperatures.

Surfactants or scaffolds? RNAs of varying lengths control the thermodynamic stability of condensates differently

Biomolecular condensates, thought to form via liquid-liquid phase separation of intracellular mixtures, are multicomponent systems that can include diverse types of proteins and RNAs. RNA is a critical modulator of RNA-protein condensate stability, as it induces an RNA concentration-dependent reentrant phase transition-increasing stability at low RNA concentrations and decreasing it at high concentrations. Beyond concentration, RNAs inside condensates can be heterogeneous in length, sequence, and structure. Here, we use multiscale simulations to understand how different RNA parameters interact with one another to modulate the properties of RNA-protein condensates. To do so, we perform residue/nucleotide resolution coarse-grained molecular dynamics simulations of multicomponent RNA-protein condensates containing RNAs of different lengths and concentrations, and either FUS or PR25 proteins. Our simulations reveal that RNA length regulates the reentrant phase behavior of RNA-protein condensates: increasing RNA length sensitively rises the maximum value that the critical temperature of the mixture reaches, and the maximum concentration of RNA that the condensate can incorporate before beginning to become unstable. Strikingly, RNAs of different lengths are organized heterogeneously inside condensates, which allows them to enhance condensate stability via two distinct mechanisms: shorter RNA chains accumulate at the condensate's surface acting as natural biomolecular surfactants, while longer RNA chains concentrate inside the core to saturate their bonds and enhance the density of molecular connections in the condensate. Using a patchy particle model, we additionally demonstrate that the combined impact of RNA length and concentration on condensate properties is dictated by the valency, binding affinity, and polymer length of the various biomolecules involved. Our results postulate that diversity on RNA parameters within condensates allows RNAs to increase condensate stability by fulfilling two different criteria: maximizing enthalpic gain and minimizing interfacial free energy; hence, RNA diversity should be considered when assessing the impact of RNA on biomolecular condensates regulation.

Theory and Simulation of Multiphase Coexistence in Biomolecular Mixtures

Biomolecular condensates constitute a newly recognized form of spatial organization in living cells. Although many condensates are believed to form as a result of phase separation, the physicochemical properties that determine the phase behavior of heterogeneous biomolecular mixtures are only beginning to be explored. Theory and simulation provide invaluable tools for probing the relationship between molecular determinants, such as protein and RNA sequences, and the emergence of phase-separated condensates in such complex environments. This review covers recent advances in the prediction and computational design of biomolecular mixtures that phase-separate into many coexisting phases. First, we review efforts to understand the phase behavior of mixtures with hundreds or thousands of species using theoretical models and statistical approaches. We then describe progress in developing analytical theories and coarse-grained simulation models to predict multiphase condensates with the molecular detail required to make contact with biophysical experiments. We conclude by summarizing the challenges ahead for modeling the inhomogeneous spatial organization of biomolecular mixtures in living cells.

RNA length has a non-trivial effect in the stability of biomolecular condensates formed by RNA-binding proteins

Biomolecular condensates formed via liquid-liquid phase separation (LLPS) play a crucial role in the spatiotemporal organization of the cell material. Nucleic acids can act as critical modulators in the stability of these protein condensates. To unveil the role of RNA length in regulating the stability of RNA binding protein (RBP) condensates, we present a multiscale computational strategy that exploits the advantages of a sequence-dependent coarse-grained representation of proteins and a minimal coarse-grained model wherein proteins are described as patchy colloids. We find that for a constant nucleotide/protein ratio, the protein fused in sarcoma (FUS), which can phase separate on its own-i.e., via homotypic interactions-only exhibits a mild dependency on the RNA strand length. In contrast, the 25-repeat proline-arginine peptide (PR25), which does not undergo LLPS on its own at physiological conditions but instead exhibits complex coacervation with RNA-i.e., via heterotypic interactions-shows a strong dependence on the length of the RNA strands. Our minimal patchy particle simulations suggest that the strikingly different effect of RNA length on homotypic LLPS versus RBP-RNA complex coacervation is general. Phase separation is RNA-length dependent whenever the relative contribution of heterotypic interactions sustaining LLPS is comparable or higher than those stemming from protein homotypic interactions. Taken together, our results contribute to illuminate the intricate physicochemical mechanisms that influence the stability of RBP condensates through RNA inclusion.

