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

Vertex model with internal dissipation enables sustained flows

Complex tissue flows in epithelia are driven by intra- and inter-cellular processes that generate, maintain, and coordinate mechanical forces. There has been growing evidence that cell shape anisotropy, manifested as nematic order, plays an important role in this process. Here we extend an active nematic vertex model by replacing substrate friction with internal viscous dissipation, dominant in epithelia not supported by a substrate or the extracellular matrix, which are found in many early-stage embryos. When coupled to cell shape anisotropy, the internal viscous dissipation allows for long-range velocity correlations and thus enables the spontaneous emergence of flows with a large degree of spatiotemporal organisation. We demonstrate sustained flow in epithelial sheets confined to a channel, providing a link between the cell-level vertex model of tissue dynamics and continuum active nematics, whose behaviour in a channel is theoretically understood and experimentally realisable. Our findings also show a simple mechanism that could account for collective cell migration correlated over distances large compared to the cell size, as observed during morphogenesis.

Confined cell migration along extracellular matrix space in vivo

Collective migration of cancer cells is often interpreted using concepts derived from the physics of active matter, but the experimental evidence is mostly restricted to observations made in vitro. Here, we study collective invasion of metastatic cancer cells injected into the mouse deep dermis using intravital multiphoton microscopy combined with a skin window technique and three-dimensional quantitative image analysis. We observe a multicellular but low-cohesive migration mode characterized by rotational patterns which self-organize into antiparallel persistent tracks with orientational nematic order. We analyze the deformations induced by the cells in the extracellular matrix and find broadly distributed strain bands with a prevalence of compression. A model of active nematic hydrodynamics is able to describe several statistical features of the experimentally observed flow, suggesting that collective cancer cell invasion can be interpreted as a nematic active fluid in the turbulent regime. Our results help elucidate the migration patterns of cancer cells in vivo and provide quantitative guidance for the development of realistic in vitro and in silico models for collective cell migration.

Cell Sorting in an Active Nematic Vertex Model

We study a mixture of extensile and contractile cells using a vertex model extended to include active nematic stresses. The two cell populations phase separate over time. While phase separation strengthens monotonically with an increasing magnitude of contractile activity, the dependence on extensile activity is nonmonotonic, so that sufficiently high values reduce the extent of sorting. We interpret this by showing that extensile activity renders the system motile, enabling cells to undergo neighbor exchanges. Contractile cells that come into contact as a result are then more likely to stay connected due to an effective attraction arising from contractile activity.

Hybrid model to simulate host cell biomechanics and infection spread during intracellular infection of epithelial monolayers

Mechanical signals are crucial in regulating the response of cells in a monolayer to both physiological and pathological stressors, including intracellular bacterial infections. In particular, during intracellular infection of epithelial cells in monolayer with the food-borne bacterial pathogen Listeria monocytogenes, cellular biomechanics dictates the degree of bacterial dissemination across the monolayer. This occurs through a process whereby surrounder uninfected cells mechanically compete and eventually extrude infected cells. However, the plethora of physical mechanisms involved and their temporal dynamics are still not fully uncovered, which could inform whether they benefit or harm the host. To further investigate these mechanisms, we propose a two-dimensional hybrid computational model that combines an agent-based model with a finite element method to simulate the kinematics and dynamics of epithelial cell monolayers in the absence or presence of infection. The model accurately replicated the impact of cell density on the mechanical behaviour of uninfected monolayers, showing that increased cell density reduces cell motility and coordination of motion, cell fluidity and monolayer stresses. Moreover, when simulating the intercellular spread of infection, the model successfully reproduced the mechanical competition between uninfected and infected cells. Infected cells showed a reduction in cell area, while the surrounder cells migrated towards the infection site, exerting increased monolayer stresses, consistent with our in vitro observations. This model offers a powerful tool for studying epithelial monolayers in health and disease, by providing in silico predictions of cell shapes, kinematics and dynamics that can then be tested experimentally.

Spontaneous flows and quantum analogies in heterogeneous active nematic films

Incorporating the inherent heterogeneity of living systems into models of active nematics is essential to provide a more realistic description of biological processes such as bacterial growth, cell dynamics and tissue development. Spontaneous flow of a confined active nematic is a fundamental feature of these systems, in which the role of heterogeneity has not yet been considered. We therefore determine the form of spontaneous flow transition for an active nematic film with heterogeneous activity, identifying a correspondence between the unstable director modes and solutions to Schrödinger's equation. We consider both activity gradients and steps between regions of distinct activity, finding that such variations can change the signature properties of the flow. The threshold activity required for the transition can be raised or lowered, the fluid flux can be reduced or reversed and interfaces in activity induce shear flows. In a biological context fluid flux influences the spread of nutrients while shear flows affect the behaviour of rheotactic microswimmers and can cause the deformation of biofilms. All the effects we identify are found to be strongly dependent on not simply the types of activity present in the film but also on how they are distributed.

Different Biomechanical Cell Behaviors in an Epithelium Drive Collective Epithelial Cell Extrusion

In vertebrates, many organs, such as the kidney and the mammary gland form ductal structures based on the folding of epithelial sheets. The development of these organs relies on coordinated sorting of different cell lineages in both time and space, through mechanisms that remain largely unclear. Tissues are composed of several cell types with distinct biomechanical properties, particularly at cell-cell and cell-substrate boundaries. One hypothesis is that adjacent epithelial layers work in a coordinated manner to shape the tissue. Using in vitro experiments on model epithelial cells, differential expression of atypical Protein Kinase C iota (aPKCi), a key junctional polarity protein, is shown to reinforce cell epithelialization and trigger sorting by tuning cell mechanical properties at the tissue level. In a broader perspective, it is shown that in a heterogeneous epithelial monolayer, in which cell sorting occurs, forces arising from epithelial cell growth under confinement by surrounding cells with different biomechanical properties are sufficient to promote collective cell extrusion and generate emerging 3D organization related to spheroids and buds. Overall, this research sheds light on the role of aPKCi and the biomechanical interplay between distinct epithelial cell lineages in shaping tissue organization, providing insights into the understanding of tissue and organ development.

