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Impact of Alan Turing's approach to morphogenesis

Impact of Alan Turing's approach to morphogenesis


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Shortly before his untimely passing, the computing pioneer Alan Turing published his most cited paper The Chemical Basis of Morphogenesis (1952).

The central question for Turing was: how does a spherically symmetric embryo develop into a non-spherically symmetric organism under the action of symmetry-preserving chemical diffusion of morphogens (as Turing calls them, an abstract term for arbitrary molecules relevant to development)? The insight that Turing made is that very small stochastic fluctuations in the chemical distribution can be amplified by diffusion to produce stable (i.e. not time varying except slow increases in intensity; although also potentially time-varying with 3 or more morphogens) patterns that break the spherical symmetry.

The theory is beautifully simple and abstract, and produces very important qualitative results (and also quantitative results through computer simulation, which unfortunately Turing did not get to fully explore). However, even in the definition Turing discusses some potential limitations such as ignoring mechanical factors, and the inability to explain preferences in handedness. The particular models he considers -- a cycle of discrete cells and a circular tissue -- do not seem particularly relevant. As far as I understand, the key feature is his observation of symmetry breaking through small stochastic noise and instability.

What was the most important contribution of Turing's paper to developmental biology? Is his approach still used, or has the field moved on to other models? If his approach is used, how was the handedness problem resolved?


This is a very interesting question. Many people have researched this topic, and many still are. But regardless, I had never heard of Alan Turing's contributions, so thank you!

First of all, I cannot actually find who first coined the term morphogen. Though people had hypothesized that chemicals could play a critical role in development through much of the 20th century, I cannot actually find the first person to use morphogen. But the most important paper really came from a guy named Lewis Wolpert, who came up with the model of a gradient of morphogens leading to differential cell fates. The idea being that if some area of an embryo produces a morphogen at a very high concentration, then as you move away from that area, the concentration goes down. So if this morphogen is required at or above a certain threshold for activity, then only those cells with that concentration will have a certain cell fate, while at lower concentrations, the cells can become something different.

But this does not really answer your question. You are asking how a single cell, which is spherically symmetrical, can determine a particular axis. Though most organisms do this is in slightly different ways, the most common feature is that sperm entry point breaks the symmetry. The best way to explain this is to show you a diagram of Xenopus (frog) eggs.

Image from: http://studentreader.com/nieuwkoop-center/

The Xenopus egg, first of all, is inherently not spherically symmetrical. There is a black animal pole, and a white vegetal pole. The sperm can only enter a marrow region of the egg about 30˚ north of the animal/vegetal line. Upon fertilization, an event occurs where the pigmented areas turn toward the sperm entry point, leaving a gray crescent. Nearby the gray crescent, in the vegetal pole, a structure called the organiser develops. This organiser creates many of the morphogens that then pattern the rest of the embryo.

Researchers have studied this a lot in many different organisms, but a few things really remain constant: eggs are not exactly spherically symmetrical, and the sperm entry point provides asymmetry.


I would think this is very much still "used." 60 years later, we finally have the first experimental support for it:

In this blog article about this journal piece the authors studied the ridges that form on the roof of mouse mouths. They manipulated the signaling molecules that induce their formation and observed changes in line with Turing's theory. Of course, this doesn't preclude other mechanisms from occurring, but supports that of Turing.


While Turing did not include mechanical effects on the differentiaton/patterning in his seminal work, other researchers have expanded on that idea. These do not necessarily change the premises that led Turing to his conclusions, nor make his contribution less relevant today. Adding a dynamic component or mechanics to the substrate in which the diffusion-driven instabilities happen can simply yield more complicated solutions.

Clear examples of this interaction between the reaction-diffusion mechanism and the mechanics or boundary conditions can be found in several places: the formation of palatal ridges in the roof of the mouth in animals, teeth formation across species, bacterial colonies both natural and synthetic and even the issue of boundary conditions has been explored in animal coating patterns.

