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Applications of vertex modelling to epithelial morphogenesis Durney, Clinton H.


During tissue morphogenesis forces at the cellular level cause deformation of tissues. Through complex interactions organs are able to develop from epithelial sheets. This work explores the role that sub-cellular organization of signalling proteins, force generation at the cellular level and collective cell behavior have during tissue morphogenesis. Using a class of biophysical model for cellular mechanics known as the vertex model, biological questions concerning two developmental processes are explored. In the first study, a two-dimensional vertex model for drosophila dorsal closure predicts the mechanics of cell oscillation and contraction from the dynamics of the PAR proteins. Using experimental observations of PAR protein dynamics, a system of differential equations models their behavior. By coupling to the vertex model for cellular mechanics, it is shown how the oscillation of cell area results from an intracellular negative feedback loop that involves myosin, an actomyosin regulator, aPKC and Bazooka. In the slow phase, gradual sequestration of apicomedial aPKC by Bazooka causes incomplete disassembly of the actomyosin network over each cycle of oscillation, producing a ratcheting effect. The fast phase of rapid cell and tissue contraction arises when aPKC is no longer able to antagonize the actomyosin network. From experimental observations, the mechanochemical model can account for all major mechanical outcomes of dorsal closure and the transition between three distinct phases. In the second study, a three-dimensional vertex-based model is presented for the study of salivary gland invagination. It is shown how the forces that drive cell shape changes within a flat epithelial sheet, results in the buckling and invagination of a tubular organ. Modelling the epithelial sheet with a 3D model allows for the quantification of how apically patterned forces cause cell shape changes in the basal compartment of the cells. It is shown how cellular constriction leads to the formation of a pit, circumferentially patterned arcs drive the invagination process and the importance of a supracellular actomyosin cable. The model is able to quantify the role that topological transitions have in invagination. The novel 3D model is able to quantify cell mechanical behavior and analyze the effect of different forces during invagination.

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