Topological defects in epithelia govern cell death and extrusion

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.

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.

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.

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.

Mechanobiology of Epithelia From the Perspective of Extracellular Matrix Heterogeneity

Understanding the complexity of the extracellular matrix (ECM) and its variability is a necessary step on the way to engineering functional (bio)materials that serve their respective purposes while relying on cell adhesion. Upon adhesion, cells receive messages which contain both biochemical and mechanical information. The main focus of mechanobiology lies in investigating the role of this mechanical coordination in regulating cellular behavior. In recent years, this focus has been additionally shifted toward cell collectives and the understanding of their behavior as a whole mechanical continuum. Collective cell phenomena very much apply to epithelia which are either simple cell-sheets or more complex three-dimensional structures. Researchers have been mostly using the organization of monolayers to observe their collective behavior in well-defined experimental setups in vitro. Nevertheless, recent studies have also reported the impact of ECM remodeling on epithelial morphogenesis in vivo. These new concepts, combined with the knowledge of ECM biochemical complexity are of key importance for engineering new interactive materials to support both epithelial remodeling and homeostasis. In this review, we summarize the structure and heterogeneity of the ECM before discussing its impact on the epithelial mechanobiology.

Role of Friction in Multidefect Ordering

We use continuum simulations to study the impact of friction on the ordering of defects in an active nematic. Even in a frictionless system, +1/2 defects tend to align side by side and orient antiparallel reflecting their propensity to form, and circulate with, flow vortices. Increasing friction enhances the effectiveness of the defect-defect interactions, and defects form dynamically evolving, large-scale, positionally, and orientationally ordered structures, which can be explained as a competition between hexagonal packing, preferred by the -1/2 defects, and rectangular packing, preferred by the +1/2 defects.

Tension heterogeneity directs form and fate to pattern the myocardial wall

How diverse cell fates and complex forms emerge and feed back to each other to sculpt functional organs remains unclear. In the developing heart, the myocardium transitions from a simple epithelium to an intricate tissue that consists of distinct layers: the outer compact and inner trabecular layers. Defects in this process, which is known as cardiac trabeculation, cause cardiomyopathies and embryonic lethality, yet how tissue symmetry is broken to specify trabecular cardiomyocytes is unknown. Here we show that local tension heterogeneity drives organ-scale patterning and cell-fate decisions during cardiac trabeculation in zebrafish. Proliferation-induced cellular crowding at the tissue scale triggers tension heterogeneity among cardiomyocytes of the compact layer and drives those with higher contractility to delaminate and seed the trabecular layer. Experimentally, increasing crowding within the compact layer cardiomyocytes augments delamination, whereas decreasing it abrogates delamination. Using genetic mosaics in trabeculation-deficient zebrafish models-that is, in the absence of critical upstream signals such as Nrg-Erbb2 or blood flow-we find that inducing actomyosin contractility rescues cardiomyocyte delamination and is sufficient to drive cardiomyocyte fate specification, as assessed by Notch reporter expression in compact layer cardiomyocytes. Furthermore, Notch signalling perturbs the actomyosin machinery in cardiomyocytes to restrict excessive delamination, thereby preserving the architecture of the myocardial wall. Thus, tissue-scale forces converge on local cellular mechanics to generate complex forms and modulate cell-fate choices, and these multiscale regulatory interactions ensure robust self-organized organ patterning.

Driven topological transitions in active nematic films

The topological properties of many materials are central to their behavior. In intrinsically out-of-equilibrium active materials, the dynamics of topological defects can be particularly important. In this paper, local manipulation of the order, dynamics, and topological properties of microtubule-based active nematic films is demonstrated in a joint experimental and simulation study. Hydrodynamic stresses created by magnetically actuated rotation of disk-shaped colloids in proximity to the films compete with internal stresses in the active nematic, influencing the local motion of +1/2 charge topological defects that are intrinsic to the nematic order in the spontaneously turbulent active films. Sufficiently large applied stresses drive the formation of +1 charge topological vortices through the merger of two +1/2 defects. The directed motion of the defects is accompanied by ordering of the vorticity and velocity of the active flows within the film that is qualitatively unlike the response of passive viscous films. Many features of the film's response to the stress are captured by lattice Boltzmann simulations, providing insight into the anomalous viscoelastic nature of the active nematic. The topological vortex formation is accompanied by a rheological instability in the film that leads to significant increase in the flow velocities. Comparison of the velocity profile in vicinity of the vortex with fluid-dynamics calculations provides an estimate of the film viscosity.

Flow States and Transitions of an Active Nematic in a Three-Dimensional Channel

We use active nematohydrodynamics to study the flow of an active fluid in a 3D microchannel, finding a transition between active turbulence and regimes where there is a net flow along the channel. We show that the net flow is only possible if the active nematic is flow aligning and that, in agreement with experiments, the appearance of the net flow depends on the aspect ratio of the channel cross section. We explain our results in terms of when the hydrodynamic screening due to the channel walls allows the emergence of vortex rolls across the channel.

