Physical principles of intracellular organization via active and passive phase transitions

Emergence of Multiphase Condensates from a Limited Set of Chemical Building Blocks

Biomolecules composed of a limited set of chemical building blocks can colocalize into distinct, spatially segregated compartments known as biomolecular condensates. While many condensates are known to form spontaneously via phase separation, it has been unclear how immiscible condensates with precisely controlled molecular compositions assemble from a small number of chemical building blocks. We address this question by establishing a connection between the specificity of biomolecular interactions and the thermodynamic stability of coexisting condensates. By computing the minimum interaction specificity required to assemble condensates with target molecular compositions, we show how to design heteropolymer mixtures that produce compositionally complex condensates by using only a small number of monomer types. Our results provide insight into how compositional specificity arises in naturally occurring multicomponent condensates and demonstrate a rational algorithm for engineering complex artificial condensates from simple chemical building blocks.

Exact analytical solution of the Flory-Huggins model and extensions to multicomponent systems

The Flory-Huggins theory describes the phase separation of solutions containing polymers. Although it finds widespread application from polymer physics to materials science to biology, the concentrations that coexist in separate phases at equilibrium have not been determined analytically, and numerical techniques are required that restrict the theory's ease of application. In this work, we derive an implicit analytical solution to the Flory-Huggins theory of one polymer in a solvent by applying a procedure that we call the implicit substitution method. While the solutions are implicit and in the form of composite variables, they can be mapped explicitly to a phase diagram in composition space. We apply the same formalism to multicomponent polymeric systems, where we find analytical solutions for polydisperse mixtures of polymers of one type. Finally, while complete analytical solutions are not possible for arbitrary mixtures, we propose computationally efficient strategies to map out coexistence curves for systems with many components of different polymer types.

The role of ER exit sites in maintaining P-body organization and transmitting ER stress response during Drosophila melanogaster oogenesis

Processing bodies (P-bodies) are cytoplasmic membrane-less organelles which host multiple mRNA processing events. While the fundamental principles of P-body organization are beginning to be elucidated in vitro, a nuanced understanding of how their assembly is regulated in vivo remains elusive. Here, we investigate the potential link between ER exit sites and P-bodies in Drosophila melanogaster egg chambers. Employing a combination of live and super-resolution imaging, we found that P-bodies associated with ER exit sites are larger and less mobile than cytoplasmic P-bodies, indicating that they constitute a distinct class of P-bodies which are more mature than their cytoplasmic counterparts. Moreover, we demonstrate that altering the composition of ER exit sites has differential effects on core P-body proteins (Me31B, Cup, and Trailer Hitch) suggesting a potential role for ER exit sites in P-body organization. We further show that in the absence of ER exit sites, P-body integrity is compromised and the stability and translational repression efficiency of the maternal mRNA, oskar, are reduced. Finally, we show that ER stress is communicated to P-bodies via ER exit sites, highlighting the pivotal role of ER exit sites as a bridge between membrane-bound and membrane-less organelles in ER stress response. Together, our data unveils the significance of ER exit sites not only in governing P-body organization, but also in facilitating inter-organellar communication during stress, potentially bearing implications for a variety of disease pathologies.

Preserving condensate structure and composition by lowering sequence complexity

Biomolecular condensates play a vital role in organizing cellular chemistry. They selectively partition biomolecules, preventing unwanted cross talk and buffering against chemical noise. Intrinsically disordered proteins (IDPs) serve as primary components of these condensates due to their flexibility and ability to engage in multivalent interactions, leading to spontaneous aggregation. Theoretical advancements are critical at connecting IDP sequences with condensate emergent properties to establish the so-called molecular grammar. We proposed an extension to the stickers and spacers model, incorporating heterogeneous, nonspecific pairwise interactions between spacers alongside specific interactions among stickers. Our investigation revealed that although spacer interactions contribute to phase separation and co-condensation, their nonspecific nature leads to disorganized condensates. Specific sticker-sticker interactions drive the formation of condensates with well-defined networked structures and molecular composition. We discussed how evolutionary pressures might emerge to affect these interactions, leading to the prevalence of low-complexity domains in IDP sequences. These domains suppress spurious interactions and facilitate the formation of biologically meaningful condensates.

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.

Chemically reactive and aging macromolecular mixtures I: Phase diagrams, spinodals, and gelation

Multicomponent macromolecular mixtures often form higher-order structures, which may display non-ideal mixing and aging behaviors. In this work, we first propose a minimal model of a quaternary system that takes into account the formation of a complex via a chemical reaction involving two macromolecular species; the complex may then phase separate from the buffer and undergo a further transition into a gel-like state. We subsequently investigate how physical parameters such as molecular size, stoichiometric coefficients, equilibrium constants, and interaction parameters affect the phase behavior of the mixture and its propensity to undergo aging via gelation. In addition, we analyze the thermodynamic stability of the system and identify the spinodal regions and their overlap with gelation boundaries. The approach developed in this work can be readily generalized to study systems with an arbitrary number of components. More broadly, it provides a physically based starting point for the investigation of the kinetics of the coupled complex formation, phase separation, and gelation processes in spatially extended systems.

Aggregation Mechanisms and Molecular Structures of Amyloid-β in Alzheimer's Disease

Amyloid plaques are a major pathological hallmark involved in Alzheimer's disease and consist of deposits of the amyloid-β peptide (Aβ). The aggregation process of Aβ is highly complex, which leads to polymorphous aggregates with different structures. In addition to aberrant aggregation, Aβ oligomers can undergo liquid-liquid phase separation (LLPS) and form dynamic condensates. It has been hypothesized that these amyloid liquid droplets affect and modulate amyloid fibril formation. In this review, we briefly introduce the relationship between stress granules and amyloid protein aggregation that is associated with neurodegenerative diseases. Then we highlight the regulatory role of LLPS in Aβ aggregation and discuss the potential relationship between Aβ phase transition and aggregation. Furthermore, we summarize the current structures of Aβ oligomers and amyloid fibrils, which have been determined using nuclear magnetic resonance (NMR) and cryo-electron microscopy (cryo-EM). The structural variations of Aβ aggregates provide an explanation for the different levels of toxicity, shed light on the aggregation mechanism and may pave the way towards structure-based drug design for both clinical diagnosis and treatment.

