A Reduction of Logical Regulatory Graphs Preserving Essential Dynamical Properties
CMSB '09 Proceedings of the 7th International Conference on Computational Methods in Systems Biology
Action-based analysis of discrete regulatory networks with short-term stimuli
Proceedings of the 8th International Conference on Computational Methods in Systems Biology
Dynamically consistent reduction of logical regulatory graphs
Theoretical Computer Science
Petri net representation of multi-valued logical regulatory graphs
Natural Computing: an international journal
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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 anterior–posterior 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 anterior–posterior 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 (ci). 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. Availability: An XML.le containing the proposed model together with annotations can be downloaded from our website ( http://gin.univ-mrs.fr/GINsim/), along with GINsim, a logical modelling and simulation software freely available to academic groups. Contact: thieffry@tagc.univ-mrs.fr