Vertex model approaches to epithelial tissues in developmental systems - Smith, A (2012)
The purpose of this thesis is to develop a vertex model framework that can be used to perform computational experiments related to the dynamics of epithelial tissues in developmental systems. We focus on three example systems: the Drosophila wing imaginal disc, the Drosophila epidermis and the visceral endoderm of the mouse embryo. Within these systems, key questions pertaining to size-control mechanisms and coordination of cell migration remain unanswered and are amenable to computational testing. The vertex model presented here builds upon existing frameworks in three key ways. Firstly, we include novel force terms, representing, for example, the reaction of a cell to being compressed and its shape becoming distorted during a highly dynamic process such as cell migration. Secondly, we incorporate a model of diffusing morphogenetic growth factors within the vertex framework, using an arbitrary Lagrangian-Eulerian formulation of the diffusion equation and solving with the finite-element method (FEM). Finally, we implement the vertex model on the surface of an ellipsoid, in order to simulate cell migration in the mouse embryo. Throughout this thesis, we validate our model by running simple simulations. We demonstrate convergence properties of the FEM scheme and discuss how the time taken to solve the system scales with tissue size. The model is applied to biological systems and its utility demonstrated in several contexts. We show that when growth is dependent on morphogen concentration in the Drosophila wing disc, proliferation occurs preferentially in regions of high concentration. In the Drosophila epidermis, we show that a recently proposed mechanism of compartment size-control, in which a growth-factor is released in limited amounts, is viable. Finally, we examine the phenomenon of rosettes in the mouse embryo, which occur when five or more cells meet at a common vertex. We show, by running simulations both with and without rosettes, that they are crucial facilitators of ordered migration, and are thus critical in the patterning of the early embryo.