Topological defects in epithelia govern cell death and extrusion

Multiphase field models for collective cell migration

Confluent cell monolayers and epithelia tissues show remarkable patterns and correlations in structural arrangements and actively driven collective flows. We simulate these properties using multiphase field models. The models are based on cell deformations and cell-cell interactions and we investigate the influence of microscopic details to incorporate active forces on emerging phenomena. We compare four different approaches, one in which the activity is determined by a random orientation, one where the activity is related to the deformation of the cells, and two models with subcellular details to resolve the mechanochemical interactions underlying cell migration. The models are compared with respect to generic features, such as coordination number distribution, cell shape variability, emerging nematic properties, as well as vorticity correlations and flow patterns in large confluent monolayers and confinements. All results are compared with experimental data for a large variety of cell cultures. The appearing qualitative differences of the models show the importance of microscopic details and provide a route towards predictive simulations of patterns and correlations in cell colonies.

Photocontrollable Crystallization at the Topological Defect of a Liquid Crystalline Droplet

Photocontrollable crystallization at topological defects in a liquid crystal (LC) droplet was demonstrated. The molecules dissolved in a surfactant solution outside the LC droplet were moved into the droplet via light absorption. Nuclei emerged tens of seconds after light irradiation and moved toward the topological defect located at the droplet center, thus forming a branch-shaped crystal. This phenomenon was reproduced for multiple different molecules; photoinduced migration, nucleation, and crystal formation were discussed as a plausible mechanism.

Digesting the mechanobiology of the intestinal epithelium

The dizzying life of the homeostatic intestinal epithelium is governed by a complex interplay between fate, form, force and function. This interplay is beginning to be elucidated thanks to advances in intravital and ex vivo imaging, organoid culture, and biomechanical measurements. Recent discoveries have untangled the intricate organization of the forces that fold the monolayer into crypts and villi, compartmentalize cell types, direct cell migration, and regulate cell identity, proliferation and death. These findings revealed that the dynamic equilibrium of the healthy intestinal epithelium relies on its ability to precisely coordinate tractions and tensions in space and time. In this review, we discuss recent findings in intestinal mechanobiology, and highlight some of the many fascinating questions that remain to be addressed in this emerging field.

Coupling Turing stripes to active flows

We numerically solve the active nematohydrodynamic equations of motion, coupled to a Turing reaction-diffusion model, to study the effect of active nematic flow on the stripe patterns resulting from a Turing instability. If the activity is uniform across the system, the Turing patterns dissociate when the flux from active advection balances that from the reaction-diffusion process. If the activity is coupled to the concentration of Turing morphogens, and neighbouring stripes have equal and opposite activity, the system self organises into a pattern of shearing flows, with stripes tending to fracture and slip sideways to join their neighbours. We discuss the role of active instabilities in controlling the crossover between these limits. Our results are of relevance to mechanochemical coupling in biological systems.

Turbulence-induced clustering in compressible active fluids

We study a novel phase of active polar fluids, which is characterized by the continuous creation and destruction of dense clusters due to self-sustained turbulence. This state arises due to the interplay between self-advection of the aligned swimmers and their defect topology. The typical cluster size is determined by the characteristic vortex size. Our results are obtained by investigating a continuum model of compressible polar active fluids, which incorporates typical experimental observations in bacterial suspensions, in particular a non-monotone dependence of speed on density.

Mechanical forces drive a reorientation cascade leading to biofilm self-patterning

In growing active matter systems, a large collection of engineered or living autonomous units metabolize free energy and create order at different length scales as they proliferate and migrate collectively. One such example is bacterial biofilms, surface-attached aggregates of bacterial cells embedded in an extracellular matrix that can exhibit community-scale orientational order. However, how bacterial growth coordinates with cell-surface interactions to create distinctive, long-range order during biofilm development remains elusive. Here we report a collective cell reorientation cascade in growing Vibrio cholerae biofilms that leads to a differentially ordered, spatiotemporally coupled core-rim structure reminiscent of a blooming aster. Cell verticalization in the core leads to a pattern of differential growth that drives radial alignment of the cells in the rim, while the growing rim generates compressive stresses that expand the verticalized core. Such self-patterning disappears in nonadherent mutants but can be restored through opto-manipulation of growth. Agent-based simulations and two-phase active nematic modeling jointly reveal the strong interdependence of the driving forces underlying the differential ordering. Our findings offer insight into the developmental processes that shape bacterial communities and provide ways to engineer phenotypes and functions in living active matter.

Transition kinetics of defect patterns in confined two-dimensional smectic liquid crystals

Topological defects in liquid crystals under confined geometries have attracted extensive research interests. Here, we perform molecular dynamics simulations to investigate the formation and transition of defect patterns in two-dimensional smectic Gay-Berne liquid crystals with a simple rectangular confinement boundary. Two typical types of defect patterns, bridge and diagonal defect patterns, are observed, which can be transformable continuously between each other over time. The transition usually starts from the line or point defect regions, and the competition between neighboring and opposite boundary effects induces the continuous realignments of the smectic layers to connect the neighboring or opposite walls. The relative stability of these two defect patterns can be controlled by changing the confinement conditions. These results deepen our understanding of transition kinetics of defect patterns in confined liquid crystals.

Orientational Correlations in Active and Passive Nematic Defects

We investigate the emergence of orientational order among +1/2 disclinations in active nematic liquid crystals. Using a combination of theoretical and experimental methods, we show that +1/2 disclinations have short-range antiferromagnetic alignment, as a consequence of the elastic torques originating from their polar structure. The presence of intermediate -1/2 disclinations, however, turns this interaction from antialigning to aligning at scales that are smaller than the typical distance between like-sign defects. No long-range orientational order is observed. Strikingly, these effects are insensitive to material properties and qualitatively similar to what is found for defects in passive nematic liquid crystals.