Review: knots and other new topological effects in liquid crystals and colloids

Humankind has been obsessed with knots in religion, culture and daily life for millennia, while physicists like Gauss, Kelvin and Maxwell already involved them in models centuries ago. Nowadays, colloidal particles can be fabricated to have shapes of knots and links with arbitrary complexity. In liquid crystals, closed loops of singular vortex lines can be knotted by using colloidal particles and laser tweezers, as well as by confining nematic fluids into micrometer-sized droplets with complex topology. Knotted and linked colloidal particles induce knots and links of singular defects, which can be interlinked (or not) with colloidal particle knots, revealing the diversity of interactions between topologies of knotted fields and topologically nontrivial surfaces of colloidal objects. Even more diverse knotted structures emerge in nonsingular molecular alignment and magnetization fields in liquid crystals and colloidal ferromagnets. The topological solitons include hopfions, skyrmions, heliknotons, torons and other spatially localized continuous structures, which are classified based on homotopy theory, characterized by integer-valued topological invariants and often contain knotted or linked preimages, nonsingular regions of space corresponding to single points of the order parameter space. A zoo of topological solitons in liquid crystals, colloids and ferromagnets promises new breeds of information displays and a plethora of data storage, electro-optic and photonic applications. Their particle-like collective dynamics echoes coherent motions in active matter, ranging from crowds of people to schools of fish. This review discusses the state of the art in the field, as well as highlights recent developments and open questions in physics of knotted soft matter. We systematically overview knotted field configurations, the allowed transformations between them, their physical stability and how one can use one form of knotted fields to model, create and imprint other forms. The large variety of symmetries accessible to liquid crystals and colloids offer insights into stability, transformation and emergent dynamics of fully nonsingular and singular knotted fields of fundamental and applied importance. The common thread of this review is the ability to experimentally visualize these knots in real space. The review concludes with a discussion of how the studies of knots in liquid crystals and colloids can offer insights into topologically related structures in other branches of physics, with answers to many open questions, as well as how these experimentally observable knots hold a strong potential for providing new inspirations to the mathematical knot theory.

Adaptive architecture and mechanoresponse of epithelial cells on a torus

Curvature is a geometric feature widely observed in the epithelia and critical to the performance of fundamental biological functions. Understanding curvature-related biophysical phenomena remains challenging partly owing to the difficulty of quantitatively tuning and measuring curvatures of interfacing individual cells. In this study, we prepared confluent wild-type Madin-Darby canine kidney cells on a torus structure presenting positive, zero, and negative Gaussian curvatures with a tubule diameter of 2-7 cells and quantified the mechanobiological characteristics of individual cells. Cells on the torus surface exhibited topological sensing ability both as an individual cell and collective cell organization. Both cell bodies and nuclei, adapted on the torus, exhibited local Gaussian curvature-dependent preferential orientation. The cells on the torus demonstrated significant adjustment in the nuclear area and exhibited asymmetric nuclear position depending on the local Gaussian curvature. Moreover, cells on top of the torus, where local Gaussian curvature is near zero, exhibited more sensitive morphological adaptations than the nuclei depending on the Gaussian curvature gradient. Furthermore, the spatial heterogeneity of intermediate filament proteins related to mechanoresponsive expression of the cell body and nucleus, vimentin, keratin and lamin A, revealed local Gaussian curvature as a key factor of cellular adaptation on curved surfaces.

Collective chemotaxis of active nematic droplets

Collective chemotaxis plays a key role in the navigation of cell clusters in, e.g., embryogenesis and cancer metastasis. Using the active nematic continuum equations, coupled to a chemical field that regulates activity, we demonstrate and explain a physical mechanism that results in collective chemotaxis. The activity naturally leads to cell polarization at the cluster interface which induces outward flows. The chemical gradient then breaks the symmetry of the flow field, leading to a net motion. The velocity is independent of the cluster size, in agreement with experiment.

Azobenzene-based sinusoidal surface topography drives focal adhesion confinement and guides collective migration of epithelial cells

Surface topography is a key parameter in regulating the morphology and behavior of single cells. At multicellular level, coordinated cell displacements drive many biological events such as embryonic morphogenesis. However, the effect of surface topography on collective migration of epithelium has not been studied in detail. Mastering the connection between surface features and collective cellular behaviour is highly important for novel approaches in tissue engineering and repair. Herein, we used photopatterned microtopographies on azobenzene-containing materials and showed that smooth topographical cues with proper period and orientation can efficiently orchestrate cell alignment in growing epithelium. Furthermore, the experimental system allowed us to investigate how the orientation of the topographical features can alter the speed of wound closure in vitro. Our findings indicate that the extracellular microenvironment topography coordinates their focal adhesion distribution and alignment. These topographic cues are able to guide the collective migration of multicellular systems, even when cell-cell junctions are disrupted.