Energetic scaling behavior of patterned epithelium

Cellular monolayers display various degrees of coordinated motion ranging from the small scale of just a few cells to large multi-cellular scales. This collective migration carries important physical cues for creating proper tissue morphology. Previous studies have demonstrated that the energetics of the epithelial monolayer show a linear variation with time in conjunction with an arrest in monolayer motion after confluency. However, little is known about how the energetics of monolayer development are affected by confined geometries. Here, we demonstrate that micropatterned epithelial monolayers display a non-linear change in energetic variables, which coincides with the large-scale coordination of migration. This non-linear scaling behavior was further seen to be associated with the biased alignment of cells and cell-cell adhesion. These findings provide a new understanding of how developing epithelia may be impacted by different conditions in vivo.

Long range juxtacrine signalling through cadherin for collective cell orientation

Many life phenomena, such as development, morphogenesis, tissue remodelling, and wound healing, are often driven by orderly and directional migration of collective cells. However, when cells are randomly oriented or localized disorder exists in orderly oriented collective cells, cell migration cannot occur in an orderly manner although various motion modes such as global rotation and local swirling and/or various motion patterns such as radial pattern and chiral pattern often occur. Therefore, it is important to control cell orientation to ensure the orderly migration of collective cells. Here, we show that it is not force transmission, but juxtacrine signalling through cadherin that plays a critical role in the orientation of collective cells. Surprisingly, juxtacrine signalling for cell orientation reached cells on a plastic dish that were not directly subjected to mechanical stimulation, up to 7 mm away from the actuator. The present study suggests that even weak mechanical stimulation is transmitted in a long range without force transmission through juxtacrine signalling. The long range juxtacrine signalling might play an important role in various life phenomena. STATEMENT OF SIGNIFICANCE: Juxtacrine signalling is direct cell-cell contact-dependent signalling, which plays a crucial role in cell behaviors such as mechanosensing, mechanotransduction and collective cell behaviors, however, there is not enough understanding about juxtacrine signalling. The present study has demonstrated that juxtacrine signalling for collective cell orientation is transmitted over a long range through cadherin. To the best of our knowledge, this is the first report of long range juxtacrine signalling. This finding may lead to the elucidation of various life phenomena such as development, morphogenesis, tissue remodelling, and wound healing.

Force-mediated recruitment and reprogramming of healthy endothelial cells drive vascular lesion growth

Force-driven cellular interactions are crucial for cancer cell invasion but remain underexplored in vascular abnormalities. Cerebral cavernous malformations (CCM), a vascular abnormality characterized by leaky vessels, involves CCM mutant cells recruiting wild-type endothelial cells to form and expand mosaic lesions. The mechanisms behind this recruitment remain poorly understood. Here, we use an in-vitro model of angiogenic invasion with traction force microscopy to reveal that hyper-angiogenic Ccm2-silenced endothelial cells enhance angiogenic invasion of neighboring wild-type cells through force and extracellular matrix-guided mechanisms. We demonstrate that mechanically hyperactive CCM2-silenced tips guide wild-type cells by transmitting pulling forces and by creating paths in the matrix, in a ROCKs-dependent manner. This is associated with reinforcement of β1 integrin and actin cytoskeleton in wild-type cells. Further, wild-type cells are reprogrammed into stalk cells and activate matrisome and DNA replication programs, thereby initiating proliferation. Our findings reveal how CCM2 mutants hijack wild-type cell functions to fuel lesion growth, providing insight into the etiology of vascular malformations. By integrating biophysical and molecular techniques, we offer tools for studying cell mechanics in tissue heterogeneity and disease progression.

Anomalous diffusion of active Brownian particles in responsive elastic gels: Nonergodicity, non-Gaussianity, and distributions of trapping times

Understanding actual transport mechanisms of self-propelled particles (SPPs) in complex elastic gels-such as in the cell cytoplasm, in in vitro networks of chromatin or of F-actin fibers, or in mucus gels-has far-reaching consequences. Implications beyond biology/biophysics are in engineering and medicine, with a particular focus on microrheology and on targeted drug delivery. Here, we examine via extensive computer simulations the dynamics of SPPs in deformable gellike structures responsive to thermal fluctuations. We treat tracer particles comparable to and larger than the mesh size of the gel. We observe distinct trapping events of active tracers at relatively short times, leading to subdiffusion; it is followed by an escape from meshwork-induced traps due to the flexibility of the network, resulting in superdiffusion. We thus find crossovers between different transport regimes. We also find pronounced nonergodicity in the dynamics of SPPs and non-Gaussianity at intermediate times. The distributions of trapping times of the tracers escaping from "cages" in our quasiperiodic gel often reveal the existence of two distinct timescales in the dynamics. At high activity of the tracers these timescales become comparable. Furthermore, we find that the mean waiting time exhibits a power-law dependence on the activity of SPPs (in terms of their Péclet number). Our results additionally showcase both exponential and nonexponential trapping events at high activities. Extensions of this setup are possible, with the factors such as anisotropy of the particles, different topologies of the gel network, and various interactions between the particles (also of a nonlocal nature) to be considered.

Intercellular friction and motility drive orientational order in cell monolayers

Spatiotemporal patterns in multicellular systems are important to understanding tissue dynamics, for instance, during embryonic development and disease. Here, we use a multiphase field model to study numerically the behavior of a near-confluent monolayer of deformable cells with intercellular friction. Varying friction and cell motility drives a solid-liquid transition, and near the transition boundary, we find the emergence of local nematic order of cell deformation driven by shear-aligning cellular flows. Intercellular friction contributes to the monolayer's viscosity, which significantly increases the spatial correlation in the flow and, concomitantly, the extent of nematic order. We also show that local hexatic and nematic order are tightly coupled and propose a mechanical-geometric model for the colocalization of [Formula: see text] nematic defects and 5-7 disclination pairs, which are the structural defects in the hexatic phase. Such topological defects coincide with regions of high cell-cell overlap, suggesting that they may mediate cellular extrusion from the monolayer, as found experimentally. Our results delineate a mechanical basis for the recent observation of nematic and hexatic order in multicellular collectives in experiments and simulations and pinpoint a generic pathway to couple topological and physical effects in these systems.