Physics of liquid crystals in cell biology

The past decade has witnessed a rapid growth in understanding of the pivotal roles of mechanical stresses and physical forces in cell biology. As a result, an integrated view of cell biology is evolving, where genetic and molecular features are scrutinised hand in hand with physical and mechanical characteristics of cells. Physics of liquid crystals has emerged as a burgeoning new frontier in cell biology over the past few years, fuelled by an increasing identification of orientational order and topological defects in cell biology, spanning scales from subcellular filaments to individual cells and multicellular tissues. Here, we provide an account of the most recent findings and developments, together with future promises and challenges in this rapidly evolving interdisciplinary research direction.

Collective effects in epithelial cell death and cell extrusion

Programmed cell death, notably apoptosis, is an essential guardian of tissue homeostasis and an active contributor of organ shaping. While the regulation of apoptosis has been mostly analysed in the framework of a cell autonomous process, recent works highlighted important collective effects which can tune cell elimination. This is particularly relevant for epithelial cell death, which requires fine coordination with the neighbours in order to maintain tissue sealing during cell expulsion. In this review, we will focus on the recent advances which outline the complex multicellular communications at play during epithelial cell death and cell extrusion. We will first focus on the new unanticipated functions of neighbouring cells during extrusion, discuss the contribution of distant neighbours, and finally highlight the complex feedbacks generated by cell elimination on neighbouring cell death.

Multiscale Microtubule Dynamics in Active Nematics

In microtubule-based active nematics, motor-driven extensile motion of microtubule bundles powers chaotic large-scale dynamics. We quantify the interfilament sliding motion both in isolated bundles and in a dense active nematic. The extension speed of an isolated microtubule pair is comparable to the molecular motor stepping speed. In contrast, the net extension in dense 2D active nematics is significantly slower; the interfilament sliding speeds are widely distributed about the average and the filaments exhibit both contractile and extensile relative motion. These measurements highlight the challenge of connecting the extension rate of isolated bundles to the multimotor and multifilament interactions present in a dense 2D active nematic. They also provide quantitative data that is essential for building multiscale models.

Grhl3 promotes retention of epidermal cells under endocytic stress to maintain epidermal architecture in zebrafish

Epithelia such as epidermis cover large surfaces and are crucial for survival. Maintenance of tissue homeostasis by balancing cell proliferation, cell size, and cell extrusion ensures epidermal integrity. Although the mechanisms of cell extrusion are better understood, how epithelial cells that round up under developmental or perturbed genetic conditions are reintegrated in the epithelium to maintain homeostasis remains unclear. Here, we performed live imaging in zebrafish embryos to show that epidermal cells that round up due to membrane homeostasis defects in the absence of goosepimples/myosinVb (myoVb) function, are reintegrated into the epithelium. Transcriptome analysis and genetic interaction studies suggest that the transcription factor Grainyhead-like 3 (Grhl3) induces the retention of rounded cells by regulating E-cadherin levels. Moreover, Grhl3 facilitates the survival of MyoVb deficient embryos by regulating cell adhesion, cell retention, and epidermal architecture. Our analyses have unraveled a mechanism of retention of rounded cells and its importance in epithelial homeostasis.

Developing vertebrate epidermis isolates and protects growing embryos from their surroundings. For performing such a crucial function under compromised physiological or genetic conditions, robust mechanisms allowing maintenance of epidermal integrity are warranted. However, such mechanisms are not fully explored. To investigate the mechanisms by which epidermis copes up with drastic cell-shape changes to maintain the epidermal integrity, we have used a mutant condition, goosepimples/myosinVb (myoVb), wherein epidermal cells round up due to defective intracellular membrane trafficking. Our in vivo confocal imaging shows that this cell rounding is transient and the rounded cells are not extruded. Instead, they are retained and reintegrated. Using next generation sequencing and in situ expression analyses, we show that grainyhead-like 3 (grhl3) gene as well as several cell adhesion genes, including e-cadherin (cdh1), are up-regulated in the epidermal regions having rounded cells. Our genetic analyses reveal that the function of grhl3, which encodes for a transcription factor shown to be crucial for epidermal differentiation and wound healing, is essential to retain rounded-up cells by increasing E-cadherin mediated cell adhesion. We further show that this retention is essential for the maintenance of epidermal homeostasis. We propose that such a mechanism may be operational whenever cells round up under developmental or perturbed genetic conditions.

Submersed micropatterned structures control active nematic flow, topology, and concentration

Coupling between flows and material properties imbues rheological matter with its wide-ranging applicability, hence the excitement for harnessing the rheology of active fluids for which internal structure and continuous energy injection lead to spontaneous flows and complex, out-of-equilibrium dynamics. We propose and demonstrate a convenient, highly tunable method for controlling flow, topology, and composition within active films. Our approach establishes rheological coupling via the indirect presence of fully submersed micropatterned structures within a thin, underlying oil layer. Simulations reveal that micropatterned structures produce effective virtual boundaries within the superjacent active nematic film due to differences in viscous dissipation as a function of depth. This accessible method of applying position-dependent, effective dissipation to the active films presents a nonintrusive pathway for engineering active microfluidic systems.

Condensation tendency and planar isotropic actin gradient induce radial alignment in confined monolayers

A monolayer of highly motile cells can establish long-range orientational order, which can be explained by hydrodynamic theory of active gels and fluids. However, it is less clear how cell shape changes and rearrangement are governed when the monolayer is in mechanical equilibrium states when cell motility diminishes. In this work, we report that rat embryonic fibroblasts (REF), when confined in circular mesoscale patterns on rigid substrates, can transition from the spindle shapes to more compact morphologies. Cells align radially only at the pattern boundary when they are in the mechanical equilibrium. This radial alignment disappears when cell contractility or cell-cell adhesion is reduced. Unlike monolayers of spindle-like cells such as NIH-3T3 fibroblasts with minimal intercellular interactions or epithelial cells like Madin-Darby canine kidney (MDCK) with strong cortical actin network, confined REF monolayers present an actin gradient with isotropic meshwork, suggesting the existence of a stiffness gradient. In addition, the REF cells tend to condense on soft substrates, a collective cell behavior we refer to as the 'condensation tendency'. This condensation tendency, together with geometrical confinement, induces tensile prestretch (i.e. an isotropic stretch that causes tissue to contract when released) to the confined monolayer. By developing a Voronoi-cell model, we demonstrate that the combined global tissue prestretch and cell stiffness differential between the inner and boundary cells can sufficiently define the cell radial alignment at the pattern boundary.

