title: Local homeoprotein diffusion can stabilize boundaries generated by graded positional cues.
abstract: Boundary formation in the developing neuroepithelium decides on the position and size of compartments in the adult nervous system. In this study, we start from the French Flag model proposed by Lewis Wolpert, in which boundaries are formed through the combination of morphogen diffusion and of thresholds in cell responses. In contemporary terms, a response is characterized by the expression of cell-autonomous transcription factors, very often of the homeoprotein family. Theoretical studies suggest that this sole mechanism results in the formation of boundaries of imprecise shapes and positions. Alan Turing, on the other hand, proposed a model whereby two morphogens that exhibit self-activation and reciprocal inhibition, and are uniformly distributed and diffuse at different rates lead to the formation of territories of unpredictable shapes and positions but with sharp boundaries (the 'leopard spots'). Here, we have combined the two models and compared the stability of boundaries when the hypothesis of local homeoprotein intercellular diffusion is, or is not, introduced in the equations. We find that the addition of homeoprotein local diffusion leads to a dramatic stabilization of the positioning of the boundary, even when other parameters are significantly modified. This novel Turing/Wolpert combined model has thus important theoretical consequences for our understanding of the role of the intercellular diffusion of homeoproteins in the developmental robustness of and the changes that take place in the course of evolution.
authors.affiliation: Collège de France, Centre for Interdisciplinary Research in Biology, UMR CNRS 7241/INSERM 1050, Labex MemoLife, 11 place Marcelin Berthelot, Paris 75231, France Laboratoire Jacques-Louis Lions, CNRS UMR 7598, Université Pierre et Marie Curie (UPMC) - Paris VI, 4 place Jussieu, Paris 75005, France.
authors.forename: Cristóbal
authors.initials: C
authors.lastname: Quiñinao
authors.affiliation: Collège de France, Centre for Interdisciplinary Research in Biology, UMR CNRS 7241/INSERM 1050, Labex MemoLife, 11 place Marcelin Berthelot, Paris 75231, France alain.prochiantz@college-de-france.fr jonathan.touboul@college-de-france.fr.
authors.forename: Alain
authors.initials: A
authors.lastname: Prochiantz
authors.affiliation: Collège de France, Centre for Interdisciplinary Research in Biology, UMR CNRS 7241/INSERM 1050, Labex MemoLife, 11 place Marcelin Berthelot, Paris 75231, France INRIA Paris Rocquencourt, MYCENAE Team, Domaine de Voluceau, Le Chesnay 78153, France alain.prochiantz@college-de-france.fr jonathan.touboul@college-de-france.fr.
authors.forename: Jonathan
authors.initials: J
authors.lastname: Touboul
mesh_terms: D018398:Homeodomain Proteins / Q000737:chemistry* / Q000378:metabolism*; D008962:Models, Theoretical; D055550:Protein Stability
chemical_list: D018398:Homeodomain Proteins
keywords: Boundary formation; Homeoprotein diffusion; Morphogenesis; Stability