'RNA modulation of transport properties and stability in phase-separated condensates

One of the key mechanisms employed by cells to control their spatiotemporal organization is the formation and dissolution of phase-separated condensates. The balance between condensate assembly and disassembly can be critically regulated by the presence of RNA. In this work, we use a chemically-accurate sequence-dependent coarse-grained model for proteins and RNA to unravel the impact of RNA in modulating the transport properties and stability of biomolecular condensates. We explore the phase behavior of several RNA-binding proteins such as FUS, hnRNPA1, and TDP-43 proteins along with that of their corresponding prion-like domains and RNA recognition motifs from absence to moderately high RNA concentration. By characterizing the phase diagram, key molecular interactions, surface tension, and transport properties of the condensates, we report a dual RNA-induced behavior: on the one hand, RNA enhances phase separation at low concentration as long as the RNA radius of gyration is comparable to that of the proteins, whereas at high concentration, it inhibits the ability of proteins to self-assemble independently of its length. On the other hand, along with the stability modulation, the viscosity of the condensates can be considerably reduced at high RNA concentration as long as the length of the RNA chains is shorter than that of the proteins. Conversely, long RNA strands increase viscosity even at high concentration, but barely modify protein self-diffusion which mainly depends on RNA concentration and on the effect RNA has on droplet density. On the whole, our work rationalizes the different routes by which RNA can regulate phase separation and condensate dynamics, as well as the subsequent aberrant rigidification implicated in the emergence of various neuropathologies and age-related diseases.

'RNA modulation of transport properties and stability in phase-separated condensates

One of the key mechanisms employed by cells to control their spatiotemporal organization is the formation and dissolution of phase-separated condensates. The balance between condensate assembly and disassembly can be critically regulated by the presence of RNA. In this work, we use a chemically-accurate sequence-dependent coarse-grained model for proteins and RNA to unravel the impact of RNA in modulating the transport properties and stability of biomolecular condensates. We explore the phase behavior of several RNA-binding proteins such as FUS, hnRNPA1, and TDP-43 proteins along with that of their corresponding prion-like domains and RNA recognition motifs from absence to moderately high RNA concentration. By characterizing the phase diagram, key molecular interactions, surface tension, and transport properties of the condensates, we report a dual RNA-induced behavior: on the one hand, RNA enhances phase separation at low concentration as long as the RNA radius of gyration is comparable to that of the proteins, whereas at high concentration, it inhibits the ability of proteins to self-assemble independently of its length. On the other hand, along with the stability modulation, the viscosity of the condensates can be considerably reduced at high RNA concentration as long as the length of the RNA chains is shorter than that of the proteins. Conversely, long RNA strands increase viscosity even at high concentration, but barely modify protein self-diffusion which mainly depends on RNA concentration and on the effect RNA has on droplet density. On the whole, our work rationalizes the different routes by which RNA can regulate phase separation and condensate dynamics, as well as the subsequent aberrant rigidification implicated in the emergence of various neuropathologies and age-related diseases.

Location of the gel-like boundary in patchy colloidal dispersions: Rigidity percolation, structure, and particle dynamics

During the past decade, there has been a hot debate about the physical mechanisms that determine when a colloidal dispersion approaches the gel transition. However, there is still no consensus on a possible unique route that leads to the conditions for the formation of a gel-like state. Based on gel states identified in experiments, Valadez-Pérez et al. [Phys. Rev. E 88, 060302(R) (2013)PLEEE81539-375510.1103/PhysRevE.88.060302] proposed rigidity percolation as the precursor of colloidal gelation in adhesive hard-sphere dispersions with coordination number 〈n_{b}〉 equal to 2.4. Although this criterion was originally established to describe mechanical transitions in network-forming molecular materials with highly directional interactions, it worked well to explain gel formation in colloidal suspensions with isotropic short-range attractive forces. Recently, this idea has also been used to account for the dynamical arrest experimentally observed in attractive spherocylinders. Then, by assuming that rigidity percolation also drives gelation in spherical colloids interacting with short-ranged and highly directional potentials, we locate the thermodynamic states where gelation seems to occur in dispersions made up of patchy colloids. To check whether the criterion 〈n_{b}〉=2.4 also holds in patchy colloidal systems, we apply the so-called bond-bending analysis to determine the fraction of floppy modes at some percolating clusters. This analysis confirms that the condition 〈n_{b}〉=2.4 is a good approximation to determine those percolating clusters that are either mechanically stable or rigid. Furthermore, our results point out that not all combinations of patches and coverages lead to a gel-like state. Additionally, we systematically study the structure and the cluster size distribution along those thermodynamic states identified as gels. We show that for high coverage values, the structure is very similar for systems that have the same coverage regardless the number or the position of the patches on the particle surface. Finally, by using dynamic Monte Carlo computer simulations, we calculate both the mean-square displacement and the intermediate scattering function at and in the neighborhood of the gel-like states.

