Speaker
Description
In this research, we are investigating the relationship between a two-dimensional, quadrilateral, vertex model based on the work of (Brown et al, 2025) and a one-dimensional cell centroid model. The aim being to derive a continuum limit PDE approximation for the behaviour of epithelial monolayers. The movement of the vertices in the two-dimensional model is determined by the minimisation of the cell energy where each cell wants to maintain a target area and perimeter, determined from the cell age. Several mechanisms are introduced to allow stability with realistic levels of cell proliferation. In order to calculate motion in the centroid model forces are computed by first reconstructing a two-dimensional cell structure (from the cell centroids) and the forces calculated on each reconstructed vertex using a vertex dynamics model. These forces are then acted on the cell centroids which allow the monolayer to be represented as a single chain of centroids aiding calculation of a continuum representation. We compare the behaviour of these two models and investigate the parameters that can be used to connect them.
Bibliography
Brown, P. J., Green, J. E. F., Binder, B. J., & Osborne, J. M. (2025). Competing mechanisms for the buckling of an epithelial monolayer identified using multicellular simulation. Mathematical Biosciences, 380, 109367.
