×

Nós usamos os cookies para ajudar a melhorar o LingQ. Ao visitar o site, você concorda com a nossa política de cookies.


image

It`s Okay To Be Smart, How the Zebra REALLY Got Its Stripes

How the Zebra REALLY Got Its Stripes

The living world is a universe of shapes and patterns. Beautiful, complex,

and sometimes strange. And beneath all of them is a mystery: How does so much variety

arise from the same simple ingredients: cells and their chemical instructions?

There is one elegant idea that describes many of biology's varied patterns,

from spots to stripes and in between. It's a code written not in the language of DNA, but in math.

Can simple equations really explain something as messy and un-predictable as the living world?

How accurately can mathematics truly predict reality?

Could there really be one universal code that explains all of this?

[OPEN]

Hey smart people, Joe here.

What color is a zebra? Black with white stripes? Or… white with black stripes?

This is not a trick question. The answer? Is black with white

stripes. And we know that because some zebras are born without their stripes.

It might make you wonder, why do zebras have stripes to begin with? A biologist might answer

that question like this: the stripes aid in camouflage from predators. And that would

be wrong. The stripes actual purpose? Is most likely to confuse bloodthirsty biting flies. Yep.

But that answer really just tells us what the stripes do.

Not where the stripes come from, or why patterns like this are even possible.

Our best answer to those questions doesn't come from a biologist at all.

In 1952, mathematician Alan Turing published a set of surprisingly simple mathematical rules

that can explain many of the patterns that we see in nature, ranging from stripes to spots

to labyrinth-like waves and even geometric mosaics. All now known as “Turing patterns”

Most people know Alan Turing as a famous wartime codebreaker, and the father of modern computing.

You might not know that many of the problems that most fascinated him throughout his life were,

well, about life: About biology.

But why would a mathematician be interested in biology in the first place?

That's a really good question!

I'm Dr. Natasha Ellison, and I'm from the University of Sheffield, which is in the UK.

I think so many mathematicians are interested in biology because it's so complicated and there's

so much we don't know about it. If you think about a living system, like a human being,

there's just so many different things going on. And really, we don't know everything.

The movements of animals, population trends, evolutionary relationships,

interactions between genes, or how diseases spread. All of these are

biological problems where mathematical models can help describe and predict what we see in

real life. But mathematical biology is also useful for describing things we can't see.

Joe (05:44) What do you say when people ask,

why should we care about math in biology?

Natasha (05:54): Why should we care

about what mathematics describes in biology?

The reason is because there's things about biology that we can't observe.

We can't follow every animal all the time in the wild, or observe their every moment.

It's impossible to measure every gene and chemical in a living thing at every instant.

Mathematical models can help make sense of these unobservable things. And one of the

most difficult things to observe in biology is the delicate process of how living things grow

and get their shape. Alan Turing called this “morphogenesis”, the “generation of form”.

In 1952, Turing published a paper called “The Chemical Basis of Morphogenesis”.

In it was a series of equations describing how complex shapes like these

can arise spontaneously from simple initial conditions.

According to Turing's model, all it takes to form these patterns is two chemicals, spreading out the

same way atoms of a gas will fill a box, and reacting with one another. Turing called these

chemicals “morphogens.” But there was one crucial difference: Instead of spreading out evenly,

these chemicals spread out at different rates. Natasha (15:49):

So the way that we create a Turing pattern is with some equations called reaction-diffusion

equations. And usually they describe how two or possibly more chemicals are moving around

and reacting with each other. So diffusion is the process of sort of spreading out.

So if you can imagine, I don't know, if you had a dish with two chemicals

in (GFX). They're both spreading out across the dish, they're both reacting with each other.

This is what reaction-diffusion equations are describing.

This was Turing's first bit of genius. To combine these two

ideas–diffusion and reaction–to explain patterns.

Because diffusion on its own doesn't create patterns. Just think of ink in water.

Simple reactions don't create patterns either. Reactants become products and… that's that.

Natasha (20:48): Everybody thought back

then that if you introduce diffusion into systems, it would stabilize it.

And that would basically make it boring. What I mean by that is you wouldn't see a lovely pattern.

You'd have an animal, just one color, but actually Turing showed that when you introduce diffusion

into these reacting chemical systems, it can destabilize and form these amazing patterns.