Salt dependent phase behavior of intrinsically disordered proteins from a coarse-grained model with explicit water and ions

Multivalent proteins and nucleic acids can self-assemble into biomolecular condensates that contribute to compartmentalize the cell interior. Computer simulations offer a unique view to elucidate the mechanisms and key intermolecular interactions behind the dynamic formation and dissolution of these condensates. In this work, we present a novel approach to include explicit water and salt in sequence-dependent coarse-grained (CG) models for proteins and RNA, enabling the study of biomolecular condensate formation in a salt-dependent manner. Our framework combines a reparameterized version of the HPS protein force field with the monoatomic mW water model and the mW-ion potential for NaCl. We show how our CG model qualitatively captures the experimental radius of the gyration trend of a subset of intrinsically disordered proteins and reproduces the experimental protein concentration and water percentage of the human fused in sarcoma (FUS) low-complexity-domain droplets at physiological salt concentration. Moreover, we perform seeding simulations as a function of salt concentration for two antagonist systems: the engineered peptide PR₂₅ and poly-uridine/poly-arginine mixtures, finding good agreement with their reported in vitro phase behavior with salt concentration in both cases. Taken together, our work represents a step forward towards extending sequence-dependent CG models to include water and salt, and to consider their key role in biomolecular condensate self-assembly.

Targeted modulation of protein liquid-liquid phase separation by evolution of amino-acid sequence

Rationally and efficiently modifying the amino-acid sequence of proteins to control their ability to undergo liquid-liquid phase separation (LLPS) on demand is not only highly desirable, but can also help to elucidate which protein features are important for LLPS. Here, we propose a computational method that couples a genetic algorithm to a sequence-dependent coarse-grained protein model to evolve the amino-acid sequences of phase-separating intrinsically disordered protein regions (IDRs), and purposely enhance or inhibit their capacity to phase-separate. We validate the predicted critical solution temperatures of the mutated sequences with ABSINTH, a more accurate all-atom model. We apply the algorithm to the phase-separating IDRs of three naturally occurring proteins, namely FUS, hnRNPA1 and LAF1, as prototypes of regions that exist in cells and undergo homotypic LLPS driven by different types of intermolecular interaction, and we find that the evolution of amino-acid sequences towards enhanced LLPS is driven in these three cases, among other factors, by an increase in the average size of the amino acids. However, the direction of change in the molecular driving forces that enhance LLPS (such as hydrophobicity, aromaticity and charge) depends on the initial amino-acid sequence. Finally, we show that the evolution of amino-acid sequences to modulate LLPS is strongly coupled to the make-up of the medium (e.g. the presence or absence of RNA), which may have significant implications for our understanding of phase separation within the many-component mixtures of biological systems.

Size conservation emerges spontaneously in biomolecular condensates formed by scaffolds and surfactant clients

Biomolecular condensates are liquid-like membraneless compartments that contribute to the spatiotemporal organization of proteins, RNA, and other biomolecules inside cells. Some membraneless compartments, such as nucleoli, are dispersed as different condensates that do not grow beyond a certain size, or do not present coalescence over time. In this work, using a minimal protein model, we show that phase separation of binary mixtures of scaffolds and low-valency clients that can act as surfactants-i.e., that significantly reduce the droplet surface tension-can yield either a single drop or multiple droplets that conserve their sizes on long timescales (herein 'multidroplet size-conserved' scenario'), depending on the scaffold to client ratio. Our simulations demonstrate that protein connectivity and condensate surface tension regulate the balance between these two scenarios. The multidroplet size-conserved scenario spontaneously arises at increasing surfactant-to-scaffold concentrations, when the interfacial penalty for creating small liquid droplets is sufficiently reduced by the surfactant proteins that are preferentially located at the interface. In contrast, low surfactant-to-scaffold concentrations enable continuous growth and fusion of droplets without restrictions. Overall, our work proposes one thermodynamic mechanism to help rationalize how size-conserved coexisting condensates can persist inside cells-shedding light on the roles of protein connectivity, binding affinity, and droplet composition in this process.

