Polar Positioning of Phase-Separated Liquid Compartments in Cells Regulated by an mRNA Competition Mechanism.

P granules are non-membrane-bound RNA-protein compartments that are involved in germline development in C. elegans. They are liquids that condense at one end of the embryo by localized phase separation, driven by gradients of polarity proteins such as the mRNA-binding protein MEX-5. To probe how polarity proteins regulate phase separation, we combined biochemistry and theoretical modeling. We reconstitute P granule-like droplets in vitro using a single protein PGL-3. By combining in vitro reconstitution with measurements of intracellular concentrations, we show that competition between PGL-3 and MEX-5 for mRNA can regulate the formation of PGL-3 droplets. Using theory, we show that, in a MEX-5 gradient, this mRNA competition mechanism can drive a gradient of P granule assembly with similar spatial and temporal characteristics to P granule assembly in vivo. We conclude that gradients of polarity proteins can position RNP granules during development by using RNA competition to regulate local phase separation.

A condensate dynamic instability orchestrates actomyosin cortex activation.

A key event at the onset of development is the activation of a contractile actomyosin cortex during the oocyte-to-embryo transition1-3. Here we report on the discovery that, in Caenorhabditis elegans oocytes, actomyosin cortex activation is supported by the emergence of thousands of short-lived protein condensates rich in F-actin, N-WASP and the ARP2/3 complex4-8 that form an active micro-emulsion. A phase portrait analysis of the dynamics of individual cortical condensates reveals that condensates initially grow and then transition to disassembly before dissolving completely. We find that, in contrast to condensate growth through diffusion9, the growth dynamics of cortical condensates are chemically driven. Notably, the associated chemical reactions obey mass action kinetics that govern both composition and size. We suggest that the resultant condensate dynamic instability10 suppresses coarsening of the active micro-emulsion11, ensures reaction kinetics that are independent of condensate size and prevents runaway F-actin nucleation during the formation of the first cortical actin meshwork.

Morphogen gradient scaling by recycling of intracellular Dpp.

Morphogen gradients are fundamental to establish morphological patterns in developing tissues1. During development, gradients scale to remain proportional to the size of growing organs2,3. Scaling is a universal gear that adjusts patterns to size in living organisms3-8, but its mechanisms remain unclear. Here, focusing on the Decapentaplegic (Dpp) gradient in the Drosophila wing disc, we uncover a cell biological basis behind scaling. From small to large discs, scaling of the Dpp gradient is achieved by increasing the contribution of the internalized Dpp molecules to Dpp transport: to expand the gradient, endocytosed molecules are re-exocytosed to spread extracellularly. To regulate the contribution of endocytosed Dpp to the spreading extracellular pool during tissue growth, it is the Dpp binding rates that are progressively modulated by the extracellular factor Pentagone, which drives scaling. Thus, for some morphogens, evolution may act on endocytic trafficking to regulate the range of the gradient and its scaling, which could allow the adaptation of shape and pattern to different sizes of organs in different species.

Liquid-liquid phase separation in biology.

Cells organize many of their biochemical reactions in non-membrane compartments. Recent evidence has shown that many of these compartments are liquids that form by phase separation from the cytoplasm. Here we discuss the basic physical concepts necessary to understand the consequences of liquid-like states for biological functions.

Cortical dynein controls microtubule dynamics to generate pulling forces that position microtubule asters.

Dynein at the cortex contributes to microtubule-based positioning processes such as spindle positioning during embryonic cell division and centrosome positioning during fibroblast migration. To investigate how cortical dynein interacts with microtubule ends to generate force and how this functional association impacts positioning, we have reconstituted the 'cortical' interaction between dynein and dynamic microtubule ends in an in vitro system using microfabricated barriers. We show that barrier-attached dynein captures microtubule ends, inhibits growth, and triggers microtubule catastrophes, thereby controlling microtubule length. The subsequent interaction with shrinking microtubule ends generates pulling forces up to several pN. By combining experiments in microchambers with a theoretical description of aster mechanics, we show that dynein-mediated pulling forces lead to the reliable centering of microtubule asters in simple confining geometries. Our results demonstrate the intrinsic ability of cortical microtubule-dynein interactions to regulate microtubule dynamics and drive positioning processes in living cells.

A cytokinetic ring-driven cell rotation achieves Hertwig's rule in early development.

Hertwig's rule states that cells divide along their longest axis, usually driven by forces acting on the mitotic spindle. Here, we show that in contrast to this rule, microtubule-based pulling forces in early Caenorhabditis elegans embryos align the spindle with the short axis of the cell. We combine theory with experiments to reveal that in order to correct this misalignment, inward forces generated by the constricting cytokinetic ring rotate the entire cell until the spindle is aligned with the cell's long axis. Experiments with slightly compressed mouse zygotes indicate that this cytokinetic ring-driven mechanism of ensuring Hertwig's rule is general for cells capable of rotating inside a confining shell, a scenario that applies to early cell divisions of many systems.

Cell flow reorients the axis of planar polarity in the wing epithelium of Drosophila.

