Rheology of the cellular vertex model with external and internal dissipation

Complex rheological properties of epithelia are the result of tissue’s ability to actively tune viscoelastic interactions between its constituent cells. While numerous studies have revealed emergent rheological properties of epithelial tissues by measuring the response to various kinds of mechanical deformations, less is known about the role played by different cellular mechanisms of dissipation. The cell-based vertex model has been widely used to describe the mechanical properties of epithelia. Most studies, however, use a simplified dissipative model with friction only due to the interaction between cells and the substrate. Our recent work [1] has shown that the linear viscoelastic properties of the vertex model with cell-substrate dissipation can be mapped to standard spring-dashpot models. Here, we show that extending the model to include dissipation due to relative motion of cells with respect to each other has non-trivial effects on rheology in the linear regime. We achieve this by combining vertex model simulations for both ordered and disordered configurations with semi-analytical calculations that offer an efficient tool to understand the rheological properties of epithelia.

[1] S. Tong, et al., arXiv:2106.12394.