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In a companion paper, we put forth a thermodynamic model for complex formation via a chemical reaction involving multiple macromolecular species, which may subsequently undergo liquid–liquid phase separation and a further transition into a gel-like state. In the present work, we formulate a thermodynamically consistent kinetic framework to study the interplay between phase separation, chemical reaction, and aging in spatially inhomogeneous macromolecular mixtures. A numerical algorithm is also proposed to simulate domain growth from collisions of liquid and gel domains via passive Brownian motion in both two and three spatial dimensions. Our results show that the coarsening behavior is significantly influenced by the degree of gelation and Brownian motion. The presence of a gel phase inside condensates strongly limits the diffusive transport processes, and Brownian motion coalescence controls the coarsening process in systems with high area/volume fractions of gel-like condensates, leading to the formation of interconnected domains with atypical domain growth rates controlled by size-dependent translational and rotational diffusivities. 

Multicomponent macromolecular mixtures often form higher-order structures, which may display non-ideal mixing and aging behaviors. In this work, we first propose a minimal model of a quaternary system that takes into account the formation of a complex via a chemical reaction involving two macromolecular species; the complex may then phase separate from the buffer and undergo a further transition into a gel-like state. We subsequently investigate how physical parameters such as molecular size, stoichiometric coefficients, equilibrium constants, and interaction parameters affect the phase behavior of the mixture and its propensity to undergo aging via gelation. In addition, we analyze the thermodynamic stability of the system and identify the spinodal regions and their overlap with gelation boundaries. The approach developed in this work can be readily generalized to study systems with an arbitrary number of components. More broadly, it provides a physically based starting point for the investigation of the kinetics of the coupled complex formation, phase separation, and gelation processes in spatially extended systems. 

Matrix-assisted pulsed laser evaporation enables precise control of polymer film deposition, facilitating the creation of well-oriented epitaxial polymer films and offering insights into confined crystallization. 

Abstract Complex fibrillar networks mediate liquid–liquid phase separation of biomolecular condensates within the cell. Mechanical interactions between these condensates and the surrounding networks are increasingly implicated in the physiology of the condensates and yet, the physical principles underlying phase separation within intracellular media remain poorly understood. Here, we elucidate the dynamics and mechanics of liquid–liquid phase separation within fibrillar networks by condensing oil droplets within biopolymer gels. We find that condensates constrained within the network pore space grow in abrupt temporal bursts. The subsequent restructuring of condensates and concomitant network deformation is contingent on the fracture of network fibrils, which is determined by a competition between condensate capillarity and network strength. As a synthetic analog to intracellular phase separation, these results further our understanding of the mechanical interactions between biomolecular condensates and fibrillar networks in the cell. 

Abstract In cells, phase-separated liquid condensates interact mechanically with surrounding elastic networks such as chromatin and cytoskeleton. By considering the trade-offs between elastic, wetting, and interfacial energies, we theoretically show that three droplet phases can be thermodynamically stable: macroscopic droplets that either cavitate or permeate the network, and mesh-size–limited microdroplets. We show that network strain stiffening further enhances this latter size-limitation effect. Our theory predicts the possibility of yet-unobserved droplet phases in the cytoplasm and nucleoplasm.