Cell motion inside dense tissues governs many biological processes, including embryonic development and cancer metastasis, and recent experiments suggest that these tissues exhibit collective glassy behavior. To make quantitative predictions about glass transitions in tissues, we study a self-propelled Voronoi (SPV) model that simultaneously captures polarized cell motility and multi-body cell-cell interactions in a confluent tissue, where there are no gaps between cells. We demonstrate that the model exhibits a jamming transition from a solid-like state to a fluid-like state that is controlled by three parameters: the single-cell motile speed, the persistence time of single-cell tracks, and a target shape index that characterizes the competition between cell-cell adhesion and cortical tension. In contrast to traditional particulate glasses, we are able to identify an experimentally accessible structural order parameter that specifies the entire jamming surface as a function of model parameters. We demonstrate that a continuum Soft Glassy Rheology model precisely captures this transition in the limit of small persistence times, and explain how it fails in the limit of large persistence times. These results provide a framework for understanding the collective solid-to-liquid transitions that have been observed in embryonic development and cancer progression, which may be associated with Epithelial-to-Mesenchymal transition in these tissues.

Cell migration is important in many biological processes, including embryonic development, cancer metastasis, and wound healing. In these tissues, a cell's motion is often strongly constrained by its neighbors, leading to glassy dynamics. While self-propelled particle models exhibit a density-driven glass transition, this does not explain liquid-to-solid transitions in confluent tissues, where there are no gaps between cells and therefore the density is constant. Here we demonstrate the existence of a new type of rigidity transition that occurs in the well-studied vertex model for confluent tissue monolayers at constant density. We find the onset of rigidity is governed by a model parameter that encodes single-cell properties such as cell-cell adhesion and cortical tension, providing an explanation for a liquid-to-solid transitions in confluent tissues and making testable predictions about how these transitions differ from those in particulate matter.Important biological processes such as embryogensis, tumorigenesis, and wound healing require cells to move collectively within a tissue. Recent experiments suggest that when cells are packed ever more densely, they start to exhibit collective motion [1][2][3] traditionally seen in non-living disordered systems such as colloids, granular matter or foams [4][5][6]. These collective behaviors exhibit growing timescales and lengthscales associated with rigidity transitions.Many of these effects are also seen in Self-Propelled Particle (SPP) models [7]. In SPP models, overdamped particles experience an active force that causes them to move at a constant speed, and particles change direction due to interactions with their neighbors or an external bath. To model cells with a cortical network of actomyosin and adhesive molecules on their surfaces, particles interact as repulsive disks or spheres, sometimes with an additional short-range attraction [8,9]. These models generically exhibit a glass transition at a critical packing density of particles, φ c , where φ c < 1 [1,8,10,11], and near the transition point they exhibit collective motion [8] that is very similar to that seen in experiments [12].An important open question is whether the density-driven glass transition in SPP models explains the glassy behavior observed in non-proliferating confluent biological tissues, where there are no gaps between cells and the packing fraction φ is fixed at precisely unity. For example, zebrafish embryonic explants are confluent three-dimensional tissues where the cells divide slowly and therefore the number of cells per unit volume remains nearly constant. Nevertheless, these tissues exhibit hallmarks of glassy dynamics such as caging behavior and viscoelasticity. Furthermore, ectoderm tissues have longer relaxation timescales than mesendoderm tissues, suggesting ectoderm tissues are closer to a glass transition, despite the fact that both tissue types have the same density [1]. This indicates that there should be an additional parameter controlling glass transitions in confluent ti...

From coffee beans flowing in a chute to cells remodelling in a living tissue, a wide variety of close-packed collective systems— both inert and living—have the potential to jam. The collective can sometimes flow like a fluid or jam and rigidify like a solid. The unjammed-to-jammed transition remains poorly understood, however, and structural properties characterizing these phases remain unknown. Using primary human bronchial epithelial cells, we show that the jamming transition in asthma is linked to cell shape, thus establishing in that system a structural criterion for cell jamming. Surprisingly, the collapse of critical scaling predicts a counter-intuitive relationship between jamming, cell shape and cell–cell adhesive stresses that is borne out by direct experimental observations. Cell shape thus provides a rigorous structural signature for classification and investigation of bronchial epithelial layer jamming in asthma, and potentially in any process in disease or development in which epithelial dynamics play a prominent role.

We analyze low-frequency vibrational modes in a two-dimensional, zero-temperature, quasistatically sheared model glass to identify a population of structural "soft spots" where particle rearrangements are initiated. The population of spots evolves slowly compared to the interval between particle rearrangements and the soft spots are structurally different from the rest of the system. Our results suggest that disordered solids flow via localized rearrangements that tend to occur at soft spots, which are analogous to dislocations in crystalline solids.

