Logical modelling of the role of the Hh pathway in the patterning of the Drosophila wing disc

Motivations: The development of most tissues and organs relies on a limited number of signal transduction pathways enabling the coordination of cellular differentiation. A proper understanding of the roles of signal transduction pathways requires the de.nition of formal models capturing the main qualitative features of these patterning processes. This is a challenging task because the underlying processes, diffusion, regulatory modi.cations, reception and sequestration of signalling molecules, transcriptional regulation of target genes, etc. are only partly characterized. In this context, qualitative models can be more readily proposed on the basis of available (molecular) genetic data. But this requires novel computational tools and proper qualitative representations of phenomena such as diffusion or sequestration. To assess the power and limits of a logical formalism in this context, we propose a multi-level model of the multi-cellular network involved in the de.nition of the anteriorposterior boundary during the development of the wing disc of Drosophila melanogaster. The morphogen Hedgehog (Hh) is the inter-cellular signal coordinating this process. It diffuses from the posterior compartment of the disc to activate its pathway in cells immediately anterior to the boundary. In these boundary cells, the Hh gradient induces target genes in distinct domains as a function of the Hh concentration. One target of Hh signalling is the gene coding for the receptor Patched (Ptc), which sequesters Hh and impedes further diffusion, thereby re.ning the boundary. Results: We have delineated a logical model of the patterning process de.ning the cellular anteriorposterior boundary in the developing imaginal disc of Drosophila melanogaster. This model qualitatively accounts for the formation of a gradient of Hh, as well as for the transduction of this signal through a balance between the activatory (CiA) and inhibitory (CiR) products of the gene cubitus interruptus (c). Wild-type and mutant simulations have been carried out to assess the coherence of the model with experimental data. Interestingly, our computational analysis provides novel insights into poorly understood processes such as the regulation of Ptc by CiR, the formation of a functional gradient of CiA across boundary cells, or yet functional En differences between anterior and posterior cells. In conclusion, our model analysis demonstrates the.exibility of the logical formalism, enabling consistent qualitative representation of diffusion, sequestration and post-transcriptional regulatory processes within and between neighbouring cells.