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

Abstract

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, cell-specific 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.

Multiscale modelling of motility wave propagation in cell migration

“…where 1/β is the characteristic persistence time of polarisation and the second term represents the reinforcement of polarisation through actual movement 15,44 , where v σ is the velocity of the center of mass of the cell σ. This is qualitatively equivalent to earlier models in which cell polarity aligns with cell velocity due to the inherent asymmetry created in a moving cell 25,29,45 ; reviewed in 26 . Thus, the displacement of the cells is determined by the intra-cellular motile force F σ in combination with other inter-cellular interactions represented in Equations (1)(2)(3)(4).…”

“…Several theoretical models have been proposed to explain the coordination between cells during collective migration 20,[22][23][24][25][26][27][28][29][30][31][32][33][34] . However, it remains elusive how the inter-and intra-cellular mechanobiology regulates the initiation and propagation of the polarization wave through a monolayer of cells.…”

The role of replication-removal spatial correlations and cellular replicative lifespan in corneal epithelium homeostasis

“…key property of the dynamics is the replicative lifespan (RLS) of corneal cells -the number of times each corneal cell can divide. Approximating the tissue as a kin of elastic network that minimize some energy function (40) was used to suggest that corneal epithelial cells can organize into centripetal patterns in the absence of external cues (41) under the assumption that stem cells are uniformly distributed, RLS of few divisions, and no correlation between replication location and cell loss location.…”

ya||a: GPU-powered Spheroid Models for Mesenchyme and Epithelium

“…Previous simulation frameworks for morphogenesis (Hoehme and Drasdo, 2010;Richmond et al, 2010;Gorochowski et al, 2012;Rudge et al, 2012;Swat et al, 2012;Mirams et al, 2013;Sütterlin et al, 2013;Kang et al, 2014;Starruß et al, 2014;Cytowski and Szymanska, 2015;Barton et al, 2017;Somogyi and Glazier, 2017;Sussman, 2017;Ghaffarizadeh et al, 2018;Song et al, 2018) often emphasized either epithelial or mesenchymal processes, e.g. vertex models describe the shapes of epithelial cells within sheets or cellular Potts models describe differential adhesion .…”