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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. Spatial and temporal organization of molecular matter is a defining hallmark of cellular ultrastructure and recent attention has focused on membraneless organelles, which are also referred to as biomolecular condensates. Of interest are condensates that form via phase transitions that combine phase separation and networking of multivalent protein and nucleic acid molecules. Building on recently recognized analogies between associative polymers and multivalent proteins, we have developed and deployed LASSI, an open source computational engine that enables the calculation of architecture-specific phase diagrams for multivalent proteins. LASSI relies on a priori identification of stickers and spacers within a multivalent protein and mapping the stickers onto a 3-dimensional lattice. A Monte Carlo engine that incorporates a suite of novel and established move sets enables simulations that track density inhomogeneities and changes to the extent of networking among stickers as a function of protein concentration and interaction strengths. Calculation of distribution functions and other order parameters allow us to compute full phase diagrams for multivalent proteins modeled using a stickers-and-spacers representation on simple cubic lattices. These calculations allow us to rationalize experimental observations and open the door to the design of protein architectures with bespoke phase behavior. LASSI can be deployed to study the phase behavior of multicomponent systems, which allows us to make direct contact with the physical principles underlying cellular biomolecular condensates. [ABSTRACT FROM AUTHOR]

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 Author(s) 2024. Published by Oxford University Press on behalf of National Academy of Sciences.)

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.

The functions of biomolecular condensates are thought to be influenced by their material properties, and these are in turn determined by the multiscale structural features within condensates. However, structural characterizations of condensates are challenging, and hence rarely reported. Here, we deploy a combination of small angle neutron scattering, fluorescence recovery after photobleaching, and bespoke coarse-grained molecular dynamics simulations to provide structural descriptions of model condensates that mimic nucleolar granular components (GCs). We show that facsimiles of GCs are network fluids featuring spatial inhomogeneities across hierarchies of 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, extracted from a combination of approaches, suggest that condensates formed by multivalent proteins share features with network fluids formed by associative systems such as patchy or hairy colloids., Competing Interests: Competing interests R.V.P. is a member of the scientific advisory board and shareholder of Dewpoint Therapeutics Inc. D.M.M. is an employee and shareholder of Dewpoint Therapeutics. The work reported here was not influenced by these affiliations. The remaining authors have no competing interests to declare.

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. Additionally, 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., Significance: Phase separation has emerged as a process of significant relevance to sorting macromolecules into distinct compartments, thereby enabling spatial and temporal control over cellular matter. Considerable effort is being invested into uncovering the driving forces that enable the separation of macromolecular solutions into coexisting phases. At its heart, this process is governed by the balance of macromolecule-solvent, inter-macromolecule, and solvent-solvent interactions. We show that the driving forces for phase separation, including the coefficients that measure interaction strengths between macromolecules, can be extracted by titrating the concentrations of crowders that enable macromolecules to phase separate at lower concentrations. Our work paves the way to leverage specific categories of measurements for quantitative characterizations of driving forces for phase separation.

Macromolecular phase separation underlies the regulated formation and dissolution of biomolecular condensates. What is unclear is how condensates of distinct and shared macromolecular compositions form and coexist within cellular milieus. Here, we use theory and computation to establish thermodynamic criteria that must be satisfied to achieve compositionally distinct condensates. We applied these criteria to an archetypal ribonucleoprotein condensate and discovered that demixing into distinct protein-RNA condensates cannot be the result of purely thermodynamic considerations. Instead, demixed, compositionally distinct condensates arise due to asynchronies in timescales that emerge from differences in long-lived protein-RNA and RNA-RNA crosslinks. This type of dynamical control is also found to be active in live cells whereby asynchronous production of molecules is required for realizing demixed protein-RNA condensates. We find that interactions that exert dynamical control provide a versatile and generalizable way to influence the compositions of coexisting condensates in live cells., Competing Interests: Additional Declarations: There is NO Competing Interest.

Cellular matter can be spatially and temporally organized into membraneless biomolecular condensates. The current thinking is that these condensates form and dissolve via phase transitions driven by one or more condensate-specific multivalent macromolecules known as scaffolds. Cells likely regulate condensate formation and dissolution by exerting control over the concentrations of regulatory molecules, which we refer to as ligands. Wyman and Gill introduced the framework of polyphasic linkage to explain how ligands can exert thermodynamic control over phase transitions. This review focuses on describing the concepts of polyphasic linkage and the relevance of such a mechanism for controlling condensate formation and dissolution. We describe how ligand-mediated control over scaffold phase behavior can be quantified experimentally. Further, we build on recent studies to highlight features of ligands that make them suppressors vs drivers of phase separation. Finally, we highlight areas where advances are needed to further understand ligand-mediated control of condensates in complex cellular environments. These advances include understanding the effects of networks of ligands on condensate behavior and how ligands modulate phase transitions controlled by different combinations of homotypic and heterotypic interactions among scaffold macromolecules. Insights gained from the application of polyphasic linkage concepts should be useful for designing novel pharmaceutical ligands to regulate condensates., (© 2021 Author(s).)

Computer simulations of model proteins with sticker-and-spacer architectures shed light on the formation of biomolecular condensates in cells., Competing Interests: FD No competing interests declared, RP is a member of the scientific advisory board of Dewpoint Therapeutics., (© 2020, Dar and Pappu.)