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 (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.

DOI: http://dx.doi.org/10.7554/eLife.14022.001

eLife digest

Developing embryos initially consist of identical cells that specialize over time to create the different parts of the adult animal. More than sixty years ago, Alan Turing proposed that this spontaneous breaking of uniformity could be controlled by two molecules that interact with each other and move by diffusion at different rates between cells. In such “reaction-diffusion” systems, the interactions between the molecules cause repeating peaks in their concentrations in different locations, which could influence how different parts of the embryo develop. However, how these hypothetical molecules relate to the genes that control embryonic development has remained largely unknown.

Marcon et al. have now developed a computational method to identify the conditions that enable periodic patterns to form spontaneously in realistic reaction-diffusion systems with mobile signaling molecules and immobile factors such as membrane-localized receptors. By computationally screening millions of biologically relevant networks, Marcon et al. found that a key requirement of classical Turing models – that the mobile signaling molecules must diffuse at different rates – does not need to be met for patterns to form. Instead, some networks can form patterns with signals that diffuse at equal rates, while others can form patterns with any combination of diffusion rates.

The computational method developed by Marcon et al. can be used to interpret the mechanisms that allow patterns to form in biological systems, such as those that control embryonic development. It can also be used to develop synthetic networks that regulate genes for the formation of tissues in particular spatial patterns.

DOI: http://dx.doi.org/10.7554/eLife.14022.002