Planar cell polarity (PCP) proteins form polarized cortical domains that govern polarity of external structures such as hairs and cilia in both vertebrate and invertebrate epithelia. The mechanisms that globally orient planar polarity are not understood, and are investigated here in the Drosophila wing using a combination of experiment and theory. Planar polarity arises during growth and PCP domains are initially oriented toward the well-characterized organizer regions that control growth and patterning. At pupal stages, the wing hinge contracts, subjecting wing-blade epithelial cells to anisotropic tension in the proximal-distal axis. This results in precise patterns of oriented cell elongation, cell rearrangement and cell division that elongate the blade proximo-distally and realign planar polarity with the proximal-distal axis. Mutation of the atypical Cadherin Dachsous perturbs the global polarity pattern by altering epithelial dynamics. This mechanism utilizes the cellular movements that sculpt tissues to align planar polarity with tissue shape.

Co-condensation of proteins with single- and double-stranded DNA.

SignificanceBiomolecular condensates are intracellular organelles that are not bounded by membranes and often show liquid-like, dynamic material properties. They typically contain various types of proteins and nucleic acids. How the interaction of proteins and nucleic acids finally results in dynamic condensates is not fully understood. Here we use optical tweezers and fluorescence microscopy to study how the prototypical prion-like protein Fused-in-Sarcoma (FUS) condenses with individual molecules of single- and double-stranded DNA. We find that FUS adsorbs on DNA in a monolayer and hence generates an effectively sticky FUS-DNA polymer that collapses and finally forms a dynamic, reversible FUS-DNA co-condensate. We speculate that protein monolayer-based protein-nucleic acid co-condensation is a general mechanism for forming intracellular membraneless organelles.

Hydraulic and electric control of cell spheroids.

We use a theoretical approach to examine the effect of a radial fluid flow or electric current on the growth and homeostasis of a cell spheroid. Such conditions may be generated by a drain of micrometric diameter. To perform this analysis, we describe the tissue as a continuum. We include active mechanical, electric, and hydraulic components in the tissue material properties. We consider a spherical geometry and study the effect of the drain on the dynamics of the cell aggregate. We show that a steady fluid flow or electric current imposed by the drain could be able to significantly change the spheroid long-time state. In particular, our work suggests that a growing spheroid can systematically be driven to a shrinking state if an appropriate external field is applied. Order-of-magnitude estimates suggest that such fields are of the order of the indigenous ones. Similarities and differences with the case of tumors and embryo development are briefly discussed.

Local thermodynamics govern formation and dissolution of Caenorhabditis elegans P granule condensates.

Membraneless compartments, also known as condensates, provide chemically distinct environments and thus spatially organize the cell. A well-studied example of condensates is P granules in the roundworm Caenorhabditis elegans that play an important role in the development of the germline. P granules are RNA-rich protein condensates that share the key properties of liquid droplets such as a spherical shape, the ability to fuse, and fast diffusion of their molecular components. An outstanding question is to what extent phase separation at thermodynamic equilibrium is appropriate to describe the formation of condensates in an active cellular environment. To address this question, we investigate the response of P granule condensates in living cells to temperature changes. We observe that P granules dissolve upon increasing the temperature and recondense upon lowering the temperature in a reversible manner. Strikingly, this temperature response can be captured by in vivo phase diagrams that are well described by a Flory-Huggins model at thermodynamic equilibrium. This finding is surprising due to active processes in a living cell. To address the impact of such active processes on intracellular phase separation, we discuss temperature heterogeneities. We show that, for typical estimates of the density of active processes, temperature represents a well-defined variable and that mesoscopic volume elements are at local thermodynamic equilibrium. Our findings provide strong evidence that P granule assembly and disassembly are governed by phase separation based on local thermal equilibria where the nonequilibrium nature of the cytoplasm is manifested on larger scales.

Random Traction Yielding Transition in Epithelial Tissues.

We investigate how randomly oriented cell traction forces lead to fluidization in a vertex model of epithelial tissues. We find that the fluidization occurs at a critical value of the traction force magnitude F_{c}. We show that this transition exhibits critical behavior, similar to the yielding transition of sheared amorphous solids. However, we find that it belongs to a different universality class, even though it satisfies the same scaling relations between critical exponents established in the yielding transition of sheared amorphous solids. Our work provides a fluidization mechanism through active force generation that could be relevant in biological tissues.

Understanding morphogenetic growth control -- lessons from flies.

Morphogens are secreted signalling molecules that control the patterning and growth of developing organs. How morphogens regulate patterning is fairly well understood; however, how they control growth is less clear. Four principal models have been proposed to explain how the morphogenetic protein Decapentaplegic (DPP) controls the growth of the wing imaginal disc in the fly. Recent studies in this model system have provided a wealth of experimental data on growth and DPP gradient properties, as well as on the interactions of DPP with other signalling pathways. These findings have allowed a more precise formulation and evaluation of morphogenetic growth models. The insights into growth control by the DPP gradient will also be useful for understanding other morphogenetic growth systems.

