LASSI: A lattice model for simulating phase transitions of multivalent proteins

Computer-Aided Drug Discovery for Undruggable Targets

Undruggable targets are those of therapeutical significance but challenging for conventional drug design approaches. Such targets often exhibit unique features, including highly dynamic structures, a lack of well-defined ligand-binding pockets, the presence of highly conserved active sites, and functional modulation by protein-protein interactions. Recent advances in computational simulations and artificial intelligence have revolutionized the drug design landscape, giving rise to innovative strategies for overcoming these obstacles. In this review, we highlight the latest progress in computational approaches for drug design against undruggable targets, present several successful case studies, and discuss remaining challenges and future directions. Special emphasis is placed on four primary target categories: intrinsically disordered proteins, protein allosteric regulation, protein-protein interactions, and protein degradation, along with discussion of emerging target types. We also examine how AI-driven methodologies have transformed the field, from applications in protein-ligand complex structure prediction and virtual screening to de novo ligand generation for undruggable targets. Integration of computational methods with experimental techniques is expected to bring further breakthroughs to overcome the hurdles of undruggable targets. As the field continues to evolve, these advancements hold great promise to expand the druggable space, offering new therapeutic opportunities for previously untreatable diseases.

Multiphasic protein condensation governed by shape and valency

Liquid-liquid phase separation (LLPS) of biological macromolecules leads to the formation of various membraneless organelles. The multilayered and multiphasic form of LLPS can mediate complex cellular functions; however, the determinants of its topological features are not fully understood. Herein, we focus on synaptic proteins consisting of Ca2+/calmodulin-dependent protein kinase II (CaMKII) and its interacting partners and present a computational model that reproduces forms of LLPS, including a form of two-phase condensates, phase-in-phase (PIP) organization. The model analyses reveal that the PIP formation requires competitive binding between the proteins. The PIP forms only when CaMKII has high valency and a short linker length. Such CaMKII exhibits low surface tension, a modular structure, and slow diffusion, enabling it to stay in small biochemical domains for a long time, which is necessary for synaptic plasticity. Thus, the computational modeling reveals new structure-function relationships for CaMKII as a synaptic memory unit.

Impact of Coiled-Coil Domains on the Phase Behavior of Biomolecular Condensates

Spatial organization is fundamental to cells, with biomolecular condensates as a key subset. Many studies show that folded domains play important roles in condensate formation by facilitating interactions. However, little is known about how the geometry and structure of folded domains impact condensate formation. Using coarse-grained simulations, we investigated a model system of two multivalent proteins, one containing a coiled-coil domain (CCD), which undergoes liquid-liquid phase separation (LLPS). We found that CCDs promote LLPS by preventing loop-closure defects, enabling protein networking. Replacing the CCD with a flexible linker abolishes LLPS due to formation of oligomeric clusters. There is a critical length of the CCD where the system rapidly changes from no LLPS to LLPS at low concentrations. This highlights their potential in regulating condensate formation and properties. This study provides insights into the phase behavior of biomolecular condensates and offers a framework for designing synthetic condensates with tunable phase behaviors.

Exploring RNA destabilization mechanisms in biomolecular condensates through atomistic simulations

Biomolecular condensates are currently recognized to play a key role in organizing cellular space and in orchestrating biochemical processes. Despite an increasing interest in characterizing their internal organization at the molecular scale, not much is known about how the densely crowded environment within these condensates affects the structural properties of recruited macromolecules. Here, we adopted explicit-solvent all-atom simulations based on a combination of enhanced sampling approaches to investigate how the conformational ensemble of an RNA hairpin is reshaped in a highly concentrated peptide solution that mimics the interior of a biomolecular condensate. Our simulations indicate that RNA structure is greatly perturbed by this distinctive physico-chemical environment, which weakens RNA secondary structure and promotes extended nonnative conformations. The resulting high-resolution picture reveals that RNA unfolding is driven by the effective solvation of nucleobases through hydrogen bonding and stacking interactions with surrounding peptides. This solvent effect can be modulated by the amino acid composition of the model condensate as proven by the differential RNA behavior observed in the case of arginine-rich and lysine-rich peptides.

Differential interactions determine anisotropies at interfaces of RNA-based biomolecular condensates

Biomolecular condensates form via macromolecular phase separation. Here, we report results from our characterization of synthetic condensates formed by phase separation of mixtures comprising two types of RNA molecules and the biocompatible polymer polyethylene glycol. Purine-rich RNAs are scaffolds that drive phase separation via heterotypic interactions. Conversely, pyrimidine-rich RNA molecules are adsorbents defined by weaker heterotypic interactions. They adsorb onto and wet the interfaces of coexisting phases formed by scaffolds. Lattice-based simulations reproduce the phenomenology observed in experiments and these simulations predict that scaffolds and adsorbents have different non-random orientational preferences at interfaces. Dynamics at interfaces were probed using single-molecule tracking of fluorogenic probes bound to RNA molecules. These experiments revealed dynamical anisotropy at interfaces whereby motions of probe molecules parallel to the interface are faster than motions perpendicular to the interface. Taken together, our findings have broad implications for designing synthetic condensates with tunable interfacial properties.

Backbone-mediated weakening of pairwise interactions enables percolation in peptide-based mimics of protein condensates

Biomolecular condensates formed by intrinsically disordered proteins (IDPs) are semidilute solutions. These can be approximated as solutions of blob-sized segments, which are peptide-sized motifs. We leveraged the blob picture and molecular dynamics simulations to quantify differences between inter-residue interactions in model compound and peptide-based mimics of dense versus dilute phases. The all-atom molecular dynamics simulations use a polarizable forcefield. In model compound solutions, the interactions between aromatic residues are stronger than interactions between cationic and aromatic residues. This holds in dilute and dense phases. Cooperativity within dense phases enhances pairwise interactions leading to finite-sized nanoscale clusters. The results for peptide-based condensates paint a different picture. Backbone amides add valence to the associating molecules. While this enhances pairwise inter-residue interactions in dilute phases, it weakens pair interactions in dense phases, doing so in a concentration-dependent manner. Weakening of pair interactions enables fluidization characterized by short-range order and long-range disorder. The higher valence afforded by the peptide backbone generates system-spanning networks. As a result, dense phases of peptides are best described as percolated network fluids. Overall, our results show how peptide backbones enhance pairwise interactions in dilute phases while weakening these interactions to enable percolation within dense phases.