Multiphase field model of cells on a substrate: From three dimensional to two dimensional

Multiphase field models have emerged as an important computational tool for understanding biological tissue while resolving single-cell properties. While they have successfully reproduced many experimentally observed behaviors of living tissue, the theoretical underpinnings have not been fully explored. We show that a two-dimensional version of the model, which is commonly employed to study tissue monolayers, can be derived from a three-dimensional version in the presence of a substrate. We also show how viscous forces, which arise from friction between different cells, can be included in the model. Finally, we numerically simulate a tissue monolayer and find that intercellular friction tends to solidify the tissue.

Perspectives in collective cell migration - moving forward

Collective cell migration, where cells move as a cohesive unit, is a vital process underlying morphogenesis and cancer metastasis. Thanks to recent advances in imaging and modelling, we are beginning to understand the intricate relationship between a cell and its microenvironment and how this shapes cell polarity, metabolism and modes of migration. The use of biophysical and mathematical models offers a fresh perspective on how cells migrate collectively, either flowing in a fluid-like state or transitioning to more static states. Continuing to unite researchers in biology, physics and mathematics will enable us to decode more complex biological behaviours that underly collective cell migration; only then can we understand how this coordinated movement of cells influences the formation and organisation of tissues and directs the spread of metastatic cancer. In this Perspective, we highlight exciting discoveries, emerging themes and common challenges that have arisen in recent years, and possible ways forward to bridge the gaps in our current understanding of collective cell migration.

Molecular Force Sensors for Biological Application

The mechanical forces exerted by cells on their surrounding microenvironment are known as cellular traction forces. These forces play crucial roles in various biological processes, such as tissue development, wound healing and cell functions. However, it is hard for traditional techniques to measure cellular traction forces accurately because their magnitude (from pN to nN) and the length scales over which they occur (from nm to μm) are extremely small. In order to fully understand mechanotransduction, highly sensitive tools for measuring cellular forces are needed. Current powerful techniques for measuring traction forces include traction force microscopy (TFM) and fluorescent molecular force sensors (FMFS). In this review, we elucidate the force imaging principles of TFM and FMFS. Then we highlight the application of FMFS in a variety of biological processes and offer our perspectives and insights into the potential applications of FMFS.

Stiffness anisotropy coordinates supracellular contractility driving long-range myotube-ECM alignment

The ability of cells to organize into tissues with proper structure and function requires the effective coordination of proliferation, migration, polarization, and differentiation across length scales. Skeletal muscle is innately anisotropic; however, few biomaterials can emulate mechanical anisotropy to determine its influence on tissue patterning without introducing confounding topography. Here, we demonstrate that substrate stiffness anisotropy coordinates contractility-driven collective cellular dynamics resulting in C2C12 myotube alignment over millimeter-scale distances. When cultured on mechanically anisotropic liquid crystalline polymer networks (LCNs) lacking topography, C2C12 myoblasts collectively polarize in the stiffest direction. Cellular coordination is amplified through reciprocal cell-ECM dynamics that emerge during fusion, driving global myotube-ECM ordering. Conversely, myotube alignment was restricted to small local domains with no directional preference on mechanically isotropic LCNs of the same chemical formulation. These findings provide valuable insights for designing biomaterials that mimic anisotropic microenvironments and underscore the importance of stiffness anisotropy in orchestrating tissue morphogenesis.

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.

Decoding Biomechanical Cues Based on DNA Sensors

Biological systems perceive and respond to mechanical forces, generating mechanical cues to regulate life processes. Analyzing biomechanical forces has profound significance for understanding biological functions. Therefore, a series of molecular mechanical techniques have been developed, mainly including single-molecule force spectroscopy, traction force microscopy, and molecular tension sensor systems, which provide indispensable tools for advancing the field of mechanobiology. DNA molecules with a programmable structure and well-defined mechanical characteristics have attached much attention to molecular tension sensors as sensing elements, and are designed for the study of biomechanical forces to present biomechanical information with high sensitivity and resolution. In this work, a comprehensive overview of molecular mechanical technology is presented, with a particular focus on molecular tension sensor systems, specifically those based on DNA. Finally, the future development and challenges of DNA-based molecular tension sensor systems are looked upon.

Stress-shape misalignment in confluent cell layers

In tissue formation and repair, the epithelium undergoes complex patterns of motion driven by the active forces produced by each cell. Although the principles governing how the forces evolve in time are not yet clear, it is often assumed that the contractile stresses within the cell layer align with the axis defined by the body of each cell. Here, we simultaneously measured the orientations of the cell shape and the cell-generated contractile stresses, observing correlated, dynamic domains in which the stresses were systematically misaligned with the cell body. We developed a continuum model that decouples the orientations of contractile stress and cell body. The model recovered the spatial and temporal dynamics of the regions of misalignment in the experiments. These findings reveal that the cell controls its contractile forces independently from its shape, suggesting that the physical rules relating cell forces and cell shape are more flexible than previously thought.

Three-Dimensional Chiral Morphogenesis of Active Fluids

Chirality is an essential nature of biological systems. However, it remains obscure how the handedness at the microscale is translated into chiral morphogenesis at the tissue level. Here, we investigate three-dimensional (3D) tissue morphogenesis using an active fluid theory invoking chirality. We show that the coordination of achiral and chiral stresses, arising from microscopic interactions and energy input of individual cells, can engender the self-organization of 3D papillary and helical structures. The achiral active stress drives the nucleation of asterlike topological defects, which initiate 3D out-of-plane budding, followed by rodlike elongation. The chiral active stress excites vortexlike topological defects, which favor the tip spheroidization and twisting of the elongated rod. These results unravel the chiral morphogenesis observed in our experiments of 3D organoids generated by human embryonic stem cells.