Wrinkling Instability in 3D Active Nematics

In nature, interactions between biopolymers and motor proteins give rise to biologically essential emergent behaviors. Besides cytoskeleton mechanics, active nematics arise from such interactions. Here we present a study on 3D active nematics made of microtubules, kinesin motors, and depleting agent. It shows a rich behavior evolving from a nematically ordered space-filling distribution of microtubule bundles toward a flattened and contracted 2D ribbon that undergoes a wrinkling instability and subsequently transitions into a 3D active turbulent state. The wrinkle wavelength is independent of the ATP concentration and our theoretical model describes its relation with the appearance time. We compare the experimental results with a numerical simulation that confirms the key role of kinesin motors in cross-linking and sliding the microtubules. Our results on the active contraction of the network and the independence of wrinkle wavelength on ATP concentration are important steps forward for the understanding of these 3D systems.

Pattern Formation and Defect Ordering in Active Chiral Nematics

Many biological systems display intriguing chiral patterns and dynamics. Here, we present an active nematic theory accounting for individual spin to explore the collective handedness in chiral rod-shaped aggregations. We show that coordinated individual spin and motility can engender a vortex-array pattern with chirality and drive ordering of topological defects. During this chiral process, the stationary trefoil-like defects self-organize into a periodic, hexagon-dominated polygonal network, which segregates persistently rotating cometlike defects in pairs within each polygon, leading to a translation symmetry at the global scale while a broken reflection symmetry at the local scale. Such defect ordering agrees exactly with the Voronoi tiling of two-dimensional space and the emergence of the hexagonal symmetry is deciphered in analogy with topological charge neutralization. We calculate energy barriers to the topological transition of the defect ordering and explain the existing metastable states with nonhexagonal polygons. Our findings shed light on the chiral morphodynamics in life processes and also suggest a potential route towards tuning self-organization in active materials.

A Biologist's Guide to Traction Force Microscopy Using Polydimethylsiloxane Substrate for Two-Dimensional Cell Cultures

Cellular traction forces influence epithelial behavior, including wound healing and cell extrusion. Here, we describe a simple in vitro traction force microscopy (TFM) protocol using ECM protein-coated polydimethylsiloxane substrate and widefield fluorescence microscopy. We include detailed steps for analysis so readers can obtain traction forces to study the mechanobiology of epithelial cells. We also provide guidelines on when to adopt another common class of TFM protocols based on polyacrylamide hydrogels. For complete details on the use and execution of this protocol, please refer to Saw et al. (2017) and Teo et al. (2020).

Dynamics of active nematic defects on the surface of a sphere

A nematic liquid crystal confined to the surface of a sphere exhibits topological defects of total charge +2 due to the topological constraint. In equilibrium, the nematic field forms four +1/2 defects, located at the corners of a regular tetrahedron inscribed within the sphere, since this minimizes the Frank elastic energy. If additionally the individual nematogens exhibit self-driven directional motion, the resulting active system creates large-scale flow that drives it out of equilibrium. In particular, the defects now follow complex dynamic trajectories which, depending on the strength of the active forcing, can be periodic (for weak forcing) or chaotic (for strong forcing). In this paper we derive an effective particle theory for this system, in which the topological defects are the degrees of freedom, whose exact equations of motion we subsequently determine. Numerical solutions of these equations confirm previously observed characteristics of their dynamics and clarify the role played by the time dependence of their global rotation. We also show that Onsager's variational principle offers an exceptionally transparent way to derive these dynamical equations, and we explain the defect mobility at the hydrodynamics level.

Active inter-cellular forces in collective cell motility

The collective behaviour of confluent cell sheets is strongly influenced both by polar forces, arising through cytoskeletal propulsion, and by active inter-cellular forces, which are mediated by interactions across cell-cell junctions. We use a phase-field model to explore the interplay between these two contributions and compare the dynamics of a cell sheet when the polarity of the cells aligns to (i) their main axis of elongation, (ii) their velocity and (iii) when the polarity direction executes a persistent random walk. In all three cases, we observe a sharp transition from a jammed state (where cell rearrangements are strongly suppressed) to a liquid state (where the cells can move freely relative to each other) when either the polar or the inter-cellular forces are increased. In addition, for case (ii) only, we observe an additional dynamical state, flocking (solid or liquid), where the majority of the cells move in the same direction. The flocking state is seen for strong polar forces, but is destroyed as the strength of the inter-cellular activity is increased.

The Role of Tricellulin in Epithelial Jamming and Unjamming via Segmentation of Tricellular Junctions

Collective cellular behavior in confluent monolayers supports physiological and pathological processes of epithelial development, regeneration, and carcinogenesis. Here, the attainment of a mature and static tissue configuration or the local reactivation of cell motility involve a dynamic regulation of the junctions established between neighboring cells. Tricellular junctions (tTJs), established at vertexes where three cells meet, are ideally located to control cellular shape and coordinate multicellular movements. However, their function in epithelial tissue dynamic remains poorly defined. To investigate the role of tTJs establishment and maturation in the jamming and unjamming transitions of epithelial monolayers, a semi-automatic image-processing pipeline is developed and validated enabling the unbiased and spatially resolved determination of the tTJ maturity state based on the localization of fluorescent reporters. The software resolves the variation of tTJ maturity accompanying collective transitions during tissue maturation, wound healing, and upon the adaptation to osmolarity changes. Altogether, this work establishes junctional maturity at tricellular contacts as a novel biological descriptor of collective responses in epithelial monolayers.