Single-fluorogen imaging reveals distinct environmental and structural features of biomolecular condensates

Biomolecular condensates are viscoelastic materials. Simulations predict that condensates formed by intrinsically disordered proteins are network fluids defined by spatially inhomogeneous organization of the underlying molecules. Here, we test these predictions and find that molecules within condensates are organized into slow-moving nanoscale clusters and fast-moving dispersed molecules. These results, obtained using single-fluorogen tracking and super-resolution imaging of different disordered protein-based condensates, affirm the predicted spatially inhomogeneous organization of molecules within condensates. We map the internal environments and interfaces of condensates using fluorogens that localize differently to the interiors versus interface between dilute phase and condensate. We show that nanoscale clusters within condensates are more hydrophobic than regions outside the clusters, and regions within condensates that lie outside clusters are more hydrophobic than coexisting dilute phases. Our findings provide a structural and dynamical basis for the viscoelasticity of condensates.

Electrostatics of salt-dependent reentrant phase behaviors highlights diverse roles of ATP in biomolecular condensates

Liquid-liquid phase separation (LLPS) involving intrinsically disordered protein regions (IDRs) is a major physical mechanism for biological membraneless compartmentalization. The multifaceted electrostatic effects in these biomolecular condensates are exemplified here by experimental and theoretical investigations of the different salt- and ATP-dependent LLPSs of an IDR of messenger RNA-regulating protein Caprin1 and its phosphorylated variant pY-Caprin1, exhibiting, for example, reentrant behaviors in some instances but not others. Experimental data are rationalized by physical modeling using analytical theory, molecular dynamics, and polymer field-theoretic simulations, indicating that interchain ion bridges enhance LLPS of polyelectrolytes such as Caprin1 and the high valency of ATP-magnesium is a significant factor for its colocalization with the condensed phases, as similar trends are observed for other IDRs. The electrostatic nature of these features complements ATP's involvement in π-related interactions and as an amphiphilic hydrotrope, underscoring a general role of biomolecular condensates in modulating ion concentrations and its functional ramifications.

Lattice Models: Non-Conventional simulation methods for mechanobiology

Computational methods represent a powerful tool to explore biophysical phenomena occurring at small scales and hence difficult to observe through experimental setups. In detail, they can provide a support to mechanobiology, with the aim of understanding the behavior of living cells interacting with the surrounding environment. To this end, lattice models can provide a simulation framework that is highly reliable and easy to implement, even for simulations involving large deformations and topological changes during time evolution. In this review article, elastic network models for studying biological molecules are described, several lattice spring models for investigating cell behaviors are discussed, and the adoption of lattice beam models for biomimetic structures design is presented. The lattice modelling approaches could be regarded as a valuable option to conduct in-silico experiments and consolidate the emergent mechanobiology research field.

Driving Forces of RNA Condensation Revealed through Coarse-Grained Modeling with Explicit Mg2

RNAs are major drivers of phase separation in the formation of biomolecular condensates, and can undergo protein-free phase separation in the presence of divalent ions or crowding agents. Much remains to be understood regarding how the complex interplay of base stacking, base pairing, electrostatics, ion interactions, and particularly structural propensities governs RNA phase behavior. Here we develop an intermediate resolution model for condensates of RNAs (iConRNA) that can capture key local and long-range structure features of dynamic RNAs and simulate their spontaneous phase transitions with Mg2+. Representing each nucleotide using 6-7 beads, iConRNA accurately captures base stacking and pairing and includes explicit Mg2+. The model does not only reproduce major conformational properties of poly(rA) and poly(rU), but also correctly folds small structured RNAs and predicts their melting temperatures. With an effective model of explicit Mg2+, iConRNA successfully recapitulates experimentally observed lower critical solution temperature phase separation of poly(rA) and triplet repeats, and critically, the nontrivial dependence of phase transitions on RNA sequence, length, concentration, and Mg2+ level. Further mechanistic analysis reveals a key role of RNA folding in modulating phase separation as well as its temperature and ion dependence, besides other driving forces such as Mg2+-phosphate interactions, base stacking, and base pairing. These studies also support iConRNA as a powerful tool for direct simulation of RNA-driven phase transitions, enabling molecular studies of how RNA conformational dynamics and its response to complex condensate environment control the phase behavior and condensate material properties.

SIGNIFICANCE STATEMENT

Dynamic RNAs and proteins are major drivers of biomolecular phase separation that has been recently discovered to underlie numerous biological processes and be involved in many human diseases. Molecular simulation has an indispensable role to play in dissecting the driving forces and regulation of biomolecular phase separation. The current work describes a high-resolution coarse-grained RNA model that is capable of describing the structure dynamics and complex sequence, concentration, temperature and ion dependent phase transitions of flexible RNAs. The study further reveals a central role of RNA folding in coordinating Mg2+-phosphate interactions, base stacking, and base pairing to drive phase separation, paving the road for studies of RNA-mediated phase separation in relevant biological contexts.

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.

