  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 \textit{Drosophila}. In this model, we consider that \textit{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
\textit{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 \textit{bicoid} mRNA is in the range 4.6\times
10^{-12}-1.5\times 10^{-11}m^2s^{-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 \textit{bicoid} mRNA in
\textit{Drosophila} [Spirov et al. (2009) Development 136:605-614].