A “reaction-diffusion system” may sound intimidating, but it's actually pretty simple:

There are two chemicals. An activator & an inhibitor. The activator makes more of itself

and makes inhibitor, while the inhibitor turns off the activator.

How can this be translated to actual biological patterns? Imagine a cheetah with no spots. We

can think of its fur as a dry forest. In this really dry forest, little fires break out.

But firefighters are also stationed throughout our forest, and they can travel faster than the

fire. The fires can't be put out from the middle, so they outrun the fire and spray it back from the

edges. We're left with blackened spots surrounded by unburned trees in our cheetah forest.

Fire is like the activator chemical: It makes more of itself. The firefighters

are the inhibitor chemical, reacting to the fire and extinguishing it. Fire

and firefighters both spread, or diffuse, throughout the forest. The key to getting

spots (and not an all-black cheetah) is that the firefighters spread faster than the fire.

And by adjusting a few simple variables like that,

Turing's simple set of mathematical rules can create a staggering variety of patterns.

Natasha (34:18): These equations that

produce spotted patterns like cheetahs, the exact same equations can also produce stripy patterns

or even a combination of the two. And that depends on different numbers inside the equations. For

example, there's a number that describes how fast the fire chemical will produce itself.

There's a number that describes how fast the fire chemical would diffuse and how fast

the water chemical would diffuse as well. And all of these different numbers inside the equations

can be altered very slightly. And then we'd see instead of a spotted pattern, a stripy pattern.

And one other thing that affects the pattern is the shape you're creating the pattern on.

A circle or a square is one thing, but animals' skins aren't simple geometric shapes. When

Turing's mathematical rules play out on irregular surfaces, different patterns can form on different

parts. And often, when we look at nature, this predicted mix of patterns is what we see.

We think of stripes and spots as very different shapes, but they might be

two versions of the same thing, identical rules playing out on different surfaces.

Turing's 1952 article was… largely ignored at the time.

Perhaps because it was overshadowed by other groundbreaking discoveries in biology,

like Watson & Crick's 1953 paper describing the double helix structure of DNA. Or perhaps

because the world simply wasn't ready to hear the ideas of a mathematician when it came to biology.

But after the 1970s, when scientists Alfred Gierer and Hans Meinhardt

rediscovered Turing patterns in a paper of their own, biologists began to take notice.

And they started to wonder: Creating biological patterns using mathematics may work on paper,

or inside of computers. But how are these patterns *actually* created in nature?

It's been a surprisingly sticky question to untangle. Turing's mathematics simply

and elegantly model reality, but to truly prove Turing right, biologists needed to

find actual morphogens: chemicals or proteins inside cells that do what Turing's model predicts.

And just recently, after decades of searching, biologists have finally begun to find molecules

that fit the math. The ridges on the roof of a mouse's mouth, the spacing of bird feathers

or the hair on your arms, even the toothlike denticle scales of sharks:

All of these patterns are sculpted in developing organisms by the diffusion

and reaction of molecular morphogens, just as Turing's math predicted.

But as simple and elegant as Turing's math is, some living systems have proven to be

a bit more complex. In the developing limbs of mammals, for example, three

different activator/inhibitor signals interact in elaborate ways to create the pattern of fingers:

Stripe-like signals, alternating on and off. Like 1s and 0s. A binary pattern of… digits.

Sadly, Alan Turing never lived to see his genius recognized. The same year he

published his paper on biological patterns, he admitted to being in a homosexual relationship,

which at the time was a criminal offense in the United Kingdom. Rather than go to prison,

he submitted to chemical castration treatment with synthetic hormones. Two years later, in

June of 1954, at the age of 41, he was found dead from cyanide poisoning, likely a suicide. In 2013,

Turing was finally pardoned by Queen Elizabeth, nearly 60 years after his tragic death.

Now I don't like to make scientists sound like mythical heroes. Even the greatest discoveries

are the result of failure after failure and are almost always built on the work of many others,

they're never plucked out of the aether and put in someone's head by some angel of genius.