Recent advances in the synthesis and application of biomolecular condensates

Biomolecular condensates (BMCs) represent a group of organized and programmed systems that participate in gene transcription, chromosome organization, cell division, tumorigenesis, and aging. However, the understanding of BMCs in terms of internal organizations and external regulations remains at an early stage. Recently, novel approaches such as synthetic biology have been used for de novo synthesis of BMCs. These synthesized BMCs (SBMCs) driven by phase separation adeptly resemble the self-assembly and dynamics of natural BMCs, offering vast potentials in basic and applied research. This review introduces recent progresses in phase separation-induced SBMCs, attempting to elaborate on the intrinsic principles and regulatory methodologies used to construct SBMCs. Furthermore, the scientific applications of SBMCs are illustrated, as indicated by the studies of chromosome structure, pathogenesis, biomanufacturing, artificial cell design, and drug delivery. The controllable SBMCs offer a powerful tool for understanding metabolic regulations, cellular organizations, and disease-associated protein aggregations, raising both opportunities and challenges in the future of biomaterial, biotechnology, and biomedicine.

Separation of sticker-spacer energetics governs the coalescence of metastable condensates

Biological condensates often emerge as a multidroplet state and never coalesce into one large droplet within the experimental timespan. Previous work revealed that the sticker-spacer architecture of biopolymers may dynamically stabilize the multidroplet state. Here, we simulate the condensate coalescence using metadynamics approach and reveal two distinct physical mechanisms underlying the fusion of droplets. Condensates made of sticker-spacer polymers readily undergo a kinetic arrest when stickers exhibit slow exchange while fast exchanging stickers at similar levels of saturation allow merger to equilibrium states. On the other hand, condensates composed of homopolymers fuse readily until they reach a threshold density. Increase in entropy upon intercondensate mixing of chains drives the fusion of sticker-spacer chains. We map the range of mechanisms of kinetic arrest from slow sticker exchange dynamics to density mediated in terms of energetic separation of stickers and spacers. Our predictions appear to be in qualitative agreement with recent experiments probing dynamic nature of protein-RNA condensates.

The RNA-dependent association of phosphatidylinositol 4,5-bisphosphate with intrinsically disordered proteins contribute to nuclear compartmentalization

The RNA content is crucial for the formation of nuclear compartments, such as nuclear speckles and nucleoli. Phosphatidylinositol 4,5-bisphosphate (PIP2) is found in nuclear speckles, nucleoli, and nuclear lipid islets and is involved in RNA polymerase I/II transcription. Intriguingly, the nuclear localization of PIP2 was also shown to be RNA-dependent. We therefore investigated whether PIP2 and RNA cooperate in the establishment of nuclear architecture. In this study, we unveiled the RNA-dependent PIP2-associated (RDPA) nuclear proteome in human cells by mass spectrometry. We found that intrinsically disordered regions (IDRs) with polybasic PIP2-binding K/R motifs are prevalent features of RDPA proteins. Moreover, these IDRs of RDPA proteins exhibit enrichment for phosphorylation, acetylation, and ubiquitination sites. Our results show for the first time that the RDPA protein Bromodomain-containing protein 4 (BRD4) associates with PIP2 in the RNA-dependent manner via electrostatic interactions, and that altered PIP2 levels affect the number of nuclear foci of BRD4 protein. Thus, we propose that PIP2 spatiotemporally orchestrates nuclear processes through association with RNA and RDPA proteins and affects their ability to form foci presumably via phase separation. This suggests the pivotal role of PIP2 in the establishment of a functional nuclear architecture competent for gene expression.

Optogenetic Control of Condensates: Principles and Applications

Biomolecular condensates appear throughout cell physiology and pathology, but the specific role of condensation or its dynamics is often difficult to determine. Optogenetics offers an expanding toolset to address these challenges, providing tools to directly control condensation of arbitrary proteins with precision over their formation, dissolution, and patterning in space and time. In this review, we describe the current state of the field for optogenetic control of condensation. We survey the proteins and their derivatives that form the foundation of this toolset, and we discuss the factors that distinguish them to enable appropriate selection for a given application. We also describe recent examples of the ways in which optogenetic condensation has been used in both basic and applied studies. Finally, we discuss important design considerations when engineering new proteins for optogenetic condensation, and we preview future innovations that will further empower this toolset in the coming years.

Accelerated Simulations Reveal Physicochemical Factors Governing Stability and Composition of RNA Clusters

Under certain conditions, RNA repeat sequences phase separate, yielding protein-free biomolecular condensates. Importantly, RNA repeat sequences have also been implicated in neurological disorders, such as Huntington's disease. Thus, mapping repeat sequences to their phase behavior, functions, and dysfunctions is an active area of research. However, despite several advances, it remains challenging to characterize the RNA phase behavior at a submolecular resolution. Here, we have implemented a residue-resolution coarse-grained model in LAMMPS─that incorporates both the RNA sequence and structure─to study the clustering propensities of protein-free RNA systems. Importantly, we achieve a multifold speedup in the simulation time compared to previous work. Leveraging this efficiency, we study the clustering propensity of all 20 nonredundant trinucleotide repeat sequences. Our results align with findings from experiments, emphasizing that canonical base-pairing and G-U wobble pairs play dominant roles in regulating cluster formation of RNA repeat sequences. Strikingly, we find strong entropic contributions to the stability and composition of RNA clusters, which is demonstrated for single-component RNA systems as well as binary mixtures of trinucleotide repeats. Additionally, we investigate the clustering behaviors of trinucleotide (odd) repeats and their quadranucleotide (even) counterparts. We observe that odd repeats exhibit stronger clustering tendencies, attributed to the presence of consecutive base pairs in their sequences that are disrupted in even repeat sequences. Altogether, our work extends the set of computational tools for probing RNA cluster formation at submolecular resolution and uncovers physicochemical principles that govern the stability and composition of the resulting clusters.

Separation of sticker-spacer energetics governs the coalescence of metastable condensates

Biological condensates often emerge as a multi-droplet state and never coalesce into one large droplet within the experimental timespan. Previous work revealed that the sticker-spacer architecture of biopolymers may dynamically stabilize the multi-droplet state. Here, we simulate the condensate coalescence using metadynamics approach and reveal two distinct physical mechanisms underlying the fusion of droplets. Condensates made of sticker-spacer polymers readily undergo a kinetic arrest when stickers exhibit slow exchange while fast exchanging stickers at similar levels of saturation allow merger to equilibrium states. On the other hand, condensates composed of homopolymers fuse readily until they reach a threshold density. Increase in entropy upon inter-condensate mixing of chains drives the fusion of sticker-spacer chains. We map the range of mechanisms of kinetic arrest from slow sticker exchange dynamics to density mediated in terms of energetic separation of stickers and spacers. Our predictions appear to be in qualitative agreement with recent experiments probing dynamic nature of protein-RNA condensates.

