Morphogenetic gradients are essential to allocate cell fates in embryos of varying sizes within and across closely related species. We previously showed that the maternal NF-κB/Dorsal (Dl) gradient has acquired different shapes in Drosophila species, which result in unequally scaled germ layers along the dorso-ventral axis and the repositioning of the neuroectodermal borders. Here we combined experimentation and mathematical modeling to investigate which factors might have contributed to the fast evolutionary changes of this gradient. To this end, we modified a previously developed model that employs differential equations of the main biochemical interactions of the Toll (Tl) signaling pathway, which regulates Dl nuclear transport. The original model simulations fit well the D. melanogaster wild type, but not mutant conditions. To broaden the applicability of this model and probe evolutionary changes in gradient distributions, we adjusted a set of 19 independent parameters to reproduce three quantified experimental conditions (i.e. Dl levels lowered, nuclear size and density increased or decreased). We next searched for the most relevant parameters that reproduce the species-specific Dl gradients. We show that adjusting parameters relative to morphological traits (i.e. embryo diameter, nuclear size and density) alone is not sufficient to reproduce the species Dl gradients. Since components of the Tl pathway simulated by the model are fast-evolving, we next asked which parameters related to Tl would most effectively reproduce these gradients and identified a particular subset. A sensitivity analysis reveals the existence of nonlinear interactions between the two fast-evolving traits tested above, namely the embryonic morphological changes and Tl pathway components. Our modeling further suggests that distinct Dl gradient shapes observed in closely related melanogaster sub-group lineages may be caused by similar sequence modifications in Tl pathway components, which are in agreement with their phylogenetic relationships.

Egg size is a fast‐evolving trait among Drosophilids expected to change the spatial distribution of morphogens that pattern the embryonic axes. Here we asked whether the patterning of the dorsal region of the embryo by the Decapentaplegic/Bone Morphogenetic Protein‐4 (DPP/BMP‐4) gradient is scaled among Drosophila species with different egg sizes. This region specifies the extra‐embryonic tissue amnioserosa and the ectoderm. We find that the entire dorsal region scales with embryo size, but the gene expression patterns regulated by DPP are not proportional, suggesting that the DPP gradient is differentially scaled during evolution. To further test whether the DPP gradient can scale or not in Drosophila melanogaster, we created embryos with expanded dorsal regions that mimic changes in scale seen in other species and measured the resulting domains of DPP‐target genes. We find that the proportions of these domains are not maintained, suggesting that the DPP gradient is unable to scale in the embryo. These and previous findings suggest that the embryonic dorso‐ventral patterning lack scaling in the ventral and dorsal sides but is robust in the lateral region where the neuroectoderm is specified and two opposing gradients, Dorsal/NFkappa‐B and DPP, intersect. We propose that the lack of scaling of the DPP gradient may contribute to changes in the size of the amnioserosa and the numbers of ectodermal cells with specific cortical tensions, which are expected to generate distinct mechanical forces for gastrulating embryos of different sizes.

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