Core-shell model of the clusters of CPEB4 isoforms preceding liquid-liquid phase separation.

Protein solutions can undergo liquid-liquid phase separation (LLPS), where a dispersed phase with a low protein concentration coexists with coacervates with a high protein concentration. We focus on the low complexity N-terminal domain of cytoplasmic polyadenylation element binding-4 protein, CPEB4, and its isoform depleted of the Exon4, CPEB4Δ4. They both exhibit LLPS, but in contrast to most systems undergoing LLPS, the single-phase regime preceding LLPS consists mainly of soluble protein clusters.

Erratum: Fluctuations and Shape Dependence of Microphase Separation in Systems with Long-Range Interactions [Phys. Rev. Lett. 131, 258401 (2023)].

This corrects the article DOI: 10.1103/PhysRevLett.131.

Mechanosensitivity of phase separation in an elastic gel.

Liquid-liquid phase separation (LLPS) in binary or multi-component solutions is a well-studied subject in soft matter with extensive applications in biological systems. In recent years, several experimental studies focused on LLPS of solutes in hydrated gels, where the formation of coexisting domains induces elastic deformations within the gel. While the experimental studies report unique physical characteristics of these systems, such as sensitivity to mechanical forces and stabilization of multiple, periodic phase-separated domains, the theoretical understanding of such systems and the role of long-range interactions have not emphasized the nonlinear nature of the equilibrium binodal for strong segregation of the solute.

Fluctuations and Shape Dependence of Microphase Separation in Systems with Long-Range Interactions.

The combination of phase separation and long-ranged, effective, Coulomb interactions results in microphase separation. We predict the sizes and shapes of such microdomains and uniquely their dependence on the macroscopic sample shape which also affects the effective interfacial tension of fluctuations of the lamellar phase. These are applied to equilibrium salt solutions and block copolymers.

Affinity hierarchies and amphiphilic proteins underlie the co-assembly of nucleolar and heterochromatin condensates.

Nucleoli are surrounded by Pericentromeric Heterochromatin (PCH), reflecting a close spatial association between the two largest biomolecular condensates in eukaryotic nuclei. This nuclear organizational feature is highly conserved and is disrupted in diseased states like senescence, however, the mechanisms driving PCH-nucleolar association are unclear. High-resolution live imaging during early Drosophila development revealed a highly dynamic process in which PCH and nucleolar formation is coordinated and interdependent.

Scaling perspectives of underscreening in concentrated electrolyte solutions.

We present a scaling view of underscreening observed in salt solutions in the range of concentrations greater than about 1 M, in which the screening length increases with concentration. The system consists of hydrated clusters of positive and negative ions with a single unpaired ion as suggested by recent simulations. The environment of this ion is more hydrated than average which leads to a self-similar situation in which the size of this environment scales with the screening length.

Affinity hierarchies and amphiphilic proteins underlie the co-assembly of nucleolar and heterochromatin condensates.

Nucleoli are surrounded by Pericentromeric Heterochromatin (PCH), reflecting a close spatial association between the two largest biomolecular condensates in eukaryotic nuclei. Nucleoli are the sites of ribosome synthesis, while the repeat-rich PCH is essential for chromosome segregation, genome stability, and transcriptional silencing. How and why these two distinct condensates co-assemble is unclear.

Regulation of chromatin microphase separation by binding of protein complexes.

We show evidence of the association of RNA polymerase II (RNAP) with chromatin in a core-shell organization, reminiscent of microphase separation where the cores comprise dense chromatin and the shell, RNAP and chromatin with low density. These observations motivate our physical model for the regulation of core-shell chromatin organization. Here, we model chromatin as a multiblock copolymer, comprising active and inactive regions (blocks) that are both in poor solvent and tend to be condensed in the absence of binding proteins.

Mesoscale, long-time mixing of chromosomes and its connection to polymer dynamics.