Membraneless organelles in health and disease: exploring the molecular basis, physiological roles and pathological implications

Once considered unconventional cellular structures, membraneless organelles (MLOs), cellular substructures involved in biological processes or pathways under physiological conditions, have emerged as central players in cellular dynamics and function. MLOs can be formed through liquid-liquid phase separation (LLPS), resulting in the creation of condensates. From neurodegenerative disorders, cardiovascular diseases, aging, and metabolism to cancer, the influence of MLOs on human health and disease extends widely. This review discusses the underlying mechanisms of LLPS, the biophysical properties that drive MLO formation, and their implications for cellular function. We highlight recent advances in understanding how the physicochemical environment, molecular interactions, and post-translational modifications regulate LLPS and MLO dynamics. This review offers an overview of the discovery and current understanding of MLOs and biomolecular condensate in physiological conditions and diseases. This article aims to deliver the latest insights on MLOs and LLPS by analyzing current research, highlighting their critical role in cellular organization. The discussion also covers the role of membrane-associated condensates in cell signaling, including those involving T-cell receptors, stress granules linked to lysosomes, and biomolecular condensates within the Golgi apparatus. Additionally, the potential of targeting LLPS in clinical settings is explored, highlighting promising avenues for future research and therapeutic interventions.

Uncovering Intermolecular Interactions Driving the Liquid-Liquid Phase Separation of the TDP-43 Low-Complexity Domain via Atomistic Dimerization Simulations

Liquid-liquid phase separation (LLPS) of transactive response DNA-binding protein of 43 kDa (TDP-43), which exerts multiple functions in the splicing, trafficking, and stabilization of RNA, mediates the formation of membraneless condensates with crucial physiological roles, while its aberrant LLPS is linked to multiple neurodegenerative diseases. However, due to the heterogeneous and dynamic nature of LLPS, major gaps remain in understanding the precise intermolecular interactions driving LLPS and how specific mutations alter LLPS dynamics. Here, we investigated the molecular mechanisms underlying the LLPS of the TDP-43 low-complexity domain (LCD) by simulating the dimerization process using all-atom discrete molecular dynamics with microsecond-long simulations. Our results showed that the TDP-43 LCD was intrinsically disordered, with helical structures consistent with prior nuclear magnetic resonance studies. Phase separation propensity was assessed by simulating the dimerization of the TDP-43 LCD and four mutants, showing that A321G, W334G, and M337V inhibited self-association, while G335D promoted it, fully consistent with experimental reports. During the dimerization process, two peptides experienced both elastic and nonelastic collisions, and the self-associated dimer featured both high- and low-contact states. These results suggested that the dimerization process of the TDP-43 LCD was accordingly dynamic and heterogeneous. Additionally, we identified crucial regions containing hydrophobic clusters and aromatic residues in the N-terminus, central region, and C-terminus that were essential for the self-association of the TDP-43 LCD. These residues with high binding affinities can act as stickers to form peptide networks in LLPS. Together, our simulation provides a comprehensive picture of the intermolecular interactions driving the phase separation of the TDP-43 LCD, offering insights into both physiological functions and pathological mechanisms.

Direct computations of viscoelastic moduli of biomolecular condensates

Biomolecular 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 that leverages information regarding intra- and inter-chain contacts, which we extract from equilibrium configurations of lattice-based Metropolis Monte Carlo (MMC) simulations of phase separation. The key ingredient of the generalized Rouse model is a graph Laplacian that we compute from equilibrium MMC simulations. We compute two flavors of graph Laplacians, one based on a single-chain graph that accounts only for intra-chain contacts, and the other referred to as a collective graph that accounts for inter-chain interactions. Calculations based on the single-chain graph systematically overestimate the storage and loss moduli, whereas calculations based on the collective graph reproduce the measured moduli with greater fidelity. However, in the long time, low-frequency domain, a mixture of the two graphs proves to be most accurate. In line with the theory of Rouse and contrary to recent assertions, we find that a continuous distribution of relaxation times exists in condensates. The single crossover frequency between dominantly elastic vs dominantly viscous behaviors does not imply a single relaxation time. Instead, it is influenced by the totality of the relaxation modes. Hence, our analysis affirms 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 the relaxation time spectra that underlie the dynamics within condensates. This is of practical importance given advancements in passive and active microrheology measurements of condensate viscoelasticity.

Balancing thermodynamic stability, dynamics, and kinetics in phase separation of intrinsically disordered proteins

Intrinsically disordered proteins (IDPs) are prevalent participants in liquid-liquid phase separation due to their inherent potential for promoting multivalent binding. Understanding the underlying mechanisms of phase separation is challenging, as phase separation is a complex process, involving numerous molecules and various types of interactions. Here, we used a simplified coarse-grained model of IDPs to investigate the thermodynamic stability of the dense phase, conformational properties of IDPs, chain dynamics, and kinetic rates of forming condensates. We focused on the IDP system, in which the oppositely charged IDPs are maximally segregated, inherently possessing a high propensity for phase separation. By varying interaction strengths, salt concentrations, and temperatures, we observed that IDPs in the dense phase exhibited highly conserved conformational characteristics, which are more extended than those in the dilute phase. Although the chain motions and global conformational dynamics of IDPs in the condensates are slow due to the high viscosity, local chain flexibility at the short timescales is largely preserved with respect to that at the free state. Strikingly, we observed a non-monotonic relationship between interaction strengths and kinetic rates for forming condensates. As strong interactions of IDPs result in high stable condensates, our results suggest that the thermodynamics and kinetics of phase separation are decoupled and optimized by the speed-stability balance through underlying molecular interactions. Our findings contribute to the molecular-level understanding of phase separation and offer valuable insights into the developments of engineering strategies for precise regulation of biomolecular condensates.

