Motility-driven glass and jamming transitions in biological tissues

Shaping epithelial tissues by stem cell mechanics in development and cancer

Adult stem cells balance self-renewal and differentiation to build, maintain and repair tissues. The role of signalling pathways and transcriptional networks in controlling stem cell function has been extensively studied, but there is increasing appreciation that mechanical forces also have a crucial regulatory role. Mechanical forces, signalling pathways and transcriptional networks must be coordinated across diverse length and timescales to maintain tissue homeostasis and function. Such coordination between stem cells and neighbouring cells dictates when cells divide, migrate and differentiate. Recent advances in measuring and manipulating the mechanical forces that act upon and are produced by stem cells are providing new insights into development and disease. In this Review, we discuss the mechanical forces involved when epithelial stem cells construct their microenvironment and what happens in cancer when stem cell niche mechanics are disrupted or dysregulated. As the skin has evolved to withstand the harsh mechanical pressures from the outside environment, we often use the stem cells of mammalian skin epithelium as a paradigm for adult stem cells shaping their surrounding tissues.

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.

Deciphering the interplay between biology and physics with a finite element method-implemented vertex organoid model: A tool for the mechanical analysis of cell behavior on a spherical organoid shell

Understanding the interplay between biology and mechanics in tissue architecture is challenging, particularly in terms of 3D tissue organization. Addressing this challenge requires a biological model enabling observations at multiple levels from cell to tissue, as well as theoretical and computational approaches enabling the generation of a synthetic model that is relevant to the biological model and allowing for investigation of the mechanical stresses experienced by the tissue. Using a monolayer human colon epithelium organoid as a biological model, freely available tools (Fiji, Cellpose, Napari, Morphonet, or Tyssue library), and the commercially available Abaqus FEM solver, we combined vertex and FEM approaches to generate a comprehensive viscoelastic finite element model of the human colon organoid and demonstrated its flexibility. We imaged human colon organoid development for 120 hours, following the evolution of the organoids from an immature to a mature morphology. According to the extracted architectural/geometric parameters of human colon organoids at various stages of tissue architecture establishment, we generated organoid active vertex models. However, this approach did not consider the mechanical aspects involved in the organoids' morphological evolution. Therefore, we applied a finite element method considering mechanical loads mimicking osmotic pressure, external solicitation, or active contraction in the vertex model by using the Abaqus FEM solver. Integration of finite element analysis (FEA) into the vertex model achieved a better fit with the biological model. Therefore, the FEM model provides a basis for depicting cell shape, tissue deformation, and cellular-level strain due to imposed stresses. In conclusion, we demonstrated that a combination of vertex and FEM approaches, combining geometrical and mechanical parameters, improves modeling of alterations in organoid morphology over time and enables better assessment of the mechanical cues involved in establishing the architecture of the human colon epithelium.

Programming the elongation of mammalian cell aggregates with synthetic gene circuits

A key goal of synthetic morphogenesis is the identification and implementation of methods to control morphogenesis. One line of research is the use of synthetic genetic circuits guiding the self-organization of cell ensembles. This approach has led to several recent successes, including control of cellular rearrangements in 3D via control of cell-cell adhesion by user-designed artificial genetic circuits. However, the methods employed to reach such achievements can still be optimized along three lines: identification of circuits happens by hand, 3D structures are spherical, and effectors are limited to cell-cell adhesion. Here we show the identification, in a computational framework, of genetic circuits for volumetric axial elongation via control of proliferation, tissue fluidity, and cell-cell signaling. We then seek to implement this design in mammalian cell aggregates in vitro. We start by identifying effectors to control tissue growth and fluidity in vitro. We then combine these new modules to construct complete circuits that control cell behaviors of interest in space and time, resulting in measurable tissue deformation along an axis that depends on the engineered signaling modules. Finally, we contextualize in vitro and in silico implementations within a unified morphospace to suggest further elaboration of this initial family of circuits towards more robust programmed axial elongation. These results and integrated in vitro/in silico pipeline demonstrate a promising method for designing, screening, and implementing synthetic genetic circuits of morphogenesis, opening the way to the programming of various user-defined tissue shapes.

Unjamming Transition as a Paradigm for Biomechanical Control of Cancer Metastasis

Tumor metastasis is a complex phenomenon that poses significant challenges to current cancer therapeutics. While the biochemical signaling involved in promoting motile phenotypes is well understood, the role of biomechanical interactions has recently begun to be incorporated into models of tumor cell migration. Specifically, we propose the unjamming transition, adapted from physical paradigms describing the behavior of granular materials, to better discern the transition toward an invasive phenotype. In this review, we introduce the jamming transition broadly and narrow our discussion to the different modes of 3D tumor cell migration that arise. Then we discuss the mechanical interactions between tumor cells and their neighbors, along with the interactions between tumor cells and the surrounding extracellular matrix. We center our discussion on the interactions that induce a motile state or unjamming transition in these contexts. By considering the interplay between biochemical and biomechanical signaling in tumor cell migration, we can advance our understanding of biomechanical control in cancer metastasis.

