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Natural mathematician
Mathematician alan turing's theory describes the primitive development toolbox shared by all vertebrates, which sets the growth model for all types of skin structures. 1952 alan turing had a bold idea long before developmental biologists talked about Hox gene and transcription factors and even understood the structure of DNA. The famous mathematician accelerated the end of World War II by cracking the Enigma code. His theory summarizes how stripes, spots and scales are formed under the interaction of two simple hypothetical chemicals or morphological factors. Decades passed before biologists realized that this mathematical theory could actually explain countless biological patterns.

Boko Garden-Popular Science: Mammalian hair, bird feathers, and even the protrusions on human mouth all evolved from Turing-like mechanism. The small dentate processes now covering the shark skin may also be included in Turing mechanism. Researchers at the University of Florida recently discovered that shark teeth are formed by a mechanism similar to rotation, which is controlled by the same genes responsible for forming feather patterns. Gareth Fraser, the researcher who led this research, believes that the developing embryos of different vertebrates determine the characteristic patterns of their outer tissues in the same way, and this pattern formation mechanism is likely to be born with the evolution of the first batch of vertebrates, and has hardly changed since then.

This is a photo of a dyed cat shark cub, showing its "leather teeth" tooth pattern. Two parallel lines near dorsal fin indicate the origin of small tooth essence. Then the essence of the small teeth unfolds, and dots are displayed in the rest of the body to match the Turing-like mechanism. Photo: University of Sheffield, Alexandre Thiery.

Alexander Schier, a developmental biologist at Harvard University, said: The beauty of this study is that everything from shark teeth to bird feathers may be very strongly protected. This study also supports a new theme of developmental biology-nature often creates something and then mutates on this theme. Turing's model is called reaction-diffusion mechanism, which only needs two interacting substances, activator and inhibitor, and can diffuse through tissues like ink in water. Activators start certain processes, such as the formation of dots, and promote their own production. Inhibitors can prevent these two effects. Inhibitors diffuse faster in tissues than activators. According to the exact time and place when the activator and inhibitor are released, the activator will be regularly arranged at intervals to form dots, strips or other patterns.

Catherine Boisvert, a developmental biologist at Curtin University in Australia, explained that the activation inhibition system is a powerful developmental motif. If you want to build a complete structure, such as feathers or small teeth, the arrangement should not be too crowded; If there is no gap, you will never get different entities. Turing model excites developmental biologists. Although simple, it can explain many different models. However, in practice, few examples of natural patterns have been proved to operate explicitly according to Turing-like mechanism. Give two examples: mouse hair follicle position and chicken feather position. On the developing chicks, the original feathers grow in turn, forming a straight line on the chicks' backs. The longest line stimulates the production of other parallel lines, which extend downward along both sides of the embryo until the embryo is covered.

Close-up of shark cub's teeth. The picture on the left shows how teeth protect the body like scales. A scan of the head teeth of the little shark shows the arrangement of Turing. Photo: Rory Cooper (left); Rendered by Rory Cooper and scanned by Kyle Martin and Amin Garbout at the Imaging and Analysis Center of the Natural History Museum in London.

Researchers know the molecules that are activated and inhibited, which proves that this process is similar to Turing model. Rory Cooper, a graduate student at Fraser Lab, thinks shark teeth seem to be developing, too. However, sharks and their close relative rays were separated from vertebrates 450 million years ago. They inhabit a very interesting place on the tree of life. Sharks provide a perspective for the development of early vertebrates. Hundreds of millions of years before mammals developed hair and birds developed feathers, shark scales covered their skin like armor. They are the oldest living vertebrates with various skin appendages. ) The patterns, shapes and functions of shark teeth are varied: densely overlapping teeth provide extra protection for some sharks, while sparse and smooth parts reduce the resistance of sharks.

In some shark species, teeth even contain luminescent bacteria, which helps communication. However, although there are some subtle differences, the similarity of development patterns among teeth, hair and feathers is undeniable. In order to prove theoretically that shark tooth patterns can be generated by Turing mechanism, Fraser's colleagues established a mathematical model of the interaction between activator and inhibitor. The researchers modified the diffusion, production and degradation rates of these two morphological factors until the model produced a pattern that matched the development of shark skin. This model tells us that, in theory, Turing-like mechanism can explain the formation of shark tooth lines. We don't know whether the molecular basis of small teeth development is the same as feathers. However, considering the similarity of development, chicken genes are a good starting point. When Cooper used in-situ hybridization technology, he found that the same gene would glow during the formation of chicken and shark patterns.

The arrangement of teeth on the shark embryo (left) is very similar to the pattern produced by the researcher's mathematical Turing model. Image: doi:10.1126/sciadv.aau5484.

These genes are expressed not only during tooth germination, but also in the same tissue layer, which is a strong protective effect. It is a good first step to show similar gene expression in similar process, but the gold standard proved in developmental biology is a simple experiment: if the expression of a gene is reduced or eliminated, and then the pattern disappears, then the gene must play an important role in pattern generation. To do this, Cooper added a chemical that inhibited chicken feather activator. Then the original teeth were implanted into shark embryos to observe the growth of sharks. Obviously, these are designed to inhibit the expression of activation genes in birds, and they can span hundreds of millions of years of evolution and produce the same effect in sharks. Cooper found that the expression of activator gene plummeted, forming a flat "dead zone" without teeth. These manipulation results strongly prove that this mechanism is highly conservative.

In order to test whether Turing-like mechanism can produce a wide range of dentate structures in other sharks and their close relatives, the researchers adjusted the production, degradation and diffusion rates of activators and inhibitors in the model. It has been found that relatively simple changes can produce patterns that match the diversity of pedigrees. For example, rays' teeth are usually sparse. By increasing the diffusion rate of inhibitors or decreasing the degradation rate of inhibitors, researchers can obtain a more sparse model. Once the initial model is set, other non-Turing mechanisms complete the transformation of these rows into fully formed teeth, feathers or other epithelial appendages. Beaufort explained: these highly conservative main regulatory mechanisms play a role in the early stage of appendage development, but downstream, species-specific mechanisms will improve this structure.

Nevertheless, in an era when little is known about molecular biology, it is a great thing for a mathematician without biological training to theorize the mechanism behind so many different biological models. Turing mechanism is not the only way to construct patterns in theory, but nature seems to prefer it. Fraser believes that the dependence of so many widely distributed biological groups on this mechanism shows that some kind of constraint may be at work: there may not be many ways to imitate something. Once a simple and powerful system like Turing Machine appears, it will naturally follow the trend and be irreversible. Generally speaking, biodiversity is based on a rather limited set of theories, which seem to be effective and have been used repeatedly in the process of evolution. Nature, with its exuberant creativity, may be more conservative than we think.