Chromosomes are arranged in distinct territories within the nucleus of animal cells. Recent experiments have shown that these territories overlap at their edges, suggesting partial mixing during interphase. Experiments that knock-down of condensin II proteins during interphase indicate increased chromosome mixing, which demonstrates control of the mixing.

The LINC Complex Inhibits Excessive Chromatin Repression.

The Linker of Nucleoskeleton and Cytoskeleton (LINC) complex transduces nuclear mechanical inputs suggested to control chromatin organization and gene expression; however, the underlying mechanism is currently unclear. We show here that the LINC complex is needed to minimize chromatin repression in muscle tissue, where the nuclei are exposed to significant mechanical inputs during muscle contraction. To this end, the genomic binding profiles of Polycomb, Heterochromatin Protein1 (HP1a) repressors, and of RNA-Pol II were studied in larval muscles lacking functional LINC complex.

Volume regulation in adhered cells: Roles of surface tension and cell swelling.

The volume of adhered cells has been shown experimentally to decrease during spreading. This effect can be understood from the pump-leak model, which we have extended to include mechano-sensitive ion transporters. We identify a novel effect that has important consequences on cellular volume loss: cells that are swollen due to a modulation of ion transport rates are more susceptible to volume loss in response to a tension increase.

Affinity and Valence Impact the Extent and Symmetry of Phase Separation of Multivalent Proteins.

Biomolecular self-assembly spatially segregates proteins with a limited number of binding sites (valence) into condensates that coexist with a dilute phase. We develop a many-body lattice model for a three-component system of proteins with fixed valence in a solvent. We compare the predictions of the model to experimental phase diagrams that we measure in vivo, which allows us to vary specifically a binding site's affinity and valency.

Balance of osmotic pressures determines the nuclear-to-cytoplasmic volume ratio of the cell.

The volume of the cell nucleus varies across cell types and species and is commonly thought to be determined by the size of the genome and degree of chromatin compaction. However, this notion has been challenged over the years by much experimental evidence. Here, we consider the physical condition of mechanical force balance as a determining condition of the nuclear volume and use quantitative, order-of-magnitude analysis to estimate the forces from different sources of nuclear and cytoplasmic pressure.

Physical theory of biological noise buffering by multicomponent phase separation.

Maintaining homeostasis is a fundamental characteristic of living systems. In cells, this is contributed to by the assembly of biochemically distinct organelles, many of which are not membrane bound but form by the physical process of liquid-liquid phase separation (LLPS). By analogy with LLPS in binary solutions, cellular LLPS was hypothesized to contribute to homeostasis by facilitating "concentration buffering," which renders the local protein concentration within the organelle robust to global variations in the average cellular concentration (e.

Live imaging of chromatin distribution reveals novel principles of nuclear architecture and chromatin compartmentalization.

The three-dimensional organization of chromatin contributes to transcriptional control, but information about native chromatin distribution is limited. Imaging chromatin in live larvae, with preserved nuclear volume, revealed that active and repressed chromatin separates from the nuclear interior and forms a peripheral layer underneath the nuclear lamina. This is in contrast to the current view that chromatin distributes throughout the nucleus.

Mesoscale phase separation of chromatin in the nucleus.

Intact-organism imaging of larvae reveals and quantifies chromatin-aqueous phase separation. The chromatin can be organized near the lamina layer of the nuclear envelope, conventionally fill the nucleus, be organized centrally, or as a wetting droplet. These transitions are controlled by changes in nuclear volume and the interaction of chromatin with the lamina (part of the nuclear envelope) at the nuclear periphery.

Long-Time Phase Correlations Reveal Regulation of Beating Cardiomyocytes.

Spontaneous contractions of cardiomyocytes are driven by calcium oscillations due to the activity of ionic calcium channels and pumps. The beating phase is related to the time-dependent deviation of the oscillations from their average frequency, due to noise and the resulting cellular response. Here, we demonstrate experimentally that, in addition to the short-time (1-2 Hz), beat-to-beat variability, there are long-time correlations (tens of minutes) in the beating phase dynamics of isolated cardiomyocytes.

