Physical theory of biological noise buffering by multicomponent phase separation

Chemically active wetting

Wetting of liquid droplets on passive surfaces is ubiquitous in our daily lives, and the governing physical laws are well understood. When surfaces become active, however, the governing laws of wetting remain elusive. Here, we propose chemically active wetting as a class of active systems where the surface is active due to a binding process that is maintained away from equilibrium. We derive the corresponding nonequilibrium thermodynamic theory and show that active binding fundamentally changes the wetting behavior, leading to steady, nonequilibrium states with droplet shapes reminiscent of a pancake or a mushroom. The origin of such anomalous shapes can be explained by mapping to electrostatics, where pairs of binding sinks and sources correspond to electrostatic dipoles along the triple line. This is an example of a more general analogy, where localized chemical activity gives rise to a multipole field of the chemical potential. The underlying physics is relevant for cells, where droplet-forming proteins can bind to membranes accompanied by the turnover of biological fuels.

Probing the Formation and Liquid-to-Solid Transition of FUS Condensates via the Lifetimes of Fluorescent Proteins

Liquid-liquid phase separation (LLPS) of biomolecules is a fundamental cellular process that is essential for maintaining homeostasis and facilitating biochemical activities. On the other hand, aberrant phase separation alters condensate fluidity and causes a transition from liquid-like condensates to solid-like condensates, which may lead to the formation of the pathological aggregations often observed in neurodegenerative diseases. Condensate fluidity is usually assessed by the fluorescence recovery after photobleaching. Here, we reveal that the fluorescence lifetimes of several fluorescent proteins are sensitive to LLPS and the liquid-to-solid transition. Furthermore, we identify several key residues that regulate the sensitivity of fluorescence lifetimes toward phase separation. Thus, we apply fluorescence lifetime imaging microscopy (FLIM) to visualize LLPS and the liquid-to-solid transition in living cells, demonstrating that FLIM is a nondestructive method for tracking changes in condensate fluidity in real time.

Concentration buffering and noise reduction in non-equilibrium phase-separating systems

Biomolecular condensates have been proposed to buffer intracellular concentrations and reduce noise. However, concentrations need not be buffered in multicomponent systems, leading to a non-constant saturation concentration (csat) when individual components are varied. Simplified equilibrium considerations suggest that noise reduction might be closely related to concentration buffering and that a fixed saturation concentration is required for noise reduction to be effective. Here, we present a theoretical analysis to demonstrate that these suggestions do not apply to mesoscopic fluctuating systems. We show that concentration buffering and noise reduction are distinct concepts, which cannot be used interchangeably. We further demonstrate that concentration buffering and a constant csat are neither necessary nor sufficient for noise reduction to be effective. Clarity about these concepts is important for studying the role of condensates in controlling cellular noise and for the interpretation of concentration relationships in cells. A record of this paper's transparent peer review process is included in the supplemental information.

Benchmarking residue-resolution protein coarse-grained models for simulations of biomolecular condensates

Intracellular liquid-liquid phase separation (LLPS) of proteins and nucleic acids is a fundamental mechanism by which cells compartmentalize their components and perform essential biological functions. Molecular simulations play a crucial role in providing microscopic insights into the physicochemical processes driving this phenomenon. In this study, we systematically compare six state-of-the-art sequence-dependent residue-resolution models to evaluate their performance in reproducing the phase behaviour and material properties of condensates formed by seven variants of the low-complexity domain (LCD) of the hnRNPA1 protein (A1-LCD)-a protein implicated in the pathological liquid-to-solid transition of stress granules. Specifically, we assess the HPS, HPS-cation-π, HPS-Urry, CALVADOS2, Mpipi, and Mpipi-Recharged models in their predictions of the condensate saturation concentration, critical solution temperature, and condensate viscosity of the A1-LCD variants. Our analyses demonstrate that, among the tested models, Mpipi, Mpipi-Recharged, and CALVADOS2 provide accurate descriptions of the critical solution temperatures and saturation concentrations for the multiple A1-LCD variants tested. Regarding the prediction of material properties for condensates of A1-LCD and its variants, Mpipi-Recharged stands out as the most reliable model. Overall, this study benchmarks a range of residue-resolution coarse-grained models for the study of the thermodynamic stability and material properties of condensates and establishes a direct link between their performance and the ranking of intermolecular interactions these models consider.

Chemically reactive and aging macromolecular mixtures. II. Phase separation and coarsening

In a companion paper, we put forth a thermodynamic model for complex formation via a chemical reaction involving multiple macromolecular species, which may subsequently undergo liquid-liquid phase separation and a further transition into a gel-like state. In the present work, we formulate a thermodynamically consistent kinetic framework to study the interplay between phase separation, chemical reaction, and aging in spatially inhomogeneous macromolecular mixtures. A numerical algorithm is also proposed to simulate domain growth from collisions of liquid and gel domains via passive Brownian motion in both two and three spatial dimensions. Our results show that the coarsening behavior is significantly influenced by the degree of gelation and Brownian motion. The presence of a gel phase inside condensates strongly limits the diffusive transport processes, and Brownian motion coalescence controls the coarsening process in systems with high area/volume fractions of gel-like condensates, leading to the formation of interconnected domains with atypical domain growth rates controlled by size-dependent translational and rotational diffusivities.

