Fluidization of tissues by cell division and apoptosis

Dynamic regulation of tissue fluidity controls skin repair during wound healing

During wound healing, different pools of stem cells (SCs) contribute to skin repair. However, how SCs become activated and drive the tissue remodeling essential for skin repair is still poorly understood. Here, by developing a mouse model allowing lineage tracing and basal cell lineage ablation, we monitor SC fate and tissue dynamics during regeneration using confocal and intravital imaging. Analysis of basal cell rearrangements shows dynamic transitions from a solid-like homeostatic state to a fluid-like state allowing tissue remodeling during repair, as predicted by a minimal mathematical modeling of the spatiotemporal dynamics and fate behavior of basal cells. The basal cell layer progressively returns to a solid-like state with re-epithelialization. Bulk, single-cell RNA, and epigenetic profiling of SCs, together with functional experiments, uncover a common regenerative state regulated by the EGFR/AP1 axis activated during tissue fluidization that is essential for skin SC activation and tissue repair.

Motility driven glassy dynamics in confluent epithelial monolayers

As wounds heal, embryos develop, cancer spreads, or asthma progresses, the cellular monolayer undergoes a glass transition between solid-like jammed and fluid-like flowing states. During some of these processes, the cells undergo an epithelial-to-mesenchymal transition (EMT): they acquire in-plane polarity and become motile. Thus, how motility drives the glassy dynamics in epithelial systems is critical for the EMT process. However, no analytical framework that is indispensable for deeper insights exists. Here, we develop such a theory inspired by a well-known glass theory. One crucial result of this work is that the confluency affects the effective persistence time-scale of active force, described by its rotational diffusivity, Deffr. Deffr differs from the bare rotational diffusivity, Dr, of the motile force due to cell shape dynamics, which acts to rectify the force dynamics: Deffr is equal to Dr when Dr is small and saturates when Dr is large. We test the theoretical prediction of Deffr and how it affects the relaxation dynamics in our simulations of the active Vertex model. This novel effect of Deffr is crucial to understanding the new and previously published simulation data of active glassy dynamics in epithelial monolayers.

Homeostasis of cytoplasmic crowding by cell wall fluidization and ribosomal counterions

In bacteria, algae, fungi, and plant cells, the wall must expand in concert with cytoplasmic biomass production, otherwise cells would experience toxic molecular crowding1,2or lyse. But how cells achieve expansion of this complex biomaterial in coordination with biosynthesis of macromolecules in the cytoplasm remains unexplained3, although recent works have revealed that these processes are indeed coupled4,5. Here, we report a striking increase of turgor pressure with growth rate in E. coli, suggesting that the speed of cell wall expansion is controlled via turgor. Remarkably, despite this increase in turgor pressure, cellular biomass density remains constant across a wide range of growth rates. By contrast, perturbations of turgor pressure that deviate from this scaling directly alter biomass density. A mathematical model based on cell wall fluidization by cell wall endopeptidases not only explains these apparently confounding observations but makes surprising quantitative predictions that we validated experimentally. The picture that emerges is that turgor pressure is directly controlled via counterions of ribosomal RNA. Elegantly, the coupling between rRNA and turgor pressure simultaneously coordinates cell wall expansion across a wide range of growth rates and exerts homeostatic feedback control on biomass density. This mechanism may regulate cell wall biosynthesis from microbes to plants and has important implications for the mechanism of action of antibiotics6.

Mechanical state transitions in the regulation of tissue form and function

From embryonic development, postnatal growth and adult homeostasis to reparative and disease states, cells and tissues undergo constant changes in genome activity, cell fate, proliferation, movement, metabolism and growth. Importantly, these biological state transitions are coupled to changes in the mechanical and material properties of cells and tissues, termed mechanical state transitions. These mechanical states share features with physical states of matter, liquids and solids. Tissues can switch between mechanical states by changing behavioural dynamics or connectivity between cells. Conversely, these changes in tissue mechanical properties are known to control cell and tissue function, most importantly the ability of cells to move or tissues to deform. Thus, tissue mechanical state transitions are implicated in transmitting information across biological length and time scales, especially during processes of early development, wound healing and diseases such as cancer. This Review will focus on the biological basis of tissue-scale mechanical state transitions, how they emerge from molecular and cellular interactions, and their roles in organismal development, homeostasis, regeneration and disease.

Emergence of cellular nematic order is a conserved feature of gastrulation in animal embryos

Cells undergo dramatic changes in morphology during embryogenesis, yet how these changes affect the formation of ordered tissues remains elusive. Here we find that the emergence of a nematic liquid crystal phase occurs in cells during gastrulation in the development of embryos of fish, frogs, and fruit flies. Moreover, the spatial correlations in all three organisms are long-ranged and follow a similar power-law decay( y ∼ x - α ) with α less than unity for the nematic order parameter, suggesting a common underlying physical mechanism unifies events in these distantly related species. All three species exhibit similar propagation of the nematic phase, reminiscent of nucleation and growth phenomena. Finally, we use a theoretical model along with disruptions of cell adhesion and cell specification to characterize the minimal features required for formation of the nematic phase. Our results provide a framework for understanding a potentially universal features of metazoan embryogenesis and shed light on the advent of ordered structures during animal development.

Emergence of cellular nematic order is a conserved feature of gastrulation in animal embryos

Cells undergo dramatic changes in morphology during embryogenesis, yet how these changes affect the formation of ordered tissues remains elusive. Here we find that the emergence of a nematic liquid crystal phase occurs in cells during gastrulation in the development of embryos of fish, frogs, and fruit flies. Moreover, the spatial correlations in all three organisms are long-ranged and follow a similar power-law decay( y ∼ x - α ) with α less than unity for the nematic order parameter, suggesting a common underlying physical mechanism unifies events in these distantly related species. All three species exhibit similar propagation of the nematic phase, reminiscent of nucleation and growth phenomena. Finally, we use a theoretical model along with disruptions of cell adhesion and cell specification to characterize the minimal features required for formation of the nematic phase. Our results provide a framework for understanding a potentially universal features of metazoan embryogenesis and shed light on the advent of ordered structures during animal development.