Taylor Dispersion-Induced Phase Separation for the Efficient Characterisation of Protein Condensate Formation

Biomolecular condensates have emerged as important structures in cellular function and disease, and are thought to form through liquid-liquid phase separation (LLPS). Thorough and efficient in vitro experiments are therefore needed to elucidate the driving forces of protein LLPS and the possibility to modulate it with drugs. Here we present Taylor dispersion-induced phase separation (TDIPS), a method to robustly measure condensation phenomena using a commercially available microfluidic platform. It uses only nanoliters of sample, does not require extrinsic fluorescent labels, and is straightforward to implement. We demonstrate TDIPS by screening the phase behaviour of two proteins that form biomolecular condensates in vivo, PGL-3 and Ddx4. Uniquely accessible to this method, we find an unexpected re-entrant behaviour at very low ionic strength, where LLPS is inhibited for both proteins. TDIPS can also probe the reversibility of assemblies, which was shown for both α-synuclein and for lysozyme, relevant for health and biotechnology, respectively. Finally, we highlight how effective inhibition concentrations and partitioning of LLPS-modifying compounds can be screened highly efficiently.

Direct computations of viscoelastic moduli of biomolecular condensates

In vitro facsimiles of biomolecular condensates are formed by different types of intrinsically disordered proteins including prion-like low complexity domains (PLCDs). PLCD condensates are viscoelastic materials defined by time-dependent, sequence-specific complex shear moduli. Here, we show that viscoelastic moduli can be computed directly using a generalization of the Rouse model and information regarding intra- and inter-chain contacts that is extracted from equilibrium configurations of lattice-based Metropolis Monte Carlo (MMC) simulations. The key ingredient of the generalized Rouse model is the Zimm matrix that we compute from equilibrium MMC simulations. We compute two flavors of Zimm matrices, one referred to as the single-chain model that accounts only for intra-chain contacts, and the other referred to as a collective model, that accounts for inter-chain interactions. The single-chain model systematically overestimates the storage and loss moduli, whereas the collective model reproduces the measured moduli with greater fidelity. However, in the long time, low-frequency domain, a mixture of the two models proves to be most accurate. In line with the theory of Rouse, we find that a continuous distribution of relaxation times exists in condensates. The single crossover frequency between dominantly elastic versus dominantly viscous behaviors is influenced by the totality of the relaxation modes. Hence, our analysis suggests that viscoelastic fluid-like condensates are best described as generalized Maxwell fluids. Finally, we show that the complex shear moduli can be used to solve an inverse problem to obtain distributions of relaxation times that underlie the dynamics within condensates.

Anomalous coarsening of coalescing nucleoli in human cells

Coarsening is a ubiquitous phenomenon in droplet systems near thermodynamic equilibrium-as an increase in droplet size lowers the system's free energy-however, coarsening of droplets in nonequilibrium systems, such as the cell nucleus, is far from understood. Liquid condensates in the cell nucleus, like nucleoli, form by liquid-liquid phase separation and play a key role in the nuclear organization. In human cells, nucleolar droplets are nucleated at the beginning of the cell cycle and coarsen with time by coalescing with each other. Upon coarsening, human nucleoli exhibit an anomalous volume distribution P(V)∼V-1, which cannot be explained by any existing theory. In this work, we investigate physical mechanisms behind the anomalous coarsening of human nucleoli. Using spinning disk confocal microscopy, we simultaneously record dynamic behavior of nucleoli and their surrounding chromatin before their coalescence in live human cells. We find that nucleolar anomalous coarsening persists during the entire cell cycle. We measure chromatin flows and density between and around nucleoli, as well as relative motion of two nucleoli before they coalesce. We find that, before nucleolar coalescence, chromatin concentration decreases in the space between nucleoli and the nucleoli move faster toward each other, resembling an effective depletion attraction between the coalescing nucleoli. Indeed, our computational simulations of nucleolar dynamics show that short-ranged attraction is sufficient to explain the observed anomalous volume distribution of human nucleoli. Overall, our results reveal a potential physical mechanism contributing to coarsening of human nucleoli. Such knowledge expands our picture of the physical behavior of liquid condensates inside the cell nucleus and our understanding of the dynamic nuclear organization.

Asymptotic analysis of particle cluster formation in the presence of anchoring sites

The aggregation or clustering of proteins and other macromolecules plays an important role in the formation of large-scale molecular assemblies within cell membranes. Examples of such assemblies include lipid rafts, and postsynaptic domains (PSDs) at excitatory and inhibitory synapses in neurons. PSDs are rich in scaffolding proteins that can transiently trap transmembrane neurotransmitter receptors, thus localizing them at specific spatial positions. Hence, PSDs play a key role in determining the strength of synaptic connections and their regulation during learning and memory. Recently, a two-dimensional (2D) diffusion-mediated aggregation model of PSD formation has been developed in which the spatial locations of the clusters are determined by a set of fixed anchoring sites. The system is kept out of equilibrium by the recycling of particles between the cell membrane and interior. This results in a stationary distribution consisting of multiple clusters, whose average size can be determined using an effective mean-field description of the particle concentration around each anchored cluster. In this paper, we derive corrections to the mean-field approximation by applying the theory of diffusion in singularly perturbed domains. The latter is a powerful analytical method for solving two-dimensional (2D) and three-dimensional (3D) diffusion problems in domains where small holes or perforations have been removed from the interior. Applications range from modeling intracellular diffusion, where interior holes could represent subcellular structures such as organelles or biological condensates, to tracking the spread of chemical pollutants or heat from localized sources. In this paper, we take the bounded domain to be the cell membrane and the holes to represent anchored clusters. The analysis proceeds by partitioning the membrane into a set of inner regions around each cluster, and an outer region where mean-field interactions occur. Asymptotically matching the inner and outer stationary solutions generates an asymptotic expansion of the particle concentration, which includes higher-order corrections to mean-field theory that depend on the positions of the clusters and the boundary of the domain. Motivated by a recent study of light-activated protein oligomerization in cells, we also develop the analogous theory for cluster formation in a three-dimensional (3D) domain. The details of the asymptotic analysis differ from the 2D case due to the contrasting singularity structure of 2D and 3D Green's functions.

Interplay Between Intracellular Transport Dynamics and Liquid‒Liquid Phase Separation

Liquid‒liquid phase separation (LLPS) is a ubiquitous process in which proteins, RNA, and biomolecules assemble into membrane-less compartments, playing important roles in many biological functions and diseases. The current knowledge on the biophysical and biochemical principles of LLPS is largely from in vitro studies; however, the physiological environment in living cells is complex and not at equilibrium. The characteristics of intracellular dynamics and their roles in physiological LLPS remain to be resolved. Here, by using single-particle tracking of quantum dots and dynamic monitoring of the formation of stress granules (SGs) in single cells, the spatiotemporal dynamics of intracellular transport in cells undergoing LLPS are quantified. It is shown that intracellular diffusion and active transport are both reduced. Furthermore, the formation of SG droplets contributes to increased spatial heterogeneity within the cell. More importantly, the study demonstrated that the LLPS of SGs can be regulated by intracellular dynamics in two stages: the reduced intracellular diffusion promotes SG assembly and the microtubule-associated transport facilitates SG coalescences. The work on intracellular dynamics not only improves the understanding of the mechanism of physiology phase separations occurring in nonequilibrium environments but also reveals an interplay between intracellular dynamics and LLPS.

