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...

This study of the reliability and validity of scales from the Child's Report of Parental Behavior (CRPBI) presents data on the utility of aggregating the ratings of multiple observers. Subjects were 680 individuals from 170 families. The participants in each family were a college freshman student, the mother, the father, and 1 sibling. The results revealed moderate internal consistency (M = .71) for all rater types on the 18 subscales of the CRPBI, but low interrater agreement (M = .30). The same factor structure was observed across the 4 rater types; however, aggregation within raters across salient scales to form estimated factor scores did not improve rater convergence appreciably (M = .36). Aggregation of factor scores across 2 raters yields much higher convergence (M = .51), and the 4-rater aggregates yielded impressive generalizability coefficients (M = .69). These and other analyses suggested that the responses of each family member contained a small proportion of true variance and a substantial proportion of factor-specific systematic error. The latter can be greatly reduced by aggregating scores across multiple raters.

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.

This study of the reliability and validity of scales from the Child's Report of Parental Behavior (CRPBI) presents data on the utility of aggregating the ratings of multiple observers. Subjects were 680 individuals from 170 families. The participants in each family were a college freshman student, the mother, the father, and 1 sibling. The results revealed moderate internal consistency (M = .71) for all rater types on the 18 subscales of the CRPBI, but low interrater agreement (M = .30). The same factor structure was observed across the 4 rater types; however, aggregation within raters across salient scales to form estimated factor scores did not improve rater convergence appreciably (M = .36). Aggregation of factor scores across 2 raters yields much higher convergence (M = .51), and the 4-rater aggregates yielded impressive generalizability coefficients (M = .69). These and other analyses suggested that the responses of each family member contained a small proportion of true variance and a substantial proportion of factor-specific systematic error. The latter can be greatly reduced by aggregating scores across multiple raters.

A theory is constructed to describe the zero-temperature jamming transition of repulsive soft spheres as the density is increased. Local mechanical stability imposes a constraint on the minimum number of bonds per particle; we argue that this constraint suggests an analogy to k-core percolation. The latter model can be solved exactly on the Bethe lattice, and the resulting transition has a mixed first-order/continuous character reminiscent of the jamming transition. In particular, the exponents characterizing the continuous parts of both transitions appear to be the same. Finally, numerical simulations suggest that in finite dimensions the k-core transition can be discontinuous with a nontrivial diverging correlation length.PACS numbers: 64.60. Ak, 64.70.Pf, 83.80.Fg Understanding a continuous phase transition is tantamount to determining the universality class to which it belongs. In contrast, understanding the nature of a discontinuous change of phase requires a detailed study of the system at hand. Under normal circumstances [1], the two categories are mutually exclusive. However, there are a few examples of continuous transitions that exhibit characteristics of first-order transitions [2,3,4,5,6,7,8,9,10]. In this Letter, we will present arguments that the jamming transition in sphere packings [11,12,13] belongs to this class and can genuinely be described as both continuous and discontinuous. Indeed, we will identify the minimal physics needed to capture the nature of the transition by analogy to the k-core percolation model, and show by exact calculation that the latter model has a true mixed transition of this type with similar exponents at the level of mean-field theory. We also present numerical evidence that k-core models can still exhibit mixed transitions in finite dimensions. We remark that, starting from a different vantage point, Toninelli, et al. [14] have arrived at a model of the k-core type and have reached similar conclusions about the nature of the transition in their studies of kineticallyconstrained models.Numerical studies [11,12,13] of sphere packings at zero temperature suggest that there is a packing density φ c (Point J) where the onset of jamming is truly sharp; i.e. the static bulk and shear moduli vanish for φ ≤ φ c and are nonzero for φ > φ c . This transition exists for spheres that repel when they overlap and otherwise do not interact. For small φ, particles easily arrange themselves so as not to overlap with any other particle and hence the total potential energy is V ≡ 0. As φ is increased, there is a particular value of φ c above which the particles can no longer "avoid" each other and V becomes nonzero. The average coordination number (the average number of overlapping neighbors per particle) is Z = 0 for φ < φ c . As φ approaches φ c from above, however, the behavior is very different:β , where β = 0.49 ± 0.04 [12]. Moreover, the singular part of the shear modulus vanishes with the exponent γ = 0.48 ± 0.05 [12] and recent simulations by Silbert, et al.[13] find a diverg...