Control of Modular Tissue Flows Shaping the Embryo in Avian Gastrulation

Avian gastrulation requires coordinated flows of thousands of cells to form the body plan. We quantified these flows using their fundamental kinematic units: one attractor and two repellers constituting its Dynamic Morphoskeleton (DM). We have also elucidated the mechanistic origin of the attractor, marking the primitive streak (PS), and controlled its shape, inducing gastrulation flows in the chick embryo that are typical of other vertebrates. However, the origins of repellers and dynamic embryo shape remain unclear. Here, we address these questions using active matter physics and experiments. Repeller 1, separating the embryo proper (EP) from extraembryonic (EE) tissues, arises from the tug-of-war between EE epiboly and EP isotropic myosin-induced active stress. Repeller 2, bisecting the anterior and posterior PS and associated with embryo shape change, arises from anisotropic myosin-induced active intercalation in the mesendoderm. Combining mechanical confinement with inhibition of mesendoderm induction, we eliminated either one or both repellers, as predicted by our model. Our results reveal a remarkable modularity of avian gastrulation flows delineated by the DM, uncovering the mechanistic roles of EE epiboly, EP active constriction, mesendoderm intercalation and ingression. These findings offer a new perspective for deconstructing morphogenetic flows, uncovering their modular origin, and aiding synthetic morphogenesis.

Cell Division and Motility Enable Hexatic Order in Biological Tissues

Biological tissues transform between solid- and liquidlike states in many fundamental physiological events. Recent experimental observations further suggest that in two-dimensional epithelial tissues these solid-liquid transformations can happen via intermediate states akin to the intermediate hexatic phases observed in equilibrium two-dimensional melting. The hexatic phase is characterized by quasi-long-range (power-law) orientational order but no translational order, thus endowing some structure to an otherwise structureless fluid. While it has been shown that hexatic order in tissue models can be induced by motility and thermal fluctuations, the role of cell division and apoptosis (birth and death) has remained poorly understood, despite its fundamental biological role. Here we study the effect of cell division and apoptosis on global hexatic order within the framework of the self-propelled Voronoi model of tissue. Although cell division naively destroys order and active motility facilitates deformations, we show that their combined action drives a liquid-hexatic-liquid transformation as the motility increases. The hexatic phase is accessed by the delicate balance of dislocation defect generation from cell division and the active binding of disclination-antidisclination pairs from motility. We formulate a mean-field model to elucidate this competition between cell division and motility and the consequent development of hexatic order.

Mechanically-driven growth and competition in a Voronoi model of tissues

The mechanisms leading cells to acquire a fitness advantage and establish themselves in a population are paramount to understanding the development and growth of cancer. Although there are many works that study separately either the evolutionary dynamics or the mechanics of cancer, little has been done to couple evolutionary dynamics to mechanics. To address this question, we study a confluent model of tissue using a Self-Propelled Voronoi (SPV) model with stochastic growth rates that depend on the mechanical variables of the system. The SPV model is an out-of-equilibrium model of tissue derived from an energy functional that has a jamming/unjamming transition between solid-like and liquid-like states. By considering several scenarios of mutants invading a resident population in both phases, we determine the range of parameters that confer a fitness advantage and show that the preferred area and perimeter are the most relevant ones. We find that the liquid-like state is more resistant to invasion and show that the outcome of the competition can be determined from the simulation of a non-growing mixture. Moreover, a mean-field approximation can accurately predict the fate of a mutation affecting mechanical properties of a cell. Our results can be used to infer evolutionary dynamics from tissue images, understand cancer-suppressing effects of tissue mechanics, and even search for mechanics-based therapies.

Homeostasis of cytoplasmic crowding by cell wall fluidization and ribosomal counterions

In bacteria, algae, fungi, and plant cells, the wall must expand in concert with cytoplasmic biomass production, otherwise cells would experience toxic molecular crowding1,2 or lyse. But how cells achieve expansion of this complex biomaterial in coordination with biosynthesis of macromolecules in the cytoplasm remains unexplained3, although recent works have revealed that these processes are indeed coupled4,5. Here, we report a striking increase of turgor pressure with growth rate in E. coli, suggesting that the speed of cell wall expansion is controlled via turgor. Remarkably, despite this increase in turgor pressure, cellular biomass density remains constant across a wide range of growth rates. By contrast, perturbations of turgor pressure that deviate from this scaling directly alter biomass density. A mathematical model based on cell wall fluidization by cell wall endopeptidases not only explains these apparently confounding observations but makes surprising quantitative predictions that we validated experimentally. The picture that emerges is that turgor pressure is directly controlled via counterions of ribosomal RNA. Elegantly, the coupling between rRNA and turgor pressure simultaneously coordinates cell wall expansion across a wide range of growth rates and exerts homeostatic feedback control on biomass density. This mechanism may regulate cell wall biosynthesis from microbes to plants and has important implications for the mechanism of action of antibiotics6.

Mechanical control of cell proliferation patterns in growing epithelial monolayers

Cell proliferation plays a crucial role in regulating tissue homeostasis and development. However, our understanding of how cell proliferation is controlled in densely packed tissues is limited. Here we develop a computational framework to predict the patterns of cell proliferation in growing epithelial tissues, connecting single-cell behaviors and cell-cell interactions to tissue-level growth. Our model incorporates probabilistic rules governing cell growth, division, and elimination, also taking into account their feedback with tissue mechanics. In particular, cell growth is suppressed and apoptosis is enhanced in regions of high cell density. With these rules and model parameters calibrated using experimental data for epithelial monolayers, we predict how tissue confinement influences cell size and proliferation dynamics and how single-cell physical properties influence the spatiotemporal patterns of tissue growth. In this model, mechanical feedback between tissue confinement and cell growth leads to enhanced cell proliferation at tissue boundaries, whereas cell growth in the bulk is arrested, recapitulating experimental observations in epithelial tissues. By tuning cellular elasticity and contact inhibition of proliferation we can regulate the emergent patterns of cell proliferation, ranging from uniform growth at low contact inhibition to localized growth at higher contact inhibition. We show that the cell size threshold at G1/S transition governs the homeostatic cell density and tissue turnover rate, whereas the mechanical state of the tissue governs the dynamics of tissue growth. In particular, we find that the cellular parameters affecting tissue pressure play a significant role in determining the overall growth rate. Our computational study thus underscores the impact of cell mechanical properties on the spatiotemporal patterns of cell proliferation in growing epithelial tissues.