Biophysics of Phase Separation of Disordered Proteins Is Governed by Balance between Short- And Long-Range Interactions

Intrinsically disordered proteins play a crucial role in cellular phase separation, yet the diverse molecular forces driving phase separation are not fully understood. It is of utmost importance to understand how peptide sequence, and particularly the balance between the peptides’ short- and long-range interactions with other peptides, may affect the stability, structure, and dynamics of liquid–liquid phase separation in protein condensates. Here, using coarse-grained molecular dynamics simulations, we studied the liquid properties of the condensate in a series of polymers in which the ratio of short-range dispersion interactions to long-range electrostatic interactions varied. As the fraction of mutations that participate in short-range interactions increases at the expense of long-range electrostatic interactions, a significant decrease in the critical temperature of phase separation is observed. Nevertheless, sequences with a high fraction of short-range interactions exhibit stabilization, which suggests compensation for the loss of long-range electrostatic interactions. Decreased condensate stability is coupled with decreased translational diffusion of the polymers in the condensate, which may result in the loss of liquid characteristics in the presence of a high fraction of uncharged residues. The effect of exchanging long-range electrostatic interactions for short-range interactions can be explained by the kinetics of breaking intermolecular contacts with neighboring polymers and the kinetics of intramolecular fluctuations. While both time scales are coupled and increase as electrostatic interactions are lost, for sequences that are dominated by short-range interactions, the kinetics of intermolecular contact breakage significantly slows down. Our study supports the contention that different types of interactions can maintain protein condensates, however, long-range electrostatic interactions enhance its liquid-like behavior.

Valency and Binding Affinity Variations Can Regulate the Multilayered Organization of Protein Condensates with Many Components

Biomolecular condensates, which assemble via the process of liquid-liquid phase separation (LLPS), are multicomponent compartments found ubiquitously inside cells. Experiments and simulations have shown that biomolecular condensates with many components can exhibit multilayered organizations. Using a minimal coarse-grained model for interacting multivalent proteins, we investigate the thermodynamic parameters governing the formation of multilayered condensates through changes in protein valency and binding affinity. We focus on multicomponent condensates formed by scaffold proteins (high-valency proteins that can phase separate on their own via homotypic interactions) and clients (proteins recruited to condensates via heterotypic scaffold-client interactions). We demonstrate that higher valency species are sequestered to the center of the multicomponent condensates, while lower valency proteins cluster towards the condensate interface. Such multilayered condensate architecture maximizes the density of LLPS-stabilizing molecular interactions, while simultaneously reducing the surface tension of the condensates. In addition, multilayered condensates exhibit rapid exchanges of low valency proteins in and out, while keeping higher valency proteins-the key biomolecules involved in condensate nucleation-mostly within. We also demonstrate how modulating the binding affinities among the different proteins in a multicomponent condensate can significantly transform its multilayered structure, and even trigger fission of a condensate into multiple droplets with different compositions.

Thermodynamics and kinetics of phase separation of protein-RNA mixtures by a minimal model

Intracellular liquid-liquid phase separation enables the formation of biomolecular condensates, such as ribonucleoprotein granules, which play a crucial role in the spatiotemporal organization of biomolecules (e.g., proteins and RNAs). Here, we introduce a patchy-particle polymer model to investigate liquid-liquid phase separation of protein-RNA mixtures. We demonstrate that at low to moderate concentrations, RNA enhances the stability of RNA-binding protein condensates because it increases the molecular connectivity of the condensed-liquid phase. Importantly, we find that RNA can also accelerate the nucleation stage of phase separation. Additionally, we assess how the capacity of RNA to increase the stability of condensates is modulated by the relative protein-protein/protein-RNA binding strengths. We find that phase separation and multiphase organization of multicomponent condensates is favored when the RNA binds with higher affinity to the lower-valency proteins in the mixture than to the cognate higher-valency proteins. Collectively, our results shed light on the roles of RNA in ribonucleoprotein granule formation and the internal structuring of stress granules.

