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The world we live in is made up of all kinds of shapes and patterns, which are beautiful, complex and even strange. And behind all these patterns is a mystery: how does such a simple ingredient produce so much diversity? There is an elegant idea that describes many different patterns of biology: from speckles to stripes and something in between. The idea is a piece of code, but not in the DNA language, but in mathematics.

Can simple equations really explain things as chaotic and unpredictable as the world of life? Can mathematics accurately predict reality? Is there really a common code that can explain all these patterns?

Turing model

What color is the zebra? Black base, white stripes? Or a white base with black stripes? The answer is black and white stripes, which we know because some zebras are born without stripes. This may make you wonder why zebras start to produce stripes. Biologists might answer this question like this: stripes help with camouflage. But this answer only tells us the function of stripes, not where the stripes come from. Why is there such a pattern?

Tuyuan Pexels our best answers to these questions don't come from biologists at all. In 1952, mathematician Alan Alan Turing published a surprisingly simple set of mathematical rules that explain many of the patterns we see in nature: from stripes to spots to labyrinthine waves, and even geometric mosaics, which are now called "Turing patterns".

Biology needs mathematics.

Most people know that Alan Turing was a famous password cracker in wartime and the father of modern computers. But you may not know that many of the most fascinating questions in his life are related to life: about biology. But why are mathematicians interested in biology? I think the reason why many mathematicians are interested in biology is that it is too complicated and there are too many things we don't know.

Animal movements, population trends, evolutionary relationships, interactions between genes or the spread of disease are all biological problems, and mathematical models can help describe and predict what we see in biology. and mathematical biology can also be used to describe things we can't see. We can't keep track of every animal in the wild or observe their every moment. We can't measure every gene and chemical in an organism all the time. Mathematical models can help to understand these unobservable things.

One of the most difficult things to observe in biology is the delicate process of how organisms grow and form shapes, which Alan Turing calls "morphogenesis". In 1952, Turing published a paper called "the Chemical basis of Morphogenesis," in which there are a series of equations describing how complex shapes arise spontaneously from simple initial conditions.

According to Turing's model, only two chemicals are needed to form these patterns, which Turing calls "morphogenetic elements". They spread and react with each other in the same way that gas atoms fill the space. But there is one key difference from gas atoms: these chemicals are not evenly distributed, but at different speeds. In other words, we create the Turing model by using equations called reaction diffusion, which usually describe how two or more chemicals move around and react to each other.

Combining these two ideas-- diffusion and reaction-- to explain that the pattern pattern is a genius idea. Because diffusion itself does not create patterns, simple reactions do not create patterns. If you introduce diffusion into the system, according to the knowledge of thermodynamics, we know that it will stabilize the system, and eventually we will not see the pattern, but only one color. But when you introduce diffusion into these reactive chemical systems, it can destabilize and form these amazing patterns.

Pattern pattern

The "reaction diffusion system" may sound scary, but it is actually very simple: there are two chemicals: activators and inhibitors. The activator produces more activators as well as inhibitors, which turn off the activators. So how do you translate this process into an actual biological model?

Imagine a cheetah without spots. We can think of its fur as a dry forest. Small fires can break out everywhere in this very dry forest, but firefighters are also stationed everywhere in the forest, and they put out the fire very quickly. The sparks of the fire will float elsewhere with the wind and start the fire, so firefighters have to put out the fire everywhere, eventually leaving black spots surrounded by unburned trees in the cheetah forest. Fires are like chemical activators. They replicate themselves. Firefighters are chemical inhibitors that react to fires and extinguish them. Fires and firefighters spread throughout the forest, and the key to getting spots (rather than all-black cheetahs) is that firefighters spread faster than the fire.

Another thing that the source Pexels affects the pattern pattern is to create the shape of the pattern: round or square, and so on. Animal skin is not a simple geometric shape. When Turing's mathematical rules work on irregular surfaces, different parts form different patterns. Usually, when we look at nature, what we see is a mixed pattern of predictions. We think that stripes and spots are very different shapes, but they may be two versions of the same thing, and the same rules work on different surfaces.

It was finally proved

Turing's 1952 article was largely ignored at the time, perhaps because it was overshadowed by other breakthroughs in biology, such as Watson and Crick's 1953 paper describing the double helix structure of DNA, or because the world was simply not ready to hear mathematicians' thoughts on biology.

But after the 1970s, when scientists Alfred Gierer and Hans Meinhardt rediscovered the Turing model in their own papers, biologists began to notice this important discovery. They began to wonder: using mathematics to create biological models may work well on paper or inside a computer, but how are these patterns actually created in nature?

Turing's mathematics simulates reality simply and elegantly, but to really prove Turing right, biologists need to find the actual morphogenetic elements: chemicals or proteins in cells, as predicted by the Turing model. Just recently, after decades of searching, biologists finally began to look for molecules suitable for mathematics. The ridges on the mouse's beak, the distance between bird feathers or the hair on the arms, and even the tooth-like scales of sharks: all of these patterns are carved through the diffusion and reaction of molecular morphogenetic elements in developing organisms, just like Turing's mathematical prediction.

Sadly, Alan Turing never lived to see his genius recognized.

This article comes from the official account of Wechat: Vientiane experience (ID:UR4351), author: Eugene Wang

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