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

TL;DR

This study investigates how Bicoid gradient formation in Drosophila embryos is influenced by its interaction with binding sites, proposing an SDID model that aligns with experimental timescales and affects gradient lengthscale estimations.

Contribution

The paper introduces an SDID model incorporating Bicoid interactions with binding sites, explaining gradient formation within observed timescales and clarifying measurement implications.

Findings

The SDID model fits experimental gradient formation times.

Bound Bicoid spans a longer lengthscale than free Bicoid.

Estimating gradient lengthscale from Bcd-GFP may overestimate actual lengthscale.

Abstract

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.