Tissue curvature and apicobasal mechanical tension imbalance instruct cancer morphogenesis.

Tubular epithelia are a basic building block of organs and a common site of cancer occurrence1-4. During tumorigenesis, transformed cells overproliferate and epithelial architecture is disrupted. However, the biophysical parameters that underlie the adoption of abnormal tumour tissue shapes are unknown. Here we show in the pancreas of mice that the morphology of epithelial tumours is determined by the interplay of cytoskeletal changes in transformed cells and the existing tubular geometry. To analyse the morphological changes in tissue architecture during the initiation of cancer, we developed a three-dimensional whole-organ imaging technique that enables tissue analysis at single-cell resolution. Oncogenic transformation of pancreatic ducts led to two types of neoplastic growth: exophytic lesions that expanded outwards from the duct and endophytic lesions that grew inwards to the ductal lumen. Myosin activity was higher apically than basally in wild-type cells, but upon transformation this gradient was lost in both lesion types. Three-dimensional vertex model simulations and a continuum theory of epithelial mechanics, which incorporate the cytoskeletal changes observed in transformed cells, indicated that the diameter of the source epithelium instructs the morphology of growing tumours. Three-dimensional imaging revealed that-consistent with theory predictions-small pancreatic ducts produced exophytic growth, whereas large ducts deformed endophytically. Similar patterns of lesion growth were observed in tubular epithelia of the liver and lung; this finding identifies tension imbalance and tissue curvature as fundamental determinants of epithelial tumorigenesis.

Spindle reorientation in response to mechanical stress is an emergent property of the spindle positioning mechanisms.

Proper orientation of the mitotic spindle plays a crucial role in embryos, during tissue development, and in adults, where it functions to dissipate mechanical stress to maintain tissue integrity and homeostasis. While mitotic spindles have been shown to reorient in response to external mechanical stresses, the subcellular cues that mediate spindle reorientation remain unclear. Here, we used a combination of optogenetics and computational modeling to investigate how mitotic spindles respond to inhomogeneous tension within the actomyosin cortex. Strikingly, we found that the optogenetic activation of RhoA only influences spindle orientation when it is induced at both poles of the cell. Under these conditions, the sudden local increase in cortical tension induced by RhoA activation reduces pulling forces exerted by cortical regulators on astral microtubules. This leads to a perturbation of the balance of torques exerted on the spindle, which causes it to rotate. Thus, spindle rotation in response to mechanical stress is an emergent phenomenon arising from the interaction between the spindle positioning machinery and the cell cortex.

Active mesh and neural network pipeline for cell aggregate segmentation.

Segmenting cells within cellular aggregates in 3D is a growing challenge in cell biology due to improvements in capacity and accuracy of microscopy techniques. Here, we describe a pipeline to segment images of cell aggregates in 3D. The pipeline combines neural network segmentations with active meshes. We apply our segmentation method to cultured mouse mammary gland organoids imaged over 24 h with oblique plane microscopy, a high-throughput light-sheet fluorescence microscopy technique. We show that our method can also be applied to images of mouse embryonic stem cells imaged with a spinning disc microscope. We segment individual cells based on nuclei and cell membrane fluorescent markers, and track cells over time. We describe metrics to quantify the quality of the automated segmentation. Our segmentation pipeline involves a Fiji plugin that implements active mesh deformation and allows a user to create training data, automatically obtain segmentation meshes from original image data or neural network prediction, and manually curate segmentation data to identify and correct mistakes. Our active meshes-based approach facilitates segmentation postprocessing, correction, and integration with neural network prediction.

Interacting active surfaces: A model for three-dimensional cell aggregates.

We introduce a modelling and simulation framework for cell aggregates in three dimensions based on interacting active surfaces. Cell mechanics is captured by a physical description of the acto-myosin cortex that includes cortical flows, viscous forces, active tensions, and bending moments. Cells interact with each other via short-range forces capturing the effect of adhesion molecules. We discretise the model equations using a finite element method, and provide a parallel implementation in C++. We discuss examples of application of this framework to small and medium-sized aggregates: we consider the shape and dynamics of a cell doublet, a planar cell sheet, and a growing cell aggregate. This framework opens the door to the systematic exploration of the cell to tissue-scale mechanics of cell aggregates, which plays a key role in the morphogenesis of embryos and organoids.