Polar swimmers induce several phases in active nematics

Swimming bacteria in passive nematics in the form of lyotropic liquid crystals are defined as a new class of active matter known as living liquid crystals in recent studies. It has also been shown that liquid crystal solutions are promising candidates for trapping and detecting bacteria. We ask the question, can a similar class of matter be designed for background nematics which are also active? Hence, we developed a minimal model for the mixture of polar particles in active nematics. It is found that the active nematics in such a mixture are highly sensitive to the presence of polar particles and show the formation of large scale higher order structures for a relatively low polar particle density. Upon increasing the density of polar particles, different phases of active nematics are found and it is observed that the system shows two phase transitions. The first phase transition is a first order transition from quasi-long-ranged ordered active nematics to disordered active nematics with larger scale structures. On further increasing density of polar particles, the system transitions to a third phase, where polar particles form large, mutually aligned clusters. These clusters sweep the whole system and enforce local order in the nematics. The current study can be helpful for detecting the presence of very low densities of polar swimmers in active nematics and can be used to design and control different structures in active nematics.

Genetically variant human pluripotent stem cells selectively eliminate wild-type counterparts through YAP-mediated cell competition

The appearance of genetic changes in human pluripotent stem cells (hPSCs) presents a concern for their use in research and regenerative medicine. Variant hPSCs that harbor recurrent culture-acquired aneuploidies display growth advantages over wild-type diploid cells, but the mechanisms that yield a drift from predominantly wild-type to variant cell populations remain poorly understood. Here, we show that the dominance of variant clones in mosaic cultures is enhanced through competitive interactions that result in the elimination of wild-type cells. This elimination occurs through corralling and mechanical compression by faster-growing variants, causing a redistribution of F-actin and sequestration of yes-associated protein (YAP) in the cytoplasm that induces apoptosis in wild-type cells. YAP overexpression or promotion of YAP nuclear localization in wild-type cells alleviates their "loser" phenotype. Our results demonstrate that hPSC fate is coupled to mechanical cues imposed by neighboring cells and reveal that hijacking this mechanism allows variants to achieve clonal dominance in cultures.

Topological braiding and virtual particles on the cell membrane

Braiding of topological structures in complex matter fields provides a robust framework for encoding and processing information, and it has been extensively studied in the context of topological quantum computation. In living systems, topological defects are crucial for the localization and organization of biochemical signaling waves, but their braiding dynamics remain unexplored. Here, we show that the spiral wave cores, which organize the Rho-GTP protein signaling dynamics and force generation on the membrane of starfish egg cells, undergo spontaneous braiding dynamics. Experimentally measured world line braiding exponents and topological entropy correlate with cellular activity and agree with predictions from a generic field theory. Our analysis further reveals the creation and annihilation of virtual quasi-particle excitations during defect scattering events, suggesting phenomenological parallels between quantum and living matter.

Properties of twisted topological defects in 2D nematic liquid crystals

Topological defects are one of the most conspicuous features of liquid crystals. In two dimensional nematics, they have been shown to behave effectively as particles with both charge and orientation, which dictate their interactions. Here, we study "twisted" defects that have a radially dependent orientation. We find that twist can be partially relaxed through the creation and annihilation of defect pairs. By solving the equations for defect motion and calculating the forces on defects, we identify four distinct elements that govern the relative relaxational motion of interacting topological defects, namely attraction, repulsion, co-rotation and co-translation. The interaction of these effects can lead to intricate defect trajectories, which can be controlled by setting relevant timescales.

Topological defects in the mesothelium suppress ovarian cancer cell clearance

We investigated an in vitro model for mesothelial clearance, wherein ovarian cancer cells invade into a layer of mesothelial cells, resulting in mesothelial retraction combined with cancer cell disaggregation and spreading. Prior to the addition of tumor cells, the mesothelial cells had an elongated morphology, causing them to align with their neighbors into well-ordered domains. Flaws in this alignment, which occur at topological defects, have been associated with altered cell density, motion, and forces. Here, we identified topological defects in the mesothelial layer and showed how they affected local cell density by producing a net flow of cells inward or outward, depending on the defect type. At locations of net inward flow, mesothelial clearance was impeded. Hence, the collective behavior of the mesothelial cells, as governed by the topological defects, affected tumor cell clearance and spreading. Importantly, our findings were consistent across multiple ovarian cancer cell types, suggesting a new physical mechanism that could impact ovarian cancer metastasis.

Investigating the nature of active forces in tissues reveals how contractile cells can form extensile monolayers

Actomyosin machinery endows cells with contractility at a single-cell level. However, within a monolayer, cells can be contractile or extensile based on the direction of pushing or pulling forces exerted by their neighbours or on the substrate. It has been shown that a monolayer of fibroblasts behaves as a contractile system while epithelial or neural progentior monolayers behave as an extensile system. Through a combination of cell culture experiments and in silico modelling, we reveal the mechanism behind this switch in extensile to contractile as the weakening of intercellular contacts. This switch promotes the build-up of tension at the cell-substrate interface through an increase in actin stress fibres and traction forces. This is accompanied by mechanotransductive changes in vinculin and YAP activation. We further show that contractile and extensile differences in cell activity sort cells in mixtures, uncovering a generic mechanism for pattern formation during cell competition, and morphogenesis.

Active flows and deformable surfaces in development

We review progress in active hydrodynamic descriptions of flowing media on curved and deformable manifolds: the state-of-the-art in continuum descriptions of single-layers of epithelial and/or other tissues during development. First, after a brief overview of activity, flows and hydrodynamic descriptions, we highlight the generic challenge of identifying the dependence on dynamical variables of so-called active kinetic coefficients- active counterparts to dissipative Onsager coefficients. We go on to describe some of the subtleties concerning how curvature and active flows interact, and the issues that arise when surfaces are deformable. We finish with a broad discussion around the utility of such theories in developmental biology. This includes limitations to analytical techniques, challenges associated with numerical integration, fitting-to-data and inference, and potential tools for the future, such as discrete differential geometry.