In the case of handedness, I think this also a question of symmetry breaking, such as with Turing patterns, but happening at different scale. Skeletal primordia are thought to be formed through a Turing-type mechanism. The "issue" with handedness would be that in Turing's formulation all fingers would be equal, but superimposing the patterning already created by the Spemman organizer which polarizes the hand, makes the fingers distinct. So, in essence, a prior symmetry breaking event (which could be caused by a different lateral inhibition process or diffusion-driven instability acting a larger scale) can modulate a downstream developmental process.


Turing patterning has had a large impact in systems biology understandings of morphogenesis. The general idea is that Turing mechanisms can be coupled with other mechanisms to build robust patterning methods.

So while not too many people would say that an entire mechanism is ONLY due to Turing patterning, a lot of regulatory networks can be understand as having the components allow for a Turing patterning mechanism (under certain parameter constraints), and thus they can understand "why" certain interactions exist and predict the behavior of perturbations. Usually there are multiple mechanisms involved in a patterning system so doing some knockouts will not get rid of patterning, but by disturbing the Turing mechanism you will many times see a decrease in the robustness of the patterning.

A lot of systems biology has focused on robustness: what kinds of network motifs allow for robust switch-like behavior? etc. The Turing mechanism is a network motif which allows for robust spatial behaviors.


Alan Turing's 'Morphogenesis' Theory Confirmed 60 Years After His Death

Alan Turing is remembered mostly for his work in computer science--and for cracking Nazi Germany's Enigma code. But the English mathematician also wrote a key biology paper in which he put forth an explanation for morphogenesis. That's the process by which identical cells in a developing organism differentiate into the various cells that make up the organism's adult form.

Now, 60 years after his suicide, scientists at Brandeis University and the University of Pittsburgh have published a study offering experimental evidence confirming Turing's theory.

Turing was the first to offer a chemical explanation of morphogenesis, study co-author Dr. Seth Fraden, a professor of physics at Brandeis, told The Huffington Post in an email. Turing theorized that cells change shape because chemicals in an embryo react with each other and diffuse across space, according to a written statement released by the University of Pittsburgh. He predicted six different patterns of morphogenesis that could arise from his model.

To test Turing's theory, Fraden and his collaborators created rings of synthetic, cell-like structures. Then Dr. G. Bard Ermentrout, a professor of computational biology and of mathematics at Pitt, used computational tools to analyze the results.


This photo montage depicts morphogenesis from an initial homogeneous state (upper left, same volume and color) through a heterogeneous state (center, same volume but different colors) and into a chemo-physical heterogeneous state (lower right, different volumes and colors). This cellular differentiation takes place exactly as Alan Turing predicted it would in his 1952 paper "The Chemical Basis of Morphogenesis.'

What happened? The researchers observed all six patterns predicted by Turing, plus a seventh that he didn't predict, according to the statement. In addition, the researchers noticed that the once identical cell-like structures started to change in size.

Turing's theory helps explains all sorts of biological phenomena, from the pigmentation of seashells to the shapes of flowers and leaves and even the geometric structures seen in drug-induced hallucinations, according to Ermentrout.

A paper describing the new research was published March 10 in Proceedings of the National Academy of Sciences.

CORRECTION: An earlier version of this story misspelled Alan Turing's last name.


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Turing's morphogenesis theory drives research into self-configuring systems

Alan Turing's ideas on morphogenesis are helping scientists to develop ways to make complex materials build themselves.

Alan Turing published in 1952 one of the most important ideas of the 20th century – a mathematical model of the chemical processes underlying cell differentiation. But it would take 60 years to be confirmed.

His aim was to answer fundamental questions about life. One of the most puzzling is how the undifferentiated cells in an early embryo decide to specialise without some overarching control. How does one become a bone cell and another a blood cell? Similarly, how did all the shapes and surface patterns we see in the huge diversity of plants, insects, and animals emerge?

Today Turing's idea has become an important starting point for thinking about systems that build themselves from a basic set of parts. Instead of having to form and assemble them using conventional top-down manufacturing, could we build synthetic systems from the bottom up from a cocktail of chemicals that mimic muscles or grow organs and build entirely new manufacturing processes?