Biomolecular condensates form spatially inhomogeneous network fluids

The functions of biomolecular condensates are thought to be influenced by their material properties, and these will be determined by the internal organization of molecules within condensates. However, structural characterizations of condensates are challenging, and rarely reported. Here, we deploy a combination of small angle neutron scattering, fluorescence recovery after photobleaching, and coarse-grained molecular dynamics simulations to provide structural descriptions of model condensates that are formed by macromolecules from nucleolar granular components (GCs). We show that these minimal facsimiles of GCs form condensates that are network fluids featuring spatial inhomogeneities across different length scales that reflect the contributions of distinct protein and peptide domains. The network-like inhomogeneous organization is characterized by a coexistence of liquid- and gas-like macromolecular densities that engenders bimodality of internal molecular dynamics. These insights suggest that condensates formed by multivalent proteins share features with network fluids formed by systems such as patchy or hairy colloids.

Untangling the Molecular Interactions Underlying Intracellular Phase Separation Using Combined Global Sensitivity Analyses

Liquid-liquid phase separation is an intracellular mechanism by which molecules, usually proteins and RNAs, interact and then rapidly demix from the surrounding matrix to form membrane-less compartments necessary for cellular function. Occurring in both the cytoplasm and the nucleus, properties of the resulting droplets depend on a variety of characteristics specific to the molecules involved, such as valency, density, and diffusion within the crowded environment. Capturing these complexities in a biologically relevant model is difficult. To understand the nuanced dynamics between proteins and RNAs as they interact and form droplets, as well as the impact of these interactions on the resulting droplet properties, we turn to sensitivity analysis. In this work, we examine a previously published mathematical model of two RNA species competing for the same protein-binding partner. We use the combined analyses of Morris Method and Sobol' sensitivity analysis to understand the impact of nine molecular parameters, subjected to three different initial conditions, on two observable LLPS outputs: the time of phase separation and the composition of the droplet field. Morris Method is a screening method capable of highlighting the most important parameters impacting a given output, while the variance-based Sobol' analysis can quantify both the importance of a given parameter, as well as the other model parameters it interacts with, to produce the observed phenomena. Combining these two techniques allows Morris Method to identify the most important dynamics and circumvent the large computational expense associated with Sobol', which then provides more nuanced information about parameter relationships. Together, the results of these combined methodologies highlight the complicated protein-RNA relationships underlying both the time of phase separation and the composition of the droplet field. Sobol' sensitivity analysis reveals that observed spatial and temporal dynamics are due, at least in part, to high-level interactions between multiple (3+) parameters. Ultimately, this work discourages using a single measurement to extrapolate the value of any single rate or parameter value, while simultaneously establishing a framework in which to analyze and assess the impact of these small-scale molecular interactions on large-scale droplet properties.

Liquid-liquid phase separation-inspired design of biomaterials

Liquid-liquid phase separation (LLPS) is a crucial biological process that governs biomolecular condensation, assembly, and functionality within phase-separated aqueous environments. This phenomenon serves as a source of inspiration for the creation of artificial designs in both structured and functional biomaterials, presenting novel strategies for manipulating the structures of functional protein aggregates in a wide range of biomedical applications. This mini review summarizes my past research endeavors, offering a panoramic overview of LLPS-inspired biomaterials utilized in the design of structured materials, the development of cell mimetics, and the advancement of intelligent biomaterials.

Effect of trimethylamine-N-oxide on the phase separation of aqueous polyethylene glycol-600-Dextran-75 two-phase systems

The emergence of phase separation in both intracellular biomolecular condensates (membrane-less organelles) and in vitro aqueous two-phase systems (ATPS) relies on the formation of immiscible water-based phases/domains. The solvent properties and arrangement of hydrogen bonds within these domains have been shown to differ and can be modulated with the addition of various inorganic salts and osmolytes. The naturally occuring osmolyte, trimethylamine-N-oxide (TMAO), is well established as a biological condensate stabilizer whose presence results in enhanced phase separation of intracellular membrane-less compartments. Here, we show the unique effect of TMAO on the mechanism of phase separation in model PEG-600-Dextran-75 ATPS using dynamic and static light scattering in conjunction with ATR-FTIR and solvatochromic analysis. We observe that the presence of TMAO may enhance or destabilize phase separation depending on the concentration of phase forming components. Additionally, the behavior and density of mesoscopic polymer agglomerates, which arise prior to macroscopic phase separation, are altered by the presence and concentration of TMAO.

Mechanism of phase condensation for chromosome architecture and function

Chromosomal phase separation is involved in a broad spectrum of chromosome organization and functional processes. Nonetheless, the intricacy of this process has left its molecular mechanism unclear. Here, we introduce the principles governing phase separation and its connections to physiological roles in this context. Our primary focus is contrasting two phase separation mechanisms: self-association-induced phase separation (SIPS) and bridging-induced phase separation (BIPS). We provide a comprehensive discussion of the distinct features characterizing these mechanisms and offer illustrative examples that suggest their broad applicability. With a detailed understanding of these mechanisms, we explore their associations with nucleosomes and chromosomal biological functions. This comprehensive review contributes to the exploration of uncharted territory in the intricate interplay between chromosome architecture and function.

Tear down this wall: phosphorylation regulates the internal interfaces of postsynaptic condensates

Can the fusion/fission of biomolecular condensates be regulated in cells? In a recent study, Wu et al. show that phosphorylation of a key scaffold protein that drives condensates in postsynaptic densities modulates the apparent miscibility of underlying components, thus enabling intracondensate demixing-to-mixing transitions.