Fractal generation in a two-dimensional active-nematic fluid

Active fluids, composed of individual self-propelled agents, can generate complex large-scale coherent flows. A particularly important laboratory realization of such an active fluid is a system composed of microtubules, aligned in a quasi-two-dimensional (2D) nematic phase and driven by adenosine-triphosphate-fueled kinesin motor proteins. This system exhibits robust chaotic advection and gives rise to a pronounced fractal structure in the nematic contours. We characterize such experimentally derived fractals using the power spectrum and discover that the power spectrum decays as k^-β for large wavenumbers k. The parameter β is measured for several experimental realizations. Though β is effectively constant in time, it does vary with experimental parameters, indicating differences in the scale-free behavior of the microtubule-based active nematic. Though the fractal patterns generated in this active system are reminiscent of passively advected dye in 2D chaotic flows, the underlying mechanism for fractal generation is more subtle. We provide a simple, physically inspired mathematical model of fractal generation in this system that relies on the material being locally compressible, though the total area of the material is conserved globally. The model also requires that large-scale density variations are injected into the material periodically. The model reproduces the power-spectrum decay k^-β seen in experiments. Linearizing the model of fractal generation about the equilibrium density, we derive an analytic relationship between β and a single dimensionless quantity r, which characterizes the compressibility.

Topological defects of integer charge in cell monolayers

Many cell types spontaneously order like nematic liquid crystals, and, as such, they form topological defects, which influence the cell organization. While defects with topological charge ±1/2 are common in cell monolayers, defects with charge ±1, which are thought to be relevant in the formation of protrusions in living systems, are more elusive. We use topographical patterns to impose topological charge of ±1 in controlled locations in cell monolayers. We study two types of cells, 3T6 fibroblasts and EpH-4 epithelial cells, and we compare their behavior on such patterns, characterizing the degree of alignment, the cell density near the defects, and their behavior at the defect core. We observe density variation in the 3T6 monolayers near both types of defects over the same length-scale. By choosing appropriate geometrical parameters of our topographical features, we identify a new behavior of 3T6 cells near the defects with topological charge +1, leading to a change in the cells' preferred shape. Our strategy allows a fine control of cell alignment near defects as a platform to study liquid crystalline properties of cells.

The EMT transcription factor Snai1 maintains myocardial wall integrity by repressing intermediate filament gene expression

The transcription factor Snai1, a well-known regulator of epithelial-to-mesenchymal transition, has been implicated in early cardiac morphogenesis as well as in cardiac valve formation. However, a role for Snai1 in regulating other aspects of cardiac morphogenesis has not been reported. Using genetic, transcriptomic, and chimeric analyses in zebrafish, we find that Snai1b is required in cardiomyocytes for myocardial wall integrity. Loss of snai1b increases the frequency of cardiomyocyte extrusion away from the cardiac lumen. Extruding cardiomyocytes exhibit increased actomyosin contractility basally as revealed by enrichment of p-myosin and α-catenin epitope α-18, as well as disrupted intercellular junctions. Transcriptomic analysis of wild-type and snai1b mutant hearts revealed the dysregulation of intermediate filament genes, including desmin b (desmb) upregulation. Cardiomyocyte-specific desmb overexpression caused increased cardiomyocyte extrusion, recapitulating the snai1b mutant phenotype. Altogether, these results indicate that Snai1 maintains the integrity of the myocardial epithelium, at least in part by repressing desmb expression.

Mechanical plasticity in collective cell migration

Collective cell migration is crucial to maintain epithelium integrity during developmental and repair processes. It requires a tight regulation of mechanical coordination between neighboring cells. This coordination embraces different features including mechanical self-propulsion of individual cells within cellular colonies and large-scale force transmission through cell-cell junctions. This review discusses how the plasticity of biomechanical interactions at cell-cell contacts could help cellular systems to perform coordinated motions and adapt to the properties of the external environment.

Spatiotemporal control of liquid crystal structure and dynamics through activity patterning

Active materials are capable of converting free energy into mechanical work to produce autonomous motion, and exhibit striking collective dynamics that biology relies on for essential functions. Controlling those dynamics and transport in synthetic systems has been particularly challenging. Here, we introduce the concept of spatially structured activity as a means of controlling and manipulating transport in active nematic liquid crystals consisting of actin filaments and light-sensitive myosin motors. Simulations and experiments are used to demonstrate that topological defects can be generated at will and then constrained to move along specified trajectories by inducing local stresses in an otherwise passive material. These results provide a foundation for the design of autonomous and reconfigurable microfluidic systems where transport is controlled by modulating activity with light.

Design of nematic liquid crystals to control microscale dynamics

The dynamics of small particles, both living such as swimming bacteria and inanimate, such as colloidal spheres, has fascinated scientists for centuries. If one could learn how to control and streamline their chaotic motion, that would open technological opportunities in the transformation of stored or environmental energy into systematic motion, with applications in micro-robotics, transport of matter, guided morphogenesis. This review presents an approach to command microscale dynamics by replacing an isotropic medium with a liquid crystal. Orientational order and associated properties, such as elasticity, surface anchoring, and bulk anisotropy, enable new dynamic effects, ranging from the appearance and propagation of particle-like solitary waves to self-locomotion of an active droplet. By using photoalignment, the liquid crystal can be patterned into predesigned structures. In the presence of the electric field, these patterns enable the transport of solid and fluid particles through nonlinear electrokinetics rooted in anisotropy of conductivity and permittivity. Director patterns command the dynamics of swimming bacteria, guiding their trajectories, polarity of swimming, and distribution in space. This guidance is of a higher level of complexity than a simple following of the director by rod-like microorganisms. Namely, the director gradients mediate hydrodynamic interactions of bacteria to produce an active force and collective polar modes of swimming. The patterned director could also be engraved in a liquid crystal elastomer. When an elastomer coating is activated by heat or light, these patterns produce a deterministic surface topography. The director gradients define an activation force that shapes the elastomer in a manner similar to the active stresses triggering flows in active nematics. The patterned elastomer substrates could be used to define the orientation of cells in living tissues. The liquid-crystal guidance holds a major promise in achieving the goal of commanding microscale active flows.

