Active suppression of Ostwald ripening: Beyond mean-field theory

Asymptotic analysis of particle cluster formation in the presence of anchoring sites

The aggregation or clustering of proteins and other macromolecules plays an important role in the formation of large-scale molecular assemblies within cell membranes. Examples of such assemblies include lipid rafts, and postsynaptic domains (PSDs) at excitatory and inhibitory synapses in neurons. PSDs are rich in scaffolding proteins that can transiently trap transmembrane neurotransmitter receptors, thus localizing them at specific spatial positions. Hence, PSDs play a key role in determining the strength of synaptic connections and their regulation during learning and memory. Recently, a two-dimensional (2D) diffusion-mediated aggregation model of PSD formation has been developed in which the spatial locations of the clusters are determined by a set of fixed anchoring sites. The system is kept out of equilibrium by the recycling of particles between the cell membrane and interior. This results in a stationary distribution consisting of multiple clusters, whose average size can be determined using an effective mean-field description of the particle concentration around each anchored cluster. In this paper, we derive corrections to the mean-field approximation by applying the theory of diffusion in singularly perturbed domains. The latter is a powerful analytical method for solving two-dimensional (2D) and three-dimensional (3D) diffusion problems in domains where small holes or perforations have been removed from the interior. Applications range from modeling intracellular diffusion, where interior holes could represent subcellular structures such as organelles or biological condensates, to tracking the spread of chemical pollutants or heat from localized sources. In this paper, we take the bounded domain to be the cell membrane and the holes to represent anchored clusters. The analysis proceeds by partitioning the membrane into a set of inner regions around each cluster, and an outer region where mean-field interactions occur. Asymptotically matching the inner and outer stationary solutions generates an asymptotic expansion of the particle concentration, which includes higher-order corrections to mean-field theory that depend on the positions of the clusters and the boundary of the domain. Motivated by a recent study of light-activated protein oligomerization in cells, we also develop the analogous theory for cluster formation in a three-dimensional (3D) domain. The details of the asymptotic analysis differ from the 2D case due to the contrasting singularity structure of 2D and 3D Green's functions.

Multiscale Modeling of Protein-RNA Condensation in and Out of Equilibrium

A vast number of intracellular membraneless bodies also known as biomolecular condensates form through a liquid-liquid phase separation (LLPS) of biomolecules. To date, phase separation has been identified as the main driving force for a membraneless organelles such as nucleoli, Cajal bodies, stress granules, and chromatin compartments. Recently, the protein-RNA condensation is receiving increased attention, because it is closely related to the biological function of cells such as transcription, translation, and RNA metabolism. Despite the multidisciplinary efforts put forth to study the biophysical properties of protein-RNA condensates, there are many fundamental unanswered questions regarding the mechanism of formation and regulation of protein-RNA condensates in eukaryotic cells. Major challenges in studying protein-RNA condensation stem from (i) the molecular heterogeneity and conformational flexibility of RNA and protein chains and (ii) the nonequilibrium nature of transcription and cellular environment. Computer simulations, bioinformatics, and mathematical models are uniquely positioned for shedding light on the microscopic nature of protein-RNA phase separation. To this end, there is an urgent need for innovative models with the right spatiotemporal resolution for confronting the experimental observables in a comprehensive and physics-based manner. In this chapter, we will summarize the currently emerging research efforts, which employ atomistic and coarse-grained molecular models and field theoretical models to understand equilibrium and nonequilibrium aspects of protein-RNA condensation.

Membrane surfaces regulate assembly of ribonucleoprotein condensates

Biomolecular condensates organize biochemistry, yet little is known about how cells control the position and scale of these structures. In cells, condensates often appear as relatively small assemblies that do not coarsen into a single droplet despite their propensity to fuse. Here we report that ribonucleoprotein condensates of the Q-rich protein Whi3 interact with the endoplasmic reticulum, prompting us to examine how membrane association controls condensate size. Reconstitution reveals that membrane recruitment promotes Whi3 condensation under physiological conditions. These assemblies rapidly arrest, resembling size distributions seen in cells. The temporal ordering of molecular interactions and the slow diffusion of membrane-bound complexes can limit condensate size. Our experiments reveal a tradeoff between locally-enhanced protein concentration at membranes, favoring condensation, and an accompanying reduction in diffusion, restricting coarsening. Given that many condensates bind endomembranes, we predict that the biophysical properties of lipid bilayers are key for controlling condensate sizes throughout the cell.

Essence determines phenomenon: Assaying the material properties of biological condensates

Intracellular spaces are partitioned into separate compartments to ensure that numerous biochemical reactions and cellular functions take place in a spatiotemporally controlled manner. Biomacromolecules including proteins and RNAs undergo liquid–liquid phase separation and subsequent phase transition to form biological condensates with diverse material states. The material/physical properties of biological condensates are crucial for fulfilling their distinct physiological functions, and abnormal material properties can cause deleterious effects under pathological conditions. Here, we review recent studies showing the role of the material properties of biological condensates in their physiological functions. We also summarize several classic methods as well as newly emerging techniques for characterization and/or measurement of the material properties of biological condensates.

Liquid-Liquid Phase Separation: Unraveling the Enigma of Biomolecular Condensates in Microbial Cells

Numerous examples of microbial phase-separated biomolecular condensates have now been identified following advances in fluorescence imaging and single molecule microscopy technologies. The structure, function, and potential applications of these microbial condensates are currently receiving a great deal of attention. By neatly compartmentalizing proteins and their interactors in membrane-less organizations while maintaining free communication between these macromolecules and the external environment, microbial cells are able to achieve enhanced metabolic efficiency. Typically, these condensates also possess the ability to rapidly adapt to internal and external changes. The biological functions of several phase-separated condensates in small bacterial cells show evolutionary convergence with the biological functions of their eukaryotic paralogs. Artificial microbial membrane-less organelles are being constructed with application prospects in biocatalysis, biosynthesis, and biomedicine. In this review, we provide an overview of currently known biomolecular condensates driven by liquid-liquid phase separation (LLPS) in microbial cells, and we elaborate on their biogenesis mechanisms and biological functions. Additionally, we highlight the major challenges and future research prospects in studying microbial LLPS.

Regulation of biomolecular condensates by interfacial protein clusters

[Figure: see text].