Modelling lipid rafts formation through chemo-mechanical interplay triggered by receptor-ligand binding

Cell membranes, mediator of many biological mechanisms from adhesion and metabolism up to mutation and infection, are highly dynamic and heterogeneous environments exhibiting a strong coupling between biochemical events and structural re-organisation. This involves conformational changes induced, at lower scales, by lipid order transitions and by the micro-mechanical interplay of lipids with transmembrane proteins and molecular diffusion. Particular attention is focused on lipid rafts, ordered lipid microdomains rich of signalling proteins, that co-localise to enhance substance trafficking and activate different intracellular biochemical pathways. In this framework, the theoretical modelling of the dynamic clustering of lipid rafts implies a full multiphysics coupling between the kinetics of phase changes and the mechanical work performed by transmembrane proteins on lipids, involving the bilayer elasticity. This mechanism produces complex interspecific dynamics in which membrane stresses and chemical potentials do compete by determining different morphological arrangements, alteration in diffusive walkways and coalescence phenomena, with a consequent influence on both signalling potential and intracellular processes. Therefore, after identifying the leading chemo-mechanical interactions, the present work investigates from a modelling perspective the spatio-temporal evolution of raft domains to theoretically explain co-localisation and synergy between proteins' activation and raft formation, by coupling diffusive and mechanical phenomena to observe different morphological patterns and clustering of ordered lipids. This could help to gain new insights into the remodelling of cell membranes and could potentially suggest mechanically based strategies to control their selectivity, by orienting intracellular functions and mechanotransduction.

Optical Control over Liquid–Liquid Phase Separation

Liquid-liquid phase separation (LLPS) is responsible for the emergence of intracellular membrane-less organelles and the development of coacervate protocells. Benefitting from the advantages of simplicity, precision, programmability, and noninvasiveness, light has become an effective tool to regulate the assembly dynamics of LLPS, and mediate various biochemical processes associated with LLPS. In this review, recent advances in optically controlling membrane-less organelles within living organisms are summarized, thereby modulating a series of biological processes including irreversible protein aggregation pathologies, transcription activation, metabolic flux, genomic rearrangements, and enzymatic reactions. Among these, the intracellular systems (i.e., optoDroplet, Corelet, PixELL, CasDrop, and other optogenetic systems) that enable the photo-mediated control over biomolecular condensation are highlighted. The design of photoactive complex coacervate protocells in laboratory settings by utilizing photochromic molecules such as azobenzene and diarylethene is further discussed. This review is expected to provide in-depth insights into phase separation-associated biochemical processes, bio-metabolism, and diseases.

Heterogeneous elasticity drives ripening and controls bursting kinetics of transcriptional condensates

Many biomolecular condensates, including transcriptional condensates, are formed in elastic mediums. In this work, we study the nonequilibrium condensate dynamics in a chromatin-like environment modeled as a heterogeneous elastic medium. We demonstrate that the ripening process in such an elastic medium exhibits a temporal power-law scaling of the average condensate radius, depending on the local stiffness distribution and different from Ostwald ripening. Moreover, we incorporate an active process to model the dissolution of transcriptional condensates upon RNA accumulation. Intriguingly, three types of kinetics of condensate growth emerge, corresponding to constitutively expressed, transcriptional-bursting, and silenced genes. Furthermore, the simulated burst frequency decreases exponentially with the local stiffness, through which we infer a lognormal distribution of local stiffness in living cells using the transcriptome-wide distribution of burst frequency. Under the inferred stiffness distribution, the simulated distributions of bursting kinetic parameters agree reasonably well with the experimental data. Our findings reveal the interplay between biomolecular condensates and elastic mediums, yielding far-reaching implications for gene expression.

The molecular basis for cellular function of intrinsically disordered protein regions

Intrinsically disordered protein regions exist in a collection of dynamic interconverting conformations that lack a stable 3D structure. These regions are structurally heterogeneous, ubiquitous and found across all kingdoms of life. Despite the absence of a defined 3D structure, disordered regions are essential for cellular processes ranging from transcriptional control and cell signalling to subcellular organization. Through their conformational malleability and adaptability, disordered regions extend the repertoire of macromolecular interactions and are readily tunable by their structural and chemical context, making them ideal responders to regulatory cues. Recent work has led to major advances in understanding the link between protein sequence and conformational behaviour in disordered regions, yet the link between sequence and molecular function is less well defined. Here we consider the biochemical and biophysical foundations that underlie how and why disordered regions can engage in productive cellular functions, provide examples of emerging concepts and discuss how protein disorder contributes to intracellular information processing and regulation of cellular function.

NAGPKin: Nucleation-and-growth parameters from the kinetics of protein phase separation

The assembly of biomolecular condensate in eukaryotic cells and the accumulation of amyloid deposits in neurons are processes involving the nucleation and growth (NAG) of new protein phases. To therapeutically target protein phase separation, drug candidates are tested in in vitro assays that monitor the increase in the mass or size of the new phase. Limited mechanistic insight is, however, provided if empirical or untestable kinetic models are fitted to these progress curves. Here we present the web server NAGPKin that quantifies NAG rates using mass-based or size-based progress curves as the input data. A report is generated containing the fitted NAG parameters and elucidating the phase separation mechanisms at play. The NAG parameters can be used to predict particle size distributions of, for example, protein droplets formed by liquid-liquid phase separation (LLPS) or amyloid fibrils formed by protein aggregation. Because minimal intervention is required from the user, NAGPKin is a good platform for standardized reporting of LLPS and protein self-assembly data. NAGPKin is useful for drug discovery as well as for fundamental studies on protein phase separation. NAGPKin is freely available (no login required) at https://nagpkin.i3s.up.pt.

Design Rules for the Sequestration of Viruses into Polypeptide Complex Coacervates

Encapsulation is a strategy that has been used to facilitate the delivery and increase the stability of proteins and viruses. Here, we investigate the encapsulation of viruses via complex coacervation, which is a liquid-liquid phase separation resulting from the complexation of oppositely charged polymers. In particular, we utilized polypeptide-based coacervates and explored the effects of peptide chemistry, chain length, charge patterning, and hydrophobicity to better understand the effects of the coacervating polypeptides on virus incorporation. Our study utilized two nonenveloped viruses, porcine parvovirus (PPV) and human rhinovirus (HRV). PPV has a higher charge density than HRV, and they both appear to be relatively hydrophobic. These viruses were compared to characterize how the charge, hydrophobicity, and patterning of chemistry on the surface of the virus capsid affects encapsulation. Consistent with the electrostatic nature of complex coacervation, our results suggest that electrostatic effects associated with the net charge of both the virus and polypeptide dominated the potential for incorporating the virus into a coacervate, with clustering of charges also playing a significant role. Additionally, the hydrophobicity of a virus appears to determine the degree to which increasing the hydrophobicity of the coacervating peptides can enhance virus uptake. Nonintuitive trends in uptake were observed with regard to both charge patterning and polypeptide chain length, with these parameters having a significant effect on the range of coacervate compositions over which virus incorporation was observed. These results provide insights into biophysical mechanisms, where sequence effects can control the uptake of proteins or viruses into biological condensates and provide insights for use in formulation strategies.

