title: Computational and mathematical methods for morphogenetic gradient analysis, boundary formation and axonal targeting.
abstract: Morphogenesis and axonal targeting are key processes during development that depend on complex interactions at molecular, cellular and tissue level. Mathematical modeling is essential to bridge this multi-scale gap in order to understand how the emergence of large structures is controlled at molecular level by interactions between various signaling pathways. We summarize mathematical modeling and computational methods for time evolution and precision of morphogenetic gradient formation. We discuss tissue patterning and the formation of borders between regions labeled by different morphogens. Finally, we review models and algorithms that reveal the interplay between morphogenetic gradients and patterned activity for axonal pathfinding and the generation of the retinotopic map in the visual system.
authors.affiliation: Group of Computational Biology and Applied Mathematics, Institute of Biology (IBENS), CNRS INSERM 1024, Ecole Normale Supérieure, 46 rue d'Ulm, 75005 Paris, France. Electronic address: reingrub@ens.fr.
authors.forename: Jürgen
authors.initials: J
authors.lastname: Reingruber
authors.affiliation: Group of Computational Biology and Applied Mathematics, Institute of Biology (IBENS), CNRS INSERM 1024, Ecole Normale Supérieure, 46 rue d'Ulm, 75005 Paris, France. Electronic address: david.holcman@ens.fr.
authors.forename: David
authors.initials: D
authors.lastname: Holcman
mesh_terms: D000465:Algorithms; D000818:Animals; D001369:Axons / Q000378:metabolism / Q000502:physiology; D001921:Brain / Q000254:growth & development / Q000378:metabolism / Q000502:physiology; D019295:Computational Biology / Q000379:methods*; D018398:Homeodomain Proteins / Q000378:metabolism / Q000502:physiology; D006801:Humans; D008959:Models, Neurological; D009024:Morphogenesis / Q000502:physiology*; D051857:Otx Transcription Factors / Q000378:metabolism / Q000502:physiology
chemical_list: C084958:GBX2 protein, human; D018398:Homeodomain Proteins; C497659:OTX2 protein, human; D051857:Otx Transcription Factors
keywords: Axon guidance; Boundary formation; Morphogenetic gradient; Patterning; Reaction–diffusion equations; Retinotopic map