Biomolecular phase boundaries are described by a solubility product that accounts for variable stoichiometry and soluble oligomers.

The solubility product is a rigorous description of the phase boundary for salt precipitation and has also been used to qualitatively describe the condensation of biomolecules. Here we present a derivation of the solubility product showing that the solubility product is also a robust description of biomolecules phase boundaries if care is taken to account for soluble oligomers and variable composition within the dense phase. Our calculation describes equilibrium between unbound monomers, the dense phase, and an ensemble of oligomer complexes with significant finite-size contributions to their free energy.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.