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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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