Dynamic heterogeneity influences the leader-follower dynamics during epithelial wound closure

Cells of epithelial tissue proliferate and pack together to attain an eventual density homeostasis. As the cell density increases, spatial distribution of velocity and force show striking similarity to the dynamic heterogeneity observed elsewhere in dense granular matter. While the physical nature of this heterogeneity is somewhat known in the epithelial cell monolayer, its biological relevance and precise connection to cell density remain elusive. Relevantly, we had demonstrated how large-scale dynamic heterogeneity in the monolayer stress field in the bulk could critically influence the emergence of leader cells at the wound margin during wound closure, but did not connect the observation to the corresponding cell density. In fact, numerous previous reports had essentially associated long-range force and velocity correlation with either cell density or dynamic heterogeneity, without any generalization. Here, we attempted to unify these two parameters under a single framework and explored their consequence on the dynamics of leader cells, which eventually affected the efficacy of collective migration and wound closure. To this end, we first quantified the dynamic heterogeneity by the peak height of four-point susceptibility. Remarkably, this quantity showed a linear relationship with cell density over many experimental samples. We then varied the heterogeneity, by changing cell density, and found this change altered the number of leader cells at the wound margin. At low heterogeneity, wound closure was slower, with decreased persistence, reduced coordination and disruptive leader-follower interactions. Finally, microscopic characterization of cell-substrate adhesions illustrated how heterogeneity influenced orientations of focal adhesions, affecting coordinated cell movements. Together, these results demonstrate the importance of dynamic heterogeneity in epithelial wound healing. This article is part of the theme issue 'Multi-scale analysis and modelling of collective migration in biological systems'.

Mechanical interplay between cell shape and actin cytoskeleton organization

We investigate the mechanical interplay between the spatial organization of the actin cytoskeleton and the shape of animal cells adhering on micropillar arrays. Using a combination of analytical work, computer simulations and in vitro experiments, we demonstrate that the orientation of the stress fibers strongly influences the geometry of the cell edge. In the presence of a uniformly aligned cytoskeleton, the cell edge can be well approximated by elliptical arcs, whose eccentricity reflects the degree of anisotropy of the cell's internal stresses. Upon modeling the actin cytoskeleton as a nematic liquid crystal, we further show that the geometry of the cell edge feeds back on the organization of the stress fibers by altering the length scale at which these are confined. This feedback mechanism is controlled by a dimensionless number, the anchoring number, representing the relative weight of surface-anchoring and bulk-aligning torques. Our model allows to predict both cellular shape and the internal structure of the actin cytoskeleton and is in good quantitative agreement with experiments on fibroblastoid (GDβ1, GDβ3) and epithelioid (GEβ1, GEβ3) cells.

Solid-Liquid Transition of Deformable and Overlapping Active Particles

Experiments and theory have shown that cell monolayers and epithelial tissues exhibit solid-liquid and glass-liquid transitions. These transitions are biologically relevant to our understanding of embryonic development, wound healing, and cancer. Current models of confluent epithelia have focused on the role of cell shape, with less attention paid to cell extrusion, which is key for maintaining homeostasis in biological tissue. Here, we use a multiphase field model to study the solid-liquid transition in a confluent monolayer of deformable cells. Cell overlap is allowed and provides a way for modeling the precursor for extrusion. When cells overlap rather than deform, we find that the melting transition changes from continuous to first order like, and that there is an intermittent regime close to the transition, where solid and liquid states alternate over time. By studying the dynamics of five- and sevenfold disclinations in the hexagonal lattice formed by the cell centers, we observe that these correlate with spatial fluctuations in the cellular overlap, and that cell extrusion tends to initiate near fivefold disclinations.

Mechanobiology of leader-follower dynamics in epithelial cell migration

Collective cell migration is fundamental to biological form and function. It is also relevant to the formation and repair of organs and to various pathological situations, including metastatic propagation of cancer. Technological, experimental, and computational advancements have allowed the researchers to explore various aspects of collective migration, spanning from biochemical signalling to inter-cellular force transduction. Here, we summarize our current understanding of the mechanobiology of collective cell migration, limiting to epithelial tissues. On the basis of recent studies, we describe how cells sense and respond to guidance signals to orchestrate various modes of migration and identify the determining factors dictating leader-follower interactions. We highlight how the inherent mechanics of dense epithelial monolayers at multicellular length scale might instruct individual cells to behave collectively. On the basis of these findings, we propose that mechanical resilience, obtained by a certain extent of cell jamming, allows the epithelium to perform efficient collective migration during wound healing.