In August 2014, a team of scientists led by James Sharpe from the Centre for Genomic Regulation in Barcelona showed that the way fingers and toes form is orchestrated by three molecules using the kind of process Turing described.

"What makes Turing special is that he takes problems and strips them to their essence. At the point he wrote his paper we didn't even know the structure of DNA," says Seth Fraden professor of physics at Brandeis University in the US. With his colleague Irv Epstein, professor of chemistry, Fraden published in March 2014 the first experimental evidence that validates Turing's theory in cell-like structures.

More than a metaphor

In Turing's model, chemicals react with each other and diffuse across space – say between cells in an embryo. These reactions are managed by the interaction of inhibitory and excitatory agents. When this interaction plays out across an embryo, it creates patterns of chemically different cells. Turing predicted six different patterns could arise from this model.

Fraden and Epstein's paper in Proceedings of the National Academy of Sciences showed how it is possible to produce these six patterns by using arrays of droplets floating in oil.

"What is clear is that one can make a system with a minimum of ingredients – just a handful of chemicals – to achieve the same kind of complexity that you have in biology. This is more than a metaphor for morphogenesis. It means we can start thinking of engineering synthetic systems," Epstein said on Boston Radio.

Fraden and Epstein used microfluidics and a cocktail of chemicals called the Belousov-Zhabotinsky (BZ) reaction (see 'The Chemical Oscillator') that switches periodically between different coloured states. They put the BZ mixture into a series of droplets each one around 100µm in diameter that were fed into a capillary tube. By adding a photosensitive catalyst, they could send individual droplets to sleep by shining a light on them. "If we release them all together it is like a set of synchronised clocks so they are all in phase. Gradually they go increasingly out of sync as each one influences its neighbour until they are all exactly 180 degrees out of phase," Fraden explains. The out-of-phase condition is more stable for the droplets.

To make more sophisticated patterns, Fraden and Epstein set up a 2D array of drops and used a digital projector coupled into a microscope so they could isolate drops or sequences of drops, pulse them with light, and look at how they oscillate and how the reaction affects neighbouring cells. Fraden comments: "We can program these like you would neurons in a neural network and get a certain collective kind of behaviour."

Dancing droplets

They tested several of Turing's predictions, including what happens if you activate even and then odd numbers of drops in a ring pattern. "If you have six rhythmically oscillating drops arranged in a circle all beating with a 4/4 metre signature, they cluster together such that every other drop beats on one half-note [minim] and the other three beat on the other half-note of the measure. However, if you have five in the ring, the drops adopt a 5/4 metre signature, like the jazz composition Take Five, performed by the Dave Brubeck Quartet, and the pattern in space along the ring traces out a pentagram," says Fraden. "We were the first to test this in a diffusive kind of system. And they were both predicted by Turing."

One other pattern Turing thought responsible for morphogenesis involves making the drops communicate so strongly that they suppress the oscillations and adopt a periodic spatial pattern in which some drops are chemically 'off' and others 'on'. In the Morphogenesis paper, he talks about the limbs of a hydra, so where a gene turns on it will grow a limb and where it doesn't there is no limb. This stationary instability has become known as the Turing instability. "The coupling strength turns out to be governed by the relative strength of the chemical reaction inside one drop to the physical diffusion of chemicals between drops," says Fraden. "To drive the transition from oscillating to stationary, we simply had to make the drops smaller. Then a field of initially identical drops make a collective decision about who's 'off' and who's 'on' in a periodic organised way as Turing predicted."

More recently, Fraden and Epstein have used the BZ oscillating reaction and embedded it in a gel so that in the oxidised state the gel swells and in the reduced state it collapses and shrinks. "You can harness this oscillating chemical reaction to make a periodic mechanical action like a heartbeat," explains Fraden.

'Self-oscillating' gels were developed ten years ago by Ryo Yoshida at the University of Tokyo, and the Brandeis team collaborated with Yoshida on some of aspects. Reducing the features to few 100µm across and making these arrays is a new area of research.