Crosstalk between protein post-translational modifications and phase separation

The phenomenon of phase separation is quite common in cells, and it is involved in multiple processes of life activities. However, the current research on the correlation between protein modifications and phase separation and the interference with the tendency of phase separation has some limitations. Here we focus on several post-translational modifications of proteins, including protein phosphorylation modification at multiple sites, methylation modification, acetylation modification, ubiquitination modification, SUMOylation modification, etc., which regulate the formation of phase separation and the stability of phase separation structure through multivalent interactions. This regulatory role is closely related to the development of neurodegenerative diseases, tumors, viral infections, and other diseases, and also plays essential functions in environmental stress, DNA damage repair, transcriptional regulation, signal transduction, and cell homeostasis of living organisms, which provides an idea to explore the interaction between novel protein post-translational modifications and phase separation. Video Abstract.

Biomolecular condensates form spatially inhomogeneous network fluids

The functions of biomolecular condensates are thought to be influenced by their material properties, and these will be determined by the internal organization of molecules within condensates. However, structural characterizations of condensates are challenging, and rarely reported. Here, we deploy a combination of small angle neutron scattering, fluorescence recovery after photobleaching, and coarse-grained molecular dynamics simulations to provide structural descriptions of model condensates that are formed by macromolecules from nucleolar granular components (GCs). We show that these minimal facsimiles of GCs form condensates that are network fluids featuring spatial inhomogeneities across different length scales that reflect the contributions of distinct protein and peptide domains. The network-like inhomogeneous organization is characterized by a coexistence of liquid- and gas-like macromolecular densities that engenders bimodality of internal molecular dynamics. These insights suggest that condensates formed by multivalent proteins share features with network fluids formed by systems such as patchy or hairy colloids.

Active smectics on a sphere

The dynamics of active smectic liquid crystals confined on a spherical surface is explored through an active phase field crystal model. Starting from an initially randomly perturbed isotropic phase, several types of topological defects are spontaneously formed, and then annihilate during a coarsening process until a steady state is achieved. The coarsening process is highly complex involving several scaling laws of defect densities as a function of time where different dynamical exponents can be identified. In general the exponent for the final stage towards the steady state is significantly larger than that in the passive and in the planar case, i.e. the coarsening is getting accelerated both by activity and by the topological and geometrical properties of the sphere. A defect type characteristic for this active system is a rotating spiral of evolving smectic layering lines. On a sphere this defect type also determines the steady state. Our results can in principle be confirmed by dense systems of synthetic or biological active particles.

Kinetic control of shape deformations and membrane phase separation inside giant vesicles

A variety of cellular processes use liquid-liquid phase separation (LLPS) to create functional levels of organization, but the kinetic pathways by which it proceeds remain incompletely understood. Here in real time, we monitor the dynamics of LLPS of mixtures of segregatively phase-separating polymers inside all-synthetic, giant unilamellar vesicles. After dynamically triggering phase separation, we find that the ensuing relaxation-en route to the new equilibrium-is non-trivially modulated by a dynamic interplay between the coarsening of the evolving droplet phase and the interactive membrane boundary. The membrane boundary is preferentially wetted by one of the incipient phases, dynamically arresting the progression of coarsening and deforming the membrane. When the vesicles are composed of phase-separating mixtures of common lipids, LLPS within the vesicular interior becomes coupled to the membrane's compositional degrees of freedom, producing microphase-separated membrane textures. This coupling of bulk and surface phase-separation processes suggests a physical principle by which LLPS inside living cells might be dynamically regulated and communicated to the cellular boundaries.

Sequence-specific interactions determine viscoelasticity and aging dynamics of protein condensates

Biomolecular condensates are viscoelastic materials. Here, we report results from investigations into molecular-scale determinants of sequence-encoded and age-dependent viscoelasticity of condensates formed by prion-like low-complexity domains (PLCDs). The terminally viscous forms of PLCD condensates are Maxwell fluids. Measured viscoelastic moduli of these condensates are reproducible using a Rouse-Zimm model that accounts for the network-like organization engendered by reversible physical crosslinks among PLCDs in the dense phase. Measurements and computations show that the strengths of aromatic inter-sticker interactions determine the sequence-specific amplitudes of elastic and viscous moduli as well as the timescales over which elastic properties dominate. PLCD condensates also undergo physical aging on sequence-specific timescales. This is driven by mutations to spacer residues that weaken the metastability of terminally viscous phases. The aging of PLCD condensates is accompanied by disorder-to-order transitions, leading to the formation of non-fibrillar, beta-sheet-containing, semi-crystalline, terminally elastic, Kelvin-Voigt solids. Our results suggest that sequence grammars, which refer to the identities of stickers versus spacers in PLCDs, have evolved to afford control over the metastabilities of terminally viscous fluid phases of condensates. This selection can, in some cases, render barriers for conversion from metastable fluids to globally stable solids to be insurmountable on functionally relevant timescales.

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.

Coarsening dynamics of ternary polymer solutions with mobility and viscosity contrasts

Using phase-field simulations, we investigate the bulk coarsening dynamics of ternary polymer solutions undergoing a glass transition for two models of phase separation: diffusion only and with hydrodynamics. The glass transition is incorporated in both models by imposing mobility and viscosity contrasts between the polymer-rich and polymer-poor phases of the evolving microstructure. For microstructures composed of polymer-poor clusters in a polymer-rich matrix, the mobility and viscosity contrasts significantly hinder coarsening, effectively leading to structural arrest. For microstructures composed of polymer-rich clusters in a polymer-poor matrix, the mobility and viscosity contrasts do not impede domain growth; rather, they change the transient concentration of the polymer-rich phase, altering the shape of the discrete domains. This effect introduces several complexities to the coarsening process, including percolation inversion of the polymer-rich and polymer-poor phases-a phenomenon normally attributed to viscoelastic phase separation.

Fluid dynamics alters liquid-liquid phase separation in confined aqueous two-phase systems

Liquid-liquid phase separation is key to understanding aqueous two-phase systems (ATPS) arising throughout cell biology, medical science, and the pharmaceutical industry. Controlling the detailed morphology of phase-separating compound droplets leads to new technologies for efficient single-cell analysis, targeted drug delivery, and effective cell scaffolds for wound healing. We present a computational model of liquid-liquid phase separation relevant to recent laboratory experiments with gelatin-polyethylene glycol mixtures. We include buoyancy and surface-tension-driven finite viscosity fluid dynamics with thermally induced phase separation. We show that the fluid dynamics greatly alters the evolution and equilibria of the phase separation problem. Notably, buoyancy plays a critical role in driving the ATPS to energy-minimizing crescent-shaped morphologies, and shear flows can generate a tenfold speedup in particle formation. Neglecting fluid dynamics produces incorrect minimum-energy droplet shapes. The model allows for optimization of current manufacturing procedures for structured microparticles and improves understanding of ATPS evolution in confined and flowing settings important in biology and biotechnology.