Regulation of epithelial cell jamming transition by cytoskeleton and cell-cell interactions

Multicellular systems, such as epithelial cell collectives, undergo transitions similar to those in inert physical systems like sand piles and foams. To remodel or maintain tissue organization during development or disease, these collectives transition between fluid-like and solid-like states, undergoing jamming or unjamming transitions. While these transitions share principles with physical systems, understanding their regulation and implications in cell biology is challenging. Although cell jamming and unjamming follow physics principles described by the jamming diagram, they are fundamentally biological processes. In this review, we explore how cellular processes and interactions regulate jamming and unjamming transitions. We begin with an overview of how these transitions control tissue remodeling in epithelial model systems and describe recent findings of the physical principles governing tissue solidification and fluidization. We then explore the mechanistic pathways that modulate the jamming phase diagram axes, focusing on the regulation of cell fluctuations and geometric compatibility. Drawing upon seminal works in cell biology, we discuss the roles of cytoskeleton and cell-cell adhesion in controlling cell motility and geometry. This comprehensive view illustrates the molecular control of cell jamming and unjamming, crucial for tissue remodeling in various biological contexts.

Assessing mechanical agency during apical apoptotic cell extrusion

Homeostasis is necessary for epithelia to maintain barrier function and prevent the accumulation of defective cells. Unfit, excess, and dying cells in the larval zebrafish tail fin epidermis are removed via controlled cell death and extrusion. Extrusion coincides with oscillations of cell area, both in the extruding cell and its neighbors. Here, we develop a biophysical model of this process to explore the role of autonomous and non-autonomous mechanics. We vary biophysical properties and oscillatory behaviors of extruding cells and their neighbors along with tissue-wide cell density and viscosity. We find that cell autonomous processes are major contributors to the dynamics of extrusion, with the mechanical microenvironment providing a less pronounced contribution. We also find that some cells initially resist extrusion, influencing the duration of the expulsion process. Our model provides insights into the cellular dynamics and mechanics that promote elimination of unwanted cells from epithelia during homeostatic tissue maintenance.

Learning Dynamics from Multicellular Graphs with Deep Neural Networks

Multicellular self-assembly into functional structures is a dynamic process that is critical in the development and diseases, including embryo development, organ formation, tumor invasion, and others. Being able to infer collective cell migratory dynamics from their static configuration is valuable for both understanding and predicting these complex processes. However, the identification of structural features that can indicate multicellular motion has been difficult, and existing metrics largely rely on physical instincts. Here we show that using a graph neural network (GNN), the motion of multicellular collectives can be inferred from a static snapshot of cell positions, in both experimental and synthetic datasets.

Interplay of geometry and mechanics in epithelial wound healing

Wound healing is a complex biological process critical for maintaining an organism's structural integrity and tissue repair following an infection or injury. Recent studies have unveiled the mechanisms involving the coordination of biochemical and mechanical responses in the tissue in wound healing. In this article, we focus on the healing property of an epithelial tissue as a material while the effects of biological mechanisms such as cell proliferation, tissue intercalation, cellular migration, cell crawling, and filopodia protrusion is minimal. We present a mathematical framework that predicts the fate of a wounded tissue based on the wound's geometrical features and the tissue's mechanical properties. Precisely, adapting the vertex model of tissue mechanics, we predict whether a wound of a specific size in an epithelial monolayer characterized by certain levels of actomyosin contractility and cell-cell adhesion will heal (i.e., close), shrink in size, or rupture the tissue further. Moreover, we show how tissue-mediated mechanisms such as purse-string tension at the wound boundary facilitate wound healing. Finally, we validate the predictions of our model by designing an experimental setup that enables us to create wounds of specific sizes in kidney epithelial cells (MDCK) monolayers. Altogether, this work sets up a basis for interpreting the interplay of mechanical and geometrical features of a tissue in the process of wound healing.

A nuclear jamming transition in vertebrate organogenesis

Jamming of cell collectives and associated rigidity transitions have been shown to play a key role in tissue dynamics, structure and morphogenesis. Cellular jamming is controlled by cellular density and the mechanics of cell-cell contacts. However, the contribution of subcellular organelles to the physical state of the emergent tissue is unclear. Here we report a nuclear jamming transition in zebrafish retina and brain tissues, where physical interactions between highly packed nuclei restrict cellular movements and control tissue mechanics and architecture. Computational modelling suggests that the nuclear volume fraction and anisotropy of cells control the emerging tissue physical state. Analysis of tissue architecture, mechanics and nuclear movements during eye development show that retina tissues undergo a nuclear jamming transition as they form, with increasing nuclear packing leading to more ordered cellular arrangements, reminiscent of the crystalline cellular packings in the functional adult eye. Our results reveal an important role of the cell nucleus in tissue mechanics and architecture.

The cellular Potts model on disordered lattices

The cellular Potts model, also known as the Glazier-Graner-Hogeweg model, is a lattice-based approach by which biological tissues at the level of individual cells can be numerically studied. Traditionally, a square or hexagonal underlying lattice structure is assumed for two-dimensional systems, and this is known to introduce artifacts in the structure and dynamics of the model tissues. That is, on regular lattices, cells can assume shapes that are dictated by the symmetries of the underlying lattice. Here, we developed a variant of this method that can be applied to a broad class of (ir)regular lattices. We show that on an irregular lattice deriving from a fluid-like configuration, two types of artifacts can be removed. We further report on the transition between a fluid-like disordered and a solid-like hexagonally ordered phase present for monodisperse confluent cells as a function of their surface tension. This transition shows the hallmarks of a first-order phase transition and is different from the glass/jamming transitions commonly reported for the vertex and active Voronoi models. We emphasize this by analyzing the distribution of shape parameters found in our state space. Our analysis provides a useful reference for the future study of epithelia using the (ir)regular cellular Potts model.

