The Turing patterning mechanism is believed to underly the formation of repetitive structures in development, such as zebra\ufb01sh stripes and mammalian digits, but it has proved di\ufb03cult to isolate the speci\ufb01c biochemical species responsible for pattern formation. Meanwhile, synthetic biologists have designed Turing systems for implementation in cell colonies, but none have yet led to visible patterns in the laboratory. In both cases, the relationship between underlying chemistry and emergent biology remains mysterious. To help resolve the mystery, this article asks the question: what kinds of biochemical systems can generate Turing patterns? We \ufb01nd general conditions for Turing pattern inception \u2013 the ability to generate unstable patterns from random noise \u2013 which may lead to the ultimate formation of stable patterns, depending on biochemical non-linearities. We \ufb01nd that a wide variety of systems can generate stable Turing patterns, including several which are currently unknown, such as two-species systems composed of two self-activators, and systems composed of a short-range inhibitor and a long-range activator. We furthermore \ufb01nd that systems which are widely believed to generate stable patterns may in fact only generate unstable patterns, which ultimately converge to spatially-homogeneous concentrations. Our results suggest that a much wider variety of systems than is commonly believed could be responsible for observed patterns in development, or could be good candidates for synthetic patterning networks.<\/p>\n","protected":false},"excerpt":{"rendered":"
The Turing patterning mechanism is believed to underly the formation of repetitive structures in development, such as zebra\ufb01sh stripes and mammalian digits, but it has proved di\ufb03cult to isolate the speci\ufb01c biochemical species responsible for pattern formation. Meanwhile, synthetic biologists have designed Turing systems for implementation in cell colonies, but none have yet led to 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