  During early development, the establishment of gradients of transcriptional
factors determines the patterning of cell fates. The case of Bicoid (Bcd) in
{\it Drosophila melanogaster} embryos is well documented and studied. There are
still controversies as to whether {\it SDD} models in which Bcd is {\it
Synthesized} at one end, then {\it Diffuses} and is {\it Degraded} can explain
the gradient formation within the timescale observed experimentally. The Bcd
gradient is observed in embryos that express a Bicoid-eGFP fusion protein
(Bcd-GFP) which cannot differentiate if Bcd is freely diffusing or bound to
immobile sites. In this work we analyze an {\it SDID} model that includes the
{\it Interaction} of Bcd with binding sites. Using previously determined
biophysical parameters we find that this model can explain the gradient
formation within the experimentally observed time. Analyzing the differences
between the free and bound Bcd distributions we observe that the latter spans
over a longer lengthscale. We conclude that deriving the lengthscale from the
distribution of Bcd-GFP can lead to an overestimation of the gradient
lengthscale and of the degree of cooperativity that explains the distribution
of the protein Hunchback whose production is regulated by Bcd.
