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Turing mechanisms can yield a large variety of patterns from noisy,homogenous initial conditions and have been proposed as patterning mechanismfor many developmental processes. However, the molecular components that giverise to Turing patterns have remained elusive, and the small size of theparameter space that permits Turing patterns to emerge makes it difficult toexplain how Turing patterns could evolve. We have recently shown that Turingpatterns can be obtained with a single ligand if the ligand-receptorinteraction is taken into account. Here we show that the general properties ofligand-receptor systems result in very large Turing spaces. Thus, therestriction of receptors to single cells, negative feedbacks, regulatoryinteractions between different ligand-receptor systems, and the clustering ofreceptors on the cell surface all greatly enlarge the Turing space. We furthershow that the feedbacks that occur in the FGF10/SHH network that controls lungbranching morphogenesis are sufficient to result in large Turing spaces. Weconclude that the cellular restriction of receptors provides a mechanism tosufficiently increase the size of the Turing space to make the evolution ofTuring patterns likely. Additional feedbacks may then have further enlarged theTuring space. Given their robustness and flexibility, we propose thatreceptor-ligand based Turing mechanisms present a general mechanism forpatterning in biology.

Feedbacks, Receptor Clustering, and Receptor Restriction to Single Cells yield large Turing Spaces for Ligand-receptor based Turing Models