mRNA diffusion explains protein gradients in \textit{Drosophila} early development

We propose a new model describing the production and the establishment of the stable gradient of the Bicoid protein along the antero-posterior axis of the embryo of Drosophila. In this model, we consider that bicoid mRNA diffuses along the antero-posterior axis of the embryo and the protein is produced in the ribosomes localized near the syncytial nuclei. Bicoid protein stays localized near the syncytial nuclei as observed in experiments. We calibrate the parameters of the mathematical model with experimental data taken during the cleavage stages 11 to 14 of the developing embryo of Drosophila. We obtain good agreement between the experimental and the model gradients, with relative errors in the range 5 − 8%. The inferred diffusion coefficient of bicoid mRNA is in the range 4.6 × 10−12−1.5×10−11 m2s−1, in agreement with the theoretical predictions and experimental measurements for the diffusion of macromolecules in the cytoplasm. We show that the model based on the mRNA diffusion hypothesis is consistent with the known observational data, supporting the recent experimental findings of the gradient of bicoid mRNA in Drosophila [Spirov et al. (2009) Development 136:605-614].