Pleomorphic ensembles: formation of large clusters composed of weakly interacting multivalent molecules

Protein interactions, calcium, phosphorylation, and cholesterol modulate CFTR cluster formation on membranes

The cystic fibrosis transmembrane conductance regulator (CFTR) is a chloride channel whose dysfunction leads to intracellular accumulation of chloride ions, dehydration of cell surfaces, and subsequent damage to airway and ductal organs. Beyond its function as a chloride channel, interactions between CFTR, epithelium sodium channel, and solute carrier (SLC) transporter family membrane proteins and cytoplasmic proteins, including calmodulin and Na+/H+ exchanger regulatory factor-1 (NHERF-1), coregulate ion homeostasis. CFTR has also been observed to form mesoscale membrane clusters. However, the contributions of multivalent protein and lipid interactions to cluster formation are not well understood. Using a combination of computational modeling and biochemical reconstitution assays, we demonstrate that multivalent interactions with CFTR protein binding partners, calcium, and membrane cholesterol can induce mesoscale CFTR cluster formation on model membranes. Phosphorylation of the intracellular domains of CFTR also promotes mesoscale cluster formation in the absence of calcium, indicating that multiple mechanisms can contribute to CFTR cluster formation. Our findings reveal that coupling of multivalent protein and lipid interactions promotes CFTR cluster formation consistent with membrane-associated biological phase separation.

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.

Modular RNA motifs for orthogonal phase separated compartments

Recent discoveries in biology have highlighted the importance of protein and RNA-based condensates as an alternative to classical membrane-bound organelles. Here, we demonstrate the design of pure RNA condensates from nanostructured, star-shaped RNA motifs. We generate condensates using two different RNA nanostar architectures: multi-stranded nanostars whose binding interactions are programmed via linear overhangs, and single-stranded nanostars whose interactions are programmed via kissing loops. Through systematic sequence design, we demonstrate that both architectures can produce orthogonal (distinct and immiscible) condensates, which can be individually tracked via fluorogenic aptamers. We also show that aptamers make it possible to recruit peptides and proteins to the condensates with high specificity. Successful co-transcriptional formation of condensates from single-stranded nanostars suggests that they may be genetically encoded and produced in living cells. We provide a library of orthogonal RNA condensates that can be modularly customized and offer a route toward creating systems of functional artificial organelles for the task of compartmentalizing molecules and biochemical reactions.

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.

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.

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.

MolClustPy: a Python package to characterize multivalent biomolecular clusters

SUMMARY

Low-affinity interactions among multivalent biomolecules may lead to the formation of molecular complexes that undergo phase transitions to become supply-limited large clusters. In stochastic simulations, such clusters display a wide range of sizes and compositions. We have developed a Python package, MolClustPy, which performs multiple stochastic simulation runs using NFsim (Network-Free stochastic simulator); MolClustPy characterizes and visualizes the distribution of cluster sizes, molecular composition, and bonds across molecular clusters. The statistical analysis offered by MolClustPy is readily applicable to other stochastic simulation software, such as SpringSaLaD and ReaDDy.

AVAILABILITY AND IMPLEMENTATION

The software is implemented in Python. A detailed Jupyter notebook is provided to enable convenient running. Code, user guide, and examples are freely available at https://molclustpy.github.io/.

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.

MolClustPy: A Python Package to Characterize Multivalent Biomolecular Clusters

S ummary

Low-affinity interactions among multivalent biomolecules may lead to the formation of molecular complexes that undergo phase transitions to become extra-large clusters. Characterizing the physical properties of these clusters is important in recent biophysical research. Due to weak interactions such clusters are highly stochastic, demonstrating a wide range of sizes and compositions. We have developed a Python package to perform multiple stochastic simulation runs using NFsim (Network-Free stochastic simulator), characterize and visualize the distribution of cluster sizes, molecular composition, and bonds across molecular clusters and individual molecules of different types.

A vailability and implementation

The software is implemented in Python. A detailed Jupyter notebook is provided to enable convenient running. Code, user guide and examples are freely available at https://molclustpy.github.io/.

C ontact

achattaraj007@gmail.com , blinov@uchc.edu.

S upplementary information

Available at https://molclustpy.github.io/.