"You can imagine taking many of the gel cells into a microfluidic channel where they all synchronise together to give concerted motion. Using a 3D printer, we have made hollow cylinders, which are then coupled to the BZ reaction, and they can beat, oscillate and contract and drive fluid flow. So we already have a proof of principle," says Fraden

As for how such a structure could be used, Fraden has the analogy of a spinal column with the autonomous nervous system hooked up to an organ, say the colon, producing contractile waves. "You don't have to think about digesting your food your colon does it automatically. When sleeping, the colon contracts slowly, but speeds up after a meal," he says. Fraden envisions that the network of drops will play the role of the neural architecture while the gel, placed underneath the drops, will play the role of the musculature.

Such a set-up could, he thinks, become a scalable architecture for building artificial materials in ways analogous to how large organisms are built out of single cells that function and communicate through diffusion. "That limits the drops to 100 microns but then you can hierarchically assemble them into tissues and organs on a larger scale. You could build up a chemo-mechanical system on a scale of humans or even dinosaurs and whales," he jokes.'

To make such systems as fully functional as living ones you need replenishment, repair, replication and evolution. But molecules like chlorophyll could, in theory, be embedded to extract energy from light and pull the carbon out of the air to make fuel, like plants, says Fraden.

Moving up the scale

Another American research group is linking up larger networks of chemical reactions. "Animals have many patterns – stripes at one size scale, legs at another size scale, and their tissues also have patterns. We've been looking at whether networks of reaction-diffusion processes, more complex than those Turing was thinking about, could organise multiple types of pattern," explains Rebecca Schulman, assistant professor of chemical and biomolecular engineering and computer science at the Schulman Lab at Johns Hopkins University (JHU) in Baltimore.

The Schulman lab is interested in how autonomous bottom-up techniques can produce form and pattern at different scales. "We know from biology that very complex forms come from simpler initial patterns, but the numbers of molecules involved in development are hundreds if not thousands. It has been hard to study those processes because we cannot engineer chemical systems of that complexity."

Schulman and co-author Dominic Scalise have taken a first step by modelling these complex systems with a set of partial differential equations. "These are the same equations Turing used but we scaled it from a set of two or three to hundreds," says Schulman.

The JHU team started with a simple initial pattern that could be formed by the reactions Turing imagined, and then added molecules to transform the pattern into something else. One computer simulation showed how chemical programs designed in this way could turn an incoherent series of dots into a symmetrical stick figure with an oval head, legs and arms.

An important feature is that patterns are produced through stages of iterative refinement. It turns out that chemical circuits that turn up in biological development share similar basic design principles.

Schulman thinks the best way to prove such results experimentally would be to use a reaction-diffusion network based on DNA strands. Erik Winfree's group at the California Institute of Technology has been using chains of synthetic DNA, using up to 130 unique species of DNA strand, to make computing circuits. Schulman proposes using the same approach to order and chain operations to operate on space.

Programming for predictability

Microsoft Research's biological computation group in Cambridge, run by Andrew Phillips, is also looking at systems that create patterns out of DNA molecules, in collaboration with the University of Washington.

"In a purely DNA-based system, we can program patterns more easily without the complication of cells. With cells it is difficult to control what is going on: they have their own metabolism and all the things they need to stay alive. With a purely chemical system, we can engineer behaviour with a much higher degree of precision," explains Neil Dalchau, a scientist in Phillips's group.

To scale up this work to living cells, the group is developing a programming language for the Genetic Engineering of Cells (GEC), which lets a programmer write a description of the function they want a cell to perform, and works out the DNA code required. "There are many things you can do with the GEC programming language," explains Phillips. "For patterning, you need the cell to make machinery that allows it to both sense signals from its environment and emit signals to neighbouring cells, depending on some internal computation."

The group is working to engineer precise communication protocols between microbial cells, tuning their DNA to produce enzymes that manufacture certain chemicals as signalling agents. In this context, a morphogen, as Turing described it, might be a signalling molecule made by a cell, which diffuses through the area between the cells. When other cells receive the morphogen they start making their own molecules.

