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

  1. Luciano Marcon
  2. Xavier Diego
  3. James Sharpe
  4. Patrick Müller  Is a corresponding author
  1. Friedrich Miescher Laboratory of the Max Planck Society, Germany
  2. The Barcelona Institute of Science and Technology, Spain

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 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.

Article and author information

Author details

  1. Luciano Marcon

    Friedrich Miescher Laboratory of the Max Planck Society, Tübingen, Germany
    Competing interests
    The authors declare that no competing interests exist.
  2. Xavier Diego

    EMBL-CRG Systems Biology Research Unit, Centre for Genomic Regulation, The Barcelona Institute of Science and Technology, Barcelona, Spain
    Competing interests
    The authors declare that no competing interests exist.
  3. James Sharpe

    EMBL-CRG Systems Biology Research Unit, Centre for Genomic Regulation, The Barcelona Institute of Science and Technology, Barcelona, Spain
    Competing interests
    The authors declare that no competing interests exist.
  4. Patrick Müller

    Friedrich Miescher Laboratory of the Max Planck Society, Tübingen, Germany
    For correspondence
    pmueller@tuebingen.mpg.de
    Competing interests
    The authors declare that no competing interests exist.

Reviewing Editor

  1. Naama Barkai, Weizmann Institute of Science, Israel

Publication history

  1. Received: December 23, 2015
  2. Accepted: April 7, 2016
  3. Accepted Manuscript published: April 8, 2016 (version 1)
  4. Accepted Manuscript updated: April 12, 2016 (version 2)
  5. Version of Record published: June 27, 2016 (version 3)

Copyright

© 2016, Marcon et al.

This article is distributed under the terms of the Creative Commons Attribution License permitting unrestricted use and redistribution provided that the original author and source are credited.

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  1. Luciano Marcon
  2. Xavier Diego
  3. James Sharpe
  4. Patrick Müller
(2016)
High-throughput mathematical analysis identifies Turing networks for patterning with equally diffusing signals
eLife 5:e14022.
https://doi.org/10.7554/eLife.14022

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