Basolateral Mechanics Prevents Rigidity Transition in Epithelial Monolayers

The mechanics of epithelial tissues, which is governed by forces generated in various cell regions, is often investigated using two-dimensional models that account for the apically positioned actomyosin structures but neglect basolateral mechanics. We employ a more detailed three-dimensional model to study how lateral surface tensions affect the structure and rigidity of such tissues. We find that cells are apicobasally asymmetric, with one side appearing more ordered than the other depending on target cell apical perimeter. In contrast to the 2D model, which predicts a rigidity transition at large target perimeters, tissues in the 3D model remain solidlike across all parameter space.

Minimal vertex model explains how the amnioserosa avoids fluidization during Drosophila dorsal closure

Dorsal closure is a process that occurs during embryogenesis of Drosophila melanogaster . During dorsal closure, the amnioserosa (AS), a one-cell thick epithelial tissue that fills the dorsal opening, shrinks as the lateral epidermis sheets converge and eventually merge. During this process, both shape index and aspect ratio of amnioserosa cells increase markedly. The standard 2-dimensional vertex model, which successfully describes tissue sheet mechanics in multiple contexts, would in this case predict that the tissue should fluidize via cell neighbor changes. Surprisingly, however, the amnioserosa remains an elastic solid with no such events. We here present a minimal extension to the vertex model that explains how the amnioserosa can achieve this unexpected behavior. We show that continuous shrinkage of the preferred cell perimeter and cell perimeter polydispersity lead to the retention of the solid state of the amnioserosa. Our model accurately captures measured cell shape and orientation changes and predicts non-monotonic junction tension that we confirm with laser ablation experiments.

Significance Statement

During embryogenesis, cells in tissues can undergo significant shape changes. Many epithelial tissues fluidize, i.e. cells exchange neighbors, when the average cell shape index increases above a threshold value, consistent with the standard vertex model. During dorsal closure in Drosophila melanogaster , however, the amnioserosa tissue remains solid even as the average cell shape index increases well above threshold. We introduce perimeter polydispersity and allow the preferred cell perimeters, usually held fixed in vertex models, to decrease linearly with time as seen experimentally. With these extensions to the standard vertex model, we capture experimental observations quantitatively. Our results demonstrate that vertex models can describe the behavior of the amnioserosa in dorsal closure by allowing normally fixed parameters to vary with time.

Temporal variability and cell mechanics control robustness in mammalian embryogenesis

How living systems achieve precision in form and function despite their intrinsic stochasticity is a fundamental yet ongoing question in biology. We generated morphomaps of preimplantation embryogenesis in mouse, rabbit, and monkey embryos, and these morphomaps revealed that although blastomere divisions desynchronized passively, 8-cell embryos converged toward robust three-dimensional shapes. Using topological analysis and genetic perturbations, we found that embryos progressively changed their cellular connectivity to a preferred topology, which could be predicted by a physical model in which actomyosin contractility and noise facilitate topological transitions, lowering surface energy. This mechanism favored regular embryo packing and promoted a higher number of inner cells in the 16-cell embryo. Synchronized division reduced embryo packing and generated substantially more misallocated cells and fewer inner-cell-mass cells. These findings suggest that stochasticity in division timing contributes to robust patterning.

A Geometric-tension-dynamics Model of Epithelial Convergent Extension

Convergent extension of epithelial tissue is a key motif of animal morphogenesis. On a coarse scale, cell motion resembles laminar fluid flow; yet in contrast to a fluid, epithelial cells adhere to each other and maintain the tissue layer under actively generated internal tension. To resolve this apparent paradox, we formulate a model in which tissue flow in the tension-dominated regime occurs through adiabatic remodeling of force balance in the network of adherens junctions. We propose that the slow dynamics within the manifold of force-balanced configurations is driven by positive feedback on myosin-generated cytoskeletal tension. Shifting force balance within a tension network causes active cell rearrangements (T1 transitions) resulting in net tissue deformation oriented by initial tension anisotropy. Strikingly, we find that the total extent of tissue deformation depends on the initial cellular packing order. T1s degrade this order so that tissue flow is self-limiting. We explain these findings by showing that coordination of T1s depends on coherence in local tension configurations, quantified by a geometric order parameter in tension space. Our model reproduces the salient tissue- and cell-scale features of germ band elongation during Drosophila gastrulation, in particular the slowdown of tissue flow after approximately twofold elongation concomitant with a loss of order in tension configurations. This suggests local cell geometry contains morphogenetic information and yields experimentally testable predictions. Defining biologically controlled active tension dynamics on the manifold of force-balanced states may provide a general approach to the description of morphogenetic flow.

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.

Origin of yield stress and mechanical plasticity in biological tissues

During development and under normal physiological conditions, biological tissues are continuously subjected to substantial mechanical stresses. In response to large deformations cells in a tissue must undergo multicellular rearrangements in order to maintain integrity and robustness. However, how these events are connected in time and space remains unknown. Here, using computational and theoretical modeling, we studied the mechanical plasticity of epithelial monolayers under large deformations. Our results demonstrate that the jamming-unjamming (solid-fluid) transition in tissues can vary significantly depending on the degree of deformation, implying that tissues are highly unconventional materials. Using analytical modeling, we elucidate the origins of this behavior. We also demonstrate how a tissue accommodates large deformations through a collective series of rearrangements, which behave similarly to avalanches in non-living materials. We find that these 'tissue avalanches' are governed by stress redistribution and the spatial distribution of vulnerable spots. Finally, we propose a simple and experimentally accessible framework to predict avalanches and infer tissue mechanical stress based on static images.