A non-cell-autonomous actin redistribution enables isotropic retinal growth.

Tissue shape is often established early in development and needs to be scaled isotropically during growth. However, the cellular contributors and ways by which cells interact tissue-wide to enable coordinated isotropic tissue scaling are not yet understood. Here, we follow cell and tissue shape changes in the zebrafish retinal neuroepithelium, which forms a cup with a smooth surface early in development and maintains this architecture as it grows. By combining 3D analysis and theory, we show how a global increase in cell height can maintain tissue shape during growth. Timely cell height increase occurs concurrently with a non-cell-autonomous actin redistribution. Blocking actin redistribution and cell height increase perturbs isotropic scaling and leads to disturbed, folded tissue shape. Taken together, our data show how global changes in cell shape enable isotropic growth of the developing retinal neuroepithelium, a concept that could also apply to other systems.

Hydrodynamic theory of active matter.

We review the general hydrodynamic theory of active soft materials that is motivated in particular by biological matter. We present basic concepts of irreversible thermodynamics of spatially extended multicomponent active systems. Starting from the rate of entropy production, we identify conjugate thermodynamic fluxes and forces and present generic constitutive equations of polar active fluids and active gels. We also discuss angular momentum conservation which plays a role in the the physics of active chiral gels. The irreversible thermodynamics of active gels provides a general framework to discuss the physics that underlies a wide variety of biological processes in cells and in multicellular tissues.

Stability and Roughness of Interfaces in Mechanically Regulated Tissues.

Cell division and death can be regulated by the mechanical forces within a tissue. We study the consequences for the stability and roughness of a propagating interface by analyzing a model of mechanically regulated tissue growth in the regime of small driving forces. For an interface driven by homeostatic pressure imbalance or leader-cell motility, long and intermediate-wavelength instabilities arise, depending, respectively, on an effective viscosity of cell number change, and on substrate friction. A further mechanism depends on the strength of directed motility forces acting in the bulk. We analyze the fluctuations of a stable interface subjected to cell-level stochasticity, and find that mechanical feedback can help preserve reproducibility at the tissue scale. Our results elucidate mechanisms that could be important for orderly interface motion in developing tissues.

Polar actomyosin contractility destabilizes the position of the cytokinetic furrow.

Cytokinesis, the physical separation of daughter cells at the end of mitosis, requires precise regulation of the mechanical properties of the cell periphery. Although studies of cytokinetic mechanics mostly focus on the equatorial constriction ring, a contractile actomyosin cortex is also present at the poles of dividing cells. Whether polar forces influence cytokinetic cell shape and furrow positioning remains an open question. Here we demonstrate that the polar cortex makes cytokinesis inherently unstable. We show that limited asymmetric polar contractions occur during cytokinesis, and that perturbing the polar cortex leads to cell shape oscillations, resulting in furrow displacement and aneuploidy. A theoretical model based on a competition between cortex turnover and contraction dynamics accurately accounts for the oscillations. We further propose that membrane blebs, which commonly form at the poles of dividing cells and whose role in cytokinesis has long been enigmatic, stabilize cell shape by acting as valves releasing cortical contractility. Our findings reveal an inherent instability in the shape of the dividing cell and unveil a novel, spindle-independent mechanism ensuring the stability of cleavage furrow positioning.

Steering cell migration by alternating blebs and actin-rich protrusions.