Demixing in Binary Mixtures with Differential Diffusivity at High Density

Spontaneous phase separation, or demixing, is important in biological phenomena such as cell sorting. In particle-based models, an open question is whether differences in diffusivity can drive such demixing. While differential-diffusivity-induced phase separation occurs in mixtures with a packing fraction up to 0.7 [S. N. Weber et al. Binary mixtures of particles with different diffusivities demix, Phys. Rev. Lett. 116, 058301 (2016)PRLTAO0031-900710.1103/PhysRevLett.116.058301], here we investigate whether demixing persists at even higher densities relevant for cells. For particle packing fractions between 0.7 and 1.0 the system demixes, but at packing fractions above unity the system remains mixed, exposing re-entrant behavior in the phase diagram that occurs when phase separation can no longer drive a change in entropy production at high densities. We also find that a confluent Voronoi model for tissues does not phase separate, consistent with particle-based simulations.

Mechanical forces across compartments coordinate cell shape and fate transitions to generate tissue architecture

Morphogenesis and cell state transitions must be coordinated in time and space to produce a functional tissue. An excellent paradigm to understand the coupling of these processes is mammalian hair follicle development, which is initiated by the formation of an epithelial invagination-termed placode-that coincides with the emergence of a designated hair follicle stem cell population. The mechanisms directing the deformation of the epithelium, cell state transitions and physical compartmentalization of the placode are unknown. Here we identify a key role for coordinated mechanical forces stemming from contractile, proliferative and proteolytic activities across the epithelial and mesenchymal compartments in generating the placode structure. A ring of fibroblast cells gradually wraps around the placode cells to generate centripetal contractile forces, which, in collaboration with polarized epithelial myosin activity, promote elongation and local tissue thickening. These mechanical stresses further enhance compartmentalization of Sox9 expression to promote stem cell positioning. Subsequently, proteolytic remodelling locally softens the basement membrane to facilitate a release of pressure on the placode, enabling localized cell divisions, tissue fluidification and epithelial invagination into the underlying mesenchyme. Together, our experiments and modelling identify dynamic cell shape transformations and tissue-scale mechanical cooperation as key factors for orchestrating organ formation.

Pulling the strings on solid-to-liquid phase transitions in cell collectives

Cell collectives must dynamically adapt to different biological contexts. For instance, in homeostatic conditions, epithelia must establish a barrier between body compartments and resist external stresses, while during development, wound healing or cancer invasion, these tissues undergo extensive remodeling. Using analogies from inert, passive materials, changes in cellular density, shape, rearrangements and/or migration were shown to result in collective transitions between solid and fluid states. However, what biological mechanisms govern these transitions remains an open question. In particular, the upstream signaling pathways and molecular effectors controlling the key physical axes determining tissue rheology and dynamics remain poorly understood. In this perspective, we focus on emerging evidence identifying the first biological signals determining the collective state of living tissues, with an emphasis on how these mechanisms are exploited for functionality across biological contexts.

Hydrodynamics and multiscale order in confluent epithelia

We formulate a hydrodynamic theory of confluent epithelia: i.e. monolayers of epithelial cells adhering to each other without gaps. Taking advantage of recent progresses toward establishing a general hydrodynamic theory of p-atic liquid crystals, we demonstrate that collectively migrating epithelia feature both nematic (i.e. p = 2) and hexatic (i.e. p = 6) orders, with the former being dominant at large and the latter at small length scales. Such a remarkable multiscale liquid crystal order leaves a distinct signature in the system's structure factor, which exhibits two different power-law scaling regimes, reflecting both the hexagonal geometry of small cells clusters and the uniaxial structure of the global cellular flow. We support these analytical predictions with two different cell-resolved models of epithelia - i.e. the self-propelled Voronoi model and the multiphase field model - and highlight how momentum dissipation and noise influence the range of fluctuations at small length scales, thereby affecting the degree of cooperativity between cells. Our construction provides a theoretical framework to conceptualize the recent observation of multiscale order in layers of Madin-Darby canine kidney cells and pave the way for further theoretical developments.

A mechanochemical model recapitulates distinct vertebrate gastrulation modes

During vertebrate gastrulation, an embryo transforms from a layer of epithelial cells into a multilayered gastrula. This process requires the coordinated movements of hundreds to tens of thousands of cells, depending on the organism. In the chick embryo, patterns of actomyosin cables spanning several cells drive coordinated tissue flows. Here, we derive a minimal theoretical framework that couples actomyosin activity to global tissue flows. Our model predicts the onset and development of gastrulation flows in normal and experimentally perturbed chick embryos, mimicking different gastrulation modes as an active stress instability. Varying initial conditions and a parameter associated with active cell ingression, our model recapitulates distinct vertebrate gastrulation morphologies, consistent with recently published experiments in the chick embryo. Altogether, our results show how changes in the patterning of critical cell behaviors associated with different force-generating mechanisms contribute to distinct vertebrate gastrulation modes via a self-organizing mechanochemical process.

Mechanochemical Active Feedback Generates Convergence Extension in Epithelial Tissue

Convergence extension, the simultaneous elongation of tissue along one axis while narrowing along a perpendicular axis, occurs during embryonic development. A fundamental process that contributes to shaping the organism, it happens in many different species and tissue types. Here, we present a minimal continuum model, that can be directly linked to the controlling microscopic biochemistry, which shows spontaneous convergence extension. It is comprised of a 2D viscoelastic active material with a mechanochemical active feedback mechanism coupled to a substrate via friction. Robust convergent extension behavior emerges beyond a critical value of the activity parameter and is controlled by the boundary conditions and the coupling to the substrate. Oscillations and spatial patterns emerge in this model when internal dissipation dominates over friction, as well as in the active elastic limit.

A toolbox to analyze collective cell migration, proliferation and cellular organization simultaneously

BACKGROUND

Analyses of collective cell migration and orientation phenomena are needed to assess the behavior of multicellular clusters. While some tools to the authors' knowledge none is capable to analyze collective migration, cellular orientation and proliferation in phase contrast images simultaneously.