The morphogenetic changes that lead to cell extrusion in development and cell competition

Cell extrusion is a morphogenetic process in which unfit or dying cells are eliminated from the tissue at the interface with healthy neighbours in homeostasis. This process is also highly associated with cell fate specification followed by differentiation in development. Spontaneous cell death occurs in development and inhibition of this process can result in abnormal development, suggesting that survival or death is part of cell fate specification during morphogenesis. Moreover, spontaneous somatic mutations in oncogenes or tumour suppressor genes can trigger new morphogenetic events at the interface with healthy cells. Cell competition is considered as the global quality control mechanism for causing unfit cells to be eliminated at the interface with healthy neighbours in proliferating tissues. In this review, I will discuss variations of cell extrusion that are coordinated by unfit cells and healthy neighbours in relation to the geometry and topology of the tissue in development and cell competition.

The cephalothoracic sucker of sea lice (Crustacea: Copepoda: Caligidae): The functional importance of cuticular membrane ultrastructure

Sea lice adhere to the body surface of host fish with a cephalothoracic sucker. Caligus adheres to this substrate using legs 2 and 3, and the action of cephalothoracic muscles. Lunules, small, paired, anterior sucker-like structures, have a vital function in the initial step of adhering and contain a unique endocuticule containing elements that may behave like active matter and serve as the actuating mechanism. Cuticular membranes bordering the cephalothorax have a unique endocuticule with an undulating dorsal surface and a smooth ventral surface. A high-speed camera revealed that this undulation likely facilitates rapid automatic application of the sucker to the substrate. The cuticular membranes on the posterior margin of the first exopodal segment of leg 2 have a specialized endocuticle with tubules each surrounded by fine fibers. This reinforcement helps them to generate a posteriorly-directed jet of water. Opening-closing of these membranes is controlled by postero-anterior motion of the distal exopodal segments of leg 2. The outer cuticular membrane of leg 3 is simple, presumably effected by powerful extrinsic muscles. The consistency of sucker morphology within Caligus implies a highly stereotyped attachment behavior that is effective across a remarkable variety of fishes.

Inference of molecular orientation/ordering change nearby topological defects by the neural network function from the microscopic color information

Topological defects in liquid crystals (LCs) dominate molecular alignment/motion in many cases. Here, the neural network (NN) function has been introduced to predict the LC orientation condition (orientation angle and order parameter) at local positions around topological defects from the phase/polarization microscopic color images. The NN function was trained in advance by using the color information of an LC in a planar alignment cell for different orientation angles and temperatures. The photo-induced changes of LC molecules around topological defects observed by the time-resolved measurement was converted into the image sequences of the orientation angle and the order parameter change. We found that each pair of brushes with different colors around topological defects showed different orientation angle and ordering changes. The photo-induced change was triggered by the photoisomerization reaction of molecules, and one pair of brushes increased in its order parameter just after light irradiation, causing gradual rotation in the brush. The molecules in the other pair of brushes were disordered and rotated by the effect of the initially affected region. This combination approach of the time-resolved phase/polarization microscopy and the NN function can provide detailed information on the molecular alignment dynamics around the topological defects.

Spatiotemporal Oscillation in Confined Epithelial Motion upon Fluid-to-Solid Transition

Fluid-to-solid phase transition in multicellular assembly is crucial in many developmental biological processes, such as embryogenesis and morphogenesis. However, biomechanical studies in this area are limited, and little is known about factors governing the transition and how cell behaviors are regulated. Due to different stresses present, cells could behave distinctively depending on the nature of tissue. Here we report a fluid-to-solid transition in geometrically confined multicellular assemblies. Under circular confinement, Madin-Darby canine kidney (MDCK) monolayers undergo spatiotemporally oscillatory motions that are strongly dependent on the confinement size and distance from the periphery of the monolayers. Nanomechanical mapping reveals that epithelial tensional stress and traction forces on the substrate are both dependent on confinement size. The oscillation pattern and cellular nanomechanics profile appear well correlated with stress fiber assembly and cell polarization. These experimental observations imply that the confinement size-dependent surface tension regulates actin fiber assembly, cellular force generation, and cell polarization. Our analyses further suggest a characteristic confinement size (approximates to MDCK's natural correlation length) below which surface tension is sufficiently high and triggers a fluid-to-solid transition of the monolayers. Our findings may shed light on the geometrical and nanomechanical control of tissue morphogenesis and growth.

Blood Flow Limits Endothelial Cell Extrusion in the Zebrafish Dorsal Aorta

Blood flow modulates endothelial cell (EC) response during angiogenesis. Shear stress is known to control gene expression related to the endothelial-mesenchymal transition and endothelial-hematopoietic transition. However, the impact of blood flow on the cellular processes associated with EC extrusion is less well understood. To address this question, we dynamically record EC movements and use 3D quantitative methods to segregate the contributions of various cellular processes to the cellular trajectories in the zebrafish dorsal aorta. We find that ECs spread toward the cell extrusion area following the tissue deformation direction dictated by flow-derived mechanical forces. Cell extrusion increases when blood flow is impaired. Similarly, the mechanosensor polycystic kidney disease 2 (pkd2) limits cell extrusion, suggesting that ECs actively sense mechanical forces in the process. These findings identify pkd2 and flow as critical regulators of EC extrusion and suggest that mechanical forces coordinate this process by maintaining ECs within the endothelium.