Ligand-independent receptor clustering modulates transmembrane signaling: a new paradigm

Cell-surface receptors mediate communication between cells and their environment. Lateral membrane organization and dynamic receptor cluster formation are fundamental in signal transduction and cell signaling. However, it is not yet fully understood how receptor clustering modulates a wide variety of physiologically relevant processes. Recent growing evidence indicates that biological responses triggered by membrane receptors can be modulated even in the absence of the natural receptor ligand. We review the most recent findings on how ligand-independent receptor clustering can regulate transmembrane signaling. We discuss the latest technologies to control receptor assembly, such as DNA nanotechnology, optogenetics, and optochemistry, focusing on the biological relevance and unraveling of ligand-independent signaling.

Nanoscale regulation of Ca2+ dependent phase transitions and real-time dynamics of SAP97/hDLG

Synapse associated protein-97/Human Disk Large (SAP97/hDLG) is a conserved, alternatively spliced, modular, scaffolding protein critical in regulating the molecular organization of cell-cell junctions in vertebrates. We confirm that the molecular determinants of first order phase transition of SAP97/hDLG is controlled by morpho-functional changes in its nanoscale organization. Furthermore, the nanoscale molecular signatures of these signalling islands and phase transitions are altered in response to changes in cytosolic Ca²⁺. Additionally, exchange kinetics of alternatively spliced isoforms of the intrinsically disordered region in SAP97/hDLG C-terminus shows differential sensitivities to Ca²⁺ bound Calmodulin, affirming that the molecular signatures of local phase transitions of SAP97/hDLG depends on their nanoscale heterogeneity and compositionality of isoforms.

SAP97/hDLG is a ubiquitous, alternatively spliced, and conserved modular scaffolding protein involved in the organization cell junctions and excitatory synapses. Here, authors confirm that SAP97/hDLG condenses in to nanosized molecular domains in both heterologous cells and hippocampal pyramidal neurons. Authors demonstrate that in vivo and in vitro condensation, molecular signatures of nanoscale condensates and exchange kinetics of SAP97/hDLG is modulated by the local availability of alternatively spliced isoforms. Additionally, SAP97/hDLG isoforms exhibits a differential sensitivity to Ca²⁺ bound Calmodulin, resulting in altered properties of nanocondensates and their real-time regulation

Different states and the associated fates of biomolecular condensates

Biomolecular condensates are functional assemblies, which can enrich intrinsically disordered proteins (IDPs) and/or RNAs at concentrations that are orders of magnitude higher than the bulk. In their native functional state, these structures can exist in multiple physical states including liquid-droplet phase, hydrogels, and solid assemblies. On the other hand, an aberrant transition between these physical states can result in loss-of-function or a gain-of-toxic-function. A prime example of such an aberrant transition is droplet aging—a phenomenon where some condensates may progressively transition into less dynamic material states at biologically relevant timescales. In this essay, we review structural and viscoelastic roots of aberrant liquid–solid transitions. Also, we highlight the different checkpoints and experimentally tunable handles, both active (ATP-dependent enzymes, post-translational modifications) and passive (colocalization of RNA molecules), that could alter the material state of assemblies.

Surface tension and super-stoichiometric surface enrichment in two-component biomolecular condensates

Cells can achieve internal organization by exploiting liquid-liquid phase separation to form biomolecular condensates. Here we focus on the surface properties of condensates composed of two multivalent associative polymers held together by one-to-one "sticker" bonds. Using coarse-grained molecular-dynamics simulations, we study the influence of component stoichiometry on condensate surface properties. We find that unequal stoichiometry results in enrichment of the majority species at the interface and a sharp reduction of surface tension. To relate these two effects, we show that the reduction in surface tension scales linearly with the excess concentration of free binding sites at the interface. Our results imply that each excess free site contributes an approximately fixed additional energy and entropy to the interface, with the latter dominating such that enrichment of free majority sites lowers the surface tension. Our work provides insight into novel physical mechanisms by which cells can regulate condensate surface properties.