But that being said, Alan Turing's work decoding

zebra stripes and leopard spots leaves no doubt that he truly was a singular mind

Natasha (37:55): The equations that produce these patterns,

we can't easily solve them with pen and paper. And in most cases we can't at all,

and we need computers to help us. So what's really amazing is that when Alan Turing was writing

these theories and studying these equations, he didn't have the computers that we have today.

Natasha (39:01):

So this here is some of Alan's Turing's notes that were found in his house when he died.

If you can see that, you'll notice that they're not actually numbers.

Joe (39:17): It's like a secret code!

Natasha (39:20): Yeah. It's like a secret

code. It's his secret code. It's in binary actually, but instead of writing binary out,

because you've got the five digits, he had this other code that kind of coded out the binary. So

Alan Turing could describe the equations in this way that required millions of

calculations by a computer, but you didn't really have, you know,

really didn't have a fast computer to do it. So it would have taken him absolutely ages.

Joe (40:15) What has

the world missed out on by the fact that we lost Alan Turing?

Natasha (40:25): It's extremely hard

to describe what the world's missed out on with losing Alan Turing. Because so often he

couldn't communicate his thoughts to other people because they were so far ahead of other people

and they were so complicated. They seemed to come out of nowhere sometimes.

Natasha (25:52) When you read accounts

of people who knew him, they were saying the same thing. We don't know where we got this idea from,

Natasha (40:42) So what, what he could have achieved.

I don't think anyone could possibly say. Natasha (42:14)

I have no idea where we would have got to, but it would have been brilliant.

One war historian estimated that the work of Turing and his fellow codebreakers shortened

World War II in Europe by more than two years, saving perhaps 14 million lives in the process.

And after the war, Turing was instrumental in developing the core logical programming at the

heart of every computer on Earth today, including the one you're watching this video on.

And decades later, his lifelong fascination with the mathematics underlying nature's beauty

has inspired completely new questions in biology.

Doing any one of these things would be worth celebrating. To do all of them is the mark

of a rare and special mind. One that could see that the true beauty of mathematics is

not just its ability to describe reality, it is to deepen our understanding of it.

Stay curious.

How the Zebra REALLY Got Its Stripes Wie das Zebra WIRKLICH seine Streifen bekam Cómo se hicieron realmente las rayas de la cebra Comment le zèbre a-t-il réellement obtenu ses rayures ? シマウマの縞模様の由来 얼룩말이 줄무늬를 갖게 된 진짜 이유 Hoe de zebra ECHT zijn strepen kreeg Jak zebra NAPRAWDĘ ma swoje paski? Como é que a zebra ganhou realmente as suas riscas Как зебра на самом деле получила свои полоски Zebra Çizgilerini Gerçekte Nasıl Aldı? Як зебра насправді отримала свої смужки 斑馬的條紋是如何形成的

The living world is a universe of  shapes and patterns. Beautiful, complex,

and sometimes strange. And beneath all of  them is a mystery: How does so much variety en soms vreemd. En onder hen allemaal schuilt een mysterie: hoe komt er zoveel variatie?

arise from the same simple ingredients:  cells and their chemical instructions? surgen de los mismos ingredientes simples: las células y sus instrucciones químicas?

There is one elegant idea that describes  many of biology's varied patterns,

from spots to stripes and in between. It's a code  written not in the language of DNA, but in math.

Can simple equations really explain something  as messy and un-predictable as the living world? ¿Pueden las ecuaciones simples explicar realmente algo tan desordenado e impredecible como el mundo vivo?

How accurately can mathematics  truly predict reality?

Could there really be one universal  code that explains all of this?

[OPEN]

Hey smart people, Joe here.

What color is a zebra? Black with white  stripes? Or… white with black stripes?

This is not a trick question.  The answer? Is black with white

stripes. And we know that because some  zebras are born without their stripes.

It might make you wonder, why do zebras have  stripes to begin with? A biologist might answer Quizás se pregunte por qué las cebras tienen rayas. Un biólogo podría responder

that question like this: the stripes aid in  camouflage from predators. And that would

be wrong. The stripes actual purpose? Is most  likely to confuse bloodthirsty biting flies. Yep.

But that answer really just  tells us what the stripes do.

Not where the stripes come from, or why  patterns like this are even possible.

Our best answer to those questions  doesn't come from a biologist at all.

