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DAVIDE MARENDUZZO watches as the synchronised swimmers rhythmically precess around the edges of the pool. He’s in charge here; he founded this troop and directs their every move. He’ll have them practising like this as long as he likes.

Even though he’s a hard taskmaster, the swimmers aren’t complaining – but then bacteria rarely do. For that’s what Marenduzzo is playing with, and it’s no swimming gala they are competing at. All that training is in aid of a quest to uncover new laws of physics.

Marenduzzo is one of a number of scientists seeking laws that govern fluids teeming with living things. It might be sperm cells on their way to an egg, a fleet of bacteria off to stir up trouble in your guts or a flock of birds heading for their wintering grounds. The idea that these disparate types of flowing life could obey universal laws of nature seems almost untenable. Yet Marenduzzo and others are uncovering some of the first hints that they might.

Turning those hints into a fully fledged theory won’t be easy, but the reward would be amazing. Technologies like self-pumping fluids could be possible and doctors might find they can understand, predict and maybe control the flow of cells – providing a powerful novel approach to medicine.

When it comes to understanding the flow of fluids like air or water, our footing is reasonably solid. The equations of fluid dynamics can predict the flow of gases and liquids, at least until they become turbulent. Measure a few basic parameters such as pressure, viscosity and flow rate, and we can predict how oil will flow along a pipeline or ketchup will ooze from its bottle. These laws are dependable: any time you take off in an aeroplane, you can be sure the crafted flow of air around the wings will keep you aloft.

All that is true only as long as the fluid is made from inanimate molecules – add in something alive and the ordinary equations go out the window. The living thing and the fluid each affect the flow of the other, with the overall result impossible to predict. “You get this incredibly complicated turbulent flow, driven by the movement of the living things,” says , a mathematician at the University of York, UK.

The heart of the problem is energy. When the molecules in a liquid absorb energy, they move faster until a predictable point at which they change phase. That means they alter the way they behave entirely, like when water boils at 100°C. But a hallmark of life is that it exchanges energy with its environment in a directed, variable fashion. The energy might be used to move around, but it might equally be stored or put into power metabolism, among other things.

No surprise, then, that finding a neat set of formulae to explain the flow of all sorts of organisms was long considered off limits. That only began to change about 15 years ago when , now at the Indian Institute of Science in Bangalore, began to think about materials that are the tiniest step away from being inanimate. Imagine, for example, something that has no senses or metabolism, but can use energy to propel itself. Work out rules for these so-called non-equilibrium systems, thought Ramaswamy, and we would at least have a start.

Ramaswamy is an expert on liquid crystals – materials used in some display screens – which can flow like a liquid but only in restricted ways. So he wondered if it would be possible to tweak the established equations we have for describing liquid crystal flow for the simplest possible non-equilibrium systems. He and his then PhD student Aditi Simha had a go. The equations they came up with predicted that as the concentration of the particles in non-equilibrium systems increased, they would start to .

By 2007, those predictions had aroused interest from experimentalists who joined Ramaswamy to put them to the test. They placed thousands of copper rods, each the size of a grain of rice, into a vibrating container and took photographs every 15 seconds. The vibrations imparted a little energy to each rod, enabling it to move around. The rods lay flat, because the container was less high than they were long. At low densities, the rods moved around randomly as expected. But at higher densities, the rods began to align into flowing clusters that were jammed together in some places and more sparse in others (see photo, below). The rods moved in an organised manner without the need for any controller. “We showed that motile but non-sentient things can produce flocking characteristics,” says Ramaswamy.

“Add something living to a liquid and fluid dynamics is out the window”

The whole thing was reminiscent of a phase change: at a certain, predictable density, the copper rods changed their behaviour fundamentally and began to flock almost like birds. It was the first sign that predicting aspects of how living things flow might be possible. Of course, copper rods aren’t that interesting in themselves – which is why Ramaswamy wanted to see if the rules applied to something closer to life.

He decided to investigate inside connective tissue cells called fibroblasts. A curious fact about them is that their nucleus slowly rotates, although we didn’t know how or why. Ramaswamy and Simha conjectured that protein filaments in the cell, driven by molecular motors, might be moving together and whipping the cell’s cytoplasm into a whirlpool that the nucleus rides. It’s a system that’s a step up in complexity from the copper rods.

The duo and their colleagues tested their whirlpool idea using a chemical to suppress the activity of the protein filaments As they added more chemicals, the rotation of the nucleus drastically slowed and became less smooth. That proved the filaments were driving the flow, and the speed and pattern of the rotation fitted the same tweaked liquid crystal equations that had worked for the rods.

By now, Ramaswamy had started something. More researchers began pitching in, trying to predict how various biochemical bits and bobs flowed. Some started to call the field “active matter”, reflecting the fact that the components didn’t just respond passively to energy but used it in directed ways. But the real goal was to develop laws that would apply to whole living things.

Graduate to that league, and the active parts of the fluid become really unpredictable. To get started, we needed to break the problem down and first understand how one living thing influences the fluid flow around it. Take Chlamydomonas reinhardtii, a microscopic green alga. This single-celled critter has two tentacle-like flagella that it uses to swim with a breaststroke motion. But it’s a wonder it gets anywhere at all. “For things this tiny, their world is dominated by viscous forces. For them, water feels like honey does to us,” says , a mathematician at the University of York.

