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Elife. 2016 Apr 8;5. pii: e14022. doi: 10.7554/eLife.14022.

High-throughput mathematical analysis identifies Turing networks for patterning with equally diffusing signals.

Author information

Friedrich Miescher Laboratory of the Max Planck Society, Tübingen, Germany.
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.


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 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.


S. cerevisiae; Turing patterns; computational biology; developmental biology; differential diffusivity; diffusion-driven instability; mouse; pattern formation; self-organization; stem cells; systems biology; zebrafish

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