1. Computational and Systems Biology
  2. Developmental Biology
Download icon

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
Tools and Resources
  • Cited 49
  • Views 4,856
  • Annotations
Cite this article as: eLife 2016;5:e14022 doi: 10.7554/eLife.14022

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.

Metrics

  • 4,856
    Page views
  • 1,245
    Downloads
  • 49
    Citations

Article citation count generated by polling the highest count across the following sources: Crossref, Scopus, PubMed Central.

Download links

A two-part list of links to download the article, or parts of the article, in various formats.

Downloads (link to download the article as PDF)

Download citations (links to download the citations from this article in formats compatible with various reference manager tools)

Open citations (links to open the citations from this article in various online reference manager services)

Further reading

    1. Computational and Systems Biology
    2. Neuroscience
    Shivesh Chaudhary et al.
    Research Article Updated

    Although identifying cell names in dense image stacks is critical in analyzing functional whole-brain data enabling comparison across experiments, unbiased identification is very difficult, and relies heavily on researchers’ experiences. Here, we present a probabilistic-graphical-model framework, CRF_ID, based on Conditional Random Fields, for unbiased and automated cell identification. CRF_ID focuses on maximizing intrinsic similarity between shapes. Compared to existing methods, CRF_ID achieves higher accuracy on simulated and ground-truth experimental datasets, and better robustness against challenging noise conditions common in experimental data. CRF_ID can further boost accuracy by building atlases from annotated data in highly computationally efficient manner, and by easily adding new features (e.g. from new strains). We demonstrate cell annotation in Caenorhabditis elegans images across strains, animal orientations, and tasks including gene-expression localization, multi-cellular and whole-brain functional imaging experiments. Together, these successes demonstrate that unbiased cell annotation can facilitate biological discovery, and this approach may be valuable to annotation tasks for other systems.

    1. Cell Biology
    2. Computational and Systems Biology
    Ryan Conrad, Kedar Narayan
    Tools and Resources

    Automated segmentation of cellular electron microscopy (EM) datasets remains a challenge. Supervised deep learning (DL) methods that rely on region-of-interest (ROI) annotations yield models that fail to generalize to unrelated datasets. Newer unsupervised DL algorithms require relevant pre-training images, however, pre-training on currently available EM datasets is computationally expensive and shows little value for unseen biological contexts, as these datasets are large and homogeneous. To address this issue, we present CEM500K, a nimble 25 GB dataset of 0.5 × 106 unique 2D cellular EM images curated from nearly 600 three-dimensional (3D) and 10,000 two-dimensional (2D) images from >100 unrelated imaging projects. We show that models pre-trained on CEM500K learn features that are biologically relevant and resilient to meaningful image augmentations. Critically, we evaluate transfer learning from these pre-trained models on six publicly available and one newly derived benchmark segmentation task and report state-of-the-art results on each. We release the CEM500K dataset, pre-trained models and curation pipeline for model building and further expansion by the EM community. Data and code are available at https://www.ebi.ac.uk/pdbe/emdb/empiar/entry/10592/ and https://git.io/JLLTz.