In 1952, mathematician Alan Turing published a  set of surprisingly simple mathematical rules

that can explain many of the patterns that we  see in nature, ranging from stripes to spots

to labyrinth-like waves and even geometric  mosaics. All now known as “Turing patterns”

Most people know Alan Turing as a famous wartime  codebreaker, and the father of modern computing. De meeste mensen kennen Alan Turing als een beroemde codekraker in oorlogstijd en de vader van moderne computers.

You might not know that many of the problems that  most fascinated him throughout his life were,

well, about life: About biology.

But why would a mathematician be  interested in biology in the first place?

That's a really good question!

I'm Dr. Natasha Ellison, and I'm from the  University of Sheffield, which is in the UK.

I think so many mathematicians are interested in  biology because it's so complicated and there's

so much we don't know about it. If you think  about a living system, like a human being,

there's just so many different things going  on. And really, we don't know everything.

The movements of animals, population  trends, evolutionary relationships,

interactions between genes, or how  diseases spread. All of these are

biological problems where mathematical models  can help describe and predict what we see in

real life. But mathematical biology is also  useful for describing things we can't see.

Joe (05:44) What do you say when people ask,

why should we care about math in biology?

Natasha (05:54): Why should we care

about what mathematics describes in biology?

The reason is because there's things  about biology that we can't observe. La razón es que hay cosas de la biología que no podemos observar.

We can't follow every animal all the time  in the wild, or observe their every moment.

It's impossible to measure every gene and  chemical in a living thing at every instant.

Mathematical models can help make sense of  these unobservable things. And one of the

most difficult things to observe in biology is  the delicate process of how living things grow

and get their shape. Alan Turing called this  “morphogenesis”, the “generation of form”.

In 1952, Turing published a paper called  “The Chemical Basis of Morphogenesis”.

In it was a series of equations  describing how complex shapes like these En él había una serie de ecuaciones que describían cómo formas complejas como estas

can arise spontaneously from  simple initial conditions.

According to Turing's model, all it takes to form  these patterns is two chemicals, spreading out the

same way atoms of a gas will fill a box, and  reacting with one another. Turing called these

chemicals “morphogens.” But there was one crucial  difference: Instead of spreading out evenly,

these chemicals spread out at different rates. Natasha (15:49):

So the way that we create a Turing pattern is  with some equations called reaction-diffusion

equations. And usually they describe how two  or possibly more chemicals are moving around

and reacting with each other. So diffusion  is the process of sort of spreading out.

So if you can imagine, I don't know,  if you had a dish with two chemicals

in (GFX). They're both spreading out across the  dish, they're both reacting with each other.

This is what reaction-diffusion  equations are describing.

This was Turing's first bit of  genius. To combine these two Esta fue la primera genialidad de Turing. Combinar estos dos Це був перший прояв геніальності Тьюрінга. Поєднати ці два

ideas–diffusion and reaction–to explain patterns.

Because diffusion on its own doesn't create  patterns. Just think of ink in water.

Simple reactions don't create patterns either.  Reactants become products and… that's that. Simpele reacties creëren ook geen patronen. Reactanten worden producten en... dat is dat.

Natasha (20:48): Everybody thought back

then that if you introduce diffusion  into systems, it would stabilize it.

And that would basically make it boring. What I  mean by that is you wouldn't see a lovely pattern. Und das würde es im Grunde langweilig machen. Was ich damit meine, ist, dass man kein schönes Muster sehen würde.

You'd have an animal, just one color, but actually  Turing showed that when you introduce diffusion

into these reacting chemical systems, it can  destabilize and form these amazing patterns.

A “reaction-diffusion system” may sound  intimidating, but it's actually pretty simple:

There are two chemicals. An activator & an  inhibitor. The activator makes more of itself Є дві хімічні речовини. Активатор та інгібітор. Активатор робить більше з себе

and makes inhibitor, while the  inhibitor turns off the activator. y hace inhibidor, mientras que el inhibidor apaga el activador.

How can this be translated to actual biological  patterns? Imagine a cheetah with no spots. We

can think of its fur as a dry forest. In this  really dry forest, little fires break out. puede pensar en su pelaje como en un bosque seco. En este bosque realmente seco, se producen pequeños incendios.