Active forces shape the metaphase spindle through a mechanical instability.

The metaphase spindle is a dynamic structure orchestrating chromosome segregation during cell division. Recently, soft matter approaches have shown that the spindle behaves as an active liquid crystal. Still, it remains unclear how active force generation contributes to its characteristic spindle-like shape. Here we combine theory and experiments to show that molecular motor-driven forces shape the structure through a barreling-type instability. We test our physical model by titrating dynein activity in Xenopus egg extract spindles and quantifying the shape and microtubule orientation. We conclude that spindles are shaped by the interplay between surface tension, nematic elasticity, and motor-driven active forces. Our study reveals how motor proteins can mold liquid crystalline droplets and has implications for the design of active soft materials.

Chemical Kinetics and Mass Action in Coexisting Phases.

The kinetics of chemical reactions are determined by the law of mass action, which has been successfully applied to homogeneous, dilute mixtures. At nondilute conditions, interactions among the components can give rise to coexisting phases, which can significantly alter the kinetics of chemical reactions. Here, we derive a theory for chemical reactions in coexisting phases at phase equilibrium. We show that phase equilibrium couples the rates of chemical reactions of components with their diffusive exchanges between the phases. Strikingly, the chemical relaxation kinetics can be represented as a flow along the phase equilibrium line in the phase diagram. A key finding of our theory is that differences in reaction rates between coexisting phases stem solely from phase-dependent reaction rate coefficients. Our theory is key to interpreting how concentration levels of reactive components in condensed phases control chemical reaction rates in synthetic and biological systems.

Long-range morphogen gradient formation by cell-to-cell signal propagation.

Morphogen gradients are a central concept in developmental biology. Their formation often involves the secretion of morphogens from a local source, that spread by diffusion in the cell field, where molecules eventually get degraded. This implies limits to both the time and length scales over which morphogen gradients can form which are set by diffusion coefficients and degradation rates. Towards the goal of identifying plausible mechanisms capable of extending the gradient range, we here use theory to explore properties of a cell-to-cell signaling relay. Inspired by the millimeter-scalewnt-expression and signaling gradients in flatworms, we consider morphogen-mediated morphogen production in the cell field. We show that such a relay can generate stable morphogen and signaling gradients that are oriented by a local, morphogen-independent source of morphogen at a boundary. This gradient formation can be related to an effective diffusion and an effective degradation that result from morphogen production due to signaling relay. If the secretion of morphogen produced in response to the relay is polarized, it further gives rise to an effective drift. We find that signaling relay can generate long-range gradients in relevant times without relying on extreme choices of diffusion coefficients or degradation rates, thus exceeding the limits set by physiological diffusion coefficients and degradation rates. A signaling relay is hence an attractive principle to conceptualize long-range gradient formation by slowly diffusing morphogens that are relevant for patterning in adult contexts such as regeneration and tissue turn-over.

Molecular Assembly Lines in Active Droplets.

Large protein complexes are assembled from protein subunits to form a specific structure. In our theoretic work, we propose that assembly into the correct structure could be reliably achieved through an assembly line with a specific sequence of assembly steps. Using droplet interfaces to position compartment boundaries, we show that an assembly line can be self-organized by active droplets. As a consequence, assembly steps can be arranged spatially so that a specific order of assembly is achieved and incorrect assembly is strongly suppressed.

Correction: Quantification of nematic cell polarity in three-dimensional tissues.

[This corrects the article DOI: 10.1371/journal.pcbi.1008412.].

Active T1 transitions in cellular networks.

In amorphous solids as in tissues, neighbor exchanges can relax local stresses and allow the material to flow. In this paper, we use an anisotropic vertex model to study T1 rearrangements in polygonal cellular networks. We consider two different physical realizations of the active anisotropic stresses: (i) anisotropic bond tension and (ii) anisotropic cell stress. Interestingly, the two types of active stress lead to patterns of relative orientation of T1 transitions and cell elongation that are different. Our work suggests that these two realizations of anisotropic active stresses can be observed in vivo. We describe and explain these results through the lens of a continuum description of the tissue as an anisotropic active material. We furthermore discuss the energetics of the dynamic tissue and express the energy balance in terms of internal elastic energy, mechanical work, chemical work and heat. This allows us to define active T1 transitions that can perform mechanical work while consuming chemical energy.

Fluid pumping and active flexoelectricity can promote lumen nucleation in cell assemblies.

We discuss the physical mechanisms that promote or suppress the nucleation of a fluid-filled lumen inside a cell assembly or a tissue. We discuss lumen formation in a continuum theory of tissue material properties in which the tissue is described as a 2-fluid system to account for its permeation by the interstitial fluid, and we include fluid pumping as well as active electric effects. Considering a spherical geometry and a polarized tissue, our work shows that fluid pumping and tissue flexoelectricity play a crucial role in lumen formation. We furthermore explore the large variety of long-time states that are accessible for the cell aggregate and its lumen. Our work reveals a role of the coupling of mechanical, electrical, and hydraulic phenomena in tissue lumen formation.