METHODS

We provide a tool based to analyze phase contrast images of dense cell layers. PIV is used to calculatevelocity fields, while the structure tensor provides cellular orientation. An artificial neural network is used to identify cell division events, allowing to correlate migratory and organizational phenomena with cell density.

CONCLUSION

The presented tool allows the simultaneous analysis of collective cell behavior from phase contrast images in terms of migration, (self-)organization and proliferation.

Epithelial apoptotic pattern emerges from global and local regulation by cell apical area

Geometry is a fundamental attribute of biological systems, and it underlies cell and tissue dynamics. Cell geometry controls cell-cycle progression and mitosis and thus modulates tissue development and homeostasis. In sharp contrast and despite the extensive characterization of the genetic mechanisms of caspase activation, we know little about whether and how cell geometry controls apoptosis commitment in developing tissues. Here, we combined multiscale time-lapse microscopy of developing Drosophila epithelium, quantitative characterization of cell behaviors, and genetic and mechanical perturbations to determine how apoptosis is controlled during epithelial tissue development. We found that early in cell lives and well before extrusion, apoptosis commitment is linked to two distinct geometric features: a small apical area compared with other cells within the tissue and a small relative apical area with respect to the immediate neighboring cells. We showed that these global and local geometric characteristics are sufficient to recapitulate the tissue-scale apoptotic pattern. Furthermore, we established that the coupling between these two geometric features and apoptotic cells is dependent on the Hippo/YAP and Notch pathways. Overall, by exploring the links between cell geometry and apoptosis commitment, our work provides important insights into the spatial regulation of cell death in tissues and improves our understanding of the mechanisms that control cell number and tissue size.

Instabilities in a growing system of active particles: scalar and vectorial systems

The physics of micron-scale biological colonies usually benefits from different out-of-equilibrium sources. In bacterial colonies and cellular tissues, the growth process is among the important active sources that determine the dynamics. In this article, we study the generic dynamical instabilities associated with the growth phenomena that may arise in both scalar and vectorial systems. In vectorial systems, where the rotational degrees of particles play a role, a phenomenological growth-mediated torque can affect the rotational dynamics of individual particles. We show that such a growth-mediated torque can result in active traveling waves in the bulk of a growing system. In addition to the bulk properties, we analyze the instabilities in the shape of growing interfaces in both scalar and vectorial systems.

Constitutive model for the rheology of biological tissue

The rheology of biological tissue is key to processes such as embryo development, wound healing, and cancer metastasis. Vertex models of confluent tissue monolayers have uncovered a spontaneous liquid-solid transition tuned by cell shape; and a shear-induced solidification transition of an initially liquidlike tissue. Alongside this jamming/unjamming behavior, biological tissue also displays an inherent viscoelasticity, with a slow time and rate-dependent mechanics. With this motivation, we combine simulations and continuum theory to examine the rheology of the vertex model in nonlinear shear across a full range of shear rates from quastistatic to fast, elucidating its nonlinear stress-strain curves after the inception of shear of finite rate, and its steady state flow curves of stress as a function of strain rate. We formulate a rheological constitutive model that couples cell shape to flow and captures both the tissue solid-liquid transition and its rich linear and nonlinear rheology.

From cells to form: A roadmap to study shape emergence in vivo

Organogenesis arises from the collective arrangement of cells into progressively 3D-shaped tissue. The acquisition of a correctly shaped organ is then the result of a complex interplay between molecular cues, responsible for differentiation and patterning, and the mechanical properties of the system, which generate the necessary forces that drive correct shape emergence. Nowadays, technological advances in the fields of microscopy, molecular biology, and computer science are making it possible to see and record such complex interactions in incredible, unforeseen detail within the global context of the developing embryo. A quantitative and interdisciplinary perspective of developmental biology becomes then necessary for a comprehensive understanding of morphogenesis. Here, we provide a roadmap to quantify the events that lead to morphogenesis from imaging to image analysis, quantification, and modeling, focusing on the discrete cellular and tissue shape changes, as well as their mechanical properties.

Changes in Tissue Fluidity Predict Tumor Aggressiveness In Vivo

Cancer progression is caused by genetic changes and associated with various alterations in cell properties, which also affect a tumor's mechanical state. While an increased stiffness has been well known for long for solid tumors, it has limited prognostic power. It is hypothesized that cancer progression is accompanied by tissue fluidization, where portions of the tissue can change position across different length scales. Supported by tabletop magnetic resonance elastography (MRE) on stroma mimicking collagen gels and microscopic analysis of live cells inside patient derived tumor explants, an overview is provided of how cancer associated mechanisms, including cellular unjamming, proliferation, microenvironment composition, and remodeling can alter a tissue's fluidity and stiffness. In vivo, state-of-the-art multifrequency MRE can distinguish tumors from their surrounding host tissue by their rheological fingerprints. Most importantly, a meta-analysis on the currently available clinical studies is conducted and universal trends are identified. The results and conclusions are condensed into a gedankenexperiment about how a tumor can grow and eventually metastasize into its environment from a physics perspective to deduce corresponding mechanical properties. Based on stiffness, fluidity, spatial heterogeneity, and texture of the tumor front a roadmap for a prognosis of a tumor's aggressiveness and metastatic potential is presented.

Alcanivorax borkumensis biofilms enhance oil degradation by interfacial tubulation

During the consumption of alkanes, Alcanivorax borkumensis will form a biofilm around an oil droplet, but the role this plays during degradation remains unclear. We identified a shift in biofilm morphology that depends on adaptation to oil consumption: Longer exposure leads to the appearance of dendritic biofilms optimized for oil consumption effected through tubulation of the interface. In situ microfluidic tracking enabled us to correlate tubulation to localized defects in the interfacial cell ordering. We demonstrate control over droplet deformation by using confinement to position defects, inducing dimpling in the droplets. We developed a model that elucidates biofilm morphology, linking tubulation to decreased interfacial tension and increased cell hydrophobicity.