But firefighters are also stationed throughout  our forest, and they can travel faster than the

fire. The fires can't be put out from the middle,  so they outrun the fire and spray it back from the fuego. Los incendios no se pueden apagar desde el centro, por lo que huyen del fuego y lo rocían desde el

edges. We're left with blackened spots surrounded  by unburned trees in our cheetah forest.

Fire is like the activator chemical: It  makes more of itself. The firefighters

are the inhibitor chemical, reacting  to the fire and extinguishing it. Fire

and firefighters both spread, or diffuse,  throughout the forest. The key to getting

spots (and not an all-black cheetah) is that  the firefighters spread faster than the fire.

And by adjusting a few simple variables like that,

Turing's simple set of mathematical rules  can create a staggering variety of patterns.

Natasha (34:18): These equations that

produce spotted patterns like cheetahs, the exact  same equations can also produce stripy patterns gevlekte patronen zoals cheeta's produceren, kunnen exact dezelfde vergelijkingen ook gestreepte patronen produceren

or even a combination of the two. And that depends  on different numbers inside the equations. For

example, there's a number that describes how  fast the fire chemical will produce itself. ejemplo, hay un número que describe la rapidez con la que el producto químico del fuego se producirá a sí mismo.

There's a number that describes how fast  the fire chemical would diffuse and how fast

the water chemical would diffuse as well. And all  of these different numbers inside the equations de waterchemicalie zou ook diffunderen. En al deze verschillende getallen in de vergelijkingen

can be altered very slightly. And then we'd see  instead of a spotted pattern, a stripy pattern. kan zeer licht gewijzigd worden. En dan zouden we in plaats van een gevlekt patroon een gestreept patroon zien.

And one other thing that affects the pattern  is the shape you're creating the pattern on.

A circle or a square is one thing, but animals'  skins aren't simple geometric shapes. When Een cirkel of een vierkant is één ding, maar dierenhuiden zijn geen eenvoudige geometrische vormen. Wanneer

Turing's mathematical rules play out on irregular  surfaces, different patterns can form on different Las reglas matemáticas de Turing se aplican a superficies irregulares, pueden formarse diferentes patrones en diferentes

parts. And often, when we look at nature,  this predicted mix of patterns is what we see.

We think of stripes and spots as very  different shapes, but they might be

two versions of the same thing, identical  rules playing out on different surfaces.

Turing's 1952 article was…  largely ignored at the time.

Perhaps because it was overshadowed by  other groundbreaking discoveries in biology,

like Watson & Crick's 1953 paper describing  the double helix structure of DNA. Or perhaps

because the world simply wasn't ready to hear the  ideas of a mathematician when it came to biology.

But after the 1970s, when scientists  Alfred Gierer and Hans Meinhardt

rediscovered Turing patterns in a paper of  their own, biologists began to take notice.

And they started to wonder: Creating biological  patterns using mathematics may work on paper,

or inside of computers. But how are these  patterns *actually* created in nature?

It's been a surprisingly sticky question  to untangle. Turing's mathematics simply

and elegantly model reality, but to truly  prove Turing right, biologists needed to

find actual morphogens: chemicals or proteins  inside cells that do what Turing's model predicts.

And just recently, after decades of searching,  biologists have finally begun to find molecules

that fit the math. The ridges on the roof of  a mouse's mouth, the spacing of bird feathers que se ajustan a las matemáticas. Las crestas del techo de la boca de un ratón, el espaciado de las plumas de los pájaros... die passen bij de wiskunde. De ribbels op het dak van de mond van een muis, de afstand tussen vogelveren

or the hair on your arms, even the  toothlike denticle scales of sharks: o el vello de los brazos, incluso las escamas dentadas de los tiburones: of het haar op je armen, zelfs de tandachtige tandschubben van haaien: або волосся на ваших руках, або навіть схожа на зуби луска акул:

All of these patterns are sculpted in  developing organisms by the diffusion Todos estos patrones se esculpen en los organismos en desarrollo por la difusión

and reaction of molecular morphogens,  just as Turing's math predicted.

But as simple and elegant as Turing's math  is, some living systems have proven to be

a bit more complex. In the developing  limbs of mammals, for example, three

different activator/inhibitor signals interact in  elaborate ways to create the pattern of fingers:

Stripe-like signals, alternating on and off.  Like 1s and 0s. A binary pattern of… digits. Señales en forma de rayas que se encienden y apagan alternativamente. Como 1s y 0s. Un patrón binario de... dígitos.