Multiple temperatures and melting of a colloidal active crystal

Thermal fluctuations constantly excite all relaxation modes in an equilibrium crystal. As the temperature rises, these fluctuations promote the formation of defects and eventually melting. In active solids, the self-propulsion of "atomic" units provides an additional source of non-equilibrium fluctuations whose effect on the melting scenario is still largely unexplored. Here we show that when a colloidal crystal is activated by a bath of swimming bacteria, solvent temperature and active temperature cooperate to define dynamic and thermodynamic properties. Our system consists of repulsive paramagnetic particles confined in two dimensions and immersed in a bath of light-driven E. coli. The relative balance between fluctuations and interactions can be adjusted in two ways: by changing the strength of the magnetic field and by tuning activity with light. When the persistence time of active fluctuations is short, a single effective temperature controls both the amplitudes of relaxation modes and the melting transition. For more persistent active noise, energy equipartition is broken and multiple temperatures emerge, whereas melting occurs before the Lindemann parameter reaches its equilibrium critical value. We show that this phenomenology is fully confirmed by numerical simulations and framed within a minimal model of a single active particle in a periodic potential.

Tunable colloidal spinners: Active chirality and hydrodynamic interactions governed by rotating external electric fields

The rotational dynamics of microparticles in liquids have a wide range of applications, including chemical microreactors, biotechnologies, microfluidic devices, tunable heat and mass transfer, and fundamental understanding of chiral active soft matter which refers to systems composed of particles that exhibit a handedness in their rotation, breaking mirror symmetry at the microscopic level. Here, we report on the study of two effects in colloids in rotating electric fields: (i) the rotation of individual colloidal particles in rotating electric field and related to that (ii) precession of pairs of particles. We show that the mechanism responsible for the rotation of individual particles is related to the time lag between the external field applied to the particle and the particle polarization. Using numerical simulations and experiments with silica particles in a water-based solvent, we prove that the observed rotation of particle pairs and triplets is governed by the tunable rotation of individual particles and can be explained and described by the action of hydrodynamic forces. Our findings demonstrate that colloidal suspensions in rotating electric fields, under some conditions, represent a novel class of chiral soft active matter-tunable colloidal spinners. The experiments and the corresponding theoretical framework we developed open novel prospects for future studies of these systems and for their potential applications.

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.

Confinement, jamming, and adhesion in cancer cells dissociating from a collectively invading strand

When cells in a primary tumor work together to invade into nearby tissue, this can lead to cell dissociations-cancer cells breaking off from the invading front-leading to metastasis. What controls the dissociation of cells, and whether they break off singly or in small groups? Can this be determined by cell-cell adhesion or chemotactic cues given to cells? We develop a physical model for this question, based on experiments that mimic aspects of cancer cell invasion using microfluidic devices with microchannels of different widths. Experimentally, most dissociation events ("ruptures") involve single cells breaking off, but we observe some ruptures of large groups ( ∼ 20 cells) in wider channels. The rupture probability is nearly independent of channel width. We recapitulate the experimental results with a phase field cell motility model by introducing three different cell states (follower, guided, and high-motility metabolically active leader cells) based on their spatial position. These leader cells may explain why single-cell rupture is the universal most probable outcome. Our simulation results show that cell-channel adhesion is necessary for cells in narrow channels to invade, and strong cell-cell adhesion leads to fewer but larger ruptures. Chemotaxis also influences the rupture behavior: Strong chemotaxis strength leads to larger and faster ruptures. Finally, we study the relationship between biological jamming transitions and cell dissociations. Our results suggest unjamming is necessary but not sufficient to create ruptures.

An emerging role for tissue plasticity in developmental precision

Reproducible tissue morphology is a fundamental feature of embryonic development. To ensure such robustness during tissue morphogenesis, inherent noise in biological processes must be buffered. While redundant genes, parallel signaling pathways and intricate network topologies are known to reduce noise, over the last few years, mechanical properties of tissues have been shown to play a vital role. Here, taking the example of somite shape changes, I will discuss how tissues are highly plastic in their ability to change shapes leading to increased precision and reproducibility.

Mechanical imbalance between normal and transformed cells drives epithelial homeostasis through cell competition

Cell competition in epithelial tissue eliminates transformed cells expressing activated oncoproteins to maintain epithelial homeostasis. Although the process is now understood to be of mechanochemical origin, direct mechanical characterization and associated biochemical underpinnings are lacking. Here, we employ tissue-scale stress and compressibility measurements and theoretical modeling to unveil a mechanical imbalance between normal and transformed cells, which drives cell competition. In the mouse intestinal epithelium and epithelial monolayer, transformed cells get compacted during competition. Stress microscopy reveals an emergent compressive stress at the transformed loci leading to this compaction. A cell-based self-propelled Voronoi model predicts that this compressive stress originates from a difference in the collective compressibility of the competing populations. A new collective compressibility measurement technique named gel compression microscopy then elucidates a two-fold higher compressibility of the transformed population than the normal population. Mechanistically, weakened cell-cell adhesions due to reduced junctional abundance of E-cadherin in the transformed cells render them collectively more compressible than normal cells. Taken together, our findings unveil a mechanical basis for epithelial homeostasis against oncogenic transformations with implications in epithelial defense against cancer.