A Hypothesis: Linking Phase Separation to Meiotic Sex Chromosome Inactivation and Sex-Body Formation

During meiotic prophase I, X and Y chromosomes in mammalian spermatocytes only stably pair at a small homologous region called the pseudoautosomal region (PAR). However, the rest of the sex chromosomes remain largely unsynapsed. The extensive asynapsis triggers transcriptional silencing - meiotic sex chromosome inactivation (MSCI). Along with MSCI, a special nuclear territory, sex body or XY body, forms. In the early steps of MSCI, DNA damage response (DDR) factors, such as BRCA1, ATR, and γH2AX, function as sensors and effectors of the silencing signals. Downstream canonical repressive histone modifications, including methylation, acetylation, ubiquitylation, and SUMOylation, are responsible for the transcriptional repression of the sex chromosomes. Nevertheless, mechanisms of the sex-body formation remain unclear. Liquid-liquid phase separation (LLPS) may drive the formation of several chromatin subcompartments, such as pericentric heterochromatin, nucleoli, inactive X chromosomes. Although several proteins involved in phase separation are found in the sex bodies, when and whether these proteins exert functions in the sex-body formation and MSCI is still unknown. Here, we reviewed recent publications on the mechanisms of MSCI and LLPS, pointed out the potential link between LLPS and the formation of sex bodies, and discussed its implications for future research.

The solubility product extends the buffering concept to heterotypic biomolecular condensates

Biomolecular condensates are formed by liquid-liquid phase separation (LLPS) of multivalent molecules. LLPS from a single ("homotypic") constituent is governed by buffering: above a threshold, free monomer concentration is clamped, with all added molecules entering the condensed phase. However, both experiment and theory demonstrate that buffering fails for the concentration dependence of multicomponent ("heterotypic") LLPS. Using network-free stochastic modeling, we demonstrate that LLPS can be described by the solubility product constant (Ksp): the product of free monomer concentrations, accounting for the ideal stoichiometries governed by the valencies, displays a threshold above which additional monomers are funneled into large clusters; this reduces to simple buffering for homotypic systems. The Ksp regulates the composition of the dilute phase for a wide range of valencies and stoichiometries. The role of Ksp is further supported by coarse-grained spatial particle simulations. Thus, the solubility product offers a general formulation for the concentration dependence of LLPS.

Designer protein assemblies with tunable phase diagrams in living cells

Protein self-organization is a hallmark of biological systems. Although the physicochemical principles governing protein-protein interactions have long been known, the principles by which such nanoscale interactions generate diverse phenotypes of mesoscale assemblies, including phase-separated compartments, remain challenging to characterize. To illuminate such principles, we create a system of two proteins designed to interact and form mesh-like assemblies. We devise a new strategy to map high-resolution phase diagrams in living cells, which provide self-assembly signatures of this system. The structural modularity of the two protein components allows straightforward modification of their molecular properties, enabling us to characterize how interaction affinity impacts the phase diagram and material state of the assemblies in vivo. The phase diagrams and their dependence on interaction affinity were captured by theory and simulations, including out-of-equilibrium effects seen in growing cells. Finally, we find that cotranslational protein binding suffices to recruit a messenger RNA to the designed micron-scale structures.

The bioenergetics of integrin-based adhesion, from single molecule dynamics to stability of macromolecular complexes

The forces actively generated by motile cells must be transmitted to their environment in a spatiotemporally regulated manner, in order to produce directional cellular motion. This task is accomplished through integrin-based adhesions, large macromolecular complexes that link the actin-cytoskelton inside the cell to its external environment. Despite their relatively large size, adhesions exhibit rapid dynamics, switching between assembly and disassembly in response to chemical and mechanical cues exerted by cytoplasmic biochemical signals, and intracellular/extracellular forces, respectively. While in material science, force typically disrupts adhesive contact, in this biological system, force has a more nuanced effect, capable of causing assembly or disassembly. This initially puzzled experimentalists and theorists alike, but investigation into the mechanisms regulating adhesion dynamics have progressively elucidated the origin of these phenomena. This review provides an overview of recent studies focused on the theoretical understanding of adhesion assembly and disassembly as well as the experimental studies that motivated them. We first concentrate on the kinetics of integrin receptors, which exhibit a complex response to force, and then investigate how this response manifests itself in macromolecular adhesion complexes. We then turn our attention to studies of adhesion plaque dynamics that link integrins to the actin-cytoskeleton, and explain how force can influence the assembly/disassembly of these macromolecular structure. Subsequently, we analyze the effect of force on integrins populations across lengthscales larger than single adhesions. Finally, we cover some theoretical studies that have considered both integrins and the adhesion plaque and discuss some potential future avenues of research.

