Vertex-based models provide a powerful tool to test hypotheses as to what processes determine the dynamics of epithelial sheets in developmental biology. They have been applied to pattern formation, growth regulation and morphogen signal interpretation in the Drosophila wing disc, to cell migration in the mouse visceral endoderm, and to wound healing. Within vertex-based models the apical surface of an epithelial sheet is approximated by a two-dimensional tessellation of polygons that represent the individual cells, and vertices of the polygons move in response to forces that are exerted by the cells. As such, this approach naturally incorporates mechanical properties of the sheet. Close collaboration with experimentalists allows us to address fundamental questions in morphogenesis, such as the regulation of tissue size via the control of cell growth and apoptosis through mechanical feedback and morphogen signalling. Based on experimental results from the Drosophila embryo epidermis, we iteratively add biologically significant detail to the vertex-based framework, such as mitotic cell rounding. We aim to develop a model of growing epithelial sheets that can be subjected to quantitative model validation and hypothesis testing. To enable quantitative model validation we develop a high-throughput data analysis pipeline to acquire characteristic spatio-temporal metrics from state of the art video microscopy data. We conduct our implementation within the Chaste computational framework (http://www.cs.ox.ac.uk/chaste). In this framework, test-driven development of open-source software ensures high code quality and model transparency. As such, our computational tools can readily be used by other researchers to directly address biological research questions.

Developmental Biology, Drosophila, Vertex-based models, Patterning, Epithelial sheets