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Abstract

One of the most intriguing aspects in developing tissues is the emergence of chemical patternswith the capability to drive cellular differentiation, provide positional information and stimuli or inhibit growth. Among these features, the study of cell specificity driven by chemical patterns requires the coupling of positional information mechanisms with the dynamics of complex genetic networks. In this work, we follow such approach to study the formation of the ocellar complex in the fruit fly Drosophila melanogaster. We present a theoretical model that fits experimental observations in both patterning and molecular regulation, and derive a simplified model, which not only recapitulates patterning features but also predicts that differences in the size of the ocellar complex among fly species might depend on differential biochemical regulation of an evolutionarily fixed regulatory network. Moreover, we discuss how this regulatory network can generate sustained spatio-temporal oscillations of some of the network's components. We also find that these oscillations can become highly complex in the presence of another oscillator, with parameter-dependent regions of multi-periodic and quasiperiodic regimes.