Mathematical Sciences: Model Mechanisms for the Formation and Spatial Patterning of Teeth Primordia

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The Principal Investigator will study possible mechanisms involved in the formation and spatial distribution of tooth primordia. The preliminary model will be closely based on experimental evidence from alligators Alligator mississippiensis and the known properties of cells. The case for the alligator as a model for research in craniofacial development is convincingly made by Ferguson (1981). In particular the PI's aim to reproduce a specific pattern, namely the positions and initiation sequence of the first seven teeth in the right half lower jaw of the alligator. The model will be a quantitative realization of a caricature of the descriptive model for tooth formation in Alligator mississippiensis described by Westergaard and Ferguson (1987). The mathematical model will involve a system of nonlinear coupled partial differential equations describing both the mechanical properties of the epithelial and mesenchymal cells as well as the reaction and diffusion of various chemicals. Thus, the model will include elements of both the reaction-diffusion and the mechanochemical approaches to pattern formation, and will incorporate tissue interaction processes. In the modelling the emphasis will be on the greatest possible biological realism at the expense of mathematical simplicity.