Mechanical convergence in mixed populations of mammalian epithelial cells

Tissues consist of cells with different molecular and/or mechanical properties. Measuring the forces and stresses in mixed-cell populations is essential for understanding the mechanisms by which tissue development, homeostasis, and disease emerge from the cooperation of distinct cell types. However, many previous studies have primarily focused their mechanical measurements on dissociated cells or aggregates of a single-cell type, leaving the mechanics of mixed-cell populations largely unexplored. In the present study, we aimed to elucidate the influence of interactions between different cell types on cell mechanics by conducting in situ mechanical measurements on a monolayer of mammalian epithelial cells. Our findings revealed that while individual cell types displayed varying magnitudes of traction and intercellular stress before mixing, these mechanical values shifted in the mixed monolayer, becoming nearly indistinguishable between the cell types. Moreover, by analyzing a mixed-phase model of active tissues, we identified physical conditions under which such mechanical convergence is induced. Overall, the present study underscores the importance of in situ mechanical measurements in mixed-cell populations to deepen our understanding of the mechanics of multicellular systems.

Cell sorting by active forces in a phase-field model of cell monolayers

Cell sorting, the segregation of cells with different properties into distinct domains, is a key phenomenon in biological processes such as embryogenesis. We use a phase-field model of a confluent cell layer to study the role of activity in cell sorting. We find that a mixture of cells with extensile or contractile dipolar activity, and which are identical apart from their activity, quickly sort into small, elongated patches which then grow slowly in time. We interpret the sorting as driven by the different diffusivity of the extensile and contractile cells, mirroring the ordering of Brownian particles connected to different hot and cold thermostats. We check that the free energy is not changed by either partial or complete sorting, thus confirming that activity can be responsible for the ordering even in the absence of thermodynamic mechanisms.

Machine learning topological defects in confluent tissues

Active nematics is an emerging paradigm for characterizing biological systems. One aspect of particularly intense focus is the role active nematic defects play in these systems, as they have been found to mediate a growing number of biological processes. Accurately detecting and classifying these defects in biological systems is, therefore, of vital importance to improving our understanding of such processes. While robust methods for defect detection exist for systems of elongated constituents, other systems, such as epithelial layers, are not well suited to such methods. Here, we address this problem by developing a convolutional neural network to detect and classify nematic defects in confluent cell layers. Crucially, our method is readily implementable on experimental images of cell layers and is specifically designed to be suitable for cells that are not rod shaped, which we demonstrate by detecting defects on experimental data using the trained model. We show that our machine learning model outperforms current defect detection techniques and that this manifests itself in our method as requiring less data to accurately capture defect properties. This could drastically improve the accuracy of experimental data interpretation while also reducing costs, advancing the study of nematic defects in biological systems.

Imaging actin organisation and dynamics in 3D

The actin cytoskeleton plays a critical role in cell architecture and the control of fundamental processes including cell division, migration and survival. The dynamics and organisation of F-actin have been widely studied in a breadth of cell types on classical two-dimensional (2D) surfaces. Recent advances in optical microscopy have enabled interrogation of these cytoskeletal networks in cells within three-dimensional (3D) scaffolds, tissues and in vivo. Emerging studies indicate that the dimensionality experienced by cells has a profound impact on the structure and function of the cytoskeleton, with cells in 3D environments exhibiting cytoskeletal arrangements that differ to cells in 2D environments. However, the addition of a third (and fourth, with time) dimension leads to challenges in sample preparation, imaging and analysis, necessitating additional considerations to achieve the required signal-to-noise ratio and spatial and temporal resolution. Here, we summarise the current tools for imaging actin in a 3D context and highlight examples of the importance of this in understanding cytoskeletal biology and the challenges and opportunities in this domain.

Extracellular Matrix Cues Regulate Mechanosensing and Mechanotransduction of Cancer Cells

Extracellular biophysical properties have particular implications for a wide spectrum of cellular behaviors and functions, including growth, motility, differentiation, apoptosis, gene expression, cell-matrix and cell-cell adhesion, and signal transduction including mechanotransduction. Cells not only react to unambiguously mechanical cues from the extracellular matrix (ECM), but can occasionally manipulate the mechanical features of the matrix in parallel with biological characteristics, thus interfering with downstream matrix-based cues in both physiological and pathological processes. Bidirectional interactions between cells and (bio)materials in vitro can alter cell phenotype and mechanotransduction, as well as ECM structure, intentionally or unintentionally. Interactions between cell and matrix mechanics in vivo are of particular importance in a variety of diseases, including primarily cancer. Stiffness values between normal and cancerous tissue can range between 500 Pa (soft) and 48 kPa (stiff), respectively. Even the shear flow can increase from 0.1-1 dyn/cm2 (normal tissue) to 1-10 dyn/cm2 (cancerous tissue). There are currently many new areas of activity in tumor research on various biological length scales, which are highlighted in this review. Moreover, the complexity of interactions between ECM and cancer cells is reduced to common features of different tumors and the characteristics are highlighted to identify the main pathways of interaction. This all contributes to the standardization of mechanotransduction models and approaches, which, ultimately, increases the understanding of the complex interaction. Finally, both the in vitro and in vivo effects of this mechanics-biology pairing have key insights and implications for clinical practice in tumor treatment and, consequently, clinical translation.

Morphogens enable interacting supracellular phases that generate organ architecture

During vertebrate organogenesis, increases in morphological complexity are tightly coupled to morphogen expression. In this work, we studied how morphogens influence self-organizing processes at the collective or "supra"-cellular scale in avian skin. We made physical measurements across length scales, which revealed morphogen-enabled material property differences that were amplified at supracellular scales in comparison to cellular scales. At the supracellular scale, we found that fibroblast growth factor (FGF) promoted "solidification" of tissues, whereas bone morphogenetic protein (BMP) promoted fluidity and enhanced mechanical activity. Together, these effects created basement membrane-less compartments within mesenchymal tissue that were mechanically primed to drive avian skin tissue budding. Understanding this multiscale process requires the ability to distinguish between proximal effects of morphogens that occur at the cellular scale and their functional effects, which emerge at the supracellular scale.