Lift force in odd compressible fluids

When a body moves through a fluid, it can experience a force orthogonal to its movement called lift force. Odd viscous fluids break parity and time-reversal symmetry, suggesting the existence of an odd lift force on tracer particles, even at vanishing Reynolds numbers and for symmetric geometries. It was previously found that an incompressible odd fluid cannot induce lift force on a tracer particle with no-slip boundary conditions, making signatures of odd viscosity in the two-dimensional bulk elusive. By computing the response matrix for a tracer particle, we show that an odd compressible fluid can produce an odd lift force. Using shell localization, we provide analytic expressions for the drag and odd lift forces acting on the tracer particle in a steady state and also at finite frequency. Importantly, we find that the existence of an odd lift force in a steady state requires taking into account the nonconservation of the fluid mass density due to the coupling between the two-dimensional surface and the three-dimensional bulk fluid.

Effective mechanical potential of cell-cell interaction explains three-dimensional morphologies during early embryogenesis

Mechanical forces are critical for the emergence of diverse three-dimensional morphologies of multicellular systems. However, it remains unclear what kind of mechanical parameters at cellular level substantially contribute to tissue morphologies. This is largely due to technical limitations of live measurements of cellular forces. Here we developed a framework for inferring and modeling mechanical forces of cell-cell interactions. First, by analogy to coarse-grained models in molecular and colloidal sciences, we approximated cells as particles, where mean forces (i.e. effective forces) of pairwise cell-cell interactions are considered. Then, the forces were statistically inferred by fitting the mathematical model to cell tracking data. This method was validated by using synthetic cell tracking data resembling various in vivo situations. Application of our method to the cells in the early embryos of mice and the nematode Caenorhabditis elegans revealed that cell-cell interaction forces can be written as a pairwise potential energy in a manner dependent on cell-cell distances. Importantly, the profiles of the pairwise potentials were quantitatively different among species and embryonic stages, and the quantitative differences correctly described the differences of their morphological features such as spherical vs. distorted cell aggregates, and tightly vs. non-tightly assembled aggregates. We conclude that the effective pairwise potential of cell-cell interactions is a live measurable parameter whose quantitative differences can be a parameter describing three-dimensional tissue morphologies.

Active cell divisions generate fourfold orientationally ordered phase in living tissue

Morphogenesis, the process through which genes generate form, establishes tissue-scale order as a template for constructing the complex shapes of the body plan. The extensive growth required to build these ordered substrates is fuelled by cell proliferation, which, naively, should destroy order. Understanding how active morphogenetic mechanisms couple cellular and mechanical processes to generate order-rather than annihilate it-remains an outstanding question in animal development. We show that cell divisions are the primary drivers of tissue flow, leading to a fourfold orientationally ordered phase. Waves of anisotropic cell proliferation propagate across the embryo with precise patterning. Defects introduced into the nascent lattice by cell divisions are moved out of the tissue bulk towards the boundary by subsequent divisions. Specific cell proliferation rates and orientations enable cell divisions to organize rather than fluidize the tissue. We observe this using live imaging and tissue cartography to analyse the dynamics of fourfold tissue ordering in the trunk segmental ectoderm of the crustacean Parhyale hawaiensis beginning 72 h after egg lay. The result is a robust, active mechanism for generating global orientational order in a non-equilibrium system that sets the stage for the subsequent development of shape and form.

MR Elastography in Cancer

ABSTRACT

The mechanical traits of cancer include abnormally high solid stress as well as drastic and spatially heterogeneous changes in intrinsic mechanical tissue properties. Whereas solid stress elicits mechanosensory signals promoting tumor progression, mechanical heterogeneity is conducive to cell unjamming and metastatic spread. This reductionist view of tumorigenesis and malignant transformation provides a generalized framework for understanding the physical principles of tumor aggressiveness and harnessing them as novel in vivo imaging markers. Magnetic resonance elastography is an emerging imaging technology for depicting the viscoelastic properties of biological soft tissues and clinically characterizing tumors in terms of their biomechanical properties. This review article presents recent technical developments, basic results, and clinical applications of magnetic resonance elastography in patients with malignant tumors.

Mechanical control of cell proliferation patterns in growing tissues

Cell proliferation plays a crucial role in regulating tissue homeostasis and development. However, our understanding of how cell proliferation is controlled in densely packed tissues is limited. Here we develop a computational framework to predict the patterns of cell proliferation in growing tissues, connecting single-cell behaviors and cell-cell interactions to tissue-level growth. Our model incorporates probabilistic rules governing cell growth, division, and elimination, while also taking into account their feedback with tissue mechanics. In particular, cell growth is suppressed and apoptosis is enhanced in regions of high cell density. With these rules and model parameters calibrated using experimental data, we predict how tissue confinement influences cell size and proliferation dynamics, and how single-cell physical properties influence the spatiotemporal patterns of tissue growth. Our findings indicate that mechanical feedback between tissue confinement and cell growth leads to enhanced cell proliferation at tissue boundaries, whereas cell growth in the bulk is arrested. By tuning cellular elasticity and contact inhibition of proliferation we can regulate the emergent patterns of cell proliferation, ranging from uniform growth at low contact inhibition to localized growth at higher contact inhibition. Furthermore, mechanical state of the tissue governs the dynamics of tissue growth, with cellular parameters affecting tissue pressure playing a significant role in determining the overall growth rate. Our computational study thus underscores the impact of cell mechanical properties on the spatiotemporal patterns of cell proliferation in growing tissues.

Migration and division in cell monolayers on substrates with topological defects

Collective movement and organization of cell monolayers are important for wound healing and tissue development. Recent experiments highlighted the importance of liquid crystal order within these layers, suggesting that +1 topological defects have a role in organizing tissue morphogenesis. We study fibroblast organization, motion, and proliferation on a substrate with micron-sized ridges that induce +1 and -1 topological defects using simulation and experiment. We model cells as self-propelled deformable ellipses that interact via a Gay-Berne potential. Unlike earlier work on other cell types, we see that density variation near defects is not explained by collective migration. We propose instead that fibroblasts have different division rates depending on their area and aspect ratio. This model captures key features of our previous experiments: the alignment quality worsens at high cell density and, at the center of the +1 defects, cells can adopt either highly anisotropic or primarily isotropic morphologies. Experiments performed with different ridge heights confirm a prediction of this model: Suppressing migration across ridges promotes higher cell density at the +1 defect. Our work enables a mechanism for tissue patterning using topological defects without relying on cell migration.

