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 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
Reviewing Editor
- Naama Barkai, Weizmann Institute of Science, Israel
Version history
- Received: December 23, 2015
- Accepted: April 7, 2016
- Accepted Manuscript published: April 8, 2016 (version 1)
- Accepted Manuscript updated: April 12, 2016 (version 2)
- 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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