Vimentin promotes collective cell migration through collagen networks via increased matrix remodeling and spheroid fluidity

The intermediate filament (IF) protein vimentin is associated with many diseases with phenotypes of enhanced cellular migration and aggressive invasion through the extracellular matrix (ECM) of tissues, but vimentin's role in in-vivo cell migration is still largely unclear. Vimentin is important for proper cellular adhesion and force generation, which are critical to cell migration; yet the vimentin cytoskeleton also hinders the ability of cells to squeeze through small pores in ECM, resisting migration. To identify the role of vimentin in collective cell migration, we generate spheroids of wide-type and vimentin-null mouse embryonic fibroblasts (mEFs) and embed them in a 3D collagen matrix. We find that loss of vimentin significantly impairs the ability of the spheroid to collectively expand through collagen networks and remodel the collagen network. Traction force analysis reveals that vimentin null spheroids exert less contractile force than their wild-type counterparts. In addition, spheroids made of mEFs with only vimentin unit length filaments (ULFs) exhibit similar behavior as vimentin-null spheroids, suggesting filamentous vimentin is required to promote 3D collective cell migration. We find the vimentin-mediated collective cell expansion is dependent on matrix metalloproteinase (MMP) degradation of the collagen matrix. Further, 3D vertex model simulation of spheroid and embedded ECM indicates that wild-type spheroids behave more fluid-like, enabling more active pulling and reconstructing the surrounding collagen network. Altogether, these results signify that VIF plays a critical role in enhancing migratory persistence in 3D matrix environments through MMP transportation and tissue fluidity.

Local Mechanical Modulation-Driven Evagination in Invaginated Epithelia

Local cells can actively create reverse bending (evagination) in invaginated epithelia, which plays a crucial role in the formation of elaborate organisms. However, the precise physical mechanism driving the evagination remains elusive. Here, we present a three-dimensional vertex model, incorporating the intrinsic cell polarity, to explore the complex morphogenesis induced by local mechanical modulations. We find that invaginated tissues can spontaneously generate local reverse bending due to the shift of the apicobasal polarity. Their exact shapes can be analytically determined by the local apicobasal differential tension and the internal stress. Our continuum theory exhibits three regions in a phase diagram controlled by these two parameters, showing curvature transitions from ordered to disordered states. Additionally, we delve into epithelial curvature transition induced by the nucleus repositioning, revealing its active contribution to the apicobasal force generation. The uncovered mechanical principles could potentially guide more studies on epithelial folding in diverse systems.

Rotational inertia-induced glassy transition in chiral particle systems

The dense active matter exhibits characteristics reminiscent of traditional glassy phenomena, yet the role of rotational inertia in glass dynamics remains elusive. In this study, we investigate the glass dynamics of chiral active particles influenced by rotational inertia. Rotational inertia endows exponential memory to particle orientation, restricting its alteration and amplifying the effective persistence time. At lower spinning frequencies, the diffusion coefficient exhibits a peak function relative to rotational inertia for shorter persistence times, while it steadily increases with rotational inertia for longer persistence times. In the realm of high-frequency spinning, the impact of rotational inertia on diffusion behavior becomes more pronounced, resulting in a nonmonotonic and intricate relationship between the diffusion coefficient and rotational inertia. Consequently, the introduction of rotational inertia significantly alters the glassy dynamics of chiral active particles, allowing for the control over transitions between fluid and glassy states by modulating rotational inertia. Moreover, our findings indicate that at a specific spinning temperature, there exists an optimal spinning frequency at which the diffusion coefficient attains its maximum value.

Discovering dynamic laws from observations: The case of self-propelled, interacting colloids

Active matter spans a wide range of time and length scales, from groups of cells and synthetic self-propelled colloids to schools of fish and flocks of birds. The theoretical framework describing these systems has shown tremendous success in finding universal phenomenology. However, further progress is often burdened by the difficulty of determining forces controlling the dynamics of individual elements within each system. Accessing this local information is pivotal for the understanding of the physics governing an ensemble of active particles and for the creation of numerical models capable of explaining the observed collective phenomena. In this work, we present ActiveNet, a machine-learning tool consisting of a graph neural network that uses the collective motion of particles to learn active and two-body forces controlling their individual dynamics. We verify our approach using numerical simulations of active Brownian particles, active particles undergoing underdamped Langevin dynamics, and chiral active Brownian particles considering different interaction potentials and values of activity. Interestingly, ActiveNet can equally learn conservative or nonconservative forces as well as torques. Moreover, ActiveNet has proven to be a useful tool to learn the stochastic contribution to the forces, enabling the estimation of the diffusion coefficients. Therefore, all coefficients of the equation of motion of Active Brownian Particles are captured. Finally, we apply ActiveNet to experiments of electrophoretic Janus particles, extracting the active and two-body forces controlling colloids' dynamics. On the one side, we have learned that the active force depends on the electric field and area fraction. On the other side, we have also discovered a dependence of the two-body interaction with the electric field that leads us to propose that the dominant force between active colloids is a screened electrostatic interaction with a constant length scale. We believe that the proposed methodological tool, ActiveNet, might open a new avenue for the study and modeling of experimental suspensions of active particles.

Large-scale control over collective cell migration using light-controlled epidermal growth factor receptors

Receptor tyrosine kinases (RTKs) are thought to play key roles in coordinating cell movement at single-cell and tissue scales. The recent development of optogenetic tools for controlling RTKs and their downstream signaling pathways suggested these responses may be amenable to engineering-based control for sculpting tissue shape and function. Here, we report that a light-controlled EGF receptor (OptoEGFR) can be deployed in epithelial cell lines for precise, programmable control of long-range tissue movements. We show that in OptoEGFR-expressing tissues, light can drive millimeter-scale cell rearrangements to densify interior regions or produce rapid outgrowth at tissue edges. Light-controlled tissue movements are driven primarily by PI 3-kinase signaling, rather than diffusible signals, tissue contractility, or ERK kinase signaling as seen in other RTK-driven migration contexts. Our study suggests that synthetic, light-controlled RTKs could serve as a powerful platform for controlling cell positions and densities for diverse applications including wound healing and tissue 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.