Configurational entropy is an intrinsic driver of tissue structural heterogeneity

Tissues comprise ordered arrangements of cells that can be surprisingly disordered in their details. How the properties of single cells and their microenvironment contribute to the balance between order and disorder at the tissue-scale remains poorly understood. Here, we address this question using the self-organization of human mammary organoids as a model. We find that organoids behave like a dynamic structural ensemble at the steady state. We apply a maximum entropy formalism to derive the ensemble distribution from three measurable parameters - the degeneracy of structural states, interfacial energy, and tissue activity (the energy associated with positional fluctuations). We link these parameters with the molecular and microenvironmental factors that control them to precisely engineer the ensemble across multiple conditions. Our analysis reveals that the entropy associated with structural degeneracy sets a theoretical limit to tissue order and provides new insight for tissue engineering, development, and our understanding of disease progression.

DeXtrusion: automatic recognition of epithelial cell extrusion through machine learning in vivo

Accurately counting and localising cellular events from movies is an important bottleneck of high-content tissue/embryo live imaging. Here, we propose a new methodology based on deep learning that allows automatic detection of cellular events and their precise xyt localisation on live fluorescent imaging movies without segmentation. We focused on the detection of cell extrusion, the expulsion of dying cells from the epithelial layer, and devised DeXtrusion: a pipeline based on recurrent neural networks for automatic detection of cell extrusion/cell death events in large movies of epithelia marked with cell contour. The pipeline, initially trained on movies of the Drosophila pupal notum marked with fluorescent E-cadherin, is easily trainable, provides fast and accurate extrusion predictions in a large range of imaging conditions, and can also detect other cellular events, such as cell division or cell differentiation. It also performs well on other epithelial tissues with reasonable re-training. Our methodology could easily be applied for other cellular events detected by live fluorescent microscopy and could help to democratise the use of deep learning for automatic event detections in developing tissues.

Proliferating active matter

The fascinating patterns of collective motion created by autonomously driven particles have fuelled active-matter research for over two decades. So far, theoretical active-matter research has often focused on systems with a fixed number of particles. This constraint imposes strict limitations on what behaviours can and cannot emerge. However, a hallmark of life is the breaking of local cell number conservation by replication and death. Birth and death processes must be taken into account, for example, to predict the growth and evolution of a microbial biofilm, the expansion of a tumour, or the development from a fertilized egg into an embryo and beyond. In this Perspective, we argue that unique features emerge in these systems because proliferation represents a distinct form of activity: not only do the proliferating entities consume and dissipate energy, they also inject biomass and degrees of freedom capable of further self-proliferation, leading to myriad dynamic scenarios. Despite this complexity, a growing number of studies document common collective phenomena in various proliferating soft-matter systems. This generality leads us to propose proliferation as another direction of active-matter physics, worthy of a dedicated search for new dynamical universality classes. Conceptual challenges abound, from identifying control parameters and understanding large fluctuations and nonlinear feedback mechanisms to exploring the dynamics and limits of information flow in self-replicating systems. We believe that, by extending the rich conceptual framework developed for conventional active matter to proliferating active matter, researchers can have a profound impact on quantitative biology and reveal fascinating emergent physics along the way.

Cell cycle dynamics control fluidity of the developing mouse neuroepithelium

As developing tissues grow in size and undergo morphogenetic changes, their material properties may be altered. Such changes result from tension dynamics at cell contacts or cellular jamming. Yet, in many cases, the cellular mechanisms controlling the physical state of growing tissues are unclear. We found that at early developmental stages, the epithelium in the developing mouse spinal cord maintains both high junctional tension and high fluidity. This is achieved via a mechanism in which interkinetic nuclear movements generate cell area dynamics that drive extensive cell rearrangements. Over time, the cell proliferation rate declines, effectively solidifying the tissue. Thus, unlike well-studied jamming transitions, the solidification uncovered here resembles a glass transition that depends on the dynamical stresses generated by proliferation and differentiation. Our finding that the fluidity of developing epithelia is linked to interkinetic nuclear movements and the dynamics of growth is likely to be relevant to multiple developing tissues.

Size-dependent response of cells in epithelial tissue modulated by contractile stress fibers

Although cells with distinct apical areas have been widely observed in epithelial tissues, how the size of cells affects their behavior during tissue deformation and morphogenesis as well as key physical factors modulating such influence remains elusive. Here, we showed that the elongation of cells within the monolayer under anisotropic biaxial stretching increases with their size because the strain released by local cell rearrangement (i.e., T1 transition) is more significant for small cells that possess higher contractility. On the other hand, by incorporating the nucleation, peeling, merging, and breakage dynamics of subcellular stress fibers into classical vertex formulation, we found that stress fibers with orientations predominantly aligned with the main stretching direction will be formed at tricellular junctions, in good agreement with recent experiments. The contractile forces generated by stress fibers help cells to resist imposed stretching, reduce the occurrence of T1 transitions, and, consequently, modulate their size-dependent elongation. Our findings demonstrate that epithelial cells could utilize their size and internal structure to regulate their physical and related biological behaviors. The theoretical framework proposed here can also be extended to investigate the roles of cell geometry and intracellular contraction in processes such as collective cell migration and embryo development.

MACC1-induced migration in tumors: Current state and perspective

Malignant tumors are still a global, heavy health burden. Many tumor types cannot be treated curatively, underlining the need for new treatment targets. In recent years, metastasis associated in colon cancer 1 (MACC1) was identified as a promising biomarker and drug target, as it is promoting tumor migration, initiation, proliferation, and others in a multitude of solid cancers. Here, we will summarize the current knowledge about MACC1-induced tumor cell migration with a special focus on the cytoskeletal and adhesive systems. In addition, a brief overview of several in vitro models used for the analysis of cell migration is given. In this context, we will point to issues with the currently most prevalent models used to study MACC1-dependent migration. Lastly, open questions about MACC1-dependent effects on tumor cell migration will be addressed.

Mechanotransduction in tumor dynamics modeling

Mechanotherapy is a groundbreaking approach to impact carcinogenesis. Cells sense and respond to mechanical stimuli, translating them into biochemical signals in a process known as mechanotransduction. The impact of stress on tumor growth has been studied in the last three decades, and many papers highlight the role of mechanics as a critical self-inducer of tumor fate at the in vitro and in vivo biological levels. Meanwhile, mathematical models attempt to determine laws to reproduce tumor dynamics. This review discusses biological mechanotransduction mechanisms and mathematical-biomechanical models together. The aim is to provide a common framework for the different approaches that have emerged in the literature from the perspective of tumor avascularity and to provide insight into emerging mechanotherapies that have attracted interest in recent years.