Phase Separation to Resolve Growth-Related Circuit Failures

Fluctuations in host cell growth poses a significant challenge to synthetic gene circuits, often disrupting circuit function. Existing solutions typically rely on circuit redesign with alternative topologies or additional control elements, yet a broadly applicable approach remains elusive. Here, we introduce a new strategy based on liquid-liquid phase separation (LLPS) to stabilize circuit performance. By engineering a self-activating circuit with transcription factors (TF) fused to an intrinsically disordered region (IDR), we enable the formation of TF condensates at the promoter region, maintaining local TF concentration despite growth-mediated dilution. This condensate formation preserves bistable memory in the self-activating circuit, demonstrating that phase separation can robustly counteract growth fluctuations, offering a novel design principle for resilient synthetic circuits.

Growing a single suspended perfect protein crystal in a fully noncontact manner

Nucleation is a fundamental process that determines the structure, morphology, and properties of crystalline materials, and is difficult to control because it is unpredictable. Here, we demonstrate a new method to control the protein crystal nucleation using a magnetic force, where we manipulate the movement and coalescence of nucleation precursors by adding paramagnetic salt into the crystallization solution to constrain the number and position of nucleation. We found that protein nucleation could be significantly affected by the magnetic force that the gradient magnetic fields generate. When the magnetization force is sufficiently enough, nucleation can be confined to the crystallization solution with no interface contact; therefore, only one crystal nucleus appears, which results in noncontact suspension growth of a single crystal in the crystallization solution system. Under these situations, the nucleation rate significantly decreases due to the coalescence of the dense liquid phase, and the crystal growth rate also decreases due to the suppression of convection, which increases the crystal quality. Our findings provide a new method for the noncontact control of crystal nucleation and demonstrate that externally applied physical environments can be used to affect the liquid-liquid phase separation process.

Selectivity of Complex Coacervation in Multiprotein Mixtures

Liquid-liquid phase separation of biomolecules is increasingly recognized as being relevant to various cellular functions, and complex coacervation of biomacromolecules, particularly proteins, is emerging as a key mechanism for this phenomenon. Complex coacervation is also being explored as a potential protein purification method due to its potential scalability, aqueous operation, and ability to produce a highly concentrated product. However, to date, most studies of complex coacervation have evaluated the phase behavior of a binary mixture of two oppositely charged macromolecules. Therefore, a comprehensive understanding of the phase behavior of complex biological mixtures is yet to be established. To address this, a panel of engineered proteins was designed to allow for quantitative analysis of the complex coacervation of individual proteins within a multicomponent mixture. The behavior of individual proteins was evaluated using a defined mixture of proteins that mimics the charge profile of the Escherichia coli proteome. To allow for the direct quantification of proteins in each phase, spectrally separated fluorescent proteins were used to construct the protein mixture. From this quantitative analysis, we observed that protein coacervation was synchronized in the mixture, which was distinctive from the behavior when each protein was evaluated in a single-protein system. Subtle differences in biophysical properties between the proteins, such as the ionization of individual charged residues and overall charge density, became noticeable in the mixture, which allowed us to elucidate parameters for protein complex coacervation. With this understanding, we successfully designed methods to enrich a range of proteins of interest from a mixture of proteins.

Where physics and biology meet

As part of this special issue on physics and biology, we invited several leading experts that bridge these disciplines to provide their views on the reciprocal contributions of each field and the benefits and challenges of working across physics and biology: introduction provided by Wallace Marshall.

Biomolecular condensates regulate cellular electrochemical equilibria

Control of the electrochemical environment in living cells is typically attributed to ion channels. Here, we show that the formation of biomolecular condensates can modulate the electrochemical environment in bacterial cells, which affects cellular processes globally. Condensate formation generates an electric potential gradient, which directly affects the electrochemical properties of a cell, including cytoplasmic pH and membrane potential. Condensate formation also amplifies cell-cell variability of their electrochemical properties due to passive environmental effect. The modulation of the electrochemical equilibria further controls cell-environment interactions, thus directly influencing bacterial survival under antibiotic stress. The condensate-mediated shift in intracellular electrochemical equilibria drives a change of the global gene expression profile. Our work reveals the biochemical functions of condensates, which extend beyond the functions of biomolecules driving and participating in condensate formation, and uncovers a role of condensates in regulating global cellular physiology.

Phase separation in soft repulsive polymer mixtures: foundation and implication for chromatin organization

Given the wide range of length scales, the analysis of polymer systems often requires coarse-graining, for which various levels of description may be possible depending on the phenomenon under consideration. Here, we provide a super-coarse grained description, where polymers are represented as a succession of mesosopic soft beads which are allowed to overlap with others. We then investigate the phase separation behaviors in a mixture of such homopolymers based on mean-field theory, and discuss universal aspects of the miscibility phase diagram in comparison with the numerical simulation. We also discuss an extension of our analysis to mixtures involving random copolymers, which might be interesting in the context of chromatin organization in a cell nucleus.