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

Biomolecular condensates are viscoelastic materials. Here, we investigate the determinants of sequence-encoded and age-dependent viscoelasticity of condensates formed by the prion-like low-complexity domain of the protein hnRNP A1 and its designed variants. We find that the dominantly viscous forms of the condensates are metastable Maxwell fluids. A Rouse-Zimm model that accounts for the network-like organization of proteins within condensates reproduces the measured viscoelastic moduli. We show that the strengths of aromatic inter-sticker interactions determine sequence-specific amplitudes of elastic and viscous moduli, and the timescales over which elastic properties dominate. These condensates undergo physical ageing on sequence-specific timescales. This is driven by mutations to spacer residues that weaken the metastability of dominantly viscous phases. The ageing of condensates is accompanied by disorder-to-order transitions, leading to the formation of non-fibrillar, beta-sheet-containing, semi-crystalline, elastic, Kelvin-Voigt solids. Our results suggest that sequence grammars, which refer to amino acid identities of stickers versus spacers in prion-like low-complexity domains, have evolved to afford control over metastabilities of dominantly viscous fluid phases of condensates. This selection is likely to render barriers for conversion from metastable fluids to globally stable solids insurmountable on functionally relevant timescales.

Measurement of solubility product reveals the interplay of oligomerization and self-association for defining condensate formation

Cellular condensates often consist of 10s to 100s of distinct interacting molecular species. Because of the complexity of these interactions, predicting the point at which they will undergo phase separation is daunting. Using experiments and computation, we therefore studied a simple model system consisting of polySH3 and polyPRM designed for pentavalent heterotypic binding. We tested whether the peak solubility product, or the product of the dilute phase concentration of each component, is a predictive parameter for the onset of phase separation. Titrating up equal total concentrations of each component showed that the maximum solubility product does approximately coincide with the threshold for phase separation in both experiments and models. However, we found that measurements of dilute phase concentration include small oligomers and monomers; therefore, a quantitative comparison of the experiments and models required inclusion of small oligomers in the model analysis. Even with the inclusion of small polyPRM and polySH3 oligomers, models did not predict experimental results. This led us to perform dynamic light scattering experiments, which revealed homotypic binding of polyPRM. Addition of this interaction to our model recapitulated the experimentally observed asymmetry. Thus, comparing experiments with simulation reveals that the solubility product can be predictive of the interactions underlying phase separation, even if small oligomers and low affinity homotypic interactions complicate the analysis.

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.

Modulation of α-synuclein aggregation amid diverse environmental perturbation

Intrinsically disordered protein α-synuclein (αS) is implicated in Parkinson's disease due to its aberrant aggregation propensity. In a bid to identify the traits of its aggregation, here we computationally simulate the multi-chain association process of αS in aqueous as well as under diverse environmental perturbations. In particular, the aggregation of αS in aqueous and varied environmental condition led to marked concentration differences within protein aggregates, resembling liquid-liquid phase separation (LLPS). Both saline and crowded settings enhanced the LLPS propensity. However, the surface tension of αS droplet responds differently to crowders (entropy-driven) and salt (enthalpy-driven). Conformational analysis reveals that the IDP chains would adopt extended conformations within aggregates and would maintain mutually perpendicular orientations to minimize inter-chain electrostatic repulsions. The droplet stability is found to stem from a diminished intra-chain interactions in the C-terminal regions of αS, fostering inter-chain residue-residue interactions. Intriguingly, a graph theory analysis identifies small-world-like networks within droplets across environmental conditions, suggesting the prevalence of a consensus interaction patterns among the chains. Together these findings suggest a delicate balance between molecular grammar and environment-dependent nuanced aggregation behavior of αS.

An activity-specificity trade-off encoded in human transcription factors

Transcription factors (TFs) control specificity and activity of gene transcription, but whether a relationship between these two features exists is unclear. Here we provide evidence for an evolutionary trade-off between the activity and specificity in human TFs encoded as submaximal dispersion of aromatic residues in their intrinsically disordered protein regions. We identified approximately 500 human TFs that encode short periodic blocks of aromatic residues in their intrinsically disordered regions, resembling imperfect prion-like sequences. Mutation of periodic aromatic residues reduced transcriptional activity, whereas increasing the aromatic dispersion of multiple human TFs enhanced transcriptional activity and reprogramming efficiency, promoted liquid-liquid phase separation in vitro and more promiscuous DNA binding in cells. Together with recent work on enhancer elements, these results suggest an important evolutionary role of suboptimal features in transcriptional control. We propose that rational engineering of amino acid features that alter phase separation may be a strategy to optimize TF-dependent processes, including cellular reprogramming.

Multi-condensate state as a functional strategy to optimize the cell signaling output

The existence of multiple biomolecular condensates inside living cells is a peculiar phenomenon not compatible with the predictions of equilibrium statistical mechanics. In this work, we address the problem of multiple condensates state (MCS) from a functional perspective. We combine Langevin dynamics, reaction-diffusion simulation, and dynamical systems theory to demonstrate that MCS can indeed be a function optimization strategy. Using Arp2/3 mediated actin nucleation pathway as an example, we show that actin polymerization is maximum at an optimal number of condensates. For a fixed amount of Arp2/3, MCS produces a greater response compared to its single condensate counterpart. Our analysis reveals the functional significance of the condensate size distribution which can be mapped to the recent experimental findings. Given the spatial heterogeneity within condensates and non-linear nature of intracellular networks, we envision MCS to be a generic functional solution, so that structures of network motifs may have evolved to accommodate such configurations.