Motility induced phase separation of deformable cells

Using a multi-phase field model, we examine how particle deformability, which is a proxy for cell stiffness, affects motility induced phase separation (MIPS). We show that purely repulsive deformable, i.e., squishy, cells phase separate more effectively than their rigid counterparts. This can be understood as due to the fact that deformability increases the effective duration of collisions. In addition, the dense regions become increasingly disordered as deformability increases. Our results contextualize the applicability of MIPS to biological systems and have implications for how cells in biological systems may self-organize.

Hexanematic crossover in epithelial monolayers depends on cell adhesion and cell density

Changes in tissue geometry during developmental processes are associated with collective migration of cells. Recent experimental and numerical results suggest that these changes could leverage on the coexistence of nematic and hexatic orientational order at different length scales. How this multiscale organization is affected by the material properties of the cells and their substrate is presently unknown. In this study, we address these questions in monolayers of Madin-Darby canine kidney cells having various cell densities and molecular repertoires. At small length scales, confluent monolayers are characterized by a prominent hexatic order, independent of the presence of E-cadherin, monolayer density, and underlying substrate stiffness. However, all three properties affect the meso-scale tissue organization. The length scale at which hexatic order transits to nematic order, the "hexanematic" crossover scale, strongly depends on cell-cell adhesions and correlates with monolayer density. Our study demonstrates how epithelial organization is affected by mechanical properties, and provides a robust description of tissue organization during developmental processes.

Active nematics with deformable particles

The hydrodynamic theory of active nematics has been often used to describe the spatio-temporal dynamics of cell flows and motile topological defects within soft confluent tissues. Those theories, however, often rely on the assumption that tissues consist of cells with a fixed, anisotropic shape and do not resolve dynamical cell shape changes due to flow gradients. In this paper we extend the continuum theory of active nematics to include cell shape deformability. We find that circular cells in tissues must generate sufficient active stress to overcome an elastic barrier to deforming their shape in order to drive tissue-scale flows. Above this threshold the systems enter a dynamical steady-state with regions of elongated cells and strong flows coexisting with quiescent regions of isotropic cells.

Stiffness anisotropy coordinates supracellular contractility driving long-range myotube-ECM alignment

In skeletal muscle tissue, injury-related changes in stiffness activate muscle stem cells through mechanosensitive signaling pathways. Functional muscle tissue regeneration also requires the effective coordination of myoblast proliferation, migration, polarization, differentiation, and fusion across multiple length scales. Here, we demonstrate that substrate stiffness anisotropy coordinates contractility-driven collective cellular dynamics resulting in C2C12 myotube alignment over millimeter-scale distances. When cultured on mechanically anisotropic liquid crystalline polymer networks (LCNs) lacking topographic features that could confer contact guidance, C2C12 myoblasts collectively polarize in the stiffest direction of the substrate. Cellular coordination is amplified through reciprocal cell-ECM dynamics that emerge during fusion, driving global myotube-ECM ordering. Conversely, myotube alignment was restricted to small local domains with no directional preference on mechanically isotropic LCNs of same chemical formulation. These findings reveal a role for stiffness anisotropy in coordinating emergent collective cellular dynamics, with implications for understanding skeletal muscle tissue development and regeneration.

Local polar order controls mechanical stress and triggers layer formation in developing Myxococcus xanthus colonies

Colonies of the social bacterium Myxococcus xanthus go through a morphological transition from a thin colony of cells to three-dimensional droplet-like fruiting bodies as a strategy to survive starvation. The biological pathways that control the decision to form a fruiting body have been studied extensively. However, the mechanical events that trigger the creation of multiple cell layers and give rise to droplet formation remain poorly understood. By measuring cell orientation, velocity, polarity, and force with cell-scale resolution, we reveal a stochastic local polar order in addition to the more obvious nematic order. Average cell velocity and active force at topological defects agree with predictions from active nematic theory, but their fluctuations are anomalously large due to polar active forces generated by the self-propelled rod-shaped cells. We find that M. xanthus cells adjust their reversal frequency to tune the magnitude of this local polar order, which in turn controls the mechanical stresses and triggers layer formation in the colonies.

Molecular-scale substrate anisotropy, crowding and division drive collective behaviours in cell monolayers

The ability of cells to reorganize in response to external stimuli is important in areas ranging from morphogenesis to tissue engineering. While nematic order is common in biological tissues, it typically only extends to small regions of cells interacting via steric repulsion. On isotropic substrates, elongated cells can co-align due to steric effects, forming ordered but randomly oriented finite-size domains. However, we have discovered that flat substrates with nematic order can induce global nematic alignment of dense, spindle-like cells, thereby influencing cell organization and collective motion and driving alignment on the scale of the entire tissue. Remarkably, single cells are not sensitive to the substrate's anisotropy. Rather, the emergence of global nematic order is a collective phenomenon that requires both steric effects and molecular-scale anisotropy of the substrate. To quantify the rich set of behaviours afforded by this system, we analyse velocity, positional and orientational correlations for several thousand cells over days. The establishment of global order is facilitated by enhanced cell division along the substrate's nematic axis, and associated extensile stresses that restructure the cells' actomyosin networks. Our work provides a new understanding of the dynamics of cellular remodelling and organization among weakly interacting cells.

Phase Separation Driven by Active Flows

We extend the continuum theories of active nematohydrodynamics to model a two-fluid mixture with separate velocity fields for each fluid component, coupled through a viscous drag. The model is used to study an active nematic fluid mixed with an isotropic fluid. We find microphase separation, and argue that this results from an interplay between active anchoring and active flows driven by concentration gradients. The results may be relevant to cell sorting and the formation of lipid rafts in cell membranes.

Engineering tools for quantifying and manipulating forces in epithelia

The integrity of epithelia is maintained within dynamic mechanical environments during tissue development and homeostasis. Understanding how epithelial cells mechanosignal and respond collectively or individually is critical to providing insight into developmental and (patho)physiological processes. Yet, inferring or mimicking mechanical forces and downstream mechanical signaling as they occur in epithelia presents unique challenges. A variety of in vitro approaches have been used to dissect the role of mechanics in regulating epithelia organization. Here, we review approaches and results from research into how epithelial cells communicate through mechanical cues to maintain tissue organization and integrity. We summarize the unique advantages and disadvantages of various reduced-order model systems to guide researchers in choosing appropriate experimental systems. These model systems include 3D, 2D, and 1D micromanipulation methods, single cell studies, and noninvasive force inference and measurement techniques. We also highlight a number of in silico biophysical models that are informed by in vitro and in vivo observations. Together, a combination of theoretical and experimental models will aid future experiment designs and provide predictive insight into mechanically driven behaviors of epithelial dynamics.