Dominance analysis to assess solute contributions to multicomponent phase equilibria

Phase separation in aqueous solutions of macromolecules underlies the generation of biomolecular condensates in cells. Condensates are membraneless bodies, representing dense, macromolecule-rich phases that coexist with the dilute, macromolecule-deficient phases. In cells, condensates comprise hundreds of different macromolecular and small molecule solutes. How do different solutes contribute to the driving forces for phase separation? To answer this question, we introduce a formalism we term energy dominance analysis. This approach rests on analysis of shapes of the dilute phase boundaries, slopes of tie lines, and changes to dilute phase concentrations in response to perturbations of concentrations of different solutes. The framework is based solely on conditions for phase equilibria in systems with arbitrary numbers of macromolecules and solution components. Its practical application relies on being able to measure dilute phase concentrations of the components of interest. The dominance framework is both theoretically facile and experimentally applicable. We present the formalism that underlies dominance analysis and establish its accuracy and flexibility by deploying it to analyze phase diagrams probed in simulations and in experiments.

Fundamental Aspects of Phase-Separated Biomolecular Condensates

Biomolecular condensates, formed through phase separation, are upending our understanding in much of molecular, cell, and developmental biology. There is an urgent need to elucidate the physicochemical foundations of the behaviors and properties of biomolecular condensates. Here we aim to fill this need by writing a comprehensive, critical, and accessible review on the fundamental aspects of phase-separated biomolecular condensates. We introduce the relevant theoretical background, present the theoretical basis for the computation and experimental measurement of condensate properties, and give mechanistic interpretations of condensate behaviors and properties in terms of interactions at the molecular and residue levels.

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.

Rules of selective condensation in cells

Liquid droplets form in cells to concentrate specific biomolecules (while excluding others) in order to perform specific functions. The molecular mechanisms that determine whether different macromolecules undergo co-partitioning or exclusion has so far remained elusive. Now, two studies uncover key principles underlying this selectivity.

Size Scaling of Condensates in Multicomponent Phase Separation

Constant proportionalities between cells and their intracellular organelles have been widely observed in various types of cells, known as intracellular size scaling. However, the mechanism underlying the size scaling and its modulation by environmental factors in multicomponent systems remain poorly understood. Here, we study the size scaling of membrane-less condensates using microdroplet-encapsulated minimalistic condensates formed by droplet microfluidics and mean-field theory. We demonstrate that the size scaling of condensates is an inherent characteristic of liquid-liquid phase separation. This concept is supported by experiments showing the occurrence of size scaling phenomena in various condensate systems and a generic lever rule acquired from mean-field theory. Moreover, it is found that the condensate-to-microdroplet scaling ratio can be affected by the solute and salt concentrations, with good agreement between experiments and predictions by theory. Notably, we identify a noise buffering mechanism whereby condensates composed of large macromolecules effectively maintain constant volumes and counteract concentration fluctuations of small molecules. This mechanism is achieved through the dynamic rearrangement of small molecules in and out of membrane-free interfaces. Our work provides crucial insights into understanding mechanistic principles that govern the size of cells and intracellular organelles as well as associated biological functions.

Charge block-driven liquid-liquid phase separation - mechanism and biological roles

Liquid-liquid phase separation (LLPS) has increasingly been found to play pivotal roles in a number of intracellular events and reactions, and has introduced a new paradigm in cell biology to explain protein-protein and enzyme-ligand interactions beyond conventional molecular and biochemical theories. LLPS is driven by the cumulative effects of weak and promiscuous interactions, including electrostatic, hydrophobic and cation-π interactions, among polypeptides containing intrinsically disordered regions (IDRs) and describes the macroscopic behaviours of IDR-containing proteins in an intracellular milieu. Recent studies have revealed that interactions between 'charge blocks' - clusters of like charges along the polypeptide chain - strongly induce LLPS and play fundamental roles in its spatiotemporal regulation. Introducing a new parameter, termed 'charge blockiness', into physicochemical models of disordered polypeptides has yielded a better understanding of how the intrinsic amino acid sequence of a polypeptide determines the spatiotemporal occurrence of LLPS within a cell. Charge blockiness might also explain why some post-translational modifications segregate within IDRs and how they regulate LLPS. In this Review, we summarise recent progress towards understanding the mechanism and biological roles of charge block-driven LLPS and discuss how this new characteristic parameter of polypeptides offers new possibilities in the fields of structural biology and cell biology.

Physical limits to acceleration of enzymatic reactions inside phase-separated compartments

We present a theoretical analysis of phase-separated compartments to facilitate enzymatic chemical reactions. While phase separation can facilitate reactions by increasing local concentration, it can also hinder the mobility of reactants. In particular, we find that the attractive interactions that concentrate reactants within the dense phase can inhibit reactions by lowering the mobility of the reactants. This mobility loss severely limits the potential to enhance reaction rates. Phase separation provides greater benefit in situations where multiple sequential reactions occur and/or high order reactions, provided the enzymes are unsaturated, transport to the condensate is not limiting, and the reactants are mobile. We show that mobility can be maintained if recruitment to the condensed phase is driven by multiple attractive moieties that can bind and release independently. However, the spacers necessary to ensure independence between stickers are prone to entangle with the dense phase scaffold. We find an optimal sticker affinity that balances the need for rapid binding/unbinding kinetics and minimal entanglement. Reaction rates can be accelerated by shrinking the size of the dense phase with a corresponding increase in the number of stickers. Our results showcase the potential capabilities of phase-separated compartments to act as biochemical reaction crucibles within living cells.

