Vertex stability and topological transitions in vertex models of foams and epithelia

Spencer, Meryl A.; Jabeen, Zahera; Lubensky, David K.

doi:10.1140/epje/i2017-11489-4

Cited by 43 publications

(56 citation statements)

References 49 publications

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“…In contrast to homogeneous vertex models where in the fluid phase four-fold vertices are generically unstable [39], we predict that in the presence of inhomogeneous line tensions (such as those we consider in this work) some geometric configurations around four-fold vertices are stable. Although not commented upon, four-fold vertices can been seen in, e.g., the vertex-model-simulation images of Ref.…”

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confidence: 78%

Soft yet Sharp Interfaces in a Vertex Model of Confluent Tissue

et al. 2018

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How can dense biological tissue maintain sharp boundaries between coexisting cell populations? We explore this question within a simple vertex model for cells, focusing on the role of topology and tissue surface tension. We show that the ability of cells to independently regulate adhesivity and tension, together with neighbor-based interaction rules, lets them support strikingly unusual interfaces. In particular, we show that mechanical-and fluctuation-based measurements of the effective surface tension of a cellular aggregate yield different results, leading to mechanically soft interfaces that are nevertheless extremely sharp.The process of compartmentalizing different cell populations, and maintaining those boundaries, is of vital importance in processes ranging from early embryonic development to tumor metastasis [1,2]. A common paradigm, the differential adhesion hypothesis, treats each cell population as an immiscible fluid and suggests that cell sorting and compartmentalization are driven by an effective surface tension [3], which is in turn governed by a competition between the repulsive and adhesive interactions between cells. The precise cellular mechanisms that govern effective surface tension are still under debate; some investigations suggest it is dominated by adhesive interactions [4], while others implicate actomyosin contractility [5] or a co-regulation of these two effects [1,6,7]. It is not even clear that different methods for measuring the effective surface tension should yield consistent results, which could explain discrepancies between observations and lead to nontrivial and unexpected dynamics for cell sorting and compartmentalization.One hint that something interesting may be happening is a set of experiments demonstrating that many tissues can support extremely sharp boundaries between compartments or coexisting cell populations [1,[8][9][10][11][12]]. Here we present a possible explanation for these observations based only on the assumption that cells interact mechanically with touching neighbors, and that they might regulate these interactions differently with "unlike" cells.For simplicity, our work focuses on models for single layers of confluent cells, with no cellular gaps or overlaps. 2D vertex models represent confluent monolayers as a polygonal tiling of space where each polygon corresponds to a cell [13][14][15]; Voronoi models, which we study here, further take the cell shapes to be given by a Voronoi tessellation of the cell positions. Vertex and Voronoi models explicitly model mechanical interactions between neighboring cells, and have successfully been used to model many biophysical processes [12,[16][17][18], ranging from embryonic development to wound healing to tumor metastasis [19][20][21][22][23]. We include an additional interfacial tension between different cell types to mimic the mechanical changes that are known to occur at so-called "heterotypic" contacts. This extra term naturally leads to a mechanism for robust cell compartmentalization.Surprisingly, we find th...

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confidence: 78%

Soft yet Sharp Interfaces in a Vertex Model of Confluent Tissue

et al. 2018

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“…i is a reference perimeter, and omit the last term in Eq (1) or completely omit the P 2 term [47,58]. Under the assumption that the values of Λ μν for all junctions of the cell i are the same, i.e., Λ μ,ν Λ i , the last term in Eq (1) becomes…”

Section: Overview Of the Vertex Modelmentioning

confidence: 99%

“…A basic implementation of the VM therefore needs to use advanced multidimensional numerical minimisation algorithms to determine the positions of vertices that minimise Eq (1) for a given set of parameters K i , Γ i and Λ μν . Most implementations [51,53,58], also introduce topology (connectivity) changing moves to model events such as cell rearrangements.…”

Section: Overview Of the Vertex Modelmentioning

confidence: 99%

“…While the introduction of dynamics alleviates some of the problems related to the quasistatic nature of the VM, one still has to implement topology changing moves if the model is to be applicable to describing cell intercalation events. This can lead to unphysical back and forth flips of the same junction and has only recently been analysed in full detail [58].…”

Section: Overview Of the Vertex Modelmentioning

confidence: 99%

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Active Vertex Model for Cell-Resolution Description of Epithelial Tissue Mechanics

Barton

Henkes

Weijer

et al. 2016

Preprint

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We introduce an Active Vertex Model (AVM) for cell-resolution studies of the mechanics of confluent epithelial tissues consisting of tens of thousands of cells, with a level of detail inaccessible to similar methods. The AVM combines the Vertex Model for confluent epithelial tissues with active matter dynamics. This introduces a natural description of the cell motion and accounts for motion patterns observed on multiple scales. Furthermore, cell contacts are generated dynamically from positions of cell centres. This not only enables efficient numerical implementation, but provides a natural description of the T1 transition events responsible for local tissue rearrangements. The AVM also includes cell alignment, cellspecific mechanical properties, cell growth, division and apoptosis. In addition, the AVM introduces a flexible, dynamically changing boundary of the epithelial sheet allowing for studies of phenomena such as the fingering instability or wound healing. We illustrate these capabilities with a number of case studies. Author summaryWe present a detailed analysis of the Active Vertex Model to study the mechanics of confluent epithelial tissues and cell monolayers. The model combines the commonly used Vertex Model for describing epithelial tissue mechanics with the active matter dynamics extensively studied in soft matter physics. We utlise an exact mathematical mapping that enables a very efficient numerical implementation using standard methods for simulating particle-based models. System sizes accessible to this model allow us to probe the dynamical motion patterns that occur in tissues over a range of length-and time-scales previously inaccessible to available simulation tools. Our model also includes a number of essential features required to properly describe actual biological systems such as cell growth, cell division and aptotsis, as well as the dynamic boundary of the epithelial sheet. This allows us to study phenomena such as the finger-like protrusions in cell monolayers and processes related to wound healing. The model is implemented into the SAMoS PLOS Computational Biology | https://doi

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“…This can lead to unphysical back and forth flips of the same junction and has only recently been analysed in full detail [58]. …”

Section: Introductionmentioning

confidence: 99%

Active Vertex Model for cell-resolution description of epithelial tissue mechanics

et al. 2017

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Vertex stability and topological transitions in vertex models of foams and epithelia

Cited by 43 publications

References 49 publications

Soft yet Sharp Interfaces in a Vertex Model of Confluent Tissue

Soft yet Sharp Interfaces in a Vertex Model of Confluent Tissue

Active Vertex Model for Cell-Resolution Description of Epithelial Tissue Mechanics

Active Vertex Model for cell-resolution description of epithelial tissue mechanics

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