The effect of reactions on the formation and readout of the gradient of Bicoid

Abstract

During early development, the establishment of gradients of transcriptional factors determinesthe patterning of cell fates. The case of Bicoid (Bcd) in Drosophila melanogaster embryos is welldocumented and studied. There are still controversies as to whether SDD models in which Bcd isSynthesized at one end, then Diffuses and is Degraded can explain the gradient formation withinthe timescale observed experimentally. The Bcd gradient is observed in embryos that express aBicoid-eGFP fusion protein (Bcd-GFP) which cannot differentiate if Bcd is freely diffusing orbound to immobile sites. In this work we analyze an SDID model that includes the Interaction ofBcd with binding sites. We simulate numerically the resulting full reaction?diffusion system in acylindrical domain using previously determined biophysical parameters and a simplified version ofthe Bcd source. In this way we obtain solutions that depend on the spatial location approximately asobserved experimentally and that reach such dependence at a time that is also compatible with theexperimental observations. Analyzing the differences between the free and bound Bcd distributionswe observe that the latter spans over a longer lengthscale. We conclude that deriving the lengthscalefrom the distribution of Bcd-GFP can lead to an overestimation of the gradient lengthscale and ofthe Hill coefficient that relates the concentrations of Bcd and of the protein, Hunchback, whoseproduction is regulated by Bcd.