Is the cell really a machine?

It has become customary to conceptualize the living cell as an intricate piece of machinery, different to a man-made machine only in terms of its superior complexity. This familiar understanding grounds the conviction that a cell's organization can be explained reductionistically, as well as the idea that its molecular pathways can be construed as deterministic circuits. The machine conception of the cell owes a great deal of its success to the methods traditionally used in molecular biology. However, the recent introduction of novel experimental techniques capable of tracking individual molecules within cells in real time is leading to the rapid accumulation of data that are inconsistent with an engineering view of the cell. This paper examines four major domains of current research in which the challenges to the machine conception of the cell are particularly pronounced: cellular architecture, protein complexes, intracellular transport, and cellular behaviour. It argues that a new theoretical understanding of the cell is emerging from the study of these phenomena which emphasizes the dynamic, self-organizing nature of its constitution, the fluidity and plasticity of its components, and the stochasticity and non-linearity of its underlying processes.

A predictive computational model reveals that GIV/girdin serves as a tunable valve for EGFR-stimulated cyclic AMP signals

Cellular levels of the versatile second messenger cyclic (c)AMP are regulated by the antagonistic actions of the canonical G protein → adenylyl cyclase pathway that is initiated by G-protein–coupled receptors (GPCRs) and attenuated by phosphodiesterases (PDEs). Dysregulated cAMP signaling drives many diseases; for example, its low levels facilitate numerous sinister properties of cancer cells. Recently, an alternative paradigm for cAMP signaling has emerged in which growth factor–receptor tyrosine kinases (RTKs; e.g., EGFR) access and modulate G proteins via a cytosolic guanine-nucleotide exchange modulator (GEM), GIV/girdin; dysregulation of this pathway is frequently encountered in cancers. In this study, we present a network-based compartmental model for the paradigm of GEM-facilitated cross-talk between RTKs and G proteins and how that impacts cellular cAMP. Our model predicts that cross-talk between GIV, Gα_s, and Gα_i proteins dampens ligand-stimulated cAMP dynamics. This prediction was experimentally verified by measuring cAMP levels in cells under different conditions. We further predict that the direct proportionality of cAMP concentration as a function of receptor number and the inverse proportionality of cAMP concentration as a function of PDE concentration are both altered by GIV levels. Taking these results together, our model reveals that GIV acts as a tunable control valve that regulates cAMP flux after growth factor stimulation. For a given stimulus, when GIV levels are high, cAMP levels are low, and vice versa. In doing so, GIV modulates cAMP via mechanisms distinct from the two most often targeted classes of cAMP modulators, GPCRs and PDEs.

Predicted amino acid motif repeats in proteins potentially encode extensive multivalent macromolecular assemblies in the human proteome

There are emerging interests in understanding higher order assemblies of biopolymers within and between cells, such as protein-protein and protein-RNA biomolecular condensates. These biomolecular condensates are thought to assemble/disassemble via multivalent interactions, including those mediated particularly by unique repeated amino acid motifs (URM). We asked how common are proteins with such URMs, their incidence and abundance, by exhaustively enumerating repeating motifs of length 3-10 in the human proteome. We found that URMs are very common and widely distributed across the human proteome. Moreover, the number of repetitions and intervals between them do not correlate with their lengths, which suggests that the number of repeats among proteins in the proteome is independent of length, contrary to the notion that short motifs are more abundant then long motifs. Finally, we describe two examples of URMs in proteins known to form higher order biopolymer assemblies: multi-PDZ domain-containing proteins and the FUS family of RNA binding proteins. For the FUS family, we predicted a known sequence 'grammar', specific motifs and interval sequence compositions that are essential to phase separation and material properties of condensates formed by this family of proteins. In PDZ domain-containing proteins we found a novel repeated motif that was surprisingly both within and between individual PDZ domains. We speculate that these motifs could be binding sites for multivalent interactions, a residual result of the mechanism by which PDZ-domain duplications occurred or that the linker sequences between PDZ domains may encode cryptic PDZ domains.

