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

Marcon, Luciano, 1983-; Diego, Xavier; Sharpe, James; Müller, Patrick

doi:http://dx.doi.org/10.7554/eLife.14022

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

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Marcon L, Diego Iñiguez J, Sharpe J, Müller P. High-throughput mathematical analysis identifies Turing networks for patterning with equally diffusing signals. 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 (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.