E-cadherin tunes tissue mechanical behavior before and during morphogenetic tissue flows

Adhesion between epithelial cells enables the remarkable mechanical behavior of epithelial tissues during morphogenesis. However, it remains unclear how cell-cell adhesion influences mechanics in static as well as in dynamically flowing epithelial tissues. Here, we systematically modulate E-cadherin-mediated adhesion in the Drosophila embryo and study the effects on the mechanical behavior of the germband epithelium before and during dramatic tissue remodeling and flow associated with body axis elongation. Before axis elongation, we find that increasing E-cadherin levels produces tissue comprising more elongated cells and predicted to be more fluid-like, providing reduced resistance to tissue flow. During axis elongation, we find that the dominant effect of E-cadherin is tuning the speed at which cells proceed through rearrangement events, revealing potential roles for E-cadherin in generating friction between cells. Before and during axis elongation, E-cadherin levels influence patterns of actomyosin-dependent forces, supporting the notion that E-cadherin tunes tissue mechanics in part through effects on actomyosin. Taken together, these findings reveal dual-and sometimes opposing-roles for E-cadherin-mediated adhesion in controlling tissue structure and dynamics in vivo that result in unexpected relationships between adhesion and flow.

Short-range correlation of stress chains near solid-to-liquid transition in active monolayers

Using a three-dimensional model of cell monolayers, we study the spatial organization of active stress chains as the monolayer transitions from a solid to a liquid state. The critical exponents that characterize this transition map the isotropic stress percolation onto the two-dimensional random percolation universality class, suggesting short-range stress correlations near this transition. This mapping is achieved via two distinct, independent pathways: (i) cell-cell adhesion and (ii) active traction forces. We unify our findings by linking the nature of this transition to high-stress fluctuations, distinctly linked to each pathway. The results elevate the importance of the transmission of mechanical information in dense active matter and provide a new context for understanding the non-equilibrium statistical physics of phase transition in active systems.

Graph topological transformations in space-filling cell aggregates

Cell rearrangements are fundamental mechanisms driving large-scale deformations of living tissues. In three-dimensional (3D) space-filling cell aggregates, cells rearrange through local topological transitions of the network of cell-cell interfaces, which is most conveniently described by the vertex model. Since these transitions are not yet mathematically properly formulated, the 3D vertex model is generally difficult to implement. The few existing implementations rely on highly customized and complex software-engineering solutions, which cannot be transparently delineated and are thus mostly non-reproducible. To solve this outstanding problem, we propose a reformulation of the vertex model. Our approach, called Graph Vertex Model (GVM), is based on storing the topology of the cell network into a knowledge graph with a particular data structure that allows performing cell-rearrangement events by simple graph transformations. Importantly, when these same transformations are applied to a two-dimensional (2D) polygonal cell aggregate, they reduce to a well-known T1 transition, thereby generalizing cell-rearrangements in 2D and 3D space-filling packings. This result suggests that the GVM's graph data structure may be the most natural representation of cell aggregates and tissues. We also develop a Python package that implements GVM, relying on a graph-database-management framework Neo4j. We use this package to characterize an order-disorder transition in 3D cell aggregates, driven by active noise and we find aggregates undergoing efficient ordering close to the transition point. In all, our work showcases knowledge graphs as particularly suitable data models for structured storage, analysis, and manipulation of tissue data.

Topological balance of cell distributions in plane monolayers

Most of normal proliferative epithelia of plants and metazoans are topologically invariant and characterized by similar cell distributions according to the number of cell neighbors (DCNs). Here we study peculiarities of these distributions and explain why the DCN obtained from the location of intercellular boundaries and that based on the Voronoi tessellation with nodes located on cell nuclei may differ from each other. As we demonstrate, special microdomains where four or more intercellular boundaries converge are topologically charged. Using this fact, we deduce a new equation describing the topological balance of the DCNs. The developed theory is applied for a series of microphotographs of non-tumoral epithelial cells of the human cervix (HCerEpiC) to improve the image processing near the edges of microphotographs and reveal the topological invariance of the examined monolayers. Special contact microdomains may be present in epithelia of various natures, however, considering the well-known vertex model of epithelium, we show that such contacts are absent in the usual solid-like state of the model and appear only in the liquid-like cancer state. Also, we discuss a possible biological role of special contacts in context of proliferative epithelium dynamics and tissue morphogenesis.

Active viscoelastic models for cell and tissue mechanics

Living cells are out of equilibrium active materials. Cell-generated forces are transmitted across the cytoskeleton network and to the extracellular environment. These active force interactions shape cellular mechanical behaviour, trigger mechano-sensing, regulate cell adaptation to the microenvironment and can affect disease outcomes. In recent years, the mechanobiology community has witnessed the emergence of many experimental and theoretical approaches to study cells as mechanically active materials. In this review, we highlight recent advancements in incorporating active characteristics of cellular behaviour at different length scales into classic viscoelastic models by either adding an active tension-generating element or adjusting the resting length of an elastic element in the model. Summarizing the two groups of approaches, we will review the formulation and application of these models to understand cellular adaptation mechanisms in response to various types of mechanical stimuli, such as the effect of extracellular matrix properties and external loadings or deformations.