Asymmetry in Polymer-Solvent Interactions Yields Complex Thermoresponsive Behavior

We introduce a lattice framework that incorporates elements of Flory-Huggins solution theory and the q-state Potts model to study the phase behavior of polymer solutions and single-chain conformational characteristics. Without empirically introducing temperature-dependent interaction parameters, standard Flory-Huggins theory describes systems that are either homogeneous across temperatures or exhibit upper critical solution temperatures. The proposed Flory-Huggins-Potts framework extends these capabilities by predicting lower critical solution temperatures, miscibility loops, and hourglass-shaped spinodal curves. We particularly show that including orientation-dependent interactions, specifically between monomer segments and solvent particles, is alone sufficient to observe such phase behavior. Signatures of emergent phase behavior are found in single-chain Monte Carlo simulations, which display heating- and cooling-induced coil-globule transitions linked to energy fluctuations. The framework also capably describes a range of experimental systems. Importantly, and by contrast to many prior theoretical approaches, the framework does not employ any temperature- or composition-dependent parameters. This work provides new insights regarding the microscopic physics that underpin complex thermoresponsive behavior in polymers.

Biomolecular condensates can function as inherent catalysts

We report the discovery that chemical reactions such as ATP hydrolysis can be catalyzed by condensates formed by intrinsically disordered proteins (IDPs), which themselves lack any intrinsic ability to function as enzymes. This inherent catalytic feature of condensates derives from the electrochemical environments and the electric fields at interfaces that are direct consequences of phase separation. The condensates we studied were capable of catalyzing diverse hydrolysis reactions, including hydrolysis and radical-dependent breakdown of ATP whereby ATP fully decomposes to adenine and multiple carbohydrates. This distinguishes condensates from naturally occurring ATPases, which can only catalyze the dephosphorylation of ATP. Interphase and interfacial properties of condensates can be tuned via sequence design, thus enabling control over catalysis through sequence-dependent electrochemical features of condensates. Incorporation of hydrolase-like synthetic condensates into live cells enables activation of transcriptional circuits that depend on products of hydrolysis reactions. Inherent catalytic functions of condensates, which are emergent consequences of phase separation, are likely to affect metabolic regulation in cells.

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.

Asymmetric oligomerization state and sequence patterning can tune multiphase condensate miscibility

Endogenous biomolecular condensates, composed of a multitude of proteins and RNAs, can organize into multiphasic structures with compositionally distinct phases. This multiphasic organization is generally understood to be critical for facilitating their proper biological function. However, the biophysical principles driving multiphase formation are not completely understood. Here we use in vivo condensate reconstitution experiments and coarse-grained molecular simulations to investigate how oligomerization and sequence interactions modulate multiphase organization in biomolecular condensates. We demonstrate that increasing the oligomerization state of an intrinsically disordered protein results in enhanced immiscibility and multiphase formation. Interestingly, we find that oligomerization tunes the miscibility of intrinsically disordered proteins in an asymmetric manner, with the effect being more pronounced when the intrinsically disordered protein, exhibiting stronger homotypic interactions, is oligomerized. Our findings suggest that oligomerization is a flexible biophysical mechanism that cells can exploit to tune the internal organization of biomolecular condensates and their associated biological functions.

Protein condensates in the the secretory pathway: Unraveling biophysical interactions and function

The emergence of phase separation phenomena among macromolecules has identified biomolecular condensates as fundamental cellular organizers. These condensates concentrate specific components and accelerate biochemical reactions without relying on membrane boundaries. Although extensive studies have revealed a large variety of nuclear and cytosolic membraneless organelles, we are witnessing a surge in the exploration of protein condensates associated with the membranes of the secretory pathway, such as the endoplasmic reticulum and the Golgi apparatus. This review focuses on protein condensates in the secretory pathway and discusses their impact on the organization and functions of this cellular process. Moreover, we explore the modes of condensate-membrane association and the biophysical and cellular consequences of protein condensate interactions with secretory pathway membranes.

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.

Crowder titrations enable the quantification of driving forces for macromolecular phase separation

Macromolecular solubility is an important contributor to the driving forces for phase separation. Formally, the driving forces in a binary mixture comprising a macromolecule dissolved in a solvent can be quantified in terms of the saturation concentration, which is the threshold macromolecular concentration above which the mixture separates into coexisting dense and dilute phases. In addition, the second virial coefficient, which measures the effective strength of solvent-mediated intermolecular interactions provides direct assessments of solvent quality. The sign and magnitude of second virial coefficients will be governed by a combination of solution conditions and the nature of the macromolecule of interest. Here, we show, using a combination of theory, simulation, and in vitro experiments, that titrations of crowders, providing they are true depletants, can be used to extract the intrinsic driving forces for macromolecular phase separation. This refers to saturation concentrations in the absence of crowders and the second virial coefficients that quantify the magnitude of the incompatibility between macromolecules and the solvent. Our results show how the depletion-mediated attractions afforded by crowders can be leveraged to obtain comparative assessments of macromolecule-specific, intrinsic driving forces for phase separation.

Aromatic and arginine content drives multiphasic condensation of protein-RNA mixtures

Multiphasic architectures are found ubiquitously in biomolecular condensates and are thought to have important implications for the organization of multiple chemical reactions within the same compartment. Many of these multiphasic condensates contain RNA in addition to proteins. Here, we investigate the importance of different interactions in multiphasic condensates comprising two different proteins and RNA using computer simulations with a residue-resolution coarse-grained model of proteins and RNA. We find that in multilayered condensates containing RNA in both phases, protein-RNA interactions dominate, with aromatic residues and arginine forming the key stabilizing interactions. The total aromatic and arginine content of the two proteins must be appreciably different for distinct phases to form, and we show that this difference increases as the system is driven toward greater multiphasicity. Using the trends observed in the different interaction energies of this system, we demonstrate that we can also construct multilayered condensates with RNA preferentially concentrated in one phase. The "rules" identified can thus enable the design of synthetic multiphasic condensates to facilitate further study of their organization and function.