BACKGROUND: High directional persistence is often assumed to enhance the efficiency of chemotactic migration. Yet, cells in vivo usually display meandering trajectories with relatively low directional persistence, and the control and function of directional persistence during cell migration in three-dimensional environments are poorly understood. RESULTS: Here, we use mesendoderm progenitors migrating during zebrafish gastrulation as a model system to investigate the control of directional persistence during migration in vivo. We show that progenitor cells alternate persistent run phases with tumble phases that result in cell reorientation. Runs are characterized by the formation of directed actin-rich protrusions and tumbles by enhanced blebbing. Increasing the proportion of actin-rich protrusions or blebs leads to longer or shorter run phases, respectively. Importantly, both reducing and increasing run phases result in larger spatial dispersion of the cells, indicative of reduced migration precision. A physical model quantitatively recapitulating the migratory behavior of mesendoderm progenitors indicates that the ratio of tumbling to run times, and thus the specific degree of directional persistence of migration, are critical for optimizing migration precision. CONCLUSIONS: Together, our experiments and model provide mechanistic insight into the control of migration directionality for cells moving in three-dimensional environments that combine different protrusion types, whereby the proportion of blebs to actin-rich protrusions determines the directional persistence and precision of movement by regulating the ratio of tumbling to run times.

Role of Turnover in Active Stress Generation in a Filament Network.

We study the effect of turnover of cross-linkers, motors, and filaments on the generation of a contractile stress in a network of filaments connected by passive cross-linkers and subjected to the forces exerted by molecular motors. We perform numerical simulations where filaments are treated as rigid rods and molecular motors move fast compared to the time scale of an exchange of cross-linkers. We show that molecular motors create a contractile stress above a critical number of cross-linkers. When passive cross-linkers are allowed to turn over, the stress exerted by the network vanishes due to the formation of clusters. When both filaments and passive cross-linkers turn over, clustering is prevented and the network reaches a dynamic contractile steady state. A maximum stress is reached for an optimum ratio of the filament and cross-linker turnover rates. Taken together, our work reveals conditions for stress generation by molecular motors in a fluid isotropic network of rearranging filaments.

Spontaneous oscillations of elastic contractile materials with turnover.

Single and collective cellular oscillations driven by the actomyosin cytoskeleton have been observed in numerous biological systems. Here, we propose that these oscillations can be accounted for by a generic oscillator model of a material turning over and contracting against an elastic element. As an example, we show that during dorsal closure of the Drosophila embryo, experimentally observed changes in actomyosin concentration and oscillatory cell shape changes can, indeed, be captured by the dynamic equations studied here. We also investigate the collective dynamics of an ensemble of such contractile elements and show that the relative contribution of viscous and friction losses yields different regimes of collective oscillations. Taking into account the diffusion of force-producing molecules between contractile elements, our theoretical framework predicts the appearance of traveling waves, resembling the propagation of actomyosin waves observed during morphogenesis.

Coupling mechanical deformations and planar cell polarity to create regular patterns in the zebrafish retina.

The orderly packing and precise arrangement of epithelial cells is essential to the functioning of many tissues, and refinement of this packing during development is a central theme in animal morphogenesis. The mechanisms that determine epithelial cell shape and position, however, remain incompletely understood. Here, we investigate these mechanisms in a striking example of planar order in a vertebrate epithelium: The periodic, almost crystalline distribution of cone photoreceptors in the adult teleost fish retina. Based on observations of the emergence of photoreceptor packing near the retinal margin, we propose a mathematical model in which ordered columns of cells form as a result of coupling between planar cell polarity (PCP) and anisotropic tissue-scale mechanical stresses. This model recapitulates many observed features of cone photoreceptor organization during retinal growth and regeneration. Consistent with the model's predictions, we report a planar-polarized distribution of Crumbs2a protein in cone photoreceptors in both unperturbed and regenerated tissue. We further show that the pattern perturbations predicted by the model to occur if the imposed stresses become isotropic closely resemble defects in the cone pattern in zebrafish lrp2 mutants, in which intraocular pressure is increased, resulting in altered mechanical stress and ocular enlargement. Evidence of interactions linking PCP, cell shape, and mechanical stresses has recently emerged in a number of systems, several of which show signs of columnar cell packing akin to that described here. Our results may hence have broader relevance for the organization of cells in epithelia. Whereas earlier models have allowed only for unidirectional influences between PCP and cell mechanics, the simple, phenomenological framework that we introduce here can encompass a broad range of bidirectional feedback interactions among planar polarity, shape, and stresses; our model thus represents a conceptual framework that can address many questions of importance to morphogenesis.