Cellular design

Actually reprogramming cells to behave the way scientists want is extremely difficult to do in practice, says Dalchau. "It requires the ability to engineer cells in a prescribed way, with precisely controlled dynamic behaviour. This precision requires a deep integration of computational design tools with laboratory experiments, which we have been working on for some time."

Phillips' group is collaborating with a number of research groups including the plant sciences team lead by Jim Haseloff of the University of Cambridge. Paul Grant, a joint postdoctoral researcher between both groups, is carrying out experiments to help determine precise dynamic properties of the genetic components needed for programmed morphogenesis. This involves putting the components into colonies of bacterial cells and studying the patterns they produce.

Grant explains: "I've carefully characterised one device that acts like a switch – it takes small differences in morphogen levels and amplifies them so that the cells switch to one state or another. As soon as you move away from a state of equilibrium so there is more of one diffusible substance than another, that sets off the system into a particular direction."

Grant is doing this work in the context of colonies of bacteria that communicate with each other on two different channels. As a measurement of gene expression, the bacteria produce fluorescent cyan or yellow proteins according to what chemical signals they receive. The goal is to be able to set up a self-organising system where only local interactions between cells produce desired emergent properties.

"Turing's idea is appealing because of its simplicity. It was an attempt to extract basic principles from the complexity of biology. What we're finding when we try to implement those principles in a designed system is that the details are important. We need to figure out ways that we can interact with those details, which requires computational software to design and build genetic circuitry. What we end up building is not quite as simple as the general principles Turing originally proposed but it takes advantage of all of our knowledge of complex biological systems," says Grant.

Ultimately the aim for all these groups is to be able to tease out design rules such that synthetic systems with the attributes of living matter can be designed on a computer in the way we design cars or computer chips.

Applications include the growth of synthetic organs and the spatial organisation of bacterial communities such as biofilms. "Biofilms are a major cause of microbial infections, since they confer antibiotic resistance. If you can understand this spatial organisation better you have the ability to disrupt it. We could also exploit the robustness of biofilms for our own applications, including the efficient production of compounds such as pharmaceuticals," says Phillips.

Self-assembly based on morphogenesis could define the surfaces of materials and some of the features that make up integrated circuits more cheaply than today's purely top-down methods. Even everyday objects such as cups could, perhaps, be 'grown' in much the same way a pitcher plant develops Haseloff has suggested.

That Alan Turing devised the general principles more than 60 years ago in his only paper on biology is a testament to his genius.

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The Chemical Basis of Morphogenesis

"The Chemical Basis of Morphogenesis" is an article that the English mathematician Alan Turing wrote in 1952. [1] It describes how patterns in nature, such as stripes and spirals, can arise naturally from a homogeneous, uniform state. The theory, which can be called a reaction–diffusion theory of morphogenesis, has become a basic model in theoretical biology. [2] Such patterns have come to be known as Turing patterns. For example, it has been postulated that the protein VEGFC can form Turing patterns to govern the formation of lymphatic vessels in the zebrafish embryo. [3]

Reaction–diffusion systems have attracted much interest as a prototype model for pattern formation. Patterns such as fronts, spirals, targets, hexagons, stripes and dissipative solitons are found in various types of reaction-diffusion systems in spite of large discrepancies e.g. in the local reaction terms. Such patterns have been dubbed "Turing patterns". [4]

Reaction–diffusion processes form one class of explanation for the embryonic development of animal coats and skin pigmentation. [5] [6] Another reason for the interest in reaction-diffusion systems is that although they represent nonlinear partial differential equations, there are often possibilities for an analytical treatment. [7] [8] [9]


Impact of Alan Turing's approach to morphogenesis - Biology

Alan Turing was long famous in computer science and then became notable due to his sexuality and its controversy in England. Less well known is his work in biology and chemistry.