APC-driven actin nucleation powers collective cell dynamics in colorectal cancer cells

Cell remodeling relies on dynamic rearrangements of cell contacts powered by the actin cytoskeleton. The tumor suppressor adenomatous polyposis coli (APC) nucleate actin filaments (F-actin) and localizes at cell junctions. Whether APC-driven actin nucleation acts in cell junction remodeling remains unknown. By combining bioimaging and genetic tools with artificial intelligence algorithms applied to colorectal cancer cell, we found that the APC-dependent actin pool contributes to sustaining levels of F-actin, as well as E-cadherin and occludin protein levels at cell junctions. Moreover, this activity preserved cell junction length and angle, as well as vertex motion and integrity. Loss of this F-actin pool led to larger cells with slow and random cell movement within a sheet. Our findings suggest that APC-driven actin nucleation promotes cell junction integrity and dynamics to facilitate collective cell remodeling and motility. This offers a new perspective to explore the relevance of APC-driven cytoskeletal function in gut morphogenesis.

4D Force Detection of Cell Adhesion and Contractility

Mechanical signals establish two-way communication between mammalian cells and their environment. Cells contacting a surface exert forces via contractility and transmit them at the areas of focal adhesions. External stimuli, such as compressive and pulling forces, typically affect the adhesion-free cell surface. Here, we demonstrate the collaborative employment of Fluidic Force Microscopy and confocal Traction Force Microscopy supported by the Cellogram solver to enable a powerful integrated force probing approach, where controlled vertical forces are applied to the free surface of individual cells, while the concomitant deformations are used to map their transmission to the substrate. Force transmission across human cells is measured with unprecedented temporal and spatial resolution, enabling the investigation of the cellular mechanisms involved in the adaptation, or maladaptation, to external mechanical stimuli. Altogether, the system enables facile and precise force interrogation of individual cells, with the capacity to perform population-based analysis.

Cellular segregation in cocultures is driven by differential adhesion and contractility on distinct timescales

Cellular sorting and pattern formation are crucial for many biological processes such as development, tissue regeneration, and cancer progression. Prominent physical driving forces for cellular sorting are differential adhesion and contractility. Here, we studied the segregation of epithelial cocultures containing highly contractile, ZO1/2-depleted MDCKII cells (dKD) and their wild-type (WT) counterparts using multiple quantitative, high-throughput methods to monitor their dynamical and mechanical properties. We observe a time-dependent segregation process governed mainly by differential contractility on short (<5 h) and differential adhesion on long (>5 h) timescales. The overly contractile dKD cells exert strong lateral forces on their WT neighbors, thereby apically depleting their surface area. Concomitantly, the tight junction-depleted, contractile cells exhibit weaker cell-cell adhesion and lower traction force. Drug-induced contractility reduction and partial calcium depletion delay the initial segregation but cease to change the final demixed state, rendering differential adhesion the dominant segregation force at longer timescales. This well-controlled model system shows how cell sorting is accomplished through a complex interplay between differential adhesion and contractility and can be explained largely by generic physical driving forces.

Hydrodynamic Enhancement of p-atic Defect Dynamics

We investigate numerically and analytically the effects of hydrodynamics on the dynamics of topological defects in p-atic liquid crystals, i.e., two-dimensional liquid crystals with p-fold rotational symmetry. Importantly, we find that hydrodynamics fuels a generic passive self-propulsion mechanism for defects of winding number s=(p-1)/p and arbitrary p. Strikingly, we discover that hydrodynamics always accelerates the annihilation dynamics of pairs of ±1/p defects and that, contrary to expectations, this effect increases with p. Our Letter paves the way toward understanding cell intercalation and other remodeling events in epithelial layers.

E-cadherin-dependent coordinated epithelial rotation on a two-dimensional discoidal pattern

In vivo, cells collectively migrate in a variety of developmental and pathological contexts. Coordinated epithelial rotation represents a unique type of collective cell migrations, which has been modeled in vitro under spatially confined conditions. Although it is known that the coordinated rotation depends on intercellular interactions, the contribution of E-cadherin, a major cell-cell adhesion molecule, has not been directly addressed on two-dimensional (2D) confined substrates. Here, using well-controlled fibronectin-coated surfaces, we tracked and compared the migratory behaviors of MDCK cells expressing or lacking E-cadherin. We observed that wild-type MDCK II cells exhibited persistent and coordinated rotations on discoidal patterns, while E-cadherin knockout cells migrated in a less coordinated manner without large-scale rotation. Our comparison of the collective dynamics between these two cell types revealed a series of changes in migratory behavior caused by the loss of E-cadherin, including a decreased global migration speed, less regularity in quantified coordination, and increased average density of topological defects. Taken together, these data demonstrate that spontaneous initiation of collective epithelial rotations depends on E-cadherin under 2D discoidal confinements.

Structure and Rheology in Vertex Models under Cell-Shape-Dependent Active Stresses

Biological cells can actively tune their intracellular architecture according to their overall shape. Here we explore the rheological implication of such coupling in a minimal model of a dense cellular material where each cell exerts an active mechanical stress along its axis of elongation. Increasing the active stress amplitude leads to several transitions. An initially hexagonal crystal motif is first destabilized into a solid with anisotropic cells whose shear modulus eventually vanishes at a first critical activity. Increasing activity beyond this first critical value, we find a re-entrant transition to a regime with finite hexatic order and finite shear modulus, in which cells arrange according to a rhombile pattern with periodically arranged rosette structures. The shear modulus vanishes again at a third threshold beyond which spontaneous tissue flows and topological defects of the nematic cell shape field arise. Flow and stress fields around the defects agree with active nematic theory, with either contractile or extensile signs, as also observed in several epithelial tissue experiments.