Solutes unmask differences in clustering versus phase separation of FET proteins

Phase separation and percolation contribute to phase transitions of multivalent macromolecules. Contributions of percolation are evident through the viscoelasticity of condensates and through the formation of heterogeneous distributions of nano- and mesoscale pre-percolation clusters in sub-saturated solutions. Here, we show that clusters formed in sub-saturated solutions of FET (FUS-EWSR1-TAF15) proteins are affected differently by glutamate versus chloride. These differences on the nanoscale, gleaned using a suite of methods deployed across a wide range of protein concentrations, are prevalent and can be unmasked even though the driving forces for phase separation remain unchanged in glutamate versus chloride. Strikingly, differences in anion-mediated interactions that drive clustering saturate on the micron-scale. Beyond this length scale the system separates into coexisting phases. Overall, we find that sequence-encoded interactions, mediated by solution components, make synergistic and distinct contributions to the formation of pre-percolation clusters in sub-saturated solutions, and to the driving forces for phase separation.

Multi-condensate state as a functional strategy to optimize the cell signaling output

The existence of multiple biomolecular condensates inside living cells is a peculiar phenomenon not compatible with the predictions of equilibrium statistical mechanics. In this work, we address the problem of multiple condensates state (MCS) from a functional perspective. We combined Langevin dynamics, reaction-diffusion simulation, and dynamical systems theory to demonstrate that MCS can indeed be a function optimization strategy. Using Arp2/3 mediated actin nucleation pathway as an example, we show that actin polymerization is maximum at an optimal number of condensates. For a fixed amount of Arp2/3, MCS produces a greater response compared to its single condensate counterpart. Our analysis reveals the functional significance of the condensate size distribution which can be mapped to the recent experimental findings. Given the spatial heterogeneity within condensates and non-linear nature of intracellular networks, we envision MCS to be a generic functional solution, so that structures of network motifs may have evolved to accommodate such configurations.

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.

Molecular determinants and signaling effects of PKA RIα phase separation

Spatiotemporal regulation of intracellular signaling molecules, such as the 3',5'-cyclic adenosine monophosphate (cAMP)-dependent protein kinase (PKA), ensures proper cellular function. Liquid-liquid phase separation (LLPS) of the ubiquitous PKA regulatory subunit RIα promotes cAMP compartmentation and signaling specificity. However, the molecular determinants of RIα LLPS remain unclear. Here, we reveal that two separate dimerization interfaces, combined with the cAMP-induced unleashing of the PKA catalytic subunit (PKA-C) from the pseudosubstrate inhibitory sequence, drive RIα condensate formation in the cytosol of mammalian cells, which is antagonized by docking to A-kinase anchoring proteins. Strikingly, we find that the RIα pseudosubstrate region is critically involved in forming a non-canonical R:C complex, which recruits active PKA-C to RIα condensates to maintain low basal PKA activity in the cytosol. Our results suggest that RIα LLPS not only facilitates cAMP compartmentation but also spatially restrains active PKA-C, thus highlighting the functional versatility of biomolecular condensates in driving signaling specificity.

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

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

Macromolecular condensation organizes nucleolar sub-phases to set up a pH gradient

Nucleoli are multicomponent condensates defined by coexisting sub-phases. We identified distinct intrinsically disordered regions (IDRs), including acidic (D/E) tracts and K-blocks interspersed by E-rich regions, as defining features of nucleolar proteins. We show that the localization preferences of nucleolar proteins are determined by their IDRs and the types of RNA or DNA binding domains they encompass. In vitro reconstitutions and studies in cells showed how condensation, which combines binding and complex coacervation of nucleolar components, contributes to nucleolar organization. D/E tracts of nucleolar proteins contribute to lowering the pH of co-condensates formed with nucleolar RNAs in vitro. In cells, this sets up a pH gradient between nucleoli and the nucleoplasm. By contrast, juxta-nucleolar bodies, which have different macromolecular compositions, featuring protein IDRs with very different charge profiles, have pH values that are equivalent to or higher than the nucleoplasm. Our findings show that distinct compositional specificities generate distinct physicochemical properties for condensates.

Multiscale Computational Framework for the Liquid-Liquid Phase Separation of Intrinsically Disordered Proteins

The reversible assembly of intrinsically disordered proteins (IDPs) to form membraneless organelles (MLOs) is a fundamental process involved in the spatiotemporal regulation in living cells. MLOs formed via liquid-liquid phase separation (LLPS) serve as molecule-enhancing hubs to regulate cell functions. Owing to the complexity and dynamic nature of the protein assembly via a network of weak inter- and intra-molecular interactions, it is challenging to describe and predict the LLPS behavior. We have developed a multiscale computational model for IDPs, using the fused in sarcoma (FUS) protein and its variants as illustrative examples. To simplify the description of protein, FUS is represented as a linear chain of stickers interspaced by spacers, as inspired by the associative polymer theory. Low-complexity aromatic-rich kinked segments (LARKS) available in FUS were identified using LARKSdb and represented as "stickers". The pairwise potential energies of each pair of stickers and their β-sheet-forming propensity were estimated via molecular docking and all atomistic molecular dynamics (AA-MD) simulations. Subsequently, FUS chains were randomly positioned in a cubic lattice as coarse-grained (CG) beads, with the bead assignment based on the Kuhn length estimation of stickers and spacers. Stochastic FUS movements were modeled by Monte Carlo (MC) simulations. In addition to the Metropolis algorithm, discretized pair potential distributions between stickers were considered in the move acceptance criteria. The chosen pair potential represents one of the possible binding energy states, with its probability determined by the frequency of the binding energy distribution histogram. The fluctuations of averaged radial distribution functions (RDFs) in successive MC trial move intervals of equilibrated lattice MC simulations were used to indicate the dynamic nature of assembly/disassembly of the protein chains. This multiscale computational framework provides an economical and efficient way of predicting and describing the LLPS behavior of IDPs.

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 .