Cell competition-induced apical elimination of transformed cells, EDAC, orchestrates the cellular homeostasis

Newly emerging transformed cells are often eliminated from the epithelium via cell competition with the surrounding normal cells. A number of recent studies using mammalian cell competition systems have demonstrated that cells with various types of oncogenic insults are extruded from the tissue in a cell death-dependent or -independent manner. Cell competition-mediated elimination of transformed cells, called EDAC (epithelial defense against cancer), represents an intrinsic anti-tumor activity within the epithelial cell society to reduce the risk of oncogenesis. Here we delineate roles and molecular mechanisms of this homeostatic process, especially focusing on mammalian models.

Revisiting the emergence of order in active matter

The emergence of orientational order plays a central role in active matter theory and is deeply based in the study of active systems with a velocity alignment mechanism, whose most prominent example is the so-called Vicsek model. Such active systems have been used to describe bird flocks, bacterial swarms, and active colloidal systems, among many other examples. Under the assumption that the large-scale properties of these models remain unchanged as long as the polar symmetry of the interactions is not affected, implementations have been performed using, out of convenience, either additive or non-additive interactions; the latter are found for instance in the original formulation of the Vicsek model. Here, we perform a careful analysis of active systems with velocity alignment, comparing additive and non-additive interactions, and show that the macroscopic properties of these active systems are fundamentally different. Our results call into question our current understanding of the onset of order in active systems.

Fluctuations can induce local nematic order and extensile stress in monolayers of motile cells

Recent experiments in various cell types have shown that two-dimensional tissues often display local nematic order, with evidence of extensile stresses manifest in the dynamics of topological defects. Using a mesoscopic model where tissue flow is generated by fluctuating traction forces coupled to the nematic order parameter, we show that the resulting tissue dynamics can spontaneously produce local nematic order and an extensile internal stress. A key element of the model is the assumption that in the presence of local nematic alignment, cells preferentially crawl along the nematic axis, resulting in anisotropy of fluctuations. Our work shows that activity can drive either extensile or contractile stresses in tissue, depending on the relative strength of the contractility of the cortical cytoskeleton and tractions by cells on the extracellular matrix.

Machine learning active-nematic hydrodynamics

Hydrodynamic theories effectively describe many-body systems out of equilibrium in terms of a few macroscopic parameters. However, such parameters are difficult to determine from microscopic information. Seldom is this challenge more apparent than in active matter, where the hydrodynamic parameters are in fact fields that encode the distribution of energy-injecting microscopic components. Here, we use active nematics to demonstrate that neural networks can map out the spatiotemporal variation of multiple hydrodynamic parameters and forecast the chaotic dynamics of these systems. We analyze biofilament/molecular-motor experiments with microtubule/kinesin and actin/myosin complexes as computer vision problems. Our algorithms can determine how activity and elastic moduli change as a function of space and time, as well as adenosine triphosphate (ATP) or motor concentration. The only input needed is the orientation of the biofilaments and not the coupled velocity field which is harder to access in experiments. We can also forecast the evolution of these chaotic many-body systems solely from image sequences of their past using a combination of autoencoders and recurrent neural networks with residual architecture. In realistic experimental setups for which the initial conditions are not perfectly known, our physics-inspired machine-learning algorithms can surpass deterministic simulations. Our study paves the way for artificial-intelligence characterization and control of coupled chaotic fields in diverse physical and biological systems, even in the absence of knowledge of the underlying dynamics.

Statistical mechanics of active Ornstein-Uhlenbeck particles

We study the statistical properties of active Ornstein-Uhlenbeck particles (AOUPs). In this simplest of models, the Gaussian white noise of overdamped Brownian colloids is replaced by a Gaussian colored noise. This suffices to grant this system the hallmark properties of active matter, while still allowing for analytical progress. We study in detail the steady-state distribution of AOUPs in the small persistence time limit and for spatially varying activity. At the collective level, we show AOUPs to experience motility-induced phase separation both in the presence of pairwise forces or due to quorum-sensing interactions. We characterize both the instability mechanism leading to phase separation and the resulting phase coexistence. We probe how, in the stationary state, AOUPs depart from their thermal equilibrium limit by investigating the emergence of ratchet currents and entropy production. In the small persistence time limit, we show how fluctuation-dissipation relations are recovered. Finally, we discuss how the emerging properties of AOUPs can be characterized from the dynamics of their collective modes.

Robustness of topological defects in discrete domains

Topological defects are singular points in vector fields, important in applications ranging from fingerprint detection to liquid crystals to biomedical imaging. In discretized vector fields, topological defects and their topological charge are identified by finite differences or finite-step paths around the tentative defect. As the topological charge is (half) integer, it cannot depend continuously on each input vector in a discrete domain. Instead, it switches discontinuously when vectors change beyond a certain amount, making the analysis of topological defects error prone in noisy data. We improve existing methods for the identification of topological defects by proposing a robustness measure for (i) the location of a defect, (ii) the existence of topological defects and the total topological charge within a given area, (iii) the annihilation of a defect pair, and (iv) the formation of a defect pair. Based on the proposed robustness measure, we show that topological defects in discrete domains can be identified with optimal trade-off between localization precision and robustness. The proposed robustness measure enables uncertainty quantification for topological defects in noisy discretized nematic fields (orientation fields) and polar fields (vector fields).

Viscoelastic control of spatiotemporal order in bacterial active matter

Active matter consists of units that generate mechanical work by consuming energy¹. Examples include living systems (such as assemblies of bacteria^2-5 and biological tissues^6,7), biopolymers driven by molecular motors^8-11 and suspensions of synthetic self-propelled particles^12-14. A central goal is to understand and control the self-organization of active assemblies in space and time. Most active systems exhibit either spatial order mediated by interactions that coordinate the spatial structure and the motion of active agents^12,14,15 or the temporal synchronization of individual oscillatory dynamics². The simultaneous control of spatial and temporal organization is more challenging and generally requires complex interactions, such as reaction-diffusion hierarchies¹⁶ or genetically engineered cellular circuits². Here we report a simple technique to simultaneously control the spatial and temporal self-organization of bacterial active matter. We confine dense active suspensions of Escherichia coli cells and manipulate a single macroscopic parameter-namely, the viscoelasticity of the suspending fluid- through the addition of purified genomic DNA. This reveals self-driven spatial and temporal organization in the form of a millimetre-scale rotating vortex with periodically oscillating global chirality of tunable frequency, reminiscent of a torsional pendulum. By combining experiments with an active-matter model, we explain this behaviour in terms of the interplay between active forcing and viscoelastic stress relaxation. Our findings provide insight into the influence of bacterial motile behaviour in complex fluids, which may be of interest in health- and ecology-related research, and demonstrate experimentally that rheological properties can be harnessed to control active-matter flows^17,18. We envisage that our millimetre-scale, tunable, self-oscillating bacterial vortex may be coupled to actuation systems to act a 'clock generator' capable of providing timing signals for rhythmic locomotion of soft robots and for programmed microfluidic pumping¹⁹, for example, by triggering the action of a shift register in soft-robotic logic devices²⁰.