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.

On shape forming by contractile filaments in the surface of growing tissues

Growing tissues are highly dynamic, and flow on sufficiently long timescales due to cell proliferation, migration, and tissue remodeling. As a consequence, growing tissues can often be approximated as viscous fluids. This means that the shape of microtissues growing in vitro is governed by their surface stress state, as in fluid droplets. Recent work showed that cells in the near-surface region of fibroblastic or osteoblastic microtissues contract with highly oriented actin filaments, thus making the surface properties highly anisotropic, in contrast to what is expected for an isotropic fluid. Here, we develop a model that includes mechanical anisotropy of the surface generated by contractile fibers and we show that mechanical equilibrium requires contractile filaments to follow geodesic lines on the surface. Constant pressure in the fluid forces these contractile filaments to be along geodesics with a constant normal curvature. We then take this into account to determine equilibrium shapes of rotationally symmetric bodies subjected to anisotropic surface stress states and derive a family of surfaces of revolution. A comparison with recently published shapes of microtissues shows that this theory accurately predicts both the surface shape and the direction of the actin filaments on the surface.

Enhanced mechanical heterogeneity of cell collectives due to temporal fluctuations in cell elasticity

Cells are dynamic systems characterized by temporal variations in biophysical properties such as stiffness and contractility. Recent studies show that the recruitment and release of actin filaments into and out of the cell cortex-a network of proteins underneath the cell membrane-leads to cell stiffening prior to division and softening immediately afterward. In three-dimensional (3D) cell collectives, it is unclear whether the stiffness change during division at the single-cell scale controls the spatial structure and dynamics at the multicellular scale. This is an important question to understand because cell stiffness variations impact cell spatial organization and cancer progression. Using a minimal 3D model incorporating cell birth, death, and cell-to-cell elastic and adhesive interactions, we investigate the effect of mechanical heterogeneity-variations in individual cell stiffnesses that make up the cell collective-on tumor spatial organization and cell dynamics. We discover that spatial mechanical heterogeneity characterized by a spheroid core composed of stiffer cells and softer cells in the periphery emerges within dense 3D cell collectives, which may be a general feature of multicellular tumor growth. We show that heightened spatial mechanical heterogeneity enhances single-cell dynamics and volumetric tumor growth driven by fluctuations in cell elasticity. Our results could have important implications in understanding how spatiotemporal variations in single-cell stiffness determine tumor growth and spread.

Jamming Transitions in Astrocytes and Glioblastoma Are Induced by Cell Density and Tension

Collective behavior of cells emerges from coordination of cell-cell-interactions and is important to wound healing, embryonic and tumor development. Depending on cell density and cell-cell interactions, a transition from a migratory, fluid-like unjammed state to a more static and solid-like jammed state or vice versa can occur. Here, we analyze collective migration dynamics of astrocytes and glioblastoma cells using live cell imaging. Furthermore, atomic force microscopy, traction force microscopy and spheroid generation assays were used to study cell adhesion, traction and mechanics. Perturbations of traction and adhesion were induced via ROCK or myosin II inhibition. Whereas astrocytes resided within a non-migratory, jammed state, glioblastoma were migratory and unjammed. Furthermore, we demonstrated that a switch from an unjammed to a jammed state was induced upon alteration of the equilibrium between cell-cell-adhesion and tension from adhesion to tension dominated, via inhibition of ROCK or myosin II. Such behavior has implications for understanding the infiltration of the brain by glioblastoma cells and may help to identify new strategies to develop anti-migratory drugs and strategies for glioblastoma-treatment.

Making sense of fragmentation and merging in lineage tracing experiments

Lineage tracing experiments give dynamic information on the functional behaviour of dividing cells. These experiments therefore have become an important tool for studying stem and progenitor cell fate behavior in vivo. When cell proliferation is high or the frequency of induced clones cannot be precisely controlled, the merging and fragmentation of clones renders the retrospective interpretation of clonal fate data highly ambiguous, potentially leading to unguarded interpretations about lineage relationships and fate behaviour. Here, we discuss and generalize statistical strategies to detect, resolve and make use of clonal fragmentation and merging. We first explain how to detect the rates of clonal fragmentation and merging using simple statistical estimates. We then discuss ways to restore the clonal provenance of labelled cells algorithmically and statistically and elaborate on how the process of clonal fragmentation can indirectly inform about cell fate. We generalize and extend results from the context of their original publication.

Broken living layers: Dislocations in active smectic liquid crystals

We show that dislocations in active two-dimensional (2D) smectic liquid crystals with underlying rotational symmetry are always unbound in the presence of noise, meaning the active smectic phase does not exist for nonzero noise in d=2. The active smectic phase can, like equilibrium smectics in 2D, be stabilized by applying rotational symmetry-breaking fields; however, even in the presence of such fields, active smectics are still much less stable against noise than equilibrium ones, when the symmetry-breaking field(s) are weak.

Stress anisotropy in confined populations of growing rods

A central feature of living matter is its ability to grow and multiply. The mechanical activity associated with growth produces both macroscopic flows shaped by confinement, and striking self-organization phenomena, such as orientational order and alignment, which are particularly prominent in populations of rod-shaped bacteria due to their nematic properties. However, how active stresses, passive mechanical interactions and flow-induced effects interact to give rise to the observed global alignment patterns remains elusive. Here, we study in silico colonies of growing rod-shaped particles of different aspect ratios confined in channel-like geometries. A spatially resolved analysis of the stress tensor reveals a strong relationship between near-perfect alignment and an inversion of stress anisotropy for particles with large length-to-width ratios. We show that, in quantitative agreement with an asymptotic theory, strong alignment can lead to a decoupling of active and passive stresses parallel and perpendicular to the direction of growth, respectively. We demonstrate the robustness of these effects in a geometry that provides less restrictive confinement and introduces natural perturbations in alignment. Our results illustrate the complexity arising from the inherent coupling between nematic order and active stresses in growing active matter, which is modulated by geometric and configurational constraints due to confinement.