Mechanical stress driven by rigidity sensing governs epithelial stability

Epithelia act as a barrier against environmental stress and abrasion and in vivo they are continuously exposed to environments of various mechanical properties. The impact of this environment on epithelial integrity remains elusive. By culturing epithelial cells on 2D hydrogels, we observe a loss of epithelial monolayer integrity through spontaneous hole formation when grown on soft substrates. Substrate stiffness triggers an unanticipated mechanical switch of epithelial monolayers from tensile on soft to compressive on stiff substrates. Through active nematic modelling, we find that spontaneous half-integer defect formation underpinning large isotropic stress fluctuations initiate hole opening events. Our data show that monolayer rupture due to high tensile stress is promoted by the weakening of cell-cell junctions that could be induced by cell division events or local cellular stretching. Our results show that substrate stiffness provides feedback on monolayer mechanical state and that topological defects can trigger stochastic mechanical failure, with potential application towards a mechanistic understanding of compromised epithelial integrity during immune response and morphogenesis.

Topological defect-mediated morphodynamics of active-active interfaces

Physical interfaces widely exist in nature and engineering. Although the formation of passive interfaces is well elucidated, the physical principles governing active interfaces remain largely unknown. Here, we combine simulation, theory, and cell-based experiment to investigate the evolution of an active-active interface. We adopt a biphasic framework of active nematic liquid crystals. We find that long-lived topological defects mechanically energized by activity display unanticipated dynamics nearby the interface, where defects perform "U-turns" to keep away from the interface, push the interface to develop local fingers, or penetrate the interface to enter the opposite phase, driving interfacial morphogenesis and cross-interface defect transport. We identify that the emergent interfacial morphodynamics stems from the instability of the interface and is further driven by the activity-dependent defect-interface interactions. Experiments of interacting multicellular monolayers with extensile and contractile differences in cell activity have confirmed our predictions. These findings reveal a crucial role of topological defects in active-active interfaces during, for example, boundary formation and tissue competition that underlie organogenesis and clinically relevant disorders.

Network model of active elastic shells swollen by hydrostatic pressure

Many organisms have an elastic skeleton that consists of a closed shell of epithelial cells that is filled with fluid, and can actively regulate both elastic forces in the shell and hydrostatic pressure inside it. In this work we introduce a simple network model of such pressure-stabilized active elastic shells in which cross-links are represented by material points connected by non-linear springs of some given equilibrium lengths and spring constants. We mimic active contractile forces in the system by changing the parameters of randomly chosen springs and use computer simulations to study the resulting local and global deformation dynamics of the network. We elucidate the statistical properties of these deformations by computing the corresponding distributions and correlation functions. We show that pressure-induced stretching of the network introduces coupling between its local and global behavior: while the network opposes the contraction of each excited spring and affects the amplitude and relaxation time of its deformation, random local excitations give rise to contraction of the network and to fluctuations of its surface area.

Compressive stress drives adhesion-dependent unjamming transitions in breast cancer cell migration

Cellular unjamming is the collective fluidization of cell motion and has been linked to many biological processes, including development, wound repair, and tumor growth. In tumor growth, the uncontrolled proliferation of cancer cells in a confined space generates mechanical compressive stress. However, because multiple cellular and molecular mechanisms may be operating simultaneously, the role of compressive stress in unjamming transitions during cancer progression remains unknown. Here, we investigate which mechanism dominates in a dense, mechanically stressed monolayer. We find that long-term mechanical compression triggers cell arrest in benign epithelial cells and enhances cancer cell migration in transitions correlated with cell shape, leading us to examine the contributions of cell–cell adhesion and substrate traction in unjamming transitions. We show that cadherin-mediated cell–cell adhesion regulates differential cellular responses to compressive stress and is an important driver of unjamming in stressed monolayers. Importantly, compressive stress does not induce the epithelial–mesenchymal transition in unjammed cells. Furthermore, traction force microscopy reveals the attenuation of traction stresses in compressed cells within the bulk monolayer regardless of cell type and motility. As traction within the bulk monolayer decreases with compressive pressure, cancer cells at the leading edge of the cell layer exhibit sustained traction under compression. Together, strengthened intercellular adhesion and attenuation of traction forces within the bulk cell sheet under compression lead to fluidization of the cell layer and may impact collective cell motion in tumor development and breast cancer progression.

Fluctuation-induced dynamics of nematic topological defects

Topological defects are increasingly being identified in various biological systems, where their characteristic flow fields and stress patterns are associated with continuous active stress generation by biological entities. Here, using numerical simulations of continuum fluctuating nematohydrodynamics, we show that even in the absence of any specific form of active stresses associated with self-propulsion, mesoscopic fluctuations in either orientational alignment or hydrodynamics can independently result in flow patterns around topological defects that resemble the ones observed in active systems. Our simulations further show the possibility of extensile- and contractile-like motion of fluctuation-induced positive half-integer topological defects. Remarkably, isotropic stress fields also reproduce the experimentally measured stress patterns around topological defects in epithelia. Our findings further reveal that extensile- or contractile-like flow and stress patterns around fluctuation-induced defects are governed by passive elastic stresses and flow-aligning behavior of the nematics.

The emergence of spontaneous coordinated epithelial rotation on cylindrical curved surfaces

Three-dimensional collective epithelial rotation around a given axis represents a coordinated cellular movement driving tissue morphogenesis and transformation. Questions regarding these behaviors and their relationship with substrate curvatures are intimately linked to spontaneous active matter processes and to vital morphogenetic and embryonic processes. Here, using interdisciplinary approaches, we study the dynamics of epithelial layers lining different cylindrical surfaces. We observe large-scale, persistent, and circumferential rotation in both concavely and convexly curved cylindrical tissues. While epithelia of inverse curvature show an orthogonal switch in actomyosin network orientation and opposite apicobasal polarities, their rotational movements emerge and vary similarly within a common curvature window. We further reveal that this persisting rotation requires stable cell-cell adhesion and Rac-1-dependent cell polarity. Using an active polar gel model, we unveil the different relationships of collective cell polarity and actin alignment with curvatures, which lead to coordinated rotational behavior despite the inverted curvature and cytoskeleton order.