Shaping Organs: Shared Structural Principles Across Kingdoms

Development encapsulates the morphogenesis of an organism from a single fertilized cell to a functional adult. A critical part of development is the specification of organ forms. Beyond the molecular control of morphogenesis, shape in essence entails structural constraints and thus mechanics. Revisiting recent results in biophysics and development, and comparing animal and plant model systems, we derive key overarching principles behind the formation of organs across kingdoms. In particular, we highlight how growing organs are active rather than passive systems and how such behavior plays a role in shaping the organ. We discuss the importance of considering different scales in understanding how organs form. Such an integrative view of organ development generates new questions while calling for more cross-fertilization between scientific fields and model system communities.

Caveolae Control Contractile Tension for Epithelia to Eliminate Tumor Cells

Epithelia are active materials where mechanical tension governs morphogenesis and homeostasis. But how that tension is regulated remains incompletely understood. We now report that caveolae control epithelial tension and show that this is necessary for oncogene-transfected cells to be eliminated by apical extrusion. Depletion of caveolin-1 (CAV1) increased steady-state tensile stresses in epithelial monolayers. As a result, loss of CAV1 in the epithelial cells surrounding oncogene-expressing cells prevented their apical extrusion. Epithelial tension in CAV1-depleted monolayers was increased by cortical contractility at adherens junctions. This reflected a signaling pathway, where elevated levels of phosphoinositide-4,5-bisphosphate (PtdIns(4,5)P₂) recruited the formin, FMNL2, to promote F-actin bundling. Steady-state monolayer tension and oncogenic extrusion were restored to CAV1-depleted monolayers when tension was corrected by depleting FMNL2, blocking PtdIns(4,5)P₂, or disabling the interaction between FMNL2 and PtdIns(4,5)P₂. Thus, caveolae can regulate active mechanical tension for epithelial homeostasis by controlling lipid signaling to the actin cytoskeleton.

Resilience of three-dimensional sinusoidal networks in liver tissue

Can three-dimensional, microvasculature networks still ensure blood supply if individual links fail? We address this question in the sinusoidal network, a plexus-like microvasculature network, which transports nutrient-rich blood to every hepatocyte in liver tissue, by building on recent advances in high-resolution imaging and digital reconstruction of adult mice liver tissue. We find that the topology of the three-dimensional sinusoidal network reflects its two design requirements of a space-filling network that connects all hepatocytes, while using shortest transport routes: sinusoidal networks are sub-graphs of the Delaunay graph of their set of branching points, and also contain the corresponding minimum spanning tree, both to good approximation. To overcome the spatial limitations of experimental samples and generate arbitrarily-sized networks, we developed a network generation algorithm that reproduces the statistical features of 0.3-mm-sized samples of sinusoidal networks, using multi-objective optimization for node degree and edge length distribution. Nematic order in these simulated networks implies anisotropic transport properties, characterized by an empirical linear relation between a nematic order parameter and the anisotropy of the permeability tensor. Under the assumption that all sinusoid tubes have a constant and equal flow resistance, we predict that the distribution of currents in the network is very inhomogeneous, with a small number of edges carrying a substantial part of the flow-a feature known for hierarchical networks, but unexpected for plexus-like networks. We quantify network resilience in terms of a permeability-at-risk, i.e., permeability as function of the fraction of removed edges. We find that sinusoidal networks are resilient to random removal of edges, but vulnerable to the removal of high-current edges. Our findings suggest the existence of a mechanism counteracting flow inhomogeneity to balance metabolic load on the liver.

Controlled Dynamics of Neural Tumor Cells by Templated Liquid Crystalline Polymer Networks

The ability to control the alignment and organization of cell populations has great potential for tissue engineering and regenerative medicine. A variety of approaches such as nano/microtopographical patterning, mechanical loading, and nanocomposite synthesis have been developed to engineer scaffolds able to control cellular properties and behaviors. In this work, a patterned liquid crystal polymer network (LCN) film is synthesized by using a nematic liquid crystal template in which the molecular orientations are predesigned by photopatterning technique. Various configurations of polymer networks such as linear and circular patterns are created. When neural tumor cells are plated onto the templated LCN films, the cell alignment, migration, and proliferation are directed in both linear and curvilinear fashions following the pattern of the aligned polymer chains. A complex LCN pattern with zigzag geometry is also fabricated and found to be capable of controlling cell alignment and collective cellular organization. The demonstrated control of cell dynamics and organization by LCN films with various molecular alignments opens new opportunities to design scaffolds to control cultured cell organization in a manner resembling that found in tissues and to develop novel advanced materials for nerve repair, tissue engineering, and regenerative medicine applications.

