Calibration and validation of a genetic regulatory network model describing the production of the gap gene protein Hunchback in \emph{Drosophila} early development

We fit the parameters of a differential equations model describing the production of gap gene proteins Hunchback and Knirps along the antero-posterior axis of the embryo of Drosophila. As initial data for the differential equations model, we take the antero-posterior distribution of the proteins Bicoid, Hunchback and Tailless at the beginning of cleavage cycle 14. We calibrate and validate the model with experimental data using single-and multi-objective evolutionary optimization techniques. In the multi-objective optimization technique, we compute the associated Pareto fronts. We analyze the cross regulation mechanism between the gap-genes protein pair Hunchback-Knirps and we show that the posterior distribution of Hunchback follow the experimental data if Hunchback is negatively regulated by the Hucke-bein protein. This approach enables to predict the posterior localiza-tion on the embryo of the protein Huckebein, and we validate with the experimental data the genetic regulatory network responsible for the antero-posterior distribution of the gap gene protein Hunchback. We discuss the importance of Pareto multi-objective optimization techniques in the calibration and validation of biological models.