The Interplay of Structural and Cellular Biophysics Controls Clustering of Multivalent Molecules

Dynamic molecular clusters are assembled through weak multivalent interactions and are platforms for cellular functions, especially receptor-mediated signaling. Clustering is also a prerequisite for liquid-liquid phase separation. It is not well understood, however, how molecular structure and cellular organization control clustering. Using coarse-grained kinetic Langevin dynamics, we performed computational experiments on a prototypical ternary system modeled after membrane-bound nephrin, the adaptor Nck1, and the actin nucleation promoting factor NWASP. Steady-state cluster size distributions favored stoichiometries that optimized binding (stoichiometry matching) but still were quite broad. At high concentrations, the system can be driven beyond the saturation boundary such that cluster size is limited only by the number of available molecules. This behavior would be predictive of phase separation. Domains close to binding sites sterically inhibited clustering much less than terminal domains because the latter effectively restrict access to the cluster interior. Increased flexibility of interacting molecules diminished clustering by shielding binding sites within compact conformations. Membrane association of nephrin increased the cluster size distribution in a density-dependent manner. These properties provide insights into how molecular ensembles function to localize and amplify cell signaling.

An Overview of Network-Based and -Free Approaches for Stochastic Simulation of Biochemical Systems

Stochastic simulation has been widely used to model the dynamics of biochemical reaction networks. Several algorithms have been proposed that are exact solutions of the chemical master equation, following the work of Gillespie. These stochastic simulation approaches can be broadly classified into two categories: network-based and -free simulation. The network-based approach requires that the full network of reactions be established at the start, while the network-free approach is based on reaction rules that encode classes of reactions, and by applying rule transformations, it generates reaction events as they are needed without ever having to derive the entire network. In this study, we compare the efficiency and limitations of several available implementations of these two approaches. The results allow for an informed selection of the implementation and methodology for specific biochemical modeling applications.

Intrinsically disordered linkers determine the interplay between phase separation and gelation in multivalent proteins

Phase transitions of linear multivalent proteins control the reversible formation of many intracellular membraneless bodies. Specific non-covalent crosslinks involving domains/motifs lead to system-spanning networks referred to as gels. Gelation transitions can occur with or without phase separation. In gelation driven by phase separation multivalent proteins and their ligands condense into dense droplets, and gels form within droplets. System spanning networks can also form without a condensation or demixing of proteins into droplets. Gelation driven by phase separation requires lower protein concentrations, and seems to be the biologically preferred mechanism for forming membraneless bodies. Here, we use coarse-grained computer simulations and the theory of associative polymers to uncover the physical properties of intrinsically disordered linkers that determine the extent to which gelation of linear multivalent proteins is driven by phase separation. Our findings are relevant for understanding how sequence-encoded information in disordered linkers influences phase transitions of multivalent proteins.

Our cells contain a variety of structures called organelles that perform specific roles within a cell. Some organelles are surrounded by a membrane, while others float inside the cell as spherical droplets made of proteins. These proteins contain several sticky regions, which are connected by flexible linker proteins. It is thought that the level of stickiness and the number of sticky regions, or domains, determine whether a protein will form a membraneless organelle. Often, proteins with similar sticky domains have different linkers, and until now, it was assumed that the linkers do not have any other purpose than stringing the domains together.

To test this further, Harmon et al. used a combination of computer simulations and physics-based theory. In these simulations, the domains were kept the same, but the properties of linkers were changed to see if this would influence how the membraneless organelles are formed.

The results showed that depending on the physical properties of the linkers, the proteins could huddle together and form dense spherical gel-like droplets similar to the membraneless organelles, or form open non-spherical gels. When the linkers were short, the proteins do not easily form droplets. Linkers that were sufficiently long but too bulky, lead to non-spherical gels. Compact linkers, however, enabled proteins to huddle and form spherical gels. The spherical droplet-spanning gels required much less protein compared to the open non-spherical gels.

This suggests that proteins important for forming membraneless organelles can be distinguished from those that are not based on the properties of their linkers – even when their domains are similar.

