Statue of Alan Turing made of layers of stacked slate, shown from the chest up.

Alan Turing, pictured in a slate sculpture by Stephen Kettle, is known as a computer scientist and codebreaker, but also made forays into mathematical biology.Credit: Steve Meddle/REX/Shutterstock

Researchers in China have developed a filter that removes salt from water up to three times as fast as conventional filters. The membrane has a unique nanostructure of tubular strands, inspired by the mathematical-biology work of codebreaker Alan Turing.

The filter is the most finely constructed example of the mathematician’s ‘Turing structures’ yet, and their first practical application, say researchers. “These 3D structures are quite extraordinary,” says Patrick Müller, a systems biologist at the Friedrich Miescher Laboratory in Tübingen, Germany. The filter’s tubular strands, just tens of nanometres in diameter, would be impossible to produce by other methods, such as 3D printing, he says. The work is published on 3 May in Science1.

British mathematician Alan Turing is best known for his codebreaking exploits for the UK government during the Second World War, and as the father of computer science and artificial intelligence. But he also produced a seminal work2 in the then-nascent field of mathematical biology in 1952, just two years before his death.

In it, he proposed a mathematical model for a process by which the cells of an embryo might begin to form structures — limbs, bones and organs. In this process, two substances continuously react with each other, but diffuse through their container at very different rates. The quicker-diffusing reactant — called the inhibitor — pushes back against the slower one, called the activator, effectively corralling the resulting product into a pattern of spots or stripes. (The terminology was coined by biologists Hans Meinhardt and Alfred Gierer, who independently formulated an equivalent theory in 1972.)

Spotting patterns

Whether such a process actually occurs at a cellular level has been hotly debated, says Müller. But this reaction-diffusion behaviour has been invoked to explain patterns in nature and society, including zebra stripes, sand ripples and the movements of financial markets.

So far, however, attempts to synthesize such structures in the lab have mostly been limited to 2D patterns.

A team led by material scientist Lin Zhang of Zhejiang University in Hangzhou, China, set out to create a 3D Turing structure out of a polyamid, a material similar to nylon, formed by a reaction between the chemicals piperazine and trimesoyl chloride. In a conventional process, trimesoyl chloride diffuses faster than piperazine, but the difference is not big enough to produce a Turing structure. Zhang’s trick was to add polyvinyl alcohol to the piperazine, further lowering its diffusion rate and allowing it to act as the activator to the trimesoyl chloride’s inhibitor.

The result is a rough, porous mesh with a nanostructure resembling a Turing pattern that can be seen under an electron microscope. The team was able to produce variants showing both dots and tubes — the two types of self-organizing structure predicted by Turing’s model.

Black and white scanning electron micrographs of the Turing-type membranes: dots on the left and tubes on the right.

Dot-based and tube-based Turing-type membranes, seen under a scanning electron microscope.Credit: Z. Tan et al./Science

The researchers were elated to produce the Turing structures, says Zhang. But they were more surprised when they found that their membranes functioned as efficient water filters — surpassing conventional nylon-like filters in some respects.

The filter’s tubular structure gives it a larger surface area compared to conventional filters, which increases the flow of water through the membrane, says Ho Bum Park, a membrane scientist at Hanyang University in Seoul. It’s an improvement on conventional membrane structures, which resemble a series of ridges and valleys, he says. “It’s a really smart approach.”

In tests performed by Zhang’s group, one pass through the tubular Turing filter reduced the table-salt content of a slightly saline solution by half. It also filtered out other salts: magnesium chloride by more than 90%; and magnesium sulfate, or Epsom salt, by more than 99%. The authors say that 1 square metre of filter can process up to 125 litres of water per hour while being pumped at a relatively low pressure of around 5 times atmospheric pressure. This is as much as three times as fast as typical commercial filters, Zhang says. The Turing filter could be used for purifying brackish water and industrial wastewater, says Zhang.

Other barriers

Although the membrane is effective at removing some impurities, Park says that its relatively low effectiveness eliminating table salt could make it impractical for desalinating seawater. Zhang says could be used to pretreat seawater in desalination plants, with the table salt removed via conventional methods, such as reverse osmosis.

Müller says that if the technique can be generalized, such tubular structures could also have applications in regenerative medicine — for instance, producing artificial veins or bones. “And once you know how to make tubules, maybe you can arrange these things into higher-order structures — maybe even organs,” he says. “Now that would be the dream application.”

But Müller also notes that because of the uncertainty in predicting whether such structures will form, they could be difficult to reproduce in other materials.

Even if that proves to be the case, the membrane is a tribute to the impact of Turing’s 1952 paper, says Zhang. “It’s a part of his legacy.”