Measuring mechanical stress in living tissues

Living tissues are active multifunctional materials capable of generating, sensing, withstanding and responding to mechanical stress. These capabilities enable tissues to adopt complex shapes during development, to sustain those shapes during homeostasis, and to restore them during healing and regeneration. Abnormal stress is associated with a broad range of pathologies, including developmental defects, inflammatory diseases, tumor growth and metastasis. Here we review techniques that measure mechanical stress in living tissues with cellular and subcellular resolution. We begin with 2D techniques to map stress in cultured cell monolayers, which provide the highest resolution and accessibility. These techniques include 2D traction microscopy, micro-pillar arrays, monolayer stress microscopy, and monolayer stretching between flexible cantilevers. We next focus on 3D traction microscopy and the micro-bulge test, which enable mapping forces in tissues cultured in 3D. Finally, we review techniques to measure stress in vivo, including servo-null methods for measuring luminal pressure, deformable inclusions, FRET sensors, laser ablation and computational methods for force inference. Whereas these techniques remain far from becoming everyday tools in biomedical laboratories, their rapid development is fostering key advances in the way we understand the role of mechanics in morphogenesis, homeostasis and disease.

Steady-state distributions and nonsteady dynamics in nonequilibrium systems

We search for steady states in a class of fluctuating and driven physical systems that exhibit sustained currents. We find that the physical concept of a steady state, well known for systems at equilibrium, must be generalized to describe such systems. In these, the generalization of a steady state is associated with a stationary probability density of microstates and a deterministic dynamical system whose trajectories the system follows on average. These trajectories are a manifestation of nonstationary macroscopic currents observed in these systems. We determine precise conditions for the steady state to exist as well as the requirements for it to be stable. We illustrate this with some examples.

The 2020 motile active matter roadmap

Activity and autonomous motion are fundamental in living and engineering systems. This has stimulated the new field of 'active matter' in recent years, which focuses on the physical aspects of propulsion mechanisms, and on motility-induced emergent collective behavior of a larger number of identical agents. The scale of agents ranges from nanomotors and microswimmers, to cells, fish, birds, and people. Inspired by biological microswimmers, various designs of autonomous synthetic nano- and micromachines have been proposed. Such machines provide the basis for multifunctional, highly responsive, intelligent (artificial) active materials, which exhibit emergent behavior and the ability to perform tasks in response to external stimuli. A major challenge for understanding and designing active matter is their inherent nonequilibrium nature due to persistent energy consumption, which invalidates equilibrium concepts such as free energy, detailed balance, and time-reversal symmetry. Unraveling, predicting, and controlling the behavior of active matter is a truly interdisciplinary endeavor at the interface of biology, chemistry, ecology, engineering, mathematics, and physics. The vast complexity of phenomena and mechanisms involved in the self-organization and dynamics of motile active matter comprises a major challenge. Hence, to advance, and eventually reach a comprehensive understanding, this important research area requires a concerted, synergetic approach of the various disciplines. The 2020 motile active matter roadmap of Journal of Physics: Condensed Matter addresses the current state of the art of the field and provides guidance for both students as well as established scientists in their efforts to advance this fascinating area.

Crystal-like order and defects in metazoan epithelia with spherical geometry

Since Robert Hooke studied cork cell patterns in 1665, scientists have been puzzled by why cells form such ordered structures. The laws underlying this type of organization are universal, and we study them comparing the living and non-living two-dimensional systems self-organizing at the spherical surface. Such-type physical systems often possess trigonal order with specific elongated defects, scars and pleats, where the 5-valence and 7-valence vertices alternate. In spite of the fact that the same physical and topological rules are involved in the structural organization of biological systems, such topological defects were never reported in epithelia. We have discovered them in the follicular spherical epithelium of ascidians that are emerging models in developmental biology. Surprisingly, the considered defects appear in the epithelium even when the number of cells in it is significantly less than the previously known threshold value. We explain this result by differences in the cell sizes and check our hypothesis considering the self-assembly of different random size particles on the spherical surface. Scars, pleats and other complex defects found in ascidian samples can play an unexpected and decisive role in the permanent renewal and reorganization of epithelia, which forms or lines many tissues and organs in metazoans.

Topology control of human fibroblast cells monolayer by liquid crystal elastomer

Eukaryotic cells in living tissues form dynamic patterns with spatially varying orientational order that affects important physiological processes such as apoptosis and cell migration. The challenge is how to impart a predesigned map of orientational order onto a growing tissue. Here, we demonstrate an approach to produce cell monolayers of human dermal fibroblasts with predesigned orientational patterns and topological defects using a photoaligned liquid crystal elastomer (LCE) that swells anisotropically in an aqueous medium. The patterns inscribed into the LCE are replicated by the tissue monolayer and cause a strong spatial variation of cells phenotype, their surface density, and number density fluctuations. Unbinding dynamics of defect pairs intrinsic to active matter is suppressed by anisotropic surface anchoring allowing the estimation of the elastic characteristics of the tissues. The demonstrated patterned LCE approach has potential to control the collective behavior of cells in living tissues, cell differentiation, and tissue morphogenesis.