Expansion of Intrinsically Disordered Proteins Increases the Range of Stability of Liquid-Liquid Phase Separation

Proteins containing intrinsically disordered regions (IDRs) are ubiquitous within biomolecular condensates, which are liquid-like compartments within cells formed through liquid-liquid phase separation (LLPS). The sequence of amino acids of a protein encodes its phase behaviour, not only by establishing the patterning and chemical nature (e.g., hydrophobic, polar, charged) of the various binding sites that facilitate multivalent interactions, but also by dictating the protein conformational dynamics. Besides behaving as random coils, IDRs can exhibit a wide-range of structural behaviours, including conformational switching, where they transition between alternate conformational ensembles. Using Molecular Dynamics simulations of a minimal coarse-grained model for IDRs, we show that the role of protein conformation has a non-trivial effect in the liquid-liquid phase behaviour of IDRs. When an IDR transitions to a conformational ensemble enriched in disordered extended states, LLPS is enhanced. In contrast, IDRs that switch to ensembles that preferentially sample more compact and structured states show inhibited LLPS. This occurs because extended and disordered protein conformations facilitate LLPS-stabilising multivalent protein-protein interactions by reducing steric hindrance; thereby, such conformations maximize the molecular connectivity of the condensed liquid network. Extended protein configurations promote phase separation regardless of whether LLPS is driven by homotypic and/or heterotypic protein-protein interactions. This study sheds light on the link between the dynamic conformational plasticity of IDRs and their liquid-liquid phase behaviour.

Model for disordered proteins with strongly sequence-dependent liquid phase behavior

Phase separation of intrinsically disordered proteins is important for the formation of membraneless organelles or biomolecular condensates, which play key roles in the regulation of biochemical processes within cells. In this work, we investigated the phase separation of different sequences of a coarse-grained model for intrinsically disordered proteins and discovered a surprisingly rich phase behavior. We studied both the fraction of total hydrophobic parts and the distribution of hydrophobic parts. Not surprisingly, sequences with larger hydrophobic fractions showed conventional liquid-liquid phase separation. The location of the critical point was systematically influenced by the terminal beads of the sequence due to changes in interfacial composition and tension. For sequences with lower hydrophobicity, we observed not only conventional liquid-liquid phase separation but also re-entrant phase behavior in which the liquid phase density decreases at lower temperatures. For some sequences, we observed the formation of open phases consisting of aggregates, rather than a normal liquid. These aggregates had overall lower densities than the conventional liquid phases and exhibited complex geometries with large interconnected string-like or membrane-like clusters. Our findings suggest that minor alterations in the ordering of residues may lead to large changes in the phase behavior of the protein, a fact of significant potential relevance for biology.

Liquid network connectivity regulates the stability and composition of biomolecular condensates with many components

One of the key mechanisms used by cells to control the spatiotemporal organization of their many components is the formation and dissolution of biomolecular condensates through liquid-liquid phase separation (LLPS). Using a minimal coarse-grained model that allows us to simulate thousands of interacting multivalent proteins, we investigate the physical parameters dictating the stability and composition of multicomponent biomolecular condensates. We demonstrate that the molecular connectivity of the condensed-liquid network-i.e., the number of weak attractive protein-protein interactions per unit of volume-determines the stability (e.g., in temperature, pH, salt concentration) of multicomponent condensates, where stability is positively correlated with connectivity. While the connectivity of scaffolds (biomolecules essential for LLPS) dominates the phase landscape, introduction of clients (species recruited via scaffold-client interactions) fine-tunes it by transforming the scaffold-scaffold bond network. Whereas low-valency clients that compete for scaffold-scaffold binding sites decrease connectivity and stability, those that bind to alternate scaffold sites not required for LLPS or that have higher-than-scaffold valencies form additional scaffold-client-scaffold bridges increasing stability. Proteins that establish more connections (via increased valencies, promiscuous binding, and topologies that enable multivalent interactions) support the stability of and are enriched within multicomponent condensates. Importantly, proteins that increase the connectivity of multicomponent condensates have higher critical points as pure systems or, if pure LLPS is unfeasible, as binary scaffold-client mixtures. Hence, critical points of accessible systems (i.e., with just a few components) might serve as a unified thermodynamic parameter to predict the composition of multicomponent condensates.