Mapping cell cortex rheology to tissue rheology and vice versa

The mechanics of biological tissues mainly proceeds from the cell cortex rheology. A direct, explicit link between cortex rheology and tissue rheology remains lacking, yet would be instrumental in understanding how modulations of cortical mechanics may impact tissue mechanical behavior. Using an ordered geometry built on 3D hexagonal, incompressible cells, we build a mapping relating the cortical rheology to the monolayer tissue rheology. Our approach shows that the tissue low-frequency elastic modulus is proportional to the rest tension of the cortex, as expected from the physics of liquid foams as well as of tensegrity structures. A fractional visco-contractile cortex rheology is predicted to yield a high-frequency fractional visco-elastic monolayer rheology, where such a fractional behavior has been recently observed experimentally at each scale separately. In particular cases, the mapping may be inverted, allowing to derive from a given tissue rheology the underlying cortex rheology. Interestingly, applying the same approach to a 2D hexagonal tiling fails, which suggests that the 2D character of planar cell cortex-based models may be unsuitable to account for realistic monolayer rheologies. We provide quantitative predictions, amenable to experimental tests through standard perturbation assays of cortex constituents, and hope to foster new, challenging mechanical experiments on cell monolayers.

A physical model for dynamic assembly of human salivary stem/progenitor microstructures

The in vitro reconstructions of human salivary glands in service of their eventual medical use represent a challenge for tissue engineering. Here, we present a theoretical approach to the dynamical formation of acinar structures from human salivary cells, focusing on observed stick-slip radial expansion as well as possible growth instabilities. Our findings demonstrate the critical importance of basement membrane remodeling in controlling the growth process.

Variational methods and deep Ritz method for active elastic solids

Variational methods have been widely used in soft matter physics for both static and dynamic problems. These methods are mostly based on two variational principles: the variational principle of minimum free energy (MFEVP) and Onsager's variational principle (OVP). Our interests lie in the applications of these variational methods to active matter physics. In our former work [H. Wang, T. Qian and X. Xu, Soft Matter, 2021, 17, 3634-3653], we have explored the applications of OVP-based variational methods for the modeling of active matter dynamics. In the present work, we explore variational (or energy) methods that are based on MFEVP for static problems in active elastic solids. We show that MFEVP can be used not only to derive equilibrium equations, but also to develop approximate solution methods, such as the Ritz method, for active solid statics. Moreover, the power of the Ritz-type method can be further enhanced using deep learning methods if we use deep neural networks to construct the trial functions of the variational problems. We then apply these variational methods and the deep Ritz method to study the spontaneous bending and contraction of a thin active circular plate that is induced by internal asymmetric active contraction. The circular plate is found to be bent towards its contracting side. The study of such a simple toy system gives implications for understanding the morphogenesis of solid-like confluent cell monolayers. In addition, we introduce a so-called activogravity length to characterize the importance of gravitational forces relative to internal active contraction in driving the bending of the active plate. When the lateral plate dimension is larger than the activogravity length (about 100 micron), gravitational forces become important. Such gravitaxis behaviors at multicellular scales may play significant roles in the morphogenesis and in the up-down symmetry broken during tissue development.

Activity gradients in two- and three-dimensional active nematics

We numerically investigate how spatial variations of extensile or contractile active stress affect bulk active nematic systems in two and three dimensions. In the absence of defects, activity gradients drive flows which re-orient the nematic director field and thus act as an effective anchoring force. At high activity, defects are created and the system transitions into active turbulence, a chaotic flow state characterized by strong vorticity. We find that in two-dimensional (2D) systems active torques robustly align +1/2 defects parallel to activity gradients, with defect heads pointing towards contractile regions. In three-dimensional (3D) active nematics disclination lines preferentially lie in the plane perpendicular to activity gradients due to active torques acting on line segments. The average orientation of the defect structures in the plane perpendicular to the line tangent depends on the defect type, where wedge-like +1/2 defects align parallel to activity gradients, while twist defects are aligned anti-parallel. Understanding the response of active nematic fluids to activity gradients is an important step towards applying physical theories to biology, where spatial variations of active stress impact morphogenetic processes in developing embryos and affect flows and deformations in growing cell aggregates, such as tumours.

Instabilities and Geometry of Growing Tissues

We present a covariant continuum formulation of a generalized two-dimensional vertexlike model of epithelial tissues which describes tissues with different underlying geometries, and allows for an analytical macroscopic description. Using a geometrical approach and out-of-equilibrium statistical mechanics, we calculate both mechanical and dynamical instabilities of a tissue, and their dependences on various variables, including activity, and cell-shape heterogeneity (disorder). We show how both plastic cellular rearrangements and the tissue elastic response depend on the existence of mechanical residual stresses at the cellular level. Even freely growing tissues may exhibit a growth instability depending on the intrinsic proliferation rate. Our main result is an explicit calculation of the cell pressure in a homeostatic state of a confined growing tissue. We show that the homeostatic pressure can be negative and depends on the existence of mechanical residual stresses. This geometric model allows us to sort out elastic and plastic effects in a growing, flowing, tissue.

Self-assembly of tessellated tissue sheets by expansion and collision

Tissues do not exist in isolation—they interact with other tissues within and across organs. While cell-cell interactions have been intensely investigated, less is known about tissue-tissue interactions. Here, we studied collisions between monolayer tissues with different geometries, cell densities, and cell types. First, we determine rules for tissue shape changes during binary collisions and describe complex cell migration at tri-tissue boundaries. Next, we propose that genetically identical tissues displace each other based on pressure gradients, which are directly linked to gradients in cell density. We present a physical model of tissue interactions that allows us to estimate the bulk modulus of the tissues from collision dynamics. Finally, we introduce TissEllate, a design tool for self-assembling complex tessellations from arrays of many tissues, and we use cell sheet engineering techniques to transfer these composite tissues like cellular films. Overall, our work provides insight into the mechanics of tissue collisions, harnessing them to engineer tissue composites as designable living materials.

Tissue boundaries in our body separate organs and enable healing, but boundary mechanics are not well known. Here, the authors define mechanical rules for colliding cell monolayers and use these rules to make complex, predictable tessellations.