Phase separation provides a mechanism to drive phenotype switching

Phenotypic switching plays a crucial role in cell fate determination across various organisms. Recent experimental findings highlight the significance of protein compartmentalization via liquid-liquid phase separation in influencing such decisions. However, the precise mechanism through which phase separation regulates phenotypic switching remains elusive. To investigate this, we established a mathematical model that couples a phase separation process and a gene expression process with feedback. We used the chemical master equation theory and mean-field approximation to study the effects of phase separation on the gene expression products. We found that phase separation can cause bistability and bimodality. Furthermore, phase separation can control the bistable properties of the system, such as bifurcation points and bistable ranges. On the other hand, in stochastic dynamics, the droplet phase exhibits double peaks within a more extensive phase separation threshold range than the dilute phase, indicating the pivotal role of the droplet phase in cell fate decisions. These findings propose an alternative mechanism that influences cell fate decisions through the phase separation process. As phase separation is increasingly discovered in gene regulatory networks, related modeling research can help build biomolecular systems with desired properties and offer insights into explaining cell fate decisions.

MolPhase, an advanced prediction algorithm for protein phase separation

We introduce MolPhase, an advanced algorithm for predicting protein phase separation (PS) behavior that improves accuracy and reliability by utilizing diverse physicochemical features and extensive experimental datasets. MolPhase applies a user-friendly interface to compare distinct biophysical features side-by-side along protein sequences. By additional comparison with structural predictions, MolPhase enables efficient predictions of new phase-separating proteins and guides hypothesis generation and experimental design. Key contributing factors underlying MolPhase include electrostatic pi-interactions, disorder, and prion-like domains. As an example, MolPhase finds that phytobacterial type III effectors (T3Es) are highly prone to homotypic PS, which was experimentally validated in vitro biochemically and in vivo in plants, mimicking their injection and accumulation in the host during microbial infection. The physicochemical characteristics of T3Es dictate their patterns of association for multivalent interactions, influencing the material properties of phase-separating droplets based on the surrounding microenvironment in vivo or in vitro. Robust integration of MolPhase's effective prediction and experimental validation exhibit the potential to evaluate and explore how biomolecule PS functions in biological systems.

GENESIS CGDYN: large-scale coarse-grained MD simulation with dynamic load balancing for heterogeneous biomolecular systems

Residue-level coarse-grained (CG) molecular dynamics (MD) simulation is widely used to investigate slow biological processes that involve multiple proteins, nucleic acids, and their complexes. Biomolecules in a large simulation system are distributed non-uniformly, limiting computational efficiency with conventional methods. Here, we develop a hierarchical domain decomposition scheme with dynamic load balancing for heterogeneous biomolecular systems to keep computational efficiency even after drastic changes in particle distribution. These schemes are applied to the dynamics of intrinsically disordered protein (IDP) droplets. During the fusion of two droplets, we find that the changes in droplet shape correlate with the mixing of IDP chains. Additionally, we simulate large systems with multiple IDP droplets, achieving simulation sizes comparable to those observed in microscopy. In our MD simulations, we directly observe Ostwald ripening, a phenomenon where small droplets dissolve and their molecules redeposit into larger droplets. These methods have been implemented in CGDYN of the GENESIS software, offering a tool for investigating mesoscopic biological processes using the residue-level CG models.

Mitigating transcription noise via protein sharing in syncytial cells

Bursty transcription allows nuclei to concentrate the work of transcribing mRNA into short, intermittent intervals, potentially reducing transcriptional interference. However, bursts of mRNA production can increase noise in protein abundances. Here, we formulate models for gene expression in syncytia, or multinucleate cells, showing that protein abundance noise may be mitigated locally via spatial averaging of diffuse proteins. Our modeling shows a universal reduction in protein noise, which increases with the average number of nuclei per cell and persists even when the number of nuclei is itself a random variable. Experimental data comparing distributions of a cyclin mRNA that is conserved between brewer's yeast and a closely related filamentous fungus Ashbya gossypii confirm that syncytism is permissive of greater levels of transcriptional noise. Our findings suggest that division of transcriptional labor between nuclei allows syncytia to sidestep tradeoffs between efficiency and precision of gene expression.

Selectivity of Complex Coacervation in Multi-Protein Mixtures

Liquid-liquid phase separation of biomolecules is increasingly recognized as relevant to various cellular functions, and complex coacervation of biomacromolecules, particularly proteins, is emerging as a key mechanism for this phenomenon. Complex coacervation is also being explored as a potential protein purification method due to its potential scalability, aqueous operation, and ability to produce a highly concentrated product. However, to date most studies of complex coacervation have evaluated the phase behavior of a binary mixture of two oppositely charged macromolecules. Therefore, a comprehensive understanding of the phase behavior of complex biological mixtures has yet to be established. To address this, a panel of engineered proteins was designed to allow for quantitative analysis of the complex coacervation of individual proteins within a multi-component mixture. The behavior of individual proteins was evaluated using a defined mixture of proteins that mimics the charge profile of the E. coli proteome. To allow for direct quantification of proteins in each phase, spectrally separated fluorescent proteins were used to construct the protein mixture. From this quantitative analysis, we observed that the coacervation behavior of individual proteins in the mixture was consistent with each other, which was distinctive from the behavior when each protein was evaluated in a single-protein system. Subtle differences in biophysical properties between the proteins became noticeable in the mixture, which allowed us to elucidate parameters for protein complex coacervation. With this understanding, we successfully designed methods to enrich a range of proteins of interest from a mixture of proteins.