Emergence, Pattern, and Frequency of Spontaneous Waves in Spreading Epithelial Monolayers

A striking phenomenon of collective cell motion is that they can exhibit a spontaneously emerging wave during epithelia expansions. However, the fundamental mechanism, governing the emergence and its crucial characteristics (e.g., the eigenfrequency and the pattern), remains an enigma. By introducing a mechanochemical feedback loop, we develop a highly efficient discrete vertex model to investigate the spatiotemporal evolution of spreading epithelia. We find both numerically and analytically that expanding cell monolayers display a power-law dependence of wave frequency on the local heterogeneities (i.e., cell density) with a scaling exponent of -1/2. Moreover, our study demonstrates the quantitative capability of the proposed model in capturing distinct X-, W-, and V-mode wave patterns. We unveil that the phase transition between these modes is governed by the distribution of active self-propulsion forces. Our work provides an avenue for rigorous quantitative investigations into the collective motion and pattern formation of cell groups.

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.

Rearrangements during slow compression of a jammed two-dimensional emulsion

As amorphous materials get jammed, both geometric and dynamic heterogeneity are observed. We investigate the correlation between the local geometric heterogeneity and local rearrangements in a slowly compressed bidisperse quasi-two-dimensional emulsion system. The compression is driven by evaporation of the continuous phase and causes the area packing fraction to increase from 0.88 to 0.99. We quantify the structural heterogeneity of the system using the radical Voronoi tessellation following the method of Rieser et al. [Phys. Rev. Lett. 116, 088001 (2016)]0031-900710.1103/PhysRevLett.116.088001. We define two structural quantities characterizing local structure, the first of which considers nearest neighbors and the second of which includes information from second-nearest neighbors. We find that droplets in heterogeneous local regions are more likely to have local rearrangements. These rearrangements are generally T1 events where two droplets converge toward a void, and two droplets move away from the void to make room for the converging droplets. Thus, the presence of the voids tends to orient the T1 events. The presence of a correlation between the structural quantities and the rearrangement dynamics remains qualitatively unchanged over the entire range of packing fractions observed.

Coordinated Motion of Epithelial Layers on Curved Surfaces

Coordinated cellular movements are key processes in tissue morphogenesis. Using a cell-based modeling approach we study the dynamics of epithelial layers lining surfaces with constant and varying curvature. We demonstrate that extrinsic curvature effects can explain the alignment of cell elongation with the principal directions of curvature. Together with specific self-propulsion mechanisms and cell-cell interactions this effect gets enhanced and can explain observed large-scale, persistent, and circumferential rotation on cylindrical surfaces. On toroidal surfaces the resulting curvature coupling is an interplay of intrinsic and extrinsic curvature effects. These findings unveil the role of curvature and postulate its importance for tissue morphogenesis.

Matrix confinement modulates 3D spheroid sorting and burst-like collective migration

While it is known that cells with differential adhesion tend to segregate and preferentially sort, the physical forces governing sorting and invasion in heterogeneous tumors remain poorly understood. To investigate this, we tune matrix confinement, mimicking changes in the stiffness and confinement of the tumor microenvironment, to explore how physical confinement influences individual and collective cell migration in 3D spheroids. High levels of confinement lead to cell sorting while reducing matrix confinement triggers the collective fluidization of cell motion. Cell sorting, which depends on cell-cell adhesion, is crucial to this phenomenon. Burst-like migration does not occur for spheroids that have not undergone sorting, regardless of the degree of matrix confinement. Using computational Self-Propelled Voronoi modeling, we show that spheroid sorting and invasion into the matrix depend on the balance between cell-generated forces and matrix resistance. The findings support a model where matrix confinement modulates 3D spheroid sorting and unjamming in an adhesion-dependent manner, providing insights into the mechanisms of cell sorting and migration in the primary tumor and toward distant metastatic sites.

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.

Discontinuous Shear Thickening in Biological Tissue Rheology

During embryonic morphogenesis, tissues undergo dramatic deformations in order to form functional organs. Similarly, in adult animals, living cells and tissues are continually subjected to forces and deformations. Therefore, the success of embryonic development and the proper maintenance of physiological functions rely on the ability of cells to withstand mechanical stresses as well as their ability to flow in a collective manner. During these events, mechanical perturbations can originate from active processes at the single-cell level, competing with external stresses exerted by surrounding tissues and organs. However, the study of tissue mechanics has been somewhat limited to either the response to external forces or to intrinsic ones. In this work, we use an active vertex model of a 2D confluent tissue to study the interplay of external deformations that are applied globally to a tissue with internal active stresses that arise locally at the cellular level due to cell motility. We elucidate, in particular, the way in which this interplay between globally external and locally internal active driving determines the emergent mechanical properties of the tissue as a whole. For a tissue in the vicinity of a solid-fluid jamming or unjamming transition, we uncover a host of fascinating rheological phenomena, including yielding, shear thinning, continuous shear thickening, and discontinuous shear thickening. These model predictions provide a framework for understanding the recently observed nonlinear rheological behaviors in vivo.

EGFR-dependent actomyosin patterning coordinates morphogenetic movements between tissues

The movements that give rise to the body's structure are powered by cell shape changes and rearrangements that are coordinated at supracellular scales. How such cellular coordination arises and integrates different morphogenetic programs is unclear. Using quantitative imaging, we found a complex pattern of adherens junction (AJ) levels in the ectoderm prior to gastrulation onset in Drosophila. AJ intensity exhibited a double-sided gradient, with peaks at the dorsal midline and ventral neuroectoderm. We show that this dorsal-ventral AJ pattern is regulated by epidermal growth factor (EGF) signaling and that this signal is required for ectoderm cell movement during mesoderm invagination and axis extension. We identify AJ levels and junctional actomyosin as downstream effectors of EGFR signaling. Overall, our study demonstrates a mechanism of coordination between tissue folding and convergent extension that facilitates embryo-wide gastrulation movements.