Active morphogenesis of patterned epithelial shells.

Shape transformations of epithelial tissues in three dimensions, which are crucial for embryonic development or in vitro organoid growth, can result from active forces generated within the cytoskeleton of the epithelial cells. How the interplay of local differential tensions with tissue geometry and with external forces results in tissue-scale morphogenesis remains an open question. Here, we describe epithelial sheets as active viscoelastic surfaces and study their deformation under patterned internal tensions and bending moments. In addition to isotropic effects, we take into account nematic alignment in the plane of the tissue, which gives rise to shape-dependent, anisotropic active tensions and bending moments. We present phase diagrams of the mechanical equilibrium shapes of pre-patterned closed shells and explore their dynamical deformations. Our results show that a combination of nematic alignment and gradients in internal tensions and bending moments is sufficient to reproduce basic building blocks of epithelial morphogenesis, including fold formation, budding, neck formation, flattening, and tubulation.

The Drosophila ecdysone receptor promotes or suppresses proliferation according to ligand level.

The steroid hormone 20-hydroxy-ecdysone (20E) promotes proliferation in Drosophila wing precursors at low titer but triggers proliferation arrest at high doses. Remarkably, wing precursors proliferate normally in the complete absence of the 20E receptor, suggesting that low-level 20E promotes proliferation by overriding the default anti-proliferative activity of the receptor. By contrast, 20E needs its receptor to arrest proliferation. Dose-response RNA sequencing (RNA-seq) analysis of ex vivo cultured wing precursors identifies genes that are quantitatively activated by 20E across the physiological range, likely comprising positive modulators of proliferation and other genes that are only activated at high doses. We suggest that some of these "high-threshold" genes dominantly suppress the activity of the pro-proliferation genes. We then show mathematically and with synthetic reporters that combinations of basic regulatory elements can recapitulate the behavior of both types of target genes. Thus, a relatively simple genetic circuit can account for the bimodal activity of this hormone.

Role of cortical tension in bleb growth.

Blebs are spherical membrane protrusions often observed during cell migration, cell spreading, cytokinesis, and apoptosis, both in cultured cells and in vivo. Bleb expansion is thought to be driven by the contractile actomyosin cortex, which generates hydrostatic pressure in the cytoplasm and can thus drive herniations of the plasma membrane. However, the role of cortical tension in bleb formation has not been directly tested, and despite the importance of blebbing, little is known about the mechanisms of bleb growth. In order to explore the link between cortical tension and bleb expansion, we induced bleb formation on cells with different tensions. Blebs were nucleated in a controlled manner by laser ablation of the cortex, mimicking endogenous bleb nucleation. Cortical tension was modified by treatments affecting the level of myosin activity or proteins regulating actin turnover. We show that there is a critical tension below which blebs cannot expand. Above this threshold, the maximal size of a bleb strongly depends on tension, and this dependence can be fitted with a model of the cortex as an active elastic material. Together, our observations and model allow us to relate bleb shape parameters to the underlying cellular mechanics and provide insights as to how bleb formation can be biochemically regulated during cell motility.

Scaling of entropy production under coarse graining in active disordered media.

Entropy production plays a fundamental role in the study of nonequilibrium systems by offering a quantitative handle on the degree of time-reversal symmetry breaking. It depends crucially on the degree of freedom considered as well as on the scale of description. How the entropy production at one resolution of the degrees of freedom is related to the entropy production at another resolution is a fundamental question which has recently attracted interest. This relationship is of particular relevance to coarse-grained and continuum descriptions of a given phenomenon. In this work, we derive the scaling of the entropy production under iterative coarse graining on the basis of the correlations of the underlying microscopic transition rates for noninteracting particles in active disordered media. Our approach unveils a natural criterion to distinguish equilibrium-like and genuinely nonequilibrium macroscopic phenomena based on the sign of the scaling exponent of the entropy production per mesostate.

Pulsations and flows in tissues as two collective dynamics with simple cellular rules.