Designer protein assemblies with tunable phase diagrams in living cells.

Protein self-organization is a hallmark of biological systems. Although the physicochemical principles governing protein-protein interactions have long been known, the principles by which such nanoscale interactions generate diverse phenotypes of mesoscale assemblies, including phase-separated compartments, remain challenging to characterize. To illuminate such principles, we create a system of two proteins designed to interact and form mesh-like assemblies.

Equilibrium size distribution and phase separation of multivalent, molecular assemblies in dilute solution.

Multivalent molecules can bind a limited number of multiple neighbors via specific interactions. In this paper, we investigate theoretically the self-assembly and phase separation of such molecules in dilute solution. We show that the equilibrium size (n) distributions of linear or branched assemblies qualitatively differ; the former decays exponentially with the relative size n/N[combining macron] (N[combining macron] = n), while the latter decays as a power law, with an exponential cutoff only for n ⪆ N[combining macron]2 ≫ N[combining macron].

Cardiomyocyte Calcium Ion Oscillations-Lessons From Physics.

We review a theoretical, coarse-grained description for cardiomyocytes calcium dynamics that is motivated by experiments on RyR channel dynamics and provides an analogy to other spontaneously oscillating systems. We show how a minimal model, that focuses on calcium channel and pump dynamics and kinetics, results in a single, easily understood equation for spontaneous calcium oscillations (the Van-der-Pol equation). We analyze experiments on isolated RyR channels to quantify how the channel dynamics depends both on the local calcium concentration, as well as its temporal behavior ("adaptation").

Active volume regulation in adhered cells.

Recent experiments reveal that the volume of adhered cells is reduced as their basal area is increased. During spreading, the cell volume decreases by several thousand cubic micrometers, corresponding to large pressure changes of the order of megapascals. We show theoretically that the volume regulation of adhered cells is determined by two concurrent conditions: mechanical equilibrium with the extracellular environment and a generalization of Donnan (electrostatic) equilibrium that accounts for active ion transport.

Screening length for finite-size ions in concentrated electrolytes.

The classical Debye-Hückel (DH) theory clearly accounts for the origin of screening in electrolyte solutions and works rather well for dilute electrolyte solutions. While the Debye screening length decreases with the ion concentration and is independent of ion size, recent surface-force measurements imply that for concentrated solutions, the screening length exhibits an opposite trend; it increases with ion concentration and depends on the ionic size. The screening length is usually defined by the response of the electrolyte solution to a test charge but can equivalently be derived from the charge-charge correlation function.

Registry Kinetics of Myosin Motor Stacks Driven by Mechanical Force-Induced Actin Turnover.

Actin filaments associated with myosin motors constitute the cytoskeletal force-generating machinery for many types of adherent cells. These actomyosin units are structurally ordered in muscle cells and, in particular, may be spatially registered across neighboring actin bundles. Such registry or stacking of myosin filaments have been recently observed in ordered actin bundles of even fibroblasts with super-resolution microscopy techniques.

Physics of Spontaneous Calcium Oscillations in Cardiac Cells and Their Entrainment.

Mechanical contraction in muscle cells requires Ca to allow myosin binding to actin. Beating cardiomyocytes contain internal Ca stores whose cytoplasmic concentration oscillates. Our theory explains observed single channel dynamics as well as cellular oscillations in spontaneously beating cardiomyocytes.

Living Matter: Mesoscopic Active Materials.

An introduction to the physical properties of living active matter at the mesoscopic scale (tens of nanometers to micrometers) and their unique features compared with "dead," nonactive matter is presented. This field of research is increasingly denoted as "biological physics" where physics includes chemical physics, soft matter physics, hydrodynamics, mechanics, and the related engineering sciences. The focus is on the emergent properties of these systems and their collective behavior, which results in active self-organization and how they relate to cellular-level biological function.