These findings further scientists’ knowledge of how specific types of proteins form membraneless organelles and will help to understand how membraneless organelles control many key aspects of how a cell works.

RNA phase transitions in repeat expansion disorders

Expansions of short nucleotide repeats produce several neurological and neuromuscular disorders including Huntington’s disease, muscular dystrophy and amyotrophic lateral sclerosis. A common pathological feature of these diseases is the accumulation of the repeat containing transcripts into aberrant foci in the nucleus. RNA foci, as well as the disease symptoms, only manifest above a critical number of nucleotide repeats, but the molecular mechanism governing foci formation above this characteristic threshold remains unresolved. Here, we show that repeat expansions create templates for multivalent base-pairing, which causes purified RNA to undergo a sol-gel transition at a similar critical repeat number as observed in the diseases. In cells, RNA foci form by phase separation of the repeat-containing RNA and can be dissolved by agents that disrupt RNA gelation in vitro. Analogous to protein aggregation disorders, our results suggest that the sequence-specific gelation of RNAs could be a contributing factor to neurological disease.

Effect of non-specific interactions on formation and stability of specific complexes

We introduce a simple model to describe the interplay between specific and non-specific interactions. We study the influence of various physical factors on the static and dynamic properties of the specific interactions of our model and show that contrary to intuitive expectations, non-specific interactions can assist in the formation of specific complexes and increase their stability. We then discuss the relevance of these results for biological systems.

Multivalent Molecules as Modulators of RNA Granule Size and Composition

RNA granules are ensembles of specific RNA and protein molecules that mediate localized translation in eukaryotic cells. The mechanisms for formation and selectivity of RNA granules are unknown. Here we present a model for assembly of one type of RNA granule based on experimentally measured binding interactions among three core multivalent molecular components necessary for such assembly: specific RNA molecules that contain a cis-acting sequence called the A2 response element (A2RE), hnRNP A2 proteins that bind specifically (with high affinity) to A2RE sequences or nonspecifically (with lower affinity) to other RNA sequences, and heptavalent protein cytoskeleton-associated protein 5 (CKAP5, an alternative name for TOG protein) that binds both hnRNP A2 molecules and RNA. Non-A2RE RNA molecules (RNA without the A2RE sequence) that may be recruited to the granules through nonspecific interactions are also considered in the model. Modeling multivalent molecular interactions in granules is challenging because of combinatorial complexity in the number of potential molecular complexes among these core components and dynamic changes in granule composition and structure in response to changes in local intracellular environment. We use a hybrid modeling approach (deterministic-stochastic-statistical) that is appropriate when the overall compositions of multimolecular ensembles are of greater importance than the specific interactions among individual molecular components. Modeling studies titrating the concentrations of various granule components and varying effective site pair affinities and RNA valency demonstrate that interactions between multivalent components (TOG and RNA) are modulated by a bivalent adaptor molecule (hnRNP A2). Formation and disruption of granules, as well as RNA selectivity in granule composition are regulated by distinct concentration regimes of A2. Our results suggest that granule assembly is tightly controlled by multivalent molecular interactions among RNA molecules, adaptor proteins, and scaffold proteins.

SpringSaLaD: A Spatial, Particle-Based Biochemical Simulation Platform with Excluded Volume

We introduce Springs, Sites, and Langevin Dynamics (SpringSaLaD), a comprehensive software platform for spatial, stochastic, particle-based modeling of biochemical systems. SpringSaLaD models biomolecules in a coarse-grained manner as a group of linked spherical sites with excluded volume. This mesoscopic approach bridges the gap between highly detailed molecular dynamics simulations and the various methods used to study network kinetics and diffusion at the cellular level. SpringSaLaD is a standalone tool that supports model building, simulation, visualization, and data analysis, all through a user-friendly graphical user interface that should make it more accessible than tools built into more comprehensive molecular dynamics infrastructures. Importantly, for bimolecular reactions we derive an exact expression relating the macroscopic on-rate to the various microscopic parameters with the inclusion of excluded volume; this makes SpringSaLaD more accurate than other tools, which rely on approximate relationships between these parameters.

