A new model for cell division and migration with spontaneous topology changes

Abstract

Tissue topology, in particular proliferating epithelium topology, is remarkably similar between various species. Understanding the mechanisms that result in the observed topologies is needed for better insight into the processes governing tissue formation. We present a two-dimensional single-cell based model for cell divisions and tissue growth. The model accounts for cell mechanics and allows cell migration. Cells do not have pre-existing shapes or topologies. Shape changes and local rearrangements occur naturally as a response to the evolving cellular environment and cell-cell interactions. We show that the commonly observed tissue topologies arise spontaneously from this model. We consider different cellular rearrangements that accompany tissue growth and study their effects on tissue topology.

Mechanical feedback and robustness of apical constrictions in Drosophila embryo ventral furrow formation

“…To evaluate cell shapes in a confluent cell layer described by the force center model, we introduce an augmented Voronoi construction that uses the force-center positions r i and the interaction-force vectors f ij to create a tessellation that is consistent with the system mechanics (Fig 4H). In previous studies [35][36][37][38][39], Voronoi tessellation was applied to infer approximate cell shapes from the positions of cell centers alone, without using any cell-shape related parameters. While this standard tessellation technique was shown to yield quite accurate representations of actual cell-shape distributions in some epithelial tissues [40], we find that it is inadequate for description of the apical constriction process.…”

Collective motion of cells modeled as ring polymers

“…These include particle models in which the units are isotropic with a polarity field, 8,10,20,22 geometrically anisotropic rigid units with their polarity determined by their anisotropy, 23–25 and flexible units composed of more than one particle. 26–31 Various other approaches have been proposed for the collective behavior of eukaryotic cells. These include Voronoi models, 32,33 phase field models 34–36 and generalizations of the Potts model.…”

Limits of Applicability of the Voronoi Tessellation Determined by Centers of Cell Nuclei to Epithelium Morphology

“…This prompted the development of in silico models, which adopt the polygonal nature of cells and are parametrized to reproduce the distributions of morphological features such as the area and the perimeters of the cells. These models typically use a free energy functional, which is minimized to yield optimal positions of points (Sulsky et al, 1984) (Mkrtchyan et al, 2014) generating the tessellation. Alternatively, vertex models optimize the cell area and the boundary-length between cells.…”