  During organogenesis, developmental programs governed by Gene Regulatory
Networks (GRN) define the functionality, size and shape of the different
constituents of living organisms. Robustness, thus, is an essential
characteristic that GRNs need to fulfill in order to maintain viability and
reproducibility in a species. In the present work we analyze the robustness of
the patterning for the ocellar complex formation in Drosophila melanogaster
fly. We have systematically pruned the GRN that drives the development of this
visual system to obtain the minimum pathway able to satisfy this pattern. We
found that the mechanism underlying the patterning obeys to the dynamics of a
3-nodes network motif with a double negative feedback loop fed by a
morphogenetic gradient that triggers the inhibition in a French flag problem
fashion. A Boolean modeling of the GRN confirms robustness in the patterning
mechanism showing the same result for different network complexity levels.
Interestingly, the network provides a steady state solution in the interocellar
part of the patterning and an oscillatory regime in the ocelli. This
theoretical result predicts that the ocellar pattern may underlie oscillatory
dynamics in its genetic regulation.