During World War II, Turing helped cracked the German Enigma Code, which made it possible to decipher enemy transmissions. After the war, he was convicted of homosexuality — a criminal offense in England — and sentenced to chemical castration. Shortly after his trial, and before he killed himself in 1954, he published a biology paper, "The Chemical Basis of Morphogenesis."

Turing proposed his hypothesis of morphogenesis, or how identical copies of a single cell differentiate, for example, into an organism with arms and legs, a head and tail, and became the first to offer an explanation of morphogenesis through chemistry. He hypothesized that identical biological cells differentiate, change shape and create patterns through a process called intercellular reaction-diffusion. In this model, a system of chemicals react with each other and diffuse across a space — say between cells in an embryo.

These chemical reactions need an inhibitory agent, to suppress the reaction, and an excitatory agent, to activate the reaction. This chemical reaction, diffused across an embryo, will create patterns of chemically different cells.

Now, 60 years after Turing's death, researchers from Brandeis University and the University of Pittsburgh writing in the Proceedings of the National Academy of Sciences
have provided the first experimental evidence that validates Turing's theory in cell-like structures.

Turing predicted six different patterns could arise from this model.

At Brandeis, Seth Fraden, professor of physics, and Irv Epstein, the Henry F. Fischbach Professor of Chemistry, created rings of synthetic, cell-like structures with activating and inhibiting chemical reactions to test Turing's model. They observed all six patterns plus a seventh unpredicted by Turing.

Just as Turing theorized, the once identical structures — now chemically different — also began to change in size due to osmosis.

This research could impact not only the study of biological development, and how similar patterns form in nature, but materials science as well. Turing's model could help grow soft robots with certain patterns and shapes.


New theory deepens understanding of Turing patterns in biology

EMBL scientists extend Turing's theory to help understand how biological patterns are created. Credit: Xavier Diego, EMBL

A team of researchers at EMBL have expanded Alan Turing's seminal theory on how patterns are created in biological systems. This work, which was partly done at the Centre for Genomic Regulation (CRG), may answer whether nature's patterns are governed by Turing's mathematical model and could have applications in tissue engineering. Their results have been published on 20 June in Physical Review X.

Alan Turing sought to explain how patterns in nature arise with his 1952 theory on morphogenesis. The stripes of a zebra, the arrangement of fingers and the radial whorls in the head of a sunflower, he proposed, are all determined through a unique interaction between molecules spreading out through space and chemically interacting with each other. Turing's famous theory can be applied to various fields, from biology to astrophysics.

Many biological patterns have been proposed to arise according to Turing's rules, but scientists have not yet been able to provide a definitive proof that these biological patterns are governed by Turing´s theory. Theoretical analysis also seemed to predict that Turing systems are intrinsically very fragile, unlikely for a mechanism that governs patterns in nature.

Going beyond Turing's theory

Xavier Diego, James Sharpe and colleagues from EMBL's new site in Barcelona analysed computational evidence that Turing systems can be much more flexible than previously thought. Following this hint, the scientists, based at the CRG and are now at EMBL, expanded Turing's original theory by using graph theory, a branch of mathematics that studies the properties of networks and makes it easier to work with complex, realistic systems. This led to the realization that network topology, the structure of the feedback between the networks' components, is what determines many fundamental properties of a Turing system. Their new topological theory provides a unifying view of many crucial properties for Turing systems that were previously not well understood and explicitly defines what is required to make a successful Turing system.

A Turing system consist of an activator that must diffuse at a much slower rate than an inhibitor to produce a pattern. The majority of Turing models require a level of parameter fine-tuning that prevents them from being a robust mechanism for any real patterning process. "We learned that studying a Turing system through the topological lens really simplifies the analysis. For example, understanding the source of the diffusion restrictions becomes straightforward, and more importantly, we can easily see what modifications are needed to relax these restrictions," explains Xavier Diego, first author of the paper.

"Our approach can be applied to general Turing systems, and the properties will be true for networks with any number of components. We can now predict if the activity in two nodes in the network is in or out of phase, and we also found out which changes are necessary to switch this around. This allows us to build networks that make any desired pair of substances overlap in space, which could have interesting applications in tissue engineering."