Biomolecular condensates in kidney physiology and disease

The regulation and preservation of distinct intracellular and extracellular solute microenvironments is crucial for the maintenance of cellular homeostasis. In mammals, the kidneys control bodily salt and water homeostasis. Specifically, the urine-concentrating mechanism within the renal medulla causes fluctuations in extracellular osmolarity, which enables cells of the kidney to either conserve or eliminate water and electrolytes, depending on the balance between intake and loss. However, relatively little is known about the subcellular and molecular changes caused by such osmotic stresses. Advances have shown that many cells, including those of the kidney, rapidly (within seconds) and reversibly (within minutes) assemble membraneless, nano-to-microscale subcellular assemblies termed biomolecular condensates via the biophysical process of hyperosmotic phase separation (HOPS). Mechanistically, osmotic cell compression mediates changes in intracellular hydration, concentration and molecular crowding, rendering HOPS one of many related phase-separation phenomena. Osmotic stress causes numerous homo-multimeric proteins to condense, thereby affecting gene expression and cell survival. HOPS rapidly regulates specific cellular biochemical processes before appropriate protective or corrective action by broader stress response mechanisms can be initiated. Here, we broadly survey emerging evidence for, and the impact of, biomolecular condensates in nephrology, where initial concentration buffering by HOPS and its subsequent cellular escalation mechanisms are expected to have important implications for kidney physiology and disease.

Preserving condensate structure and composition by lowering sequence complexity

Biological condensates play a vital role in organizing cellular chemistry. They selectively partition biomolecules, preventing unwanted cross-talk and buffering against chemical noise. Intrinsically disordered proteins (IDPs) serve as primary components of these condensates due to their flexibility and ability to engage in multivalent, non-specific interactions, leading to spontaneous aggregation. Theoretical advancements are critical at connecting IDP sequences with condensate emergent properties to establish the so-called molecular grammar. We proposed an extension to the stickers and spacers model, incorporating non-specific pairwise interactions between spacers alongside specific interactions among stickers. Our investigation revealed that while spacer interactions contribute to phase separation and co-condensation, their non-specific nature leads to disorganized condensates. Specific sticker-sticker interactions drive the formation of condensates with well-defined structures and molecular composition. We discussed how evolutionary pressures might emerge to affect these interactions, leading to the prevalence of low complexity domains in IDP sequences. These domains suppress spurious interactions and facilitate the formation of biologically meaningful condensates.

Molecular mechanisms of phase separation and amyloidosis of ALS/FTD-linked FUS and TDP-43

FUS and TDP-43, two RNA-binding proteins from the heterogeneous nuclear ribonucleoprotein family, have gained significant attention in the field of neurodegenerative diseases due to their association with amyotrophic lateral sclerosis (ALS) and frontotemporal degeneration (FTD). They possess folded domains for binding ATP and various nucleic acids including DNA and RNA, as well as substantial intrinsically disordered regions (IDRs) including prion-like domains (PLDs) and RG-/RGG-rich regions. They play vital roles in various cellular processes, including transcription, splicing, microRNA maturation, RNA stability and transport and DNA repair. In particular, they are key components for forming ribonucleoprotein granules and stress granules (SGs) through homotypic or heterotypic liquid-liquid phase separation (LLPS). Strikingly, liquid-like droplets formed by FUS and TDP-43 may undergo aging to transform into less dynamic assemblies such as hydrogels, inclusions, and amyloid fibrils, which are the pathological hallmarks of ALS and FTD. This review aims to synthesize and consolidate the biophysical knowledge of the sequences, structures, stability, dynamics, and inter-domain interactions of FUS and TDP-43 domains, so as to shed light on the molecular mechanisms underlying their liquid-liquid phase separation (LLPS) and amyloidosis. The review further delves into the mechanisms through which ALS-causing mutants of the well-folded hPFN1 disrupt the dynamics of LLPS of FUS prion-like domain, providing key insights into a potential mechanism for misfolding/aggregation-prone proteins to cause neurodegenerative diseases and aging by gain of functions. With better understanding of different biophysical aspects of FUS and TDP-43, the ultimate goal is to develop drugs targeting LLPS and amyloidosis, which could mediate protein homeostasis within cells and lead to new treatments for currently intractable diseases, particularly neurodegenerative diseases such as ALS, FTD and aging. However, the study of membrane-less organelles and condensates is still in its infancy and therefore the review also highlights key questions that require future investigation.

Triblock Proteins with Weakly Dimerizing Terminal Blocks and an Intrinsically Disordered Region for Rational Design of Condensate Properties

Condensates are molecular assemblies that are formed through liquid-liquid phase separation and play important roles in many biological processes. The rational design of condensate formation and their properties is central to applications, such as biosynthetic materials, synthetic biology, and for understanding cell biology. Protein engineering is used to make a triblock structure with varying terminal blocks of folded proteins on both sides of an intrinsically disordered mid-region. Dissociation constants are determined in the range of micromolar to millimolar for a set of proteins suitable for use as terminal blocks. Varying the weak dimerization of terminal blocks leads to an adjustable tendency for condensate formation while keeping the intrinsically disordered region constant. The dissociation constants of the terminal domains correlate directly with the tendency to undergo liquid-liquid phase separation. Differences in physical properties, such as diffusion rate are not directly correlated with the strength of dimerization but can be understood from the properties and interplay of the constituent blocks. The work demonstrates the importance of weak interactions in condensate formation and shows a principle for protein design that will help in fabricating functional condensates in a predictable and rational way.

Chemical reaction motifs driving non-equilibrium behaviours in phase separating materials

Chemical reactions that couple to systems that phase separate have been implicated in diverse contexts from biology to materials science. However, how a particular set of chemical reactions (chemical reaction network, CRN) would affect the behaviours of a phase separating system is difficult to fully predict theoretically. In this paper, we analyse a mean field theory coupling CRNs to a combined system of phase separating and non-phase separating materials and analyse how the properties of the CRNs affect different classes of non-equilibrium behaviour: microphase separation or temporally oscillating patterns. We examine the problem of achieving microphase separated condensates by statistical analysis of the Jacobians, of which the most important motifs are negative feedback of the phase separating component and combined inhibition/activation by the non-phase separating components. We then identify CRN motifs that are likely to yield microphase by examining randomly generated networks and parameters. Molecular sequestration of the phase separating motif is shown to be the most robust towards yielding microphase separation. Subsequently, we find that dynamics of the phase separating species is promoted most easily by inducing oscillations in the diffusive components coupled to the phase separating species. Our results provide guidance towards the design of CRNs that manage the formation, dissolution and organization of compartments.

