A Comprehensive Network Atlas Reveals That Turing Patterns Are Common but Not Robust

Turing patterns (TPs) underlie many fundamental developmental processes, but they operate over narrow parameter ranges, raising the conundrum of how evolution can ever discover them. Here we explore TP design space to address this question and to distill design rules. We exhaustively analyze 2- and 3-node biological candidate Turing systems, amounting to 7,625 networks and more than 3 × 1011 analyzed scenarios. We find that network structure alone neither implies nor guarantees emergent TPs. A large fraction (>61%) of network design space can produce TPs, but these are sensitive to even subtle changes in parameters, network structure, and regulatory mechanisms. This implies that TP networks are more common than previously thought, and evolution might regularly encounter prototypic solutions. We deduce compositional rules for TP systems that are almost necessary and sufficient (96% of TP networks contain them, and 92% of networks implementing them produce TPs). This comprehensive network atlas provides the blueprints for identifying natural TPs and for engineering synthetic systems. [Display omitted] •Turing pattern mechanisms are highly sensitive to perturbations•Regulatory mechanisms profoundly influence pattern generation capability•Many more molecular mechanisms can generate Turing patterns than previously thought•We derive simple but surprisingly powerful heuristics for designing Turing patterns Turing patterns are stable spatial patterns resulting from the interplay of chemical reactions and molecular diffusion and underlie many developmental processes. Here, we perform an exhaustive analysis of potential Turing pattern generating mechanisms for systems with two or three molecular species. The resulting atlas contains the blueprints of Turing pattern generating mechanisms, and shows that while we expect these patterns to be common, they can also be sensitive to even subtle changes.