Reduction of endocytic activity accelerates cell elimination during tissue remodeling of the Drosophila epidermal epithelium

Epithelial tissues undergo cell turnover both during development and for homeostatic maintenance. Cells that are no longer needed are quickly removed without compromising the barrier function of the tissue. During metamorphosis, insects undergo developmentally programmed tissue remodeling. However, the mechanisms that regulate this rapid tissue remodeling are not precisely understood. Here, we show that the temporal dynamics of endocytosis modulate physiological cell properties to prime larval epidermal cells for cell elimination. Endocytic activity gradually reduces as tissue remodeling progresses. This reduced endocytic activity accelerates cell elimination through the regulation of Myosin II subcellular reorganization, junctional E-cadherin levels, and caspase activation. Whereas the increased Myosin II dynamics accelerates cell elimination, E-cadherin plays a protective role against cell elimination. Reduced E-cadherin is involved in the amplification of caspase activation by forming a positive-feedback loop with caspase. These findings reveal the role of endocytosis in preventing cell elimination and in the cell-property switching initiated by the temporal dynamics of endocytic activity to achieve rapid cell elimination during tissue remodeling.

A Mechanical Instability in Planar Epithelial Monolayers Leads to Cell Extrusion

In cell extrusion, a cell embedded in an epithelial monolayer loses its apical or basal surface and is subsequently squeezed out of the monolayer by neighboring cells. Cell extrusions occur during apoptosis, epithelial-mesenchymal transition, or precancerous cell invasion. They play important roles in embryogenesis, homeostasis, carcinogenesis, and many other biological processes. Although many of the molecular factors involved in cell extrusion are known, little is known about the mechanical basis of cell extrusion. We used a three-dimensional (3D) vertex model to investigate the mechanical stability of cells arranged in a monolayer with 3D foam geometry. We found that when the cells composing the monolayer have homogeneous mechanical properties, cells are extruded from the monolayer when the symmetry of the 3D geometry is broken because of an increase in cell density or a decrease in the number of topological neighbors around single cells. Those results suggest that mechanical instability inherent in the 3D foam geometry of epithelial monolayers is sufficient to drive epithelial cell extrusion. In the situation in which cells in the monolayer actively generate contractile or adhesive forces under the control of intrinsic genetic programs, the forces act to break the symmetry of the monolayer, leading to cell extrusion that is directed to the apical or basal side of the monolayer by the balance of contractile and adhesive forces on the apical and basal sides. Although our analyses are based on a simple mechanical model, our results are in accordance with observations of epithelial monolayers in vivo and consistently explain cell extrusions under a wide range of physiological and pathophysiological conditions. Our results illustrate the importance of a mechanical understanding of cell extrusion and provide a basis by which to link molecular regulation to physical processes.

A theoretical model of collective cell polarization and alignment

Collective cell polarization and alignment play important roles in tissue morphogenesis, wound healing and cancer metastasis. How cells sense the direction and position in these processes, however, has not been fully understood. Here we construct a theoretical model based on describing cell layer as a nemato-elastic medium, by which the cell polarization, cell alignment and cell active contraction are explicitly expressed as functions of components of the nematic order parameter. To determine the order parameter we derive two sets of governing equations, one for the force equilibrium of the system, and the other for the minimization of the system's free energy including the energy of cell polarization and alignment. By solving these coupled governing equations, we can predict the effects of substrate stiffness, geometries of cell layers, external forces and myosin activity on the direction- and position-dependent cell aspect ratio and cell orientation. Moreover, the axisymmetric problem with cells on a ring-like pattern is solved analytically, and the analytical solution for cell aspect ratio are governed by parameter groups which include the stiffness of the cell and the substrate, the strength of myosin activity and the external forces. Our predictions of the cell aspect ratio and orientation are generally comparable to experimental observations. These results show that the pattern of cell polarization is determined by the anisotropic degree of active contractile stress, and suggest a stress-driven polarization mechanism that enables cells to sense their spatial positions to develop direction- and position-dependent behavior. This, in turn, sheds light on the ways to control pattern formation in tissue engineering for potential biomedical applications.

EphA7 is required for otic epithelial homeostasis by modulating Claudin6 in Xenopus

Receptor tyrosine kinase EphA7 is specifically expressed in otic region in Xenopus early development. However, its role in otocyst development remains unknown. Knockdown of EphA7 by a specific morpholino oligonucleotide (MO) reduced the size of the otocyst and triggered otic epithelial cell extrusion. Interestingly, EphA7 depletion attenuated the membrane level of the tight junction protein Claudin6 (CLDN6). Utilizing the Cldn6 MO, we further confirmed that CLDN6 attenuation also led to otic epithelial cell extrusion. Our work suggested that EphA7 modulates the otic epithelial homeostasis through stabilizing the CLDN6 membrane level.

Topological structure and dynamics of three-dimensional active nematics

Topological structures are effective descriptors of the nonequilibrium dynamics of diverse many-body systems. For example, motile, point-like topological defects capture the salient features of two-dimensional active liquid crystals composed of energy-consuming anisotropic units. We dispersed force-generating microtubule bundles in a passive colloidal liquid crystal to form a three-dimensional active nematic. Light-sheet microscopy revealed the temporal evolution of the millimeter-scale structure of these active nematics with single-bundle resolution. The primary topological excitations are extended, charge-neutral disclination loops that undergo complex dynamics and recombination events. Our work suggests a framework for analyzing the nonequilibrium dynamics of bulk anisotropic systems as diverse as driven complex fluids, active metamaterials, biological tissues, and collections of robots or organisms.