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.

Liquid-liquid phase separation within fibrillar networks

Complex fibrillar networks mediate liquid-liquid phase separation of biomolecular condensates within the cell. Mechanical interactions between these condensates and the surrounding networks are increasingly implicated in the physiology of the condensates and yet, the physical principles underlying phase separation within intracellular media remain poorly understood. Here, we elucidate the dynamics and mechanics of liquid-liquid phase separation within fibrillar networks by condensing oil droplets within biopolymer gels. We find that condensates constrained within the network pore space grow in abrupt temporal bursts. The subsequent restructuring of condensates and concomitant network deformation is contingent on the fracture of network fibrils, which is determined by a competition between condensate capillarity and network strength. As a synthetic analog to intracellular phase separation, these results further our understanding of the mechanical interactions between biomolecular condensates and fibrillar networks in the cell.

Mechanical Slowing Down of Network-Forming Phase Separation of Polymer Solutions

Phase separation is a fundamental phenomenon leading to spatially heterogeneous material distribution, which is critical in nature, biology, material science, and industry. In ordinary phase separation, the minority phase always forms droplets. Contrary to this common belief, even the minority phase can form a network structure in viscoelastic phase separation (VPS). VPS can occur in any mixture with significant mobility differences between their components and is highly relevant to soft matter and biomatter. In contrast to classical phase separation, experiments have shown that VPS in polymer solutions lacks self-similar coarsening, resulting in the absence of a domain-coarsening scaling law. However, the underlying microscopic mechanism of this behavior remains unknown. To this end, we perform fluid particle dynamics simulations of bead-spring polymers, incorporating many-body hydrodynamic interactions between polymers through a solvent. We discover that polymers in the dense-network-forming phase are stretched and store elastic energy when the deformation speed exceeds the polymer dynamics. This self-generated viscoelastic stress mechanically interferes with phase separation and slows its dynamics, disrupting self-similar growth. We also highlight the essential role of many-body hydrodynamic interactions in VPS. The implications of our findings may hold importance in areas such as biological phase separation, porous material formation, and other fields where network structures play a pivotal role.

Comprehensive Regulation of Liquid-Liquid Phase Separation of Polypeptides

The elucidation of the molecular driving forces responsible for Liquid-liquid Phase Separation (LLPS) of proteins and nucleic acids within living cells is crucial for understanding its biological functions and its role in related diseases. In the present study, we investigated the regulation of LLPS in a series of polypeptides with repetitive proline and arginine (PR) sequences by modifying their length and the salt concentration in the solution. Our findings indicate that higher salt concentrations are necessary for LLPS of repetitive PR peptides longer than eight PRs, which emerges as a threshold value. To pinpoint the molecular forces driving the LLPS in peptides, we sequentially introduced various concentrations of hydrophobic disruptors, such as 1,6-hexanediol, and electrostatic regulators, such as ethyl alcohol and 6-Aminocaproic acid. We further modulated the electrostatic interaction by introducing ethyl alcohol and 6-Aminocaproic acid to alter the dielectric constant of the solution. The inclusion of ethyl alcohol intensified the electrostatic interaction between arginine molecules, facilitating LLPS of PR15, while 6-Aminocaproic acid yielded the reverse effect. We deduced that the phase separation in peptide systems is conjointly driven by hydrophobicity and electrostatic interactions. These insights can guide the regulation of LLPS in other peptide and protein systems, and could be pivotal in addressing abnormal aggregations of proteins and nucleic acids.

Pattern formation by bacteria-phage interactions

The interactions between bacteria and phages-viruses that infect bacteria-play critical roles in agriculture, ecology, and medicine; however, how these interactions influence the spatial organization of both bacteria and phages remain largely unexplored. Here, we address this gap in knowledge by developing a theoretical model of motile, proliferating bacteria that aggregate via motility-induced phase separation (MIPS) and encounter phage that infect and lyse the cells. We find that the non-reciprocal predator-prey interactions between phage and bacteria strongly alter spatial organization, in some cases giving rise to a rich array of finite-scale stationary and dynamic patterns in which bacteria and phage coexist. We establish principles describing the onset and characteristics of these diverse behaviors, thereby helping to provide a biophysical basis for understanding pattern formation in bacteria-phage systems, as well as in a broader range of active and living systems with similar predator-prey or other non-reciprocal interactions.

Critical Assessment of Condensate Boundaries in Dual-Color Single Particle Tracking

Biomolecular condensates are membraneless cellular compartments generated by phase separation that regulate a broad variety of cellular functions by enriching some biomolecules while excluding others. Live-cell single particle tracking of individual fluorophore-labeled condensate components has provided insights into a condensate's mesoscopic organization and biological functions, such as revealing the recruitment, translation, and decay of RNAs within ribonucleoprotein (RNP) granules. Specifically, during dual-color tracking, one imaging channel provides a time series of individual biomolecule locations, while the other channel monitors the location of the condensate relative to these molecules. Therefore, an accurate assessment of a condensate's boundary is critical for combined live-cell single particle-condensate tracking. Despite its importance, a quantitative benchmarking and objective comparison of the various available boundary detection methods is missing due to the lack of an absolute ground truth for condensate images. Here, we use synthetic data of defined ground truth to generate noise-overlaid images of condensates with realistic phase separation parameters to benchmark the most commonly used methods for condensate boundary detection, including an emerging machine-learning method. We find that it is critical to carefully choose an optimal boundary detection method for a given dataset to obtain accurate measurements of single particle-condensate interactions. The criteria proposed in this study to guide the selection of an optimal boundary detection method can be broadly applied to imaging-based studies of condensates.

Tube geometry controls protein cluster conformation and stability on the endoplasmic reticulum surface

The endoplasmic reticulum (ER), a cellular organelle that forms a cell-spanning network of tubes and sheets, is an important location of protein synthesis and folding. When the ER experiences sustained unfolded protein stress, IRE1 proteins embedded in the ER membrane activate and assemble into clusters as part of the unfolded protein response (UPR). We use kinetic Monte Carlo simulations to explore IRE1 clustering dynamics on the surface of ER tubes. While initially growing clusters are approximately round, once a cluster is sufficiently large a shorter interface length can be achieved by 'wrapping' around the ER tube. A wrapped cluster can grow without further interface length increases. Relative to wide tubes, narrower tubes enable cluster wrapping at smaller cluster sizes. Our simulations show that wrapped clusters on narrower tubes grow more rapidly, evaporate more slowly, and require a lower protein concentration to grow compared to equal-area round clusters on wider tubes. These results suggest that cluster wrapping, facilitated by narrower tubes, could be an important factor in the growth and stability of IRE1 clusters and thus impact the persistence of the UPR, connecting geometry to signaling behavior. This work is consistent with recent experimental observations of IRE1 clusters wrapped around narrow tubes in the ER network.