Collective Polarization of Cancer Cells at the Monolayer Boundary

Cell polarization, a process depending on both intracellular and intercellular interactions, is crucial for collective cell migration that commonly emerges in embryonic development, tissue morphogenesis, wound healing and cancer metastasis. Although invasive cancer cells display weak cell-cell interactions, they can invade host tissues through a collective mode. Yet, how cancer cells without stable cell-cell junctions polarize collectively to migrate and invade is not fully understood. Here, using a wound-healing assay, we elucidate the polarization of carcinoma cells at the population level. We show that with loose intercellular connections, the highly polarized leader cells can induce the polarization of following cancer cells and subsequent transmission of polarity information by membrane protrusions, leading to gradient polarization at the monolayer boundary. Unlike the polarization of epithelial monolayer where Rac1/Cdc42 pathway functions primarily, our data show that collective polarization of carcinoma cells is predominantly controlled by Golgi apparatus, a disruption of which results in the destruction of collective polarization over a large scale. We reveal that the Golgi apparatus can sustain membrane protrusion formation, polarized secretion, intracellular trafficking, and F-actin polarization, which contribute to collective cancer cell polarization and its transmission between cells. These findings could advance our understanding of collective cancer invasion in tumors.

Quantifying Material Properties of Cell Monolayers by Analyzing Integer Topological Defects

In developing organisms, internal cellular processes generate mechanical stresses at the tissue scale. The resulting deformations depend on the material properties of the tissue, which can exhibit long-ranged orientational order and topological defects. It remains a challenge to determine these properties on the time scales relevant for developmental processes. Here, we build on the physics of liquid crystals to determine material parameters of cell monolayers. Specifically, we use a hydrodynamic description to characterize the stationary states of compressible active polar fluids around defects. We illustrate our approach by analyzing monolayers of C2C12 cells in small circular confinements, where they form a single topological defect with integer charge. We find that such monolayers exert compressive stresses at the defect centers, where localized cell differentiation and formation of three-dimensional shapes is observed.

Apoptotic cell extrusion depends on single-cell synthesis of sphingosine-1-phosphate by sphingosine kinase 2

Collecting duct cells are physiologically subject to the hypertonic environment of the kidney. This condition is necessary for kidney maturation and function but represents a stress condition that requires active strategies to ensure epithelial integrity. Madin-Darby Canine Kidney (MDCK) cells develop the differentiated phenotype of collecting duct cells when subject to hypertonicity, serving as a model to study epithelial preservation and homeostasis in this particular environment. The integrity of epithelia is essential to achieve the required functional barrier. One of the mechanisms that ensure integrity is cell extrusion, a process initiated by sphingosine-1-phosphate (S1P) to remove dying or surplus cells while maintaining the epithelium barrier. Both types start with the activation of S1P receptor type 2, located in neighboring cells. In this work, we studied the effect of cell differentiation induced by hypertonicity on cell extrusion in MDCK cells, and we provide new insights into the associated molecular mechanism. We found that the different stages of differentiation influence the rate of apoptotic cell extrusion. Besides, we used a novel methodology to demonstrate that S1P increase in extruding cells of differentiated monolayers. These results show for first time that cell extrusion is triggered by the single-cell synthesis of S1P by sphingosine kinase 2 (SphK2), but not SphK1, of the extruding cell itself. Moreover, the inhibition or knockdown of SphK2 prevents cell extrusion and cell-cell junction protein degradation, but not apoptotic nuclear fragmentation. Thus, we propose SphK2 as the biochemical key to ensure the preservation of the epithelial barrier under hypertonic stress.

Adhesion-mediated heterogeneous actin organization governs apoptotic cell extrusion

Apoptotic extrusion is crucial in maintaining epithelial homeostasis. Current literature supports that epithelia respond to extrusion by forming a supracellular actomyosin purse-string in the neighbors. However, whether other actin structures could contribute to extrusion and how forces generated by these structures can be integrated are unknown. Here, we found that during extrusion, a heterogeneous actin network composed of lamellipodia protrusions and discontinuous actomyosin cables, was reorganized in the neighboring cells. The early presence of basal lamellipodia protrusion participated in both basal sealing of the extrusion site and orienting the actomyosin purse-string. The co-existence of these two mechanisms is determined by the interplay between the cell-cell and cell-substrate adhesions. A theoretical model integrates these cellular mechanosensitive components to explain why a dual-mode mechanism, which combines lamellipodia protrusion and purse-string contractility, leads to more efficient extrusion than a single-mode mechanism. In this work, we provide mechanistic insight into extrusion, an essential epithelial homeostasis process.

Integer topological defects of cell monolayers: Mechanics and flows

Monolayers of anisotropic cells exhibit long-ranged orientational order and topological defects. During the development of organisms, orientational order often influences morphogenetic events. However, the linkage between the mechanics of cell monolayers and topological defects remains largely unexplored. This holds specifically at the timescales relevant for tissue morphogenesis. Here, we build on the physics of liquid crystals to determine material parameters of cell monolayers. In particular, we use a hydrodynamical description of an active polar fluid to study the steady-state mechanical patterns at integer topological defects. Our description includes three distinct sources of activity: traction forces accounting for cell-substrate interactions as well as anisotropic and isotropic active nematic stresses accounting for cell-cell interactions. We apply our approach to C2C12 cell monolayers in small circular confinements, which form isolated aster or spiral topological defects. By analyzing the velocity and orientational order fields in spirals as well as the forces and cell number density fields in asters, we determine mechanical parameters of C2C12 cell monolayers. Our work shows how topological defects can be used to fully characterize the mechanical properties of biological active matter.

