Cellular Oscillations in Models of Biological Tissues

Abstract

Tissue mechanics controls biological processes such as cancer metastasis, embryonic development and wound healing. Recent studies have examined jamming transitions in tissues to determine how they become fluid-like, which is considered key to understanding these phenomena. Here, two models of biological cells are used to describe the dynamics of epithelial tissue and to study the effect of oscillations on the onset of flow in tissues. The first model treats cells as soft deformable disks interacting via the Hertz potential and imposes oscillations in the size of the particles. The second model describes cells as polygons through a Voronoi diagram, allowing changes in size and shape. We found that oscillations in diameter enhance motion of crystallised 'Hertzian cells' and hinder the motion of cells in dense tissues. The Voronoi model was implemented with a flip algorithm, but stability issues were found. Further analysis of these issues is required to investigate the role of shape oscillations in fluidisation of the tissue as described by the Voronoi model.