Sadly, Alan Turing never lived to see  his genius recognized. The same year he

published his paper on biological patterns, he  admitted to being in a homosexual relationship,

which at the time was a criminal offense in  the United Kingdom. Rather than go to prison,

he submitted to chemical castration treatment  with synthetic hormones. Two years later, in se sometió a un tratamiento de castración química con hormonas sintéticas. Dos años más tarde, en

June of 1954, at the age of 41, he was found dead  from cyanide poisoning, likely a suicide. In 2013, En junio de 1954, a la edad de 41 años, fue encontrado muerto por envenenamiento con cianuro, probablemente un suicidio. En 2013,

Turing was finally pardoned by Queen Elizabeth,  nearly 60 years after his tragic death.

Now I don't like to make scientists sound like  mythical heroes. Even the greatest discoveries

are the result of failure after failure and are  almost always built on the work of many others, son el resultado de un fracaso tras otro y casi siempre se construyen sobre el trabajo de muchos otros,

they're never plucked out of the aether and  put in someone's head by some angel of genius. nunca son arrancadas del éter y metidas en la cabeza de alguien por un ángel genial.

But that being said, Alan Turing's work decoding

zebra stripes and leopard spots leaves no  doubt that he truly was a singular mind

Natasha (37:55): The equations that produce these patterns,

we can't easily solve them with pen and  paper. And in most cases we can't at all,

and we need computers to help us. So what's really  amazing is that when Alan Turing was writing

these theories and studying these equations, he  didn't have the computers that we have today.

Natasha (39:01):

So this here is some of Alan's Turing's notes  that were found in his house when he died.

If you can see that, you'll notice  that they're not actually numbers.

Joe (39:17): It's like a secret code!

Natasha (39:20): Yeah. It's like a secret

code. It's his secret code. It's in binary  actually, but instead of writing binary out,

because you've got the five digits, he had this  other code that kind of coded out the binary. So

Alan Turing could describe the equations  in this way that required millions of

calculations by a computer, but  you didn't really have, you know,

really didn't have a fast computer to do it.  So it would have taken him absolutely ages. realmente no tenía un ordenador rápido para hacerlo. Así que le habría llevado muchísimo tiempo.

Joe (40:15) What has

the world missed out on by the  fact that we lost Alan Turing? que se ha perdido el mundo por haber perdido a Alan Turing?

Natasha (40:25): It's extremely hard

to describe what the world's missed out on  with losing Alan Turing. Because so often he om te beschrijven wat de wereld heeft gemist door Alan Turing te verliezen. Omdat hij zo vaak

couldn't communicate his thoughts to other people  because they were so far ahead of other people no podía comunicar sus pensamientos a otras personas porque iban muy por delante de los demás

and they were so complicated. They  seemed to come out of nowhere sometimes. y eran tan complicados. A veces parecían salir de la nada.

Natasha (25:52) When you read accounts

of people who knew him, they were saying the same  thing. We don't know where we got this idea from,

Natasha (40:42) So what, what he could have achieved.

I don't think anyone could possibly say. Natasha (42:14)

I have no idea where we would have got  to, but it would have been brilliant.

One war historian estimated that the work of  Turing and his fellow codebreakers shortened Un historiador de la guerra estimó que el trabajo de Turing y sus compañeros acortó

World War II in Europe by more than two years,  saving perhaps 14 million lives in the process.

And after the war, Turing was instrumental in  developing the core logical programming at the Y después de la guerra, Turing desempeñó un papel decisivo en el desarrollo del núcleo de la programación lógica en la

heart of every computer on Earth today,  including the one you're watching this video on.

And decades later, his lifelong fascination  with the mathematics underlying nature's beauty Y décadas más tarde, su fascinación de toda la vida por las matemáticas que subyacen a la belleza de la naturaleza

has inspired completely new questions in biology.

Doing any one of these things would be worth  celebrating. To do all of them is the mark

of a rare and special mind. One that could  see that the true beauty of mathematics is

not just its ability to describe reality,  it is to deepen our understanding of it.

Stay curious.