Phase separation of protein mixtures is driven by the interplay of homotypic and heterotypic interactions

Prion-like low-complexity domains (PLCDs) are involved in the formation and regulation of distinct biomolecular condensates that form via phase separation coupled to percolation. Intracellular condensates often encompass numerous distinct proteins with PLCDs. Here, we combine simulations and experiments to study mixtures of PLCDs from two RNA-binding proteins, hnRNPA1 and FUS. Using simulations and experiments, we find that 1:1 mixtures of A1-LCD and FUS-LCD undergo phase separation more readily than either of the PLCDs on their own due to complementary electrostatic interactions. Tie line analysis reveals that stoichiometric ratios of different components and their sequence-encoded interactions contribute jointly to the driving forces for condensate formation. Simulations also show that the spatial organization of PLCDs within condensates is governed by relative strengths of homotypic versus heterotypic interactions. We uncover rules for how interaction strengths and sequence lengths modulate conformational preferences of molecules at interfaces of condensates formed by mixtures of proteins.

Nonreciprocal Cahn-Hilliard Model Emerges as a Universal Amplitude Equation

Oscillatory behavior is ubiquitous in out-of-equilibrium systems showing spatiotemporal pattern formation. Starting from a linear large-scale oscillatory instability-a conserved-Hopf instability-that naturally occurs in many active systems with two conservation laws, we derive a corresponding amplitude equation. It belongs to a hierarchy of such universal equations for the eight types of instabilities in homogeneous isotropic systems resulting from the combination of three features: large-scale vs small-scale instability, stationary vs oscillatory instability, and instability without and with conservation law(s). The derived universal equation generalizes a phenomenological model of considerable recent interest, namely, the nonreciprocal Cahn-Hilliard model, and may be of a similar relevance for the classification of pattern forming systems as the complex Ginzburg-Landau equation.

Viscoelasticity and advective flow of RNA underlies nucleolar form and function

The nucleolus is the largest biomolecular condensate and facilitates transcription, processing, and assembly of ribosomal RNA (rRNA). Although nucleolar function is thought to require multiphase liquid-like properties, nucleolar fluidity and its connection to the highly coordinated transport and biogenesis of ribosomal subunits are poorly understood. Here, we use quantitative imaging, mathematical modeling, and pulse-chase nucleotide labeling to examine nucleolar material properties and rRNA dynamics. The mobility of rRNA is several orders of magnitude slower than that of nucleolar proteins, with rRNA steadily moving away from the transcriptional sites in a slow (∼1 Å/s), radially directed fashion. This constrained but directional mobility, together with polymer physics-based calculations, suggests that nascent rRNA forms an entangled gel, whose constant production drives outward flow. We propose a model in which progressive maturation of nascent rRNA reduces its initial entanglement, fluidizing the nucleolar periphery to facilitate the release of assembled pre-ribosomal particles.

Visualizing Formation and Dynamics of a Three-Dimensional Sponge-like Network of a Coacervate in Real Time

Coacervates, which are formed by liquid-liquid phase separation, have been extensively explored as models for synthetic cells and membraneless organelles, so their in-depth structural analysis is crucial. However, both the inner structure dynamics and formation mechanism of coacervates remain elusive. Herein, we demonstrate real-time confocal observation of a three-dimensional sponge-like network in a dipeptide-based coacervate. In situ generation of the dipeptide allowed us to capture the emergence of the sponge-like network via unprecedented membrane folding of vesicle-shaped intermediates. We also visualized dynamic fluctuation of the network, including reversible engagement/disengagement of cross-links and a stochastic network kissing event. Photoinduced transient formation of a multiphase coacervate was achieved with a thermally responsive phase transition. Our findings expand the fundamental understanding of synthetic coacervates and provide opportunities to manipulate their physicochemical properties by engineering the inner network for potential applications in development of artificial cells and life-like material fabrication.

Composition Dependent Instabilities in Mixtures with Many Components

Understanding the phase behavior of mixtures with many components is important in many contexts, including as a key step toward a physics-based description of intracellular compartmentalization. Here, we study phase ordering instabilities in a paradigmatic model that represents the complexity of-e.g., biological-mixtures via random second virial coefficients. Using tools from free probability theory we obtain the exact spinodal curve and the nature of instabilities for a mixture with an arbitrary composition, thus lifting an important restriction in previous work. We show that, by controlling the concentration of only a few components, one can systematically change the nature of the spinodal instability and achieve demixing for realistic scenarios by a strong composition imbalance amplification. This results from a nontrivial interplay of interaction complexity and entropic effects due to the nonuniform composition. Our approach can be extended to include additional systematic interactions, leading to a competition between different forms of demixing as density is varied.

Decoupling of Interactions between Model-Charged Peptides Reveals Key Factors Responsible for Liquid-Liquid Phase Separation

Liquid-liquid phase separation (LLPS) by disordered proteins has been shown to govern biological processes and cause numerous diseases. Therefore, a deeper understanding of the interactions and their variation with external factors is key to modulating the LLPS behavior of different systems and protecting proteins from pathological aggregation. In this context, we have looked at interactions between similarly charged peptides to understand the molecular features that may drive or prevent condensate formation under various conditions. We have studied dimer formation for model peptides where charged and noncharged amino acids have been placed alternatively. Using arginine and glutamic acid as the charged residues and varying the other residues with glycine, alanine, and proline to alter hydrophobicity, we have obtained the free-energy surface (FES) for the dimer formation for these systems under high salt concentration at two different temperatures using all-atom molecular dynamics simulations and the well-tempered metadynamics method. Our results indicate that a combination of effects such as hydrophobicity, arginine-arginine interactions, or water release from the solvation shell makes dimerization free energy more favorable for the positively charged peptides with lower flexibility. For the negatively charged peptides, the crucial role of water has been found in governing the FES. Systems having charged residues and phenylalanine in the peptide sequence also have been studied at high salt concentrations using unbiased simulations. In this case, only the positively charged peptides were found to aggregate through temperature-dependent hydrophobic and cation-π interactions. Overall, our study indicates that the negatively charged peptides are more likely to remain in the dilute phase under various conditions compared to the positively charged systems. The findings from our study would be helpful in designing and controlling systems to obtain LLPS behavior for therapeutic usage.