Recent studies have shown in fine detail how the algae overcome the viscosity by twisting their bodies as they swim. Armed with that knowledge, Pushkin wanted to look at how the algae affect the way the fluid flows around them. He and his team added thousands of microscopic polystyrene beads to a tank of the cells and then took photographs 500 times a second. If the fluid were inanimate, you would expect the beads to be randomly buffeted by the water molecules, a process called diffusion. Pushkin expected that the movement of the algae might make the beads spread out a bit faster than that – perhaps 10 times faster.

In the zone

When the results came in, the beads actually dispersed about 500 times faster than diffusion would allow. Pushkin thought the experiment must be faulty, so he reran it several times. He realised that although most of beads followed loop-like patterns, surfing the currents created by the flagella, about one in five was caught in a dead zone in front of the swimming cells and . “It is quite a rare occurrence,” says Pushkin. “But the effect it has is enormous.”

That dead zone might prove to have been evolutionarily important. The flagella-breaststroke technique is common in algae, perhaps because having morsels of food trapped in the dead zone makes it easier for the cells to eat.

Pushkin’s work is also edging us towards equations for describing how the algae affect the fluid. Taking the equations that describe diffusion, Pushkin added a term to describe the dead-spot effect and produced a formula that could predict the patterns of fluid flow around the cell.

That equation is a far cry from a fully fledged description of active matter. Still, we’re already beginning to see how these sorts of things could be handy in real life.

That much is apparent just down the corridor from Pushkin’s lab, where Gadêlha is studying sperm. We know that the little swimmers swish their tails 20 times a second to move themselves along, but again it is a mystery how they get anywhere, because the fluid feels so thick to them. Gadêlha has been documenting the sperm movements with greater precision than ever before and feeding the information into a computer to . He plans to use those models to improve the way we assess fertility.

Male fertility is normally measured by counting sperm and assessing their swimming ability by monitoring the path their head follows. But using that method, “it’s really hard to determine whether someone is going to have trouble or not”, says Gadêlha. His model would instead identify the sperm that are best at powering through the fluid, which he thinks will be more accurate.

However, if we want laws that explain the whole shebang – fluid and multiple cells at once – the maths Gadêlha and Pushkin are working on isn’t enough. It only describes the effects of one cell on its surrounding fluid. In reality, cells often move in swarms, and it’s their collective motion that affects the overall flow. That’s why is watching his synchronised swimmers.

He began with an experiment reminiscent of Ramaswamy’s jiggling copper rods. In 2011, Marenduzzo and his colleague , both at the University of Edinburgh, UK, showed that when they increased the concentration of a soup of E. coli beyond a certain threshold, the bacteria suddenly began to cluster. Once again, it was a bit like a phase change. “Once some bacteria slow down, they start to accumulate, which leads to more bacteria slowing down and accumulating,” says Marenduzzo. Curiously, the clusters always .

“How they work is still uncertain, but these are self-pumping fluids”

This got Marenduzzo and others wondering if, once we have understood these flows, we could put them to work. One way to get started is to capitalise on the fact that E. coli instinctively avoid light. Marenduzzo did some computer simulations that suggested it would be possible to use light beams to herd the bacteria into small areas, whereupon they would become concentrated and start to swirl.

In an unpublished experiment, at the Sapienza University of Rome has made this real. He took E. coli that have been genetically modified to respond to particular wavelengths of light and herded them into pockets on a custom-built, microscopic Ferris wheel, which rotates as they push.

Roberto Di Leonardo at the Sapienza University of Rome has designed motors driven by bacteria. This prototype version is driven by particles that use hydrogen peroxide as a fuel to power themselves along. Credit: Roberto Di Leonardo

Arrays of these rotors might one day be tools in medicine. Di Leonardo imagines capsules equipped with arrays of these motors, some to propel them through the bloodstream and others to pump out a payload of drugs when they find biomolecular cues signalling disease.

That is a while off, but the motors could soon be used in microfluidic chips. These tiny devices are etched with even tinier channels. Water flows very neatly when confined in these channels, meaning several chemical reactions can be done one after another in a minuscule space. Such chips are used as simple kits for checking water quality or diagnosing disease. “But currently we have to find ways of pumping fluid around the chip,” says Di Leonardo. He reckons the bacterial pumps might be the perfect solution, because they can be engineered to self-regulate, adjusting the pressure they pump at for different tasks.

Despite these advances, those hunting the laws of living flows still have a long way to go. It’s not clear whether any of the equations so far developed could apply to multicellular life.

But the rules of active matter don’t have to be used to describe natural things – there is also a world of synthetic active matter to be explored.

Marenduzzo and his colleagues have a research programme to design new classes of . The idea is to create materials that will flow in response to stimuli in programmed ways, for example, repairing themselves by backfilling after a fracture.

It’s early days, but the potential was illustrated in a recent breakthrough from the lab of at Brandeis University in Waltham, Massachusetts. His team had previously combined fibre-like biomolecules called microtubules, a protein called kinesin that walks along them and a fuel molecule. The resulting material united natural components in an unnatural way and flowed by itself in intricate whorls.

In 2012, Zvonimir Dogic created a protein goo that could flow on its own. He has now shown that, when added to water, the goo creates a self-pumping liquid (see main story). Credit: Zvonimir Dogic

A few months ago, Dogic showed the same material can be used to drive water through a microscopic pipe. He doped water with 0.1 per cent of the mixture and injected it into doughnut-shaped tubes. In tubes with a rectangular cross section, the motion was random, but in roughly square tubes, the . By cutting microscopic notches in the tube, the researchers could also control the direction of the flow, which was about as rapid as typical microfluidic devices and persisted for at least a metre. “We still need to pin down the theory,” says Dogic. “But essentially we’ve invented self-pumping fluids.”

This article appeared in print under the headline “Find the flow”