Dominance Analysis: A formalism to uncover dominant energetic contributions to biomolecular condensate formation in multicomponent systems

Phase separation in aqueous solutions of macromolecules is thought to underlie the generation of biomolecular condensates in cells. Condensates are membraneless bodies, representing dense, macromolecule-rich phases that coexist with the dilute, macromolecule-deficient phase. In cells, condensates comprise hundreds of different macromolecular and small molecule solutes. Do all components contribute equally or very differently to the driving forces for phase separation? Currently, we lack a coherent formalism to answer this question, a gap we remedy in this work through the introduction of a formalism we term energy dominance analysis. This approach rests on model-free analysis of shapes of the dilute arms of phase boundaries, slopes of tie lines, and changes to dilute phase concentrations in response to perturbations of concentrations of different solutes. We present the formalism that underlies dominance analysis, and establish its accuracy and flexibility by deploying it to analyse phase spaces probed in silico, in vitro , and in cellulo .

Thermodynamic modulation of gephyrin condensation by inhibitory synapse components

Phase separation drives compartmentalization of intracellular contents into various biomolecular condensates. Individual condensate components are thought to differentially contribute to the organization and function of condensates. However, how intermolecular interactions among constituent biomolecules modulate the phase behaviors of multicomponent condensates remains unclear. Here, we used core components of the inhibitory postsynaptic density (iPSD) as a model system to quantitatively probe how the network of intra- and intermolecular interactions defines the composition and cellular distribution of biomolecular condensates. We found that oligomerization-driven phase separation of gephyrin, an iPSD-specific scaffold, is critically modulated by an intrinsically disordered linker region exhibiting minimal homotypic attractions. Other iPSD components, such as neurotransmitter receptors, differentially promote gephyrin condensation through distinct binding modes and affinities. We further demonstrated that the local accumulation of scaffold-binding proteins at the cell membrane promotes the nucleation of gephyrin condensates in neurons. These results suggest that in multicomponent systems, the extent of scaffold condensation can be fine-tuned by scaffold-binding factors, a potential regulatory mechanism for self-organized compartmentalization in cells.

Mechanosensitivity of phase separation in an elastic gel

Liquid-liquid phase separation (LLPS) in binary or multi-component solutions is a well-studied subject in soft matter with extensive applications in biological systems. In recent years, several experimental studies focused on LLPS of solutes in hydrated gels, where the formation of coexisting domains induces elastic deformations within the gel. While the experimental studies report unique physical characteristics of these systems, such as sensitivity to mechanical forces and stabilization of multiple, periodic phase-separated domains, the theoretical understanding of such systems and the role of long-range interactions have not emphasized the nonlinear nature of the equilibrium binodal for strong segregation of the solute. In this paper, we formulate a generic, mean-field theory of a hydrated gel in the presence of an additional solute which changes the elastic properties of the gel. We derive equations for the equilibrium binodal of the phase separation of the solvent and solute and show that the deformations induced by the solute can result in effective long-range interactions between phase-separating solutes that can either enhance or, in the case of externally applied pressure, suppress phase separation of the solute relative to the case where there is no gel. This causes the coexisting concentrations at the binodal to depend on the system-wide average concentration, in contrast to the situation for phase separation in the absence of the gel.

Haploinsufficient Transcription Factors in Myeloid Neoplasms

Many transcription factors (TFs) function as tumor suppressor genes with heterozygous phenotypes, yet haploinsufficiency generally has an underappreciated role in neoplasia. This is no less true in myeloid cells, which are normally regulated by a delicately balanced and interconnected transcriptional network. Detailed understanding of TF dose in this circuitry sheds light on the leukemic transcriptome. In this review, we discuss the emerging features of haploinsufficient transcription factors (HITFs). We posit that: (a) monoallelic and biallelic losses can have distinct cellular outcomes; (b) the activity of a TF exists in a greater range than the traditional Mendelian genetic doses; and (c) how a TF is deleted or mutated impacts the cellular phenotype. The net effect of a HITF is a myeloid differentiation block and increased intercellular heterogeneity in the course of myeloid neoplasia.

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.

Phase-Diagram Observation of Liquid-Liquid Phase Separation in the Poly(l-lysine)/ATP System and a Proposal for Diagram-Based Application Strategy

Liquid-liquid phase separation (LLPS) is essential to understanding the biomacromolecule compartmentalization in living cells and to developing soft-matter structures for chemical reactions and drug delivery systems. However, the importance of detailed experimental phase diagrams of modern LLPS systems tends to be overlooked in recent times. Even for the poly(l-lysine) (PLL)/ATP system, which is one of the most widely used LLPS models, any detailed phase diagram of LLPS has not been reported. Herein, we report the first phase diagram of the PLL/ATP system and demonstrate the feasibility of phase-diagram-based research design for understanding the physical properties of LLPS systems and realizing biophysical and medical applications. We established an experimentally handy model for the droplet formation-disappearance process by generating a concentration gradient in a chamber for extracting a suitable condition on the phase diagram, including the two-phase droplet region. As a proof of concept of pharmaceutical application, we added a human immunoglobulin G (IgG) solution to the PLL/ATP system. Using the knowledge from the phase diagram, we realized the formation of IgG/PLL droplets in a pharmaceutically required IgG concentration of ca. 10 mg/mL. Thus, this study provides guidance for using the phase diagram to analyze and utilize LLPS.