Minimal vertex model explains how the amnioserosa avoids fluidization during Drosophila dorsal closure

Dorsal closure is a process that occurs during embryogenesis of Drosophila melanogaster. During dorsal closure, the amnioserosa (AS), a one-cell thick epithelial tissue that fills the dorsal opening, shrinks as the lateral epidermis sheets converge and eventually merge. During this process, the aspect ratio of amnioserosa cells increases markedly. The standard 2-dimensional vertex model, which successfully describes tissue sheet mechanics in multiple contexts, would in this case predict that the tissue should fluidize via cell neighbor changes. Surprisingly, however, the amnioserosa remains an elastic solid with no such events. We here present a minimal extension to the vertex model that explains how the amnioserosa can achieve this unexpected behavior. We show that continuous shrink-age of the preferred cell perimeter and cell perimeter polydispersity lead to the retention of the solid state of the amnioserosa. Our model accurately captures measured cell shape and orientation changes and predicts non-monotonic junction tension that we confirm with laser ablation experiments.

Integrating mechanical cues with engineered platforms to explore cardiopulmonary development and disease

Mechanical forces provide critical biological signals to cells during healthy and aberrant organ development as well as during disease processes in adults. Within the cardiopulmonary system, mechanical forces, such as shear, compressive, and tensile forces, act across various length scales, and dysregulated forces are often a leading cause of disease initiation and progression such as in bronchopulmonary dysplasia and cardiomyopathies. Engineered in vitro models have supported studies of mechanical forces in a number of tissue and disease-specific contexts, thus enabling new mechanistic insights into cardiopulmonary development and disease. This review first provides fundamental examples where mechanical forces operate at multiple length scales to ensure precise lung and heart function. Next, we survey recent engineering platforms and tools that have provided new means to probe and modulate mechanical forces across in vitro and in vivo settings. Finally, the potential for interdisciplinary collaborations to inform novel therapeutic approaches for a number of cardiopulmonary diseases are discussed.

Pulsating Active Matter

We reveal that the mechanical pulsation of locally synchronized particles is a generic route to propagate deformation waves. We consider a model of dense repulsive particles whose activity drives periodic change in size of each individual. The dynamics is inspired by biological tissues where cells consume fuel to sustain active deformation. We show that the competition between repulsion and synchronization triggers an instability which promotes a wealth of dynamical patterns, ranging from spiral waves to defect turbulence. We identify the mechanisms underlying the emergence of patterns, and characterize the corresponding transitions. By coarse-graining the dynamics, we propose a hydrodynamic description of an assembly of pulsating particles, and discuss an analogy with reaction-diffusion systems.

Using Histologic Image Analysis to Understand Biophysical Regulations of Epithelial Cell Morphology

Epithelial mechanics and mechanobiology have become 2 important research fields in life sciences and bioengineering. These fields investigate how physical factors induced by cell adhesion and collective behaviors can directly regulate biologic processes, such as organ development and disease progression. Cell mechanics and mechanobiology thus make exciting biophysics education topics to illustrate how fundamental physics principles play a role in regulating cell biology. However, the field currently lacks hands-on activities that engage students in learning science and outreach programs in these topics. One such area is the development of robust hands-on modules that allow students to observe features of cell shape and mechanics and connect them to fundamental physics principles. Here, we demonstrate a workflow that engages students in studying epithelial cell mechanics by using commercial histology slides of frog skin. We show that by using recently developed artificial intelligence-based image-segmentation tools, students can easily quantify different cell morphologic features in a high-throughput manner. Using our workflow, students can reproduce 2 essential findings in cell mechanics: the common gamma distribution of normalized cell aspect ratio in jammed epithelia and the constant ratio between the nuclear and cellular area. Importantly, because the only required instrument for this active learning module is a readily available light microscope and a computer, our module is relatively low cost, as well as portable. These features make the module scalable for students at various education levels and outreach programs. This highly accessible education module provides a fun and engaging way to introduce students to the world of epithelial tissue mechanics.

Effect of contact inhibition locomotion on confined cellular organization

Experiments performed using micro-patterned one dimensional collision assays have allowed a precise quantitative analysis of the collective manifestation of contact inhibition locomotion (CIL) wherein, individual migrating cells reorient their direction of motion when they come in contact with other cells. Inspired by these experiments, we present a discrete, minimal 1D Active spin model that mimics the CIL interaction between cells in one dimensional channels. We analyze the emergent collective behaviour of migrating cells in such confined geometries, as well as the sensitivity of the emergent patterns to driving forces that couple to cell motion. In the absence of vacancies, akin to dense cell packing, the translation dynamics is arrested and the model reduces to an equilibrium spin model which can be solved exactly. In the presence of vacancies, the interplay of activity-driven translation, cell polarity switching, and CIL results in an exponential steady cluster size distribution. We define a dimensionless Péclet number Q-the ratio of the translation rate and directional switching rate of particles in the absence of CIL. While the average cluster size increases monotonically as a function of Q, it exhibits a non-monotonic dependence on CIL strength, when the Q is sufficiently high. In the high Q limit, an analytical form of average cluster size can be obtained approximately by effectively mapping the system to an equivalent equilibrium process involving clusters of different sizes wherein the cluster size distribution is obtained by minimizing an effective Helmholtz free energy for the system. The resultant prediction of exponential dependence on CIL strength of the average cluster size and [Formula: see text] dependence of the average cluster size is borne out to reasonable accuracy as long as the CIL strength is not very large. The consequent prediction of a single scaling function of Q, particle density and CIL interaction strength, characterizing the distribution function of the cluster sizes and resultant data collapse is observed for a range of parameters.