Many biomolecular condensates form via spontaneous phase transitions that are driven by multivalent proteins. These molecules are biological instantiations of associative polymers that conform to a so-called stickers-and-spacers architecture. The stickers are protein-protein or protein-RNA interaction motifs and / or domains that can form reversible, non-covalent crosslinks with one another. Spacers are interspersed between stickers and their preferential interactions with solvent molecules determine the cooperativity of phase transitions. Here, we report the development of an open source computational engine known as LASSI (LAttice simulation engine for Sticker and Spacer Interactions) that enables the calculation of full phase diagrams for multicomponent systems comprising of coarse-grained representations of multivalent proteins. LASSI is designed to enable computationally efficient phenomenological modeling of spontaneous phase transitions of multicomponent mixtures comprising of multivalent proteins and RNA molecules. We demonstrate the application of LASSI using simulations of linear and branched multivalent proteins. We show that dense phases are best described as droplet-spanning networks that are characterized by reversible physical crosslinks among multivalent proteins. We connect recent observations regarding correlations between apparent stoichiometry and dwell times of condensates to being proxies for the internal structural organization, specifically the convolution of internal density and extent of networking, within condensates. Finally, we demonstrate that the concept of saturation concentration thresholds does not apply to multicomponent systems where obligate heterotypic interactions drive phase transitions. This emerges from the ellipsoidal structures of phase diagrams for multicomponent systems and it has direct implications for the regulation of biomolecular condensates in vivo.

Multivalent proteins and nucleic acids, collectively referred to as multivalent associative biomacromolecules, provide the driving forces for the formation and compositional regulation of biomolecular condensates. Here, we review the key concepts of phase transitions of aqueous solutions of associative biomacromolecules, specifically proteins that include folded domains and intrinsically disordered regions. The phase transitions of these systems come under the rubric of coupled associative and segregative transitions. The concepts underlying these processes are presented, and their relevance to biomolecular condensates is discussed.

Biomolecular condensates enable spatial and temporal control over cellular processes by concentrating biomolecules into nonstoichiometric assemblies. Many condensates form via reversible phase transitions of condensate-specific multivalent macromolecules known as scaffolds. Phase transitions of scaffolds can be regulated by changing the concentrations of ligands, which are defined as nonscaffold molecules that bind to specific sites on scaffolds. Here, we use theory and computation to uncover rules that underlie ligand-mediated control over scaffold phase behavior. We use the stickers-and-spacers model wherein reversible noncovalent cross-links among stickers drive phase transitions of scaffolds, and spacers modulate the driving forces for phase transitions. We find that the modulatory effects of ligands are governed by the valence of ligands, whether they bind directly to stickers versus spacers, and the relative affinities of ligand–scaffold versus scaffold–scaffold interactions. In general, all ligands have a diluting effect on the concentration of scaffolds within condensates. Whereas monovalent ligands destabilize condensates, multivalent ligands can stabilize condensates by binding directly to spacers or destabilize condensates by binding directly to stickers. Bipartite ligands that bind to stickers and spacers can alter the structural organization of scaffold molecules within condensates even when they have a null effect on condensate stability. Our work highlights the importance of measuring dilute phase concentrations of scaffolds as a function of ligand concentration in cells. This can reveal whether ligands modulate scaffold phase behavior by enabling or suppressing phase separation at endogenous levels, thereby regulating the formation and dissolution of condensates in vivo.