Dense active matter model of motion patterns in confluent cell monolayers

Epithelial cell monolayers show remarkable displacement and velocity correlations over distances of ten or more cell sizes that are reminiscent of supercooled liquids and active nematics. We show that many observed features can be described within the framework of dense active matter, and argue that persistent uncoordinated cell motility coupled to the collective elastic modes of the cell sheet is sufficient to produce swirl-like correlations. We obtain this result using both continuum active linear elasticity and a normal modes formalism, and validate analytical predictions with numerical simulations of two agent-based cell models, soft elastic particles and the self-propelled Voronoi model together with in-vitro experiments of confluent corneal epithelial cell sheets. Simulations and normal mode analysis perfectly match when tissue-level reorganisation occurs on times longer than the persistence time of cell motility. Our analytical model quantitatively matches measured velocity correlation functions over more than a decade with a single fitting parameter.

Tissue mechanical properties modulate cell extrusion in the Drosophila abdominal epidermis

The replacement of cells is a common strategy during animal development. In the Drosophila pupal abdomen, larval epidermal cells (LECs) are replaced by adult progenitor cells (histoblasts). Previous work showed that interactions between histoblasts and LECs result in apoptotic extrusion of LECs during early pupal development. Extrusion of cells is closely preceded by caspase activation and is executed by contraction of a cortical actomyosin cable. Here, we identify a population of LECs that extrudes independently of the presence of histoblasts during late pupal development. Extrusion of these LECs is not closely preceded by caspase activation, involves a pulsatile medial actomyosin network, and correlates with a developmental time period when mechanical tension and E-cadherin turnover at adherens junctions is particularly high. Our work reveals a developmental switch in the cell extrusion mechanism that correlates with changes in tissue mechanical properties.

Three-Dimensional Active Defect Loops

We describe the flows and morphological dynamics of topological defect lines and loops in three-dimensional active nematics and show, using theory and numerical modeling, that they are governed by the local profile of the orientational order surrounding the defects. Analyzing a continuous span of defect loop profiles, ranging from radial and tangential twist to wedge ±1/2 profiles, we show that the distinct geometries can drive material flow perpendicular or along the local defect loop segment, whose variation around a closed loop can lead to net loop motion, elongation, or compression of shape, or buckling of the loops. We demonstrate a correlation between local curvature and the local orientational profile of the defect loop, indicating dynamic coupling between geometry and topology. To address the general formation of defect loops in three dimensions, we show their creation via bend instability from different initial elastic distortions.

Nucleation and shape dynamics of model nematic tactoids around adhesive colloids

Recent experiments have shown how nematically ordered tactoid shaped actin droplets can be reorganized and divided by the action of myosin molecular motors. In this paper, we consider how similar morphological changes can potentially be achieved under equilibrium conditions. Using simulations, both atomistic and continuum, and a simple macroscopic model, we explore how the nucleation dynamics, shape changes, and the final steady state of a nematic tactoid droplet can be modified by interactions with model adhesive colloids that mimic a myosin motor cluster. We show how tactoid reorganization may occur in an equilibrium colloidal-nematic setting. We then suggest based on the simple macroscopic model how the simulation models may be extended to potentially stabilize divided tactoids.

Active nematics with anisotropic friction: the decisive role of the flow aligning parameter

We use continuum simulations to study the impact of anisotropic hydrodynamic friction on the emergent flows of active nematics. We show that, depending on whether the active particles align with or tumble in their collectively self-induced flows, anisotropic friction can result in markedly different patterns of motion. In a flow-aligning regime and at high anisotropic friction, the otherwise chaotic flows are streamlined into flow lanes with alternating directions, reproducing the experimental laning state that has been obtained by interfacing microtubule-motor protein mixtures with smectic liquid crystals. Within a flow-tumbling regime, however, we find that no such laning state is possible. Instead, the synergistic effects of friction anisotropy and flow tumbling can lead to the emergence of bound pairs of topological defects that align at an angle to the easy flow direction and navigate together throughout the domain. In addition to confirming the mechanism behind the laning states observed in experiments, our findings emphasise the role of the flow aligning parameter in the dynamics of active nematics.

3D-printable cell crowding device enables imaging of live cells in compression

We designed and fabricated, using low-cost 3D printing technologies, a device that enables direct control of cell density in epithelial monolayers. The device operates by varying the tension of a silicone substrate upon which the cells are adhered. Multiple devices can be manufactured easily and placed in any standard incubator. This allows long-term culturing of cells on pretensioned substrates until the user decreases the tension, thereby inducing compressive forces in plane and subsequent instantaneous cell crowding. Moreover, the low-profile device is completely portable and can be mounted directly onto an inverted optical microscope. This enables visualization of the morphology and dynamics of living cells in stretched or compressed conditions using a wide range of high-resolution microscopy techniques.