title: High-throughput mathematical analysis identifies Turing networks for patterning with equally diffusing signals.
abstract: The Turing reaction-diffusion model explains how identical cells can self-organize to form spatial patterns. It has been suggested that extracellular signaling molecules with different diffusion coefficients underlie this model, but the contribution of cell-autonomous signaling components is largely unknown. We developed an automated mathematical analysis to derive a catalog of realistic Turing networks. This analysis reveals that in the presence of cell-autonomous factors, networks can form a pattern with equally diffusing signals and even for any combination of diffusion coefficients. We provide a software (available at http://www.RDNets.com) to explore these networks and to constrain topologies with qualitative and quantitative experimental data. We use the software to examine the self-organizing networks that control embryonic axis specification and digit patterning. Finally, we demonstrate how existing synthetic circuits can be extended with additional feedbacks to form Turing reaction-diffusion systems. Our study offers a new theoretical framework to understand multicellular pattern formation and enables the wide-spread use of mathematical biology to engineer synthetic patterning systems.
authors.affiliation: Friedrich Miescher Laboratory of the Max Planck Society, Tübingen, Germany.
authors.forename: Luciano
authors.identifier: 0000-0003-0957-9170
authors.initials: L
authors.lastname: Marcon
authors.affiliation: EMBL-CRG Systems Biology Research Unit, Centre for Genomic Regulation, The Barcelona Institute of Science and Technology, Barcelona, Spain.|Universitat Pompeu Fabra, Barcelona, Spain.
authors.forename: Xavier
authors.initials: X
authors.lastname: Diego
authors.affiliation: EMBL-CRG Systems Biology Research Unit, Centre for Genomic Regulation, The Barcelona Institute of Science and Technology, Barcelona, Spain.|Universitat Pompeu Fabra, Barcelona, Spain.|Institucio Catalana de Recerca i Estudis Avançats, Barcelona, Spain.
authors.forename: James
authors.initials: J
authors.lastname: Sharpe
authors.affiliation: Friedrich Miescher Laboratory of the Max Planck Society, Tübingen, Germany.
authors.forename: Patrick
authors.identifier: 0000-0002-0702-6209
authors.initials: P
authors.lastname: Müller
mesh_terms: D019521:Body Patterning; D004626:Embryology / Q000379:methods*; D008962:Models, Theoretical; D012984:Software
keywords: S. cerevisiae; Turing patterns; computational biology; developmental biology; differential diffusivity; diffusion-driven instability; mouse; pattern formation; self-organization; stem cells; systems biology; zebrafish