Quantitative description of the phase-separation behavior of the multivalent SLP65-CIN85 complex

Biomolecular condensates play a major role in cell compartmentalization, besides membrane-enclosed organelles. The multivalent SLP65 and CIN85 proteins are proximal B-cell antigen receptor (BCR) signal effectors and critical for proper immune responses. In association with intracellular vesicles, the two effector proteins form phase separated condensates prior to antigen stimulation, thereby preparing B lymphocytes for rapid and effective activation upon BCR ligation. Within this tripartite system, 6 proline-rich motifs (PRMs) of SLP65 interact promiscuously with 3 SH3 domains of the CIN85 monomer, establishing 18 individual SH3-PRM interactions whose individual dissociation constants we determined. Based on these 18 dissociation constants, we measured the phase-separation properties of the natural SLP65/CIN85 system as well as designer constructs that emphasize the strongest SH3/PRM interactions. By modeling these various SLP65/CIN85 constructs with the program LASSI (LAttice simulation engine for Sticker and Spacer Interactions), we reproduced the observed phase-separation properties. In addition, LASSI revealed a deviation in the experimental measurement, which was independently identified as a previously unknown intramolecular interaction. Thus, thermodynamic properties of the individual PRM/SH3 interactions allow us to model the phase-separation behavior of the SLP65/CIN85 system faithfully.

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.

Determinants of viscoelasticity and flow activation energy in biomolecular condensates

The form and function of biomolecular condensates are intimately linked to their material properties. Here, we integrate microrheology with molecular simulations to dissect the physical determinants of condensate fluid phase dynamics. By quantifying the timescales and energetics of network relaxation in a series of heterotypic viscoelastic condensates, we uncover distinctive roles of sticker motifs, binding energy, and chain length in dictating condensate dynamical properties. We find that the mechanical relaxation times of condensate-spanning networks are determined by both intermolecular interactions and chain length. We demonstrate, however, that the energy barrier for network reconfiguration, termed flow activation energy, is independent of chain length and only varies with the strengths of intermolecular interactions. Biomolecular diffusion in the dense phase depends on a complex interplay between viscoelasticity and flow activation energy. Our results illuminate distinctive roles of chain length and sequence-specific multivalent interactions underlying the complex material and transport properties of biomolecular condensates.

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.

Surface Charge Can Modulate Phase Separation of Multidomain Proteins

Phase separation has emerged as an important mechanism explaining the formation of certain biomolecular condensates. Biological phase separation is often driven by the multivalent interactions of modular protein domains. Beyond valency, the physical features of folded domains that promote phase separation are poorly understood. We used a model system─the small ubiquitin modifier (SUMO) and its peptide ligand, the SUMO interaction motif (SIM)─to examine how domain surface charge influences multivalency-driven phase separation. Phase separation of polySUMO and polySIM was altered by pH via a change in the protonation state of SUMO surface histidines. These effects were recapitulated by histidine mutations, which modulated SUMO solubility and polySUMO-polySIM phase separation in parallel and were quantitatively explained by atomistic modeling of weak interactions among proteins in the system. Thus, surface charge can tune the phase separation of multivalent proteins, suggesting a means of controlling phase separation biologically, evolutionarily, and therapeutically.

Measurement of solubility product in a model condensate reveals the interplay of small oligomerization and self-association

Cellular condensates often consist of 10s to 100s of distinct interacting molecular species. Because of the complexity of these interactions, predicting the point at which they will undergo phase separation into discrete compartments is daunting. Using experiments and computation, we therefore studied a simple model system consisting of 2 proteins, polySH3 and polyPRM, designed for pentavalent heterotypic binding. We tested whether the peak solubility product, the product of dilute phase monomer concentrations, is a predictive parameter for the onset of phase separation. Titrating up equal total concentrations of each component showed that the maximum solubility product does approximately coincide with the threshold for phase separation in both the experiments and models. However, we found that measurements of dilute phase concentration include contributions from small oligomers, not just monomers; therefore, a quantitative comparison of the experiments and models required inclusion of small oligomers in the model analysis. We also examined full phase diagrams where the model results were almost symmetric along the diagonal, but the experimental results were highly asymmetric. This led us to perform dynamic light scattering experiments, where we discovered a weak homotypic interaction for polyPRM; when this was added to the computational model, it was able to recapitulate the experimentally observed asymmetry. Thus, comparing experiments to simulation reveals that the solubility product can be predictive of phase separation, even if small oligomers and low affinity homotypic interactions preclude experimental measurement of monomer concentration.

Toward Accurate Simulation of Coupling between Protein Secondary Structure and Phase Separation

Intrinsically disordered proteins (IDPs) frequently mediate phase separation that underlies the formation of a biomolecular condensate. Together with theory and experiment, efficient coarse-grained (CG) simulations have been instrumental in understanding the sequence-specific phase separation of IDPs. However, the widely used Cα-only models are limited in capturing the peptide nature of IDPs, particularly backbone-mediated interactions and effects of secondary structures, in phase separation. Here, we describe a hybrid resolution (HyRes) protein model toward a more accurate description of the backbone and transient secondary structures in phase separation. With an atomistic backbone and coarse-grained side chains, HyRes can semiquantitatively capture the residue helical propensity and overall chain dimension of monomeric IDPs. Using GY-23 as a model system, we show that HyRes is efficient enough for the direct simulation of spontaneous phase separation and, at the same time, appears accurate enough to resolve the effects of single His to Lys mutations. HyRes simulations also successfully predict increased β-structure formation in the condensate, consistent with available experimental CD data. We further utilize HyRes to study the phase separation of TPD-43, where several disease-related mutants in the conserved region (CR) have been shown to affect residual helicities and modulate the phase separation propensity as measured by the saturation concentration. The simulations successfully recapitulate the effect of these mutants on the helicity and phase separation propensity of TDP-43 CR. Analyses reveal that the balance between backbone and side chain-mediated interactions, but not helicity itself, actually determines phase separation propensity. These results support that HyRes represents an effective protein model for molecular simulation of IDP phase separation and will help to elucidate the coupling between transient secondary structures and phase separation.