Metallic Scaffold with Micron-Scale Geometrical Cues Promotes Osteogenesis and Angiogenesis via the ROCK/Myosin/YAP Pathway

The advent of precision manufacturing has enabled the creation of pores in metallic scaffolds with feature size in the range of single microns. In orthopedic implants, pore geometries at the micron scale could regulate bone formation by stimulating osteogenic differentiation and the coupling of osteogenesis and angiogenesis. However, the biological response to pore geometry at the cellular level is not clear. As cells are sensitive to curvature of the pore boundary, this study aimed to investigate osteogenesis in high- vs low-curvature environments by utilizing computer numerical control laser cutting to generate triangular and circular precision manufactured micropores (PMpores). We fabricated PMpores on 100 μm-thick stainless-steel discs. Triangular PMpores had a 30° vertex angle and a 300 μm base, and circular PMpores had a 300 μm diameter. We found triangular PMpores significantly enhanced the elastic modulus, proliferation, migration, and osteogenic differentiation of MC3T3-E1 preosteoblasts through Yes-associated protein (YAP) nuclear translocation. Inhibition of Rho-associated kinase (ROCK) and Myosin II abolished YAP translocation in all pore types and controls. Inhibition of YAP transcriptional activity reduced the proliferation, pore closure, collagen secretion, alkaline phosphatase (ALP), and Alizarin Red staining in MC3T3-E1 cultures. In C166 vascular endothelial cells, PMpores increased the VEGFA mRNA expression even without an angiogenic differentiation medium and induced tubule formation and maintenance. In terms of osteogenesis-angiogenesis coupling, a conditioned medium from MC3T3-E1 cells in PMpores promoted the expression of angiogenic genes in C166 cells. A coculture with MC3T3-E1 induced tubule formation and maintenance in C166 cells and tubule alignment along the edges of pores. Together, curvature cues in micropores are important stimuli to regulate osteogenic differentiation and osteogenesis-angiogenesis coupling. This study uncovered key mechanotransduction signaling components activated by curvature differences in a metallic scaffold and contributed to the understanding of the interaction between orthopedic implants and cells.

Bridging microscopic cell dynamics to nematohydrodynamics of cell monolayers

It is increasingly being realized that liquid-crystalline features can play an important role in the properties and dynamics of cell monolayers. Here, we present a cell-based model of cell layers, based on the phase-field formulation, that connects cell-cell interactions specified at the single cell level to large-scale nematic and hydrodynamic properties of the tissue. In particular, we present a minimal formulation that reproduces the well-known bend and splay hydrodynamic instabilities of the continuum nemato-hydrodynamic formulation of active matter, together with an analytical description of the instability threshold in terms of activity and elasticity of the cells. Furthermore, we provide a quantitative characterisation and comparison of flows and topological defects for extensile and contractile stress generation mechanisms, and demonstrate activity-induced heterogeneity and spontaneous formation of gaps within a confluent monolayer. Together, these results contribute to bridging the gap between cell-scale dynamics and tissue-scale collective cellular organisation.

Thickness of epithelia on wavy substrates: measurements and continuous models

We measured the thickness of MDCK epithelia grown on substrates with a sinusoidal profile. We show that while at long wavelength the profile of the epithelium follows that of the substrate, at short wavelengths cells are thicker in valleys than on ridges. This is reminiscent of the so-called «healing length in the case of a thin liquid film wetting a rough solid substrate. We explore the ability of continuum mechanics models to account for these observations. Modeling the epithelium as a thin liquid film, with surface tension, does not fully account for the measurements. Neither does modeling the epithelium as a thin incompressible elastic film. On the contrary, the addition of an apical active stress gives satisfactory agreement with measurements, with one fitting parameter, the ratio between the active stress and the elastic modulus.

Self-rotation regulates interface evolution in biphasic active matter through taming defect dynamics

Chirality can endow nonequilibrium active matter with unique features and functions. Here, we explore the chiral dynamics in biphasic active nematics composed of self-rotating units that continuously inject energy and angular momentum at the microscale. We show that the self-rotation of units can regularize the boundaries between two phases, rendering sinusoidal-like interfaces, which allow lateral wave propagation and are characterized by chains of ordered antiferromagnetic cross-interface flow vortices. Through the spontaneous coordination of counter-rotating units across the interfaces, topological defects excited by activity are sorted spatiotemporally, where positive defects are locally trapped at the interfaces but, unexpectedly, are transported laterally in a unidirectional rather than wavy mode, whereas inertial negative defects remain spinning in the bulks. Our findings reveal that individual chirality could be harnessed to modulate interfacial morphodynamics in active systems and suggest a potential approach toward controlling topological defects for programmable microfluidics and logic operations.

Differences in cell death and division rules can alter tissue rigidity and fluidization

Tissue mechanical properties such as rigidity and fluidity, and changes in these properties driven by jamming-unjamming transitions (UJT), have come under recent highlight as mechanical markers of health and disease in various biological processes including cancer. However, most analyses of these mechanical properties and UJT have sidestepped the effect of cellular death and division in these systems. Cellular apoptosis (programmed cell death) and mitosis (cell division) can drive significant changes in tissue properties. The balance between the two is crucial in maintaining tissue function, and an imbalance between the two is seen in situations such as cancer progression, wound healing and necrosis. In this work we investigate the impact of cell death and division on tissue mechanical properties, by incorporating specific mechanosensitive triggers of cell death and division based on the size and geometry of the cell within in silico models of tissue dynamics. Specifically, we look at cell migration, tissue response to external stress, tissue extrusion propensity and self-organization of different cell types within the tissue, as a function of cell death and division and the rules that trigger these events. We find that not only do cell death and division events significantly alter tissue mechanics when compared to systems without these events, but that the choice of triggers driving these cell death and division events also alters the predicted tissue mechanics and overall system behavior.