Turing hieroglyphs for experimental groups

The researchers also provide a pictorial method that enables researchers to easily analyse existing networks or to come up with new network designs. "We call them 'Turing hieroglyphs' in the lab," says EMBL Barcelona group leader James Sharpe, who led the work. "By using these hieroglyphs, we hope that our methods will be adopted by both theoreticians and by experimental groups that are trying to implement Turing networks in biological cells."

This expanded theory provides experimental research groups with a new approach to making biological cells develop in patterns in the lab. If experimental groups are successful in this, the questions over whether Turing's theory of morphogenesis applies to biological systems will finally be answered.


Turing’s Theory of Morphogenesis Validated 60 Years After His Death

British />mathematician Alan Turing’s accomplishments in computer science are well known—he’s the man who cracked the German Enigma code, expediting the Allies’ victory in World War II. He also had a tremendous impact on biology and chemistry. In his only paper in biology, Turing proposed a theory of morphogenesis, or how identical copies of a single cell differentiate, for example, into an organism with arms and legs, a head and tail.

Now, 60 years after Turing’s death, researchers from the University of Pittsburgh and Brandeis University have provided the first experimental evidence that validates Turing’s theory in cell-like structures.

The team published their findings in the Proceedings of the National Academy of Sciences on March 10.

Turing, in 1952, was the first to offer an explanation of morphogenesis through chemistry. He theorized that identical biological cells differentiate and change shape through a process called intercellular reaction-diffusion. In this model, chemicals react with each other and diffuse across space—say between cells in an embryo. These chemical reactions are managed by the interaction of inhibitory and excitatory agents. When this interaction plays out across an embryo, it creates patterns of chemically different cells. Turing predicted six different patterns could arise from this model.

At Brandeis, Seth Fraden, professor of physics, and Irv Epstein, professor of chemistry, created rings of synthetic, cell-like structures with activating and inhibiting chemical reactions to test Turing’s model. Pitt’s G. Bard Ermentrout, University Professor of Computational Biology and professor of mathematics in the Kenneth P. Dietrich School of Arts and Sciences, undertook mathematical analysis of the experiments.

The researchers observed all six patterns plus a seventh unpredicted by Turing.

In addition, they noticed that, as Turing theorized in the 1950s, the once identical cell-like structures—now chemically different—also began to change in size due to osmosis. This may explain how some cells, further down the development assembly line, become large egg cells or tiny sperm cells.

The research “tells you how a zebra gets its stripes,” says Ermentrout. Turing’s theory underlies pattern formation in every biological area from pigmentation of seashells to the shapes of flowers and leaves and to the geometric structures seen in drug-induced hallucinations, he adds. Thus, validating Turing’s theory could have an impact on future research in fields ranging from embryology to neurology to cardiology. This research could impact not only the study of biological development but the study of materials science as well.


The Impact of Alan Turing

The 2012 centenary of Alan Turing’s birth has enjoyed a level of public awareness that is remarkable for any scientific figure. This is in part due to the great change in the perception of his homosexuality since the 1990s: young people can scarcely believe that British criminal law was as it was in 1952, and there has been much agitation for some sort of posthumous adjustment to his conviction. Unfortunately, just as Roger Bannister and the Comet crashes represented that particular era in Britain, so too did Turing’s conviction. This is an immutable historical fact.

In parallel, also since the 1990s, the public understanding of computers has changed. Computers are not remote installations, but hubs of free personal communication, and are becoming increasingly in tune with Turing’s vision. In fact it is only recently, with general-purpose chips taking over ever more functions, that the idea of the universal Turing machine has really been vindicated. When he died in 1954, Turing would hardly have been seen as a towering figure — and not just because his war work remained totally secret until the 1970s. When elected Fellow of the Royal Society (FRS) in 1951 for his 1936 work on computability, his work was barely appreciated outside a small academic field, and was not considered of practical importance. In 1953 the first British book on computers ridiculed Turing machines as ”incomprehensible”.