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.

Membrane-less compartments in the nucleus: Separated or connected phases?

In recent years, it has become increasingly clear that many nuclear membrane-less compartments have liquid-like properties and may form through the physicochemical process of phase separation. In this review, we will first discuss how various nuclear compartments, such as the genome, transcription compartments, and nuclear bodies are formed through phase separation. Then, we propose that inter-compartmental communications can also be prevalent and may be mediated by inter-compartmental diffusion of macromolecules, fusion among different compartments, and transient or stable contacts among nuclear compartments. Understanding how nuclear compartments communicate with each other represents an exciting new area of research and may reveal important insights about cellular functions and uncover previously under-appreciated disease mechanisms.

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.

Condensation Goes Viral: A Polymer Physics Perspective

The past decade has seen a revolution in our understanding of how the cellular environment is organized, where an incredible body of work has provided new insights into the role played by membraneless organelles. These rapid advancements have been made possible by an increasing awareness of the peculiar physical properties that give rise to such bodies and the complex biology that enables their function. Viral infections are not extraneous to this. Indeed, in host cells, viruses can harness existing membraneless compartments or, even, induce the formation of new ones. By hijacking the cellular machinery, these intracellular bodies can assist in the replication, assembly, and packaging of the viral genome as well as in the escape of the cellular immune response. Here, we provide a perspective on the fundamental polymer physics concepts that may help connect and interpret the different observed phenomena, ranging from the condensation of viral genomes to the phase separation of multicomponent solutions. We complement the discussion of the physical basis with a description of biophysical methods that can provide quantitative insights for testing and developing theoretical and computational models.

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.

The maximum solubility product marks the threshold for condensation of multivalent biomolecules

Clustering of weakly interacting multivalent biomolecules underlies the formation of membraneless compartments known as condensates. As opposed to single-component (homotypic) systems, the concentration dependence of multicomponent (heterotypic) condensate formation is not well understood. We previously proposed the solubility product (SP), the product of monomer concentrations in the dilute phase, as a tool for understanding the concentration dependence of multicomponent systems. In this study, we further explore the limits of the SP concept using spatial Langevin dynamics and rule-based stochastic simulations. We show, for a variety of idealized molecular structures, how the maximum SP coincides with the onset of the phase transition, i.e., the formation of large clusters. We reveal the importance of intracluster binding in steering the free and cluster phase molecular distributions. We also show how structural features of biomolecules shape the SP profiles. The interplay of flexibility, length, and steric hindrance of linker regions controls the phase transition threshold. Remarkably, when SPs are normalized to nondimensional variables and plotted against the concentration scaled to the threshold for phase transition, the curves all coincide independent of the structural features of the binding partners. Similar coincidence is observed for the normalized clustering versus concentration plots. Overall, the principles derived from these systematic models will help guide and interpret in vitro and in vivo experiments on the biophysics of biomolecular condensates.

Developments in describing equilibrium phase transitions of multivalent associative macromolecules

Biomolecular condensates are distinct cellular bodies that form and dissolve reversibly to organize cellular matter and biochemical reactions in space and time. Condensates are thought to form and dissolve under the influence of spontaneous and driven phase transitions of multivalent associative macromolecules. These include phase separation, which is defined by segregation of macromolecules from the solvent or from one another, and percolation or gelation, which is an inclusive networking transition driven by reversible associations among multivalent macromolecules. Considerable progress has been made to model sequence-specific phase transitions, especially for intrinsically disordered proteins. Here, we summarize the state-of-the-art of theories and computations aimed at understanding and modeling sequence-specific, thermodynamically controlled, coupled associative and segregative phase transitions of archetypal multivalent macromolecules.

Membrane reshaping by protein condensates

Proteins can organize into dynamic, functionally important assemblies on fluid membrane surfaces. Phase separation has emerged as an important mechanism for forming such protein assemblies on the membrane during cell signaling, endocytosis, and cytoskeleton regulation. Protein-protein phase separation thus adds novel fluid mosaics to the classical Singer and Nicolson model. Protein condensates formed in this process can modulate membrane morphologies. This is evident from recent reports of protein condensate-driven membrane reshaping in processes such as endocytosis, autophagosome formation, and protein storage vacuole morphogenesis in plants. Lateral phase separation (on the membrane surface) of peripheral curvature coupling proteins can modulate such membrane morphological transitions. Additionally, three-dimensional protein phase separation can result in droplets that through adhesion can affect membrane shape changes. How do these condensate-driven curvature generation mechanisms contrast with the classically recognized scaffolding and amphipathic helix insertion activities of specific membrane remodeling proteins? A salient feature of these condensate-driven membrane activities is that they depend upon both macroscopic features (such as interfacial energies of the condensate, membrane, and cytosol) as well as microscopic, molecular-level interactions (such as protein-lipid binding). This review highlights the current understanding of the mechanisms underlying curvature generation by protein condensates in various biological pathways.