We simulate a model of self-propelled disks with soft repulsive interactions confined to a box in two dimensions. For small rotational diffusion rates, monodisperse disks spontaneously accumulate at the walls. At low densities, interaction forces between particles are strongly inhomogeneous, and a simple model predicts how these inhomogeneities alter the equation of state. At higher densities, collective effects become important. We observe signatures of a jamming transition at a packing fraction ϕ ∼ 0.88, which is also the jamming point for non-active athermal monodisperse disks. At this ϕ, the system develops a critical finite active speed necessary for wall aggregation. At packing fractions above ϕ ∼ 0.6, the pressure decreases with increasing density, suggesting that strong interactions between particles are affecting the equation of state well below the jamming transition. A mixture of bidisperse disks segregates in the absence of any adhesion, identifying a new mechanism that could contribute to cell sorting in embryonic development.

In the course of animal morphogenesis, large-scale cell movements occur, which involve the rearrangement, mutual spreading, and compartmentalization of cell populations in specific configurations. Morphogenetic cell rearrangements such as cell sorting and mutual tissue spreading have been compared with the behaviors of immiscible liquids, which they closely resemble. Based on this similarity, it has been proposed that tissues behave as liquids and possess a characteristic surface tension, which arises as a collective, macroscopic property of groups of mobile, cohering cells. But how are tissue surface tensions generated? Different theories have been proposed to explain how mesoscopic cell properties such as cell-cell adhesion and contractility of cell interfaces may underlie tissue surface tensions. Although recent work suggests that both may be contributors, an explicit model for the dependence of tissue surface tension on these mesoscopic parameters has been missing. Here we show explicitly that the ratio of adhesion to cortical tension determines tissue surface tension. Our minimal model successfully explains the available experimental data and makes predictions, based on the feedback between mechanical energy and geometry, about the shapes of aggregate surface cells, which we verify experimentally. This model indicates that there is a crossover from adhesion dominated to cortical-tension dominated behavior as a function of the ratio between these two quantities.differential adhesion hypothesis | differential interfacial tension hypothesis | mathematical modeling | cell aggregate geometry | self-assembly I t is well established that many tissues behave like liquids on long timescales. Cell tracking in vivo and in vitro highlights (i) largescale flows, (ii) exchange of nearest neighbors in a cellular aggregate, and (iii) rounding-up and fusion of aggregates (1). Macroscopic rheological properties such as surface tension can be measured using a tissue surface tensiometer (TST) (1-8) or micropipette aspiration (9), and surface tension can be used to explain tissue self-organization in embryogenesis (8, 10-12) or cancer (13,14). In particular, cell sorting and tissue spreading can be explained in terms of tissue surface tensions that differ among cell types (1, 3-5, 8, 15, 16).A full understanding of tissue surface tension as a driving force for biological processes is important, and knowledge of its cellular origins would allow us to intelligently design drugs and treatments to alter tissue organization. Two opposing theories about the mesoscopic origin of tissue surface tension have coexisted over the last 30 years. One, the differential adhesion hypothesis (DAH), postulates that in analogy to ordinary fluids, tissue surface tension is proportional to the intensity of the adhesive energy between the constituent cells, which are treated as point objects. The DAH has proven successful in a variety of studies with cell lines (2-5, 15) , malignant (13, 14) and embryonic tissues (1,5,8,16) and is widely accepted (12...

We model a sheared disordered solid using the theory of Shear Transformation Zones (STZs). In this mean-field continuum model the density of zones is governed by an effective temperature that approaches a steady state value as energy is dissipated. We compare the STZ model to simulations by Shi, et al.[Y. Shi et al. PRL 98, 185505 (2007)], finding that the model generates solutions that fit the data, exhibit strain localization, and capture important features of the localization process. We show that perturbations to the effective temperature grow due to an instability in the transient dynamics, but unstable systems do not always develop shear bands. Nonlinear energy dissipation processes interact with perturbation growth to determine whether a material exhibits strain localization. By estimating the effects of these interactions, we derive a criterion that determines which materials exhibit shear bands based on the initial conditions alone. We also show that the shear band width is not set by an inherent diffusion length scale but instead by a dynamical scale that depends on the imposed strain rate.

Recent observations demonstrate that confluent tissues exhibit features of glassy dynamics, such as caging behavior and dynamical heterogeneities, although it has remained unclear how single-cell properties control this behavior. Here we develop numerical and theoretical models to calculate energy barriers to cell rearrangements, which help govern cell migration in cell monolayers. In contrast to work on sheared foams, we find that energy barrier heights are exponentially distributed and depend systematically on the cell's number of neighbors. Based on these results, we predict glassy two-time correlation functions for cell motion, with a timescale that increases rapidly as cell activity decreases. These correlation functions are used to construct simple random walks that reproduce the caging behavior observed for cell trajectories in experiments. This work provides a theoretical framework for predicting collective motion of cells in wound-healing, embryogenesis and cancer tumorogenesis.