Mathematical problems in Drosophila morphogenesis

par Prof. Rui DILAO (Instituto Superior Técnico & IHÉS)

vendredi 25 janv. 2013, 11:00 → 12:00 Europe/Paris

Amphithéâtre Léon Motchane (IHES)

A formal approach (mathematical models) describing the first two hours of development of the embryo of Drosophila (fruit fly) is presented. The first part of the talk is centered on the biological and biochemical events and processes that determine the form and shape (morphogenesis) of the embryo of Drosophila. Then we show the basic equations associated to some of the developmental processes and discuss the calibration and validation of the mathematical models with real experimental data. The models describe all the biochemical morphogenetic parameters measured in the Drosophila embryo with a relative error below 5% and account for the observed phenotypic plasticity and resilience. This approach leads to a precise mathematical definition of resilience, which we associate to the existence of a continuous family of Pareto optimal solutions of the models. Problems associated with conservation laws (symmetries) and optimization for ill posed problems and noisy objective functions will also be discussed.