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...

A broad class of disordered materials including foams, glassy molecular systems, colloids and granular materials can form jammed states. A jammed system can resist small stresses without deforming irreversibly, whereas unjammed systems flow under any applied stresses. The broad applicability of the Liu-Nagel jamming concept has attracted intensive theoretical and modelling interest but has prompted less experimental effort. In the Liu-Nagel framework, jammed states of athermal systems exist only above a certain critical density. Although numerical simulations for particles that do not experience friction broadly support this idea, the nature of the jamming transition for frictional grains is less clear. Here we show that jamming of frictional, disk-shaped grains can be induced by the application of shear stress at densities lower than the critical value, at which isotropic (shear-free) jamming occurs. These jammed states have a much richer phenomenology than the isotropic jammed states: for small applied shear stresses, the states are fragile, with a strong force network that percolates only in one direction. A minimum shear stress is needed to create robust, shear-jammed states with a strong force network percolating in all directions. The transitions from unjammed to fragile states and from fragile to shear-jammed states are controlled by the fraction of force-bearing grains. The fractions at which these transitions occur are statistically independent of the density. Jammed states with densities lower than the critical value have an anisotropic fabric (contact network). The minimum anisotropy of shear-jammed states vanishes as the density approaches the critical value from below, in a manner reminiscent of an order-disorder transition.

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.