An Introduction to the Stickers-and-Spacers Framework as Applied to Biomolecular Condensates

Cellular organization is determined by a combination of membrane-bound and membrane-less biomolecular assemblies that range from clusters of tens of molecules to micrometer-sized cellular bodies. Over the last decade, membrane-less assemblies have come to be referred to as biomolecular condensates, reflecting their ability to condense specific molecules with respect to the remainder of the cell. In many cases, the physics of phase transitions provides a conceptual framework and a mathematical toolkit to describe the assembly, maintenance, and dissolution of biomolecular condensates. Among the various quantitative and qualitative models applied to understand intracellular phase transitions, the stickers-and-spacers framework offers an intuitive yet rigorous means to map biomolecular sequences and structure to the driving forces needed for higher-order assembly. This chapter introduces the fundamental concepts behind the stickers-and-spacers model, considers its application to different biological systems, and discusses limitations and misconceptions around the model.

Analytical Formulation and Field-Theoretic Simulation of Sequence-Specific Phase Separation of Protein-Like Heteropolymers with Short- and Long-Spatial-Range Interactions

A theory for sequence-dependent liquid-liquid phase separation (LLPS) of intrinsically disordered proteins (IDPs) in the study of biomolecular condensates is formulated by extending the random phase approximation (RPA) and field-theoretic simulation (FTS) of heteropolymers with spatially long-range Coulomb interactions to include the fundamental effects of short-range, hydrophobic-like interactions between amino acid residues. To this end, short-range effects are modeled by Yukawa interactions between multiple nonelectrostatic charges derived from an eigenvalue decomposition of pairwise residue-residue contact energies. Chain excluded volume is afforded by incompressibility constraints. A mean-field approximation leads to an effective Flory-Huggins χ parameter, which, in conjunction with RPA, accounts for the contact-interaction effects of amino acid composition and the sequence-pattern effects of long-range electrostatics in IDP LLPS, whereas FTS based on the formulation provides full sequence dependence for both short- and long-range interactions. This general approach is illustrated here by applications to variants of a natural IDP in the context of several different amino-acid interaction schemes as well as a set of different model hydrophobic-polar sequences sharing the same composition. Effectiveness of the methodology is verified by coarse-grained explicit-chain molecular dynamics simulations.

The stoichiometric interaction model for mesoscopic MD simulations of liquid-liquid phase separation

Liquid-liquid phase separation (LLPS) has received considerable attention in recent years for explaining the formation of cellular biomolecular condensates. The fluidity and the complexity of their components make molecular simulation approaches indispensable for gaining structural insights. Domain-resolution mesoscopic model simulations have been explored for cases in which condensates are formed by multivalent proteins with tandem domains. One problem with this approach is that interdomain pairwise interactions cannot regulate the valency of the binding domains. To overcome this problem, we propose a new potential, the stoichiometric interaction (SI) potential. First, we verified that the SI potential maintained the valency of the interacting domains for the test systems. We then examined a well-studied LLPS model system containing tandem repeats of SH3 domains and proline-rich motifs. We found that the SI potential alone cannot reproduce the phase diagram of LLPS quantitatively. We had to combine the SI and a pairwise interaction; the former and the latter represent the specific and nonspecific interactions, respectively. Biomolecular condensates with the mixed SI and pairwise interaction exhibited fluidity, whereas those with the pairwise interaction alone showed no detectable diffusion. We also compared the phase diagrams of the systems containing different numbers of tandem domains with those obtained from the experiments and found quantitative agreement in all but one case.

Affinity and Valence Impact the Extent and Symmetry of Phase Separation of Multivalent Proteins

Biomolecular self-assembly spatially segregates proteins with a limited number of binding sites (valence) into condensates that coexist with a dilute phase. We develop a many-body lattice model for a three-component system of proteins with fixed valence in a solvent. We compare the predictions of the model to experimental phase diagrams that we measure in vivo, which allows us to vary specifically a binding site's affinity and valency. We find that the extent of phase separation varies exponentially with affinity and increases with valency. Valency alone determines the symmetry of the phase diagram.

Model biomolecular condensates have heterogeneous structure quantitatively dependent on the interaction profile of their constituent macromolecules

Biomolecular condensates play numerous roles in cells by selectively concentrating client proteins while excluding others. These functions are likely to be sensitive to the spatial organization of the scaffold proteins forming the condensate. We use coarse-grained molecular simulations to show that model intrinsically-disordered proteins phase separate into a heterogeneous, structured fluid characterized by a well-defined length scale. The proteins are modelled as semi-flexible polymers with punctate, multifunctional binding sites in good solvent conditions. Their dense phase is highly solvated with a spatial structure that is more sensitive to the separation of the binding sites than their affinity. We introduce graph theoretic measures to quantify their heterogeneity, and find that it increases with increasing binding site number, and exhibits multi-timescale dynamics. The model proteins also swell on passing from the dilute solution to the dense phase. The simulations predict that the structure of the dense phase is modulated by the location and affinity of binding sites distant from the termini of the proteins, while sites near the termini more strongly affect its phase behaviour. The relations uncovered between the arrangement of weak interaction sites on disordered proteins and the material properties of their dense phase can be experimentally tested to give insight into the biophysical properties, pathological effects, and rational design of biomolecular condensates.

