There are signs that all living things sit on the knife-edge of criticality – something that could help them adapt to complex and unpredictable events
WHEN physicists take an interest in the living world, some biologists fear the worst. After all, goes the bad joke, there’s only so much you can gain by modelling a cow as a sphere. But one crucial idea from physics may hold valuable insights into complex biological behaviour in everything from birds to gene networks. There is increasing evidence that many systems we observe in living things are close to what’s called a critical point – they sit on a knife-edge, precariously poised between order and disorder. Odd as it may sound, this strategy could confer a variety of benefits, in particular the flexibility to deal with a complex and unpredictable environment.
Some of the most convincing evidence comes from neuroscience. For a decade now, we have been seeing clues that neurons in the brain sit near a critical point. On one side, they are stable and ready to respond to stimuli. On the other, they fire in an uncontrolled cascade, triggering a seizure. Neuroscientists believe that being poised in between can help explain basic aspects of the brain’s functions.
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Similar behaviour has been spotted in bird flocks, insect swarms and even inside cells. This proximity to “criticality” could help creatures adapt rapidly, says physicist Jim Sethna of Cornell University in Ithaca, New York. “At the critical point, everything is about to go crazy. You get massively more sensitive behaviour.” It is, he says, like having some general-purpose knobs that living things can adjust to cope with change without needing to reconfigure their genomes. According to Manfred Eigen, who won the 1967 Nobel prize for chemistry, critical states might even help to explain how evolution works.
At criticality, the bird flock remains coordinated but responsive to danger (Image: Composite image: Chris Helgren / Reuters, Bruno D’Amicis/NaturePL)
All this raises a profound question. Is the presence of criticality in all these systems just a coincidence, or a sign of a unifying physical law for all life?
The idea that critical states might underlie many processes in the natural world hit the headlines