Collective motions of epithelial cells are essential for morphogenesis. Tissues elongate, contract, flow, and oscillate, thus sculpting embryos. These tissue level dynamics are known, but the physical mechanisms at the cellular level are unclear. Here, we demonstrate that a single epithelial monolayer of MDCK cells can exhibit two types of local tissue kinematics, pulsations and long range coherent flows, characterized by using quantitative live imaging. We report that these motions can be controlled with internal and external cues such as specific inhibitors and substrate friction modulation. We demonstrate the associated mechanisms with a unified vertex model. When cell velocity alignment and random diffusion of cell polarization are comparable, a pulsatile flow emerges whereas tissue undergoes long-range flows when velocity alignment dominates which is consistent with cytoskeletal dynamics measurements. We propose that environmental friction, acto-myosin distributions, and cell polarization kinetics are important in regulating dynamics of tissue morphogenesis.

Mechanical constraints to cell-cycle progression in a pseudostratified epithelium.

As organs and tissues approach their normal size during development or regeneration, growth slows down, and cell proliferation progressively comes to a halt. Among the various processes suggested to contribute to growth termination,1-10 mechanical feedback, perhaps via adherens junctions, has been suggested to play a role.11-14 However, since adherens junctions are only present in a narrow plane of the subapical region, other structures are likely needed to sense mechanical stresses along the apical-basal (A-B) axis, especially in a thick pseudostratified epithelium. This could be achieved by nuclei, which have been implicated in mechanotransduction in tissue culture.15 In addition, mechanical constraints imposed by nuclear crowding and spatial confinement could affect interkinetic nuclear migration (IKNM),16 which allows G2 nuclei to reach the apical surface, where they normally undergo mitosis.17-25 To explore how mechanical constraints affect IKNM, we devised an individual-based model that treats nuclei as deformable objects constrained by the cell cortex and the presence of other nuclei. The model predicts changes in the proportion of cell-cycle phases during growth, which we validate with the cell-cycle phase reporter FUCCI (Fluorescent Ubiquitination-based Cell Cycle Indicator).26 However, this model does not preclude indefinite growth, leading us to postulate that nuclei must migrate basally to access a putative basal signal required for S phase entry. With this refinement, our updated model accounts for the observed progressive slowing down of growth and explains how pseudostratified epithelia reach a stereotypical thickness upon completion of growth.

ECM degradation in the Drosophila abdominal epidermis initiates tissue growth that ceases with rapid cell-cycle exit.

During development, multicellular organisms undergo stereotypical patterns of tissue growth in space and time. How developmental growth is orchestrated remains unclear, largely due to the difficulty of observing and quantitating this process in a living organism. Drosophila histoblast nests are small clusters of progenitor epithelial cells that undergo extensive growth to give rise to the adult abdominal epidermis and are amenable to live imaging. Our quantitative analysis of histoblast proliferation and tissue mechanics reveals that tissue growth is driven by cell divisions initiated through basal extracellular matrix degradation by matrix metalloproteases secreted by the neighboring larval epidermal cells. Laser ablations and computational simulations show that tissue mechanical tension does not decrease as the histoblasts fill the abdominal epidermal surface. During tissue growth, the histoblasts display oscillatory cell division rates until growth termination occurs through the rapid emergence of G0/G1 arrested cells, rather than a gradual increase in cell-cycle time as observed in other systems such as the Drosophila wing and mouse postnatal epidermis. Different developing tissues can therefore achieve their final size using distinct growth termination strategies. Thus, adult abdominal epidermal development is characterized by changes in the tissue microenvironment and a rapid exit from the cell cycle.

Tissue hydraulics: Physics of lumen formation and interaction.

Lumen formation plays an essential role in the morphogenesis of tissues during development. Here we review the physical principles that play a role in the growth and coarsening of lumens. Solute pumping by the cell, hydraulic flows driven by differences of osmotic and hydrostatic pressures, balance of forces between extracellular fluids and cell-generated cytoskeletal forces, and electro-osmotic effects have been implicated in determining the dynamics and steady-state of lumens. We use the framework of linear irreversible thermodynamics to discuss the relevant force, time and length scales involved in these processes. We focus on order of magnitude estimates of physical parameters controlling lumen formation and coarsening.