Multivalent interactions between molecular components involved in fast endophilin mediated endocytosis drive protein phase separation

A specific group of transmembrane receptors, including the β1-adrenergic receptor (β1-AR), is internalized through a non-clathrin pathway known as Fast Endophilin Mediated Endocytosis (FEME). A key question is: how does the endocytic machinery assemble and how is it modulated by activated receptors during FEME. Here we show that endophilin, a major regulator of FEME, undergoes a phase transition into liquid-like condensates, which facilitates the formation of multi-protein assemblies by enabling the phase partitioning of endophilin binding proteins. The phase transition can be triggered by specific multivalent binding partners of endophilin in the FEME pathway such as the third intracellular loop (TIL) of the β1-AR, and the C-terminal domain of lamellipodin (LPD). Other endocytic accessory proteins can either partition into, or target interfacial regions of, these condensate droplets, and LPD also phase separates with the actin polymerase VASP. On the membrane, TIL promotes protein clustering in the presence of endophilin and LPD C-terminal domain. Our results demonstrate how the multivalent interactions between endophilin, LPD, and TIL regulate protein assembly formation on the membrane, providing mechanistic insights into the priming and initiation steps of FEME.

Here the authors show that protein phase separation is a key mechanism in cellular receptor internalization via fast endophilin mediated endocytosis (FEME). Phase separation facilitates multivalent FEME-protein assembly in this clathrin-independent pathway.

Analytical Solution to the Flory-Huggins Model

A self-consistent analytical solution for binodal concentrations of the two-component Flory-Huggins phase separation model is derived. We show that this form extends the validity of the Ginzburg-Landau expansion away from the critical point to cover the whole phase space. Furthermore, this analytical solution reveals an exponential scaling law of the dilute phase binodal concentration as a function of the interaction strength and chain length. We demonstrate explicitly the power of this approach by fitting experimental protein liquid-liquid phase separation boundaries to determine the effective chain length and solute-solvent interaction energies. Moreover, we demonstrate that this strategy allows us to resolve differences in interaction energy contributions of individual amino acids. This analytical framework can serve as a new way to decode the protein sequence grammar for liquid-liquid phase separation.

Connected Peptide Modules Enable Controlled Co-Existence of Self-Assembled Fibers Inside Liquid Condensates

Supramolecular self-assembly of fibrous components and liquid-liquid phase separation are at the extremes of the order-to-disorder spectrum. They collectively play key roles in cellular organization. It is still a major challenge to design systems where both highly ordered nanostructures and liquid-liquid phase-separated domains can coexist. We present a three-component assembly approach that generates fibrous domains that exclusively form inside globally disordered, liquid condensates. This is achieved by creating amphiphilic peptides that combine the features of fibrillar assembly (the amyloid domain LVFFA) and complex coacervation (oligo-arginine and adenosine triphosphate (ATP)) in one peptide, namely, LVFFAR₉. When this hybrid peptide is mixed in different ratios with R₉ and ATP, we find that conditions can be created where fibrous assembly is exclusively observed inside liquid coacervates. Through fluorescence and atomic force microscopy characterization, we investigate the dynamic evolution of ordered and disordered features over time. It was observed that the fibers nucleate and mature inside the droplets and that these fiber-containing liquid droplets can also undergo fusion, showing that the droplets remain liquid-like. Our work thus generates opportunities for the design of ordered structures within the confined environment of biomolecular condensates, which may be useful to create supramolecular materials in defined compartments and as model systems that can enhance understanding of ordering principles in biology.

Evolved interactions stabilize many coexisting phases in multicomponent liquids

Phase separation has emerged as an essential concept for the spatial organization inside biological cells. However, despite the clear relevance to virtually all physiological functions, we understand surprisingly little about what phases form in a system of many interacting components, like in cells. Here we introduce a numerical method based on physical relaxation dynamics to study the coexisting phases in such systems. We use our approach to optimize interactions between components, similar to how evolution might have optimized the interactions of proteins. These evolved interactions robustly lead to a defined number of phases, despite substantial uncertainties in the initial composition, while random or designed interactions perform much worse. Moreover, the optimized interactions are robust to perturbations, and they allow fast adaption to new target phase counts. We thus show that genetically encoded interactions of proteins provide versatile control of phase behavior. The phases forming in our system are also a concrete example of a robust emergent property that does not rely on fine-tuning the parameters of individual constituents.

Liquid-Liquid Phase Separation in Cancer Signaling, Metabolism and Anticancer Therapy

The cancer state is thought to be maintained by genetic and epigenetic changes that drive a cancer-promoting gene expression program. However, recent results show that cellular states can be also stably maintained by the reorganization of cell structure leading to the formation of biological condensates via the process of liquid-liquid phase separation. Here, we review the data showing cancer-specific biological condensates initiated by mutant oncoproteins, RNA-binding proteins, or lincRNAs that regulate oncogenic gene expression programs and cancer metabolism. Effective anticancer drugs may specifically partition into oncogenic biological condensates (OBC).

Rich Phase Separation Behavior of Biomolecules

Phase separation is a thermodynamic process leading to the formation of compositionally distinct phases. For the past few years, numerous works have shown that biomolecular phase separation serves as biogenesis mechanisms of diverse intracellular condensates, and aberrant phase transitions are associated with disease states such as neurodegenerative diseases and cancers. Condensates exhibit rich phase behaviors including multiphase internal structuring, noise buffering, and compositional tunability. Recent studies have begun to uncover how a network of intermolecular interactions can give rise to various biophysical features of condensates. Here, we review phase behaviors of biomolecules, particularly with regard to regular solution models of binary and ternary mixtures. We discuss how these theoretical frameworks explain many aspects of the assembly, composition, and miscibility of diverse biomolecular phases, and highlight how a model-based approach can help elucidate the detailed thermodynamic principle for multicomponent intracellular phase separation.