Foams

Weaire, D.; Hutzler, Stefan

doi:10.1093/oxfordhb/9780199667925.013.4

Cited by 96 publications

(142 citation statements)

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“…However, cells are self-propelled and even in the absence of external forces, cells in confluent tissues regularly intercalate, or exchange neighbors [26,27]. In an isotropic confluent tissue monolayer where mitosis (cell division) or apoptosis (cell death) are rare, cell neighbor exchange must happen through intercalation processes known as T1 transitions [28,29], where an edge between two cells shrinks to a point and a new edge arises between two neighboring cells as illustrated in Fig. 1 (a).…”

Section: Figmentioning

confidence: 99%

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A density-independent rigidity transition in biological tissues

Bi¹,

Lopez²,

Schwarz³

et al. 2015

Nature Phys

709

1,033

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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...

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Section: Figmentioning

confidence: 99%

“…To answer this question, we first study a simple mean-field model for a T1 topological swap. In an infinite confluent tissue, the topological Gauss-Bonnet theorem requires each cell to have six neighbors on average [28]. Therefore our mean-field model consists of four adjacent sixsided cells.…”

Section: Figmentioning

confidence: 99%

A density-independent rigidity transition in biological tissues

Bi¹,

Lopez²,

Schwarz³

et al. 2015

Nature Phys

709

1,033

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“…With only a few degenerate exceptions (described in Section IV), most of the grains observed in the simulated grain growth microstructures (or in other space-filling cellular structures, e.g. foams [6]) have the combinatorial types of simple 3-polytopes. These obey the constraints that two faces meet on at most one edge and exactly three faces meet at each vertex.…”

Section: Combinatorial Analysis Of Cellular Microstructures a Simentioning

confidence: 99%

Roundness of grains in cellular microstructures

et al. 2017

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Many physical systems are composed of polyhedral cells of varying sizes and shapes. These structures are simple in the sense that no more than three faces meet at an edge and no more than four edges meet at a vertex. This means that individual cells can usually be considered as simple, three-dimensional polyhedra. This paper is concerned with determining the distribution of combinatorial types of such polyhedral cells. We introduce the terms fundamental and vertextruncated types and apply these concepts to the grain growth microstructure as a testing ground. For these microstructures we demonstrate that most grains are of particular fundamental types, whereas the frequency of vertex-truncated types decreases exponentially with the number of truncations. This can be explained by the evolutionary process through which grain growth structures are formed, and in which energetically unfavorable surfaces are quickly eliminated. Furthermore, we observe that these grain types are 'round' in a combinatorial sense: there are no 'short' separating cycles that partition the polyhedra into two parts of similar sizes. A particular microstructure derived from the Poisson-Voronoi initial condition is identified as containing an unusually large proportion of round grains. This Round microstructure has an average of 14.036 faces per grain, and is conjectured to be more resistant to topological change than the steady-state grain growth microstructure.

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“…These conditions together, that there is neither disclination nor dislocation charge, are necessary and sufficient for the production of a self-consistent perturbation. These perturbations take the form of a disclination quadrupole, also known as a T1 topological rearrangement [27] [ Fig. 6(b)].…”

Section: Statistical Arguments For the Cycle-merger Choicementioning

confidence: 99%

Extracting Hidden Hierarchies in 3D Distribution Networks

2016

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Natural and man-made transport webs are frequently dominated by dense sets of nested cycles. The architecture of these networks, as defined by the topology and edge weights, determines how efficiently the networks perform their function. Yet, the set of tools that can characterize such a weighted cycle-rich architecture in a physically relevant, mathematically compact way is sparse. In order to fill this void, we have developed a new algorithm that rests on an abstraction of the physical "tiling" in the case of a twodimensional network to an effective tiling of an abstract surface in 3-space that the network may be thought to sit in. Generically, these abstract surfaces are richer than the flat plane because there are now two families of fundamental units that may aggregate upon cutting weakest links-the plaquettes of the tiling and the longer "topological" cycles associated with the abstract surface itself. Upon sequential removal of the weakest links, as determined by a physically relevant edge weight, such as flow volume or capacity, neighboring plaquettes merge and a new tree graph characterizing this merging process results. The properties of this characteristic tree can provide the physical and topological data required to describe the architecture of the network and to build physical models. The new algorithm can be used for automated phenotypic characterization of any weighted network whose structure is dominated by cycles, such as mammalian vasculature in the organs or the force networks in jammed granular matter.

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Foams

Cited by 96 publications

References 0 publications

A density-independent rigidity transition in biological tissues

A density-independent rigidity transition in biological tissues

Roundness of grains in cellular microstructures

Extracting Hidden Hierarchies in 3D Distribution Networks

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