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.

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

Biopolymer condensates often emerge as a multi-droplet state and never coalesce into one large droplet within the experimental timespan. This contradicts the prediction of classical polymer physics which suggests the existence of one large droplet beyond the phase transition. 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. We also show that the inter-condensate exchange of chains offers a general mechanism that drives the fusion. 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 excellent agreement with recent experiments probing dynamic nature of protein-RNA condensates.

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/.

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.

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.