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Colloquium, Winter 2005

Day: Monday February 7th Time: 4:00pm Place: BH 112 Title: Dynamical Mechanisms and Simulations for Skeletal Pattern Formation in the Embryonic Chick Limb Speaker: Tilmann Glimm, Emory University In the early stages of the development of the embryonic chick limb, the sites of future skeletal elements are marked by a prepattern formed by condensations of precartilage cells. A number of different theories have been proposed as to what mechanism determines the characteristic size, shape and number of these condensations. Nevertheless, there is still little definite knowledge on this question. In this talk, we present a model of the limb based on recent experiments and additional hypotheses. In this model, it is a "reactor-diffusion" mechanism which gives rise to precartilage condensation. The model consists of a system of nonlinear partial differential equations which govern the spatiotemporal distribution of various types of mesenchymal cells and relevant biomolecules. Special emphasis is put on the mathematical analysis of the system of PDEs. We discuss the conditions under which the equations give rise to patterns and we present the results of numerical simulations. The stability of Turing type patterns in three dimensions is investigated using bifurcation theory. We also briefly talk about extensions of the model, namely modeling cells via the cellular Potts model, a cellular automata type model. This allows for more realistic treatment of cell shapes and cell-cell interactions. Parts of this talk are based on joint work with H.G.E. Hentschel, S. Newman, M. Alber, and others. Cookies: In BH 300 at 3:30pm.