Epithelial colonies in vitro elongate through collective effects

Epithelial tissues of the developing embryos elongate by different mechanisms, such as neighbor exchange, cell elongation, and oriented cell division. Since autonomous tissue self-organization is influenced by external cues such as morphogen gradients or neighboring tissues, it is difficult to distinguish intrinsic from directed tissue behavior. The mesoscopic processes leading to the different mechanisms remain elusive. Here, we study the spontaneous elongation behavior of spreading circular epithelial colonies in vitro. By quantifying deformation kinematics at multiple scales, we report that global elongation happens primarily due to cell elongations, and its direction correlates with the anisotropy of the average cell elongation. By imposing an external time-periodic stretch, the axis of this global symmetry breaking can be modified and elongation occurs primarily due to orientated neighbor exchange. These different behaviors are confirmed using a vertex model for collective cell behavior, providing a framework for understanding autonomous tissue elongation and its origins.

Defective nematogenesis: Gauss curvature in programmable shape-responsive sheets with topological defects

Flat sheets encoded with patterns of contraction/elongation morph into curved surfaces. If the surfaces bear Gauss curvature, the resulting actuation can be strong and powerful. We deploy the Gauss-Bonnet theorem to deduce the Gauss curvature encoded in a pattern of uniform-magnitude contraction/elongation with spatially varying direction, as is commonly implemented in patterned liquid crystal elastomers. This approach reveals two fundamentally distinct contributions: a structural curvature which depends on the precise form of the pattern, and a topological curvature generated by defects in the contractile direction. These curvatures grow as different functions of the contraction/elongation magnitude, explaining the apparent contradiction between previous calculations for simple +1 defects, and smooth defect-free patterns. We verify these structural and topological contributions by conducting numerical shell calculations on sheets encoded with simple higher-order contractile defects to reveal their activated morphology. Finally we calculate the Gauss curvature generated by patterns with spatially varying magnitude and direction, which leads to additional magnitude gradient contributions to the structural term. We anticipate this form will be useful whenever magnitude and direction are natural variables, including in describing the contraction of a muscle along its patterned fiber direction, or a tissue growing by elongating its cells.

Active nematics with quenched disorder

We introduce a two-dimensional active nematic with quenched disorder. We write the coarse-grained hydrodynamic equations of motion for slow variables, viz. density and orientation. Disorder strength is tuned from zero to large values. Results from the numerical solution of equations of motion as well as the calculation of two-point orientation correlation function using linear approximation shows that the ordered steady state follows a disorder dependent crossover from quasi-long-range order to short-range order. Such crossover is due to the pinning of ±1/2 topological defects in the presence of finite disorder, which breaks the system in uncorrelated domains. Finite disorder slows the dynamics of +1/2 defect, and it leads to slower growth dynamics. The two-point correlation functions for the density and orientation fields show good dynamic scaling but no static scaling for the different disorder strengths. Our findings can motivate experimentalists to verify the results and find applications in living and artificial apolar systems in the presence of a quenched disorder.

Quantification of nematic cell polarity in three-dimensional tissues

How epithelial cells coordinate their polarity to form functional tissues is an open question in cell biology. Here, we characterize a unique type of polarity found in liver tissue, nematic cell polarity, which is different from vectorial cell polarity in simple, sheet-like epithelia. We propose a conceptual and algorithmic framework to characterize complex patterns of polarity proteins on the surface of a cell in terms of a multipole expansion. To rigorously quantify previously observed tissue-level patterns of nematic cell polarity (Morales-Navarrete et al., eLife 2019), we introduce the concept of co-orientational order parameters, which generalize the known biaxial order parameters of the theory of liquid crystals. Applying these concepts to three-dimensional reconstructions of single cells from high-resolution imaging data of mouse liver tissue, we show that the axes of nematic cell polarity of hepatocytes exhibit local coordination and are aligned with the biaxially anisotropic sinusoidal network for blood transport. Our study characterizes liver tissue as a biological example of a biaxial liquid crystal. The general methodology developed here could be applied to other tissues and in-vitro organoids.

Defect patterns on the curved surface of fish retinae suggest a mechanism of cone mosaic formation

The outer epithelial layer of zebrafish retinae contains a crystalline array of cone photoreceptors, called the cone mosaic. As this mosaic grows by mitotic addition of new photoreceptors at the rim of the hemispheric retina, topological defects, called "Y-Junctions", form to maintain approximately constant cell spacing. The generation of topological defects due to growth on a curved surface is a distinct feature of the cone mosaic not seen in other well-studied biological patterns like the R8 photoreceptor array in the Drosophila compound eye. Since defects can provide insight into cell-cell interactions responsible for pattern formation, here we characterize the arrangement of cones in individual Y-Junction cores as well as the spatial distribution of Y-junctions across entire retinae. We find that for individual Y-junctions, the distribution of cones near the core corresponds closely to structures observed in physical crystals. In addition, Y-Junctions are organized into lines, called grain boundaries, from the retinal center to the periphery. In physical crystals, regardless of the initial distribution of defects, defects can coalesce into grain boundaries via the mobility of individual particles. By imaging in live fish, we demonstrate that grain boundaries in the cone mosaic instead appear during initial mosaic formation, without requiring defect motion. Motivated by this observation, we show that a computational model of repulsive cell-cell interactions generates a mosaic with grain boundaries. In contrast to paradigmatic models of fate specification in mostly motionless cell packings, this finding emphasizes the role of cell motion, guided by cell-cell interactions during differentiation, in forming biological crystals. Such a route to the formation of regular patterns may be especially valuable in situations, like growth on a curved surface, where the resulting long-ranged, elastic, effective interactions between defects can help to group them into grain boundaries.