The segmentation process in the early Drosophila embryo results from the dynamic establishment of patterned mRNA and protein profiles. The recent availability of spatio-temporal mRNA and protein expression atlases on the full 2D surface of the syncetium opens new possibilities for modeling this complex process. Until now, most models have assumed a one-dimensional geometry along a portion of the anterior-posterior axis, motivated by the nearly rotationally symmetrical observed patterns along this axis. While this approximation has been fruitful, the new data from the whole surface of the blastoderm justifies an extension of the models to the full geometry of the embryo.
Figure 1 : Side view of the Gap genes data (mRNA). Time flows from top to bottom. Time zero denotes beginning of cleavage cycle 14A. Red is high concentration and blue low concentration.
Here, we develop a reaction diffusion model for the gap gene network on the curved surface of the blastoderm. We model the dynamics of both mRNA and protein of four trunk gap genes expression during the cleavage cycles 12, 13 and 14A: hunchback, Kruppel, giant and knirps (Figure 1). The model takes as a regulatory inputs the protein expression of the maternal bicoid and caudal gradients, plus the zygotic tailless and huckebein. The model is calibrated using non-linear optimization showing that the main features of spatio-temporal patterning on the whole embryo are well captured. However, anterior domains, e.g. those in the giant gene, are the most difficult to reproduce probably reflecting oversimplifying assumptions or missing genes in the network. A detailed analysis of hunchback suggests that it has concentration dependent activity. We implement this possibility and show that it leads to significant improvements (Figure 2). The model is further assessed by comparing predictions for gap gene mutants with experimental patterns showing satisfactory agreement. However, the current model is less successful at quantitatively predicting the shifts observed in bicoid dosage mutants.
Figure 2 : Model prediction (green) and data (red) for the mRNA. Time flows from top to bottom. Time zero denotes beginning of cleavage cycle 14A.
Covariance analysis around the optimal model identifies the stiff and soft directions in parameter space, showing e.g. that the regulation of Kruppel by the maternal gradient has to be tightly controlled.
In conclusion, modeling patterning on the full egg captures and predicts both qualitative and quantitative aspects of early drosophila patterning, while uncovering important design properties of the regulatory network.
Figure 3 : Solution of diffusion equation on the surface of the egg. Left : initial condition is Kr protein. The time goes from left to right (0 min, 2.5 min, 5 min, 7.5 min).
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