Perhaps what is most distinctive about Turing is that although in 1936 he addressed the very abstract and unfashionable material of mathematical logic, unmotivated by any prospect of economic benefit, he never spurned down-to-earth application. The commonplace picture of him as a dreaming theorist misses the mark. His codebreaking work, turning logic and probability into engineering, made a critical contribution to 1945 and indeed the post-1945 world of Anglo-American dominance. His 1945 design for the ACE computer, now the centrepiece of a special Science Museum exhibition, makes visible his eagerness to engage with technical electronics — although his prospectus for what would now be called software development was really the most powerful aspect of his plan.

This was never really followed up and one weakness of Turing’s scientific career was that he did not publish more of his far-sighted ideas. When he chose, he could make a great impact with published papers, and he was not shy about explaining Artificial Intelligence in radio talks. But he was impatient with the more routine work of pressing home his arguments, always eager to move on to new explorations. Many scientists today, serial writers of research proposals, will sympathise.

The questions that most excited Turing are still alive and well. After writing a classic work on Artificial Intelligence in 1950, he turned to mathematical biology, and his models of growth are now the focus of much exciting research. In his last period, Turing was also looking afresh at quantum mechanics, and the connection of logic and physics remains a fundamental problem in modern scientific thought. There is much about Alan Turing’s centenary that speaks not to 1912, but to 2012.


Turing's theory of chemical morphogenesis validated 60 years after his death

This illustration is a montage of photographs, taken from Figure 4 of 'Testing Turing's Theory of Morphogenesis in Chemical Cells,' depicting the evolution of physical morphogenesis from an initial homogeneous state (upper left, same volume and color) through a chemically heterogeneous state (center, same volume but different colors) and into a chemo-physical heterogeneous state (lower right, different volumes and colors). This cellular differentiation takes place exactly as Alan Turing predicted it would in his 1952 paper, 'The Chemical Basis of Morphogenesis.' Credit: Seth Fraden

Alan Turing's accomplishments in computer science are well known, but lesser known is his impact on biology and chemistry. In his only paper on biology, Turing proposed a theory of morphogenesis, or how identical copies of a single cell differentiate, for example, into an organism with arms and legs, a head and tail.

Now, 60 years after Turing's death, researchers from Brandeis University and the University of Pittsburgh have provided the first experimental evidence that validates Turing's theory in cell-like structures.

The team published their findings in the Proceedings of the National Academy of Sciences on Monday, March 10.

Turing was the first to offer an explanation of morphogenesis through chemistry. He theorized that identical biological cells differentiate, change shape and create patterns through a process called intercellular reaction-diffusion. In this model, a system of chemicals react with each other and diffuse across a space—say between cells in an embryo. These chemical reactions need an inhibitory agent, to suppress the reaction, and an excitatory agent, to activate the reaction. This chemical reaction, diffused across an embryo, will create patterns of chemically different cells.

Turing predicted six different patterns could arise from this model.

At Brandeis, Seth Fraden, professor of physics, and Irv Epstein, the Henry F. Fischbach Professor of Chemistry, created rings of synthetic, cell-like structures with activating and inhibiting chemical reactions to test Turing's model. They observed all six patterns plus a seventh unpredicted by Turing.

Just as Turing theorized, the once identical structures—now chemically different—also began to change in size due to osmosis.

This research could impact not only the study of biological development, and how similar patterns form in nature, but materials science as well. Turing's model could help grow soft robots with certain patterns and shapes.

More than anything, this research further validates Turing as a pioneer across many different fields, Fraden says. After cracking the German Enigma code, expediting the Allies' victory in World War II, Turing was shamed and ostracized by the British government. He was convicted of homosexuality—a crime in 1950s England—and sentenced to chemical castration. He published "The Chemical Basis of Morphogenesis" shortly after his trial and killed himself less than two years later, in June 1954. He was 41 years old.


Watch the video: Philip Ball discusses Alan Turings research on morphogenesis (October 2022).