Second Messenger-Operated Calcium Entry Through TRPC6

Canonical transient receptor potential 6 (TRPC6) proteins assemble into heteromultimeric structures forming non-selective cation channels. In addition, many TRPC6-interacting proteins have been identified like some enzymes, channels, pumps, cytoskeleton-associated proteins, immunophilins, or cholesterol-binding proteins, indicating that TRPC6 are engaged into macromolecular complexes. Depending on the cell type and the experimental conditions used, TRPC6 activity has been reported to be controlled by diverse modalities. For instance, the second messenger diacylglycerol, store-depletion, the plant extract hyperforin or H2O2 have all been shown to trigger the opening of TRPC6 channels. A well-characterized consequence of TRPC6 activation is the elevation of the cytosolic concentration of Ca(2+). This latter response can reflect the entry of Ca(2+) through open TRPC6 channels but it can also be due to the Na(+)/Ca(2+) exchanger (operating in its reverse mode) or voltage-gated Ca(2+) channels (recruited in response to a TRPC6-mediated depolarization). Although TRPC6 controls a diverse array of biological functions in many tissues and cell types, its pathophysiological functions are far from being fully understood. This chapter covers some key features of TRPC6, with a special emphasis on their biological significance in kidney and blood cells.

Assemblages: functional units formed by cellular phase separation

The partitioning of intracellular space beyond membrane-bound organelles can be achieved with collections of proteins that are multivalent or contain low-complexity, intrinsically disordered regions. These proteins can undergo a physical phase change to form functional granules or other entities within the cytoplasm or nucleoplasm that collectively we term “assemblage.” Intrinsically disordered proteins (IDPs) play an important role in forming a subset of cellular assemblages by promoting phase separation. Recent work points to an involvement of assemblages in disease states, indicating that intrinsic disorder and phase transitions should be considered in the development of therapeutics.

Exact hybrid particle/population simulation of rule-based models of biochemical systems

Detailed modeling and simulation of biochemical systems is complicated by the problem of combinatorial complexity, an explosion in the number of species and reactions due to myriad protein-protein interactions and post-translational modifications. Rule-based modeling overcomes this problem by representing molecules as structured objects and encoding their interactions as pattern-based rules. This greatly simplifies the process of model specification, avoiding the tedious and error prone task of manually enumerating all species and reactions that can potentially exist in a system. From a simulation perspective, rule-based models can be expanded algorithmically into fully-enumerated reaction networks and simulated using a variety of network-based simulation methods, such as ordinary differential equations or Gillespie's algorithm, provided that the network is not exceedingly large. Alternatively, rule-based models can be simulated directly using particle-based kinetic Monte Carlo methods. This “network-free” approach produces exact stochastic trajectories with a computational cost that is independent of network size. However, memory and run time costs increase with the number of particles, limiting the size of system that can be feasibly simulated. Here, we present a hybrid particle/population simulation method that combines the best attributes of both the network-based and network-free approaches. The method takes as input a rule-based model and a user-specified subset of species to treat as population variables rather than as particles. The model is then transformed by a process of “partial network expansion” into a dynamically equivalent form that can be simulated using a population-adapted network-free simulator. The transformation method has been implemented within the open-source rule-based modeling platform BioNetGen, and resulting hybrid models can be simulated using the particle-based simulator NFsim. Performance tests show that significant memory savings can be achieved using the new approach and a monetary cost analysis provides a practical measure of its utility.

Rule-based modeling is a modeling paradigm that addresses the problem of combinatorial complexity in biochemical systems. The key idea is to specify only those components of a biological macromolecule that are directly involved in a biochemical transformation. Until recently, this “pattern-based” approach greatly simplified the process of model building but did nothing to improve the performance of model simulation. This changed with the introduction of “network-free” simulation methods, which operate directly on the compressed rule set of a rule-based model rather than on a fully-enumerated set of reactions and species. However, these methods represent every molecule in a system as a particle, limiting their use to systems containing less than a few million molecules. Here, we describe an extension to the network-free approach that treats rare, complex species as particles and plentiful, simple species as population variables, while retaining the exact dynamics of the model system. By making more efficient use of computational resources for species that do not require the level of detail of a particle representation, this hybrid particle/population approach can simulate systems much larger than is possible using network-free methods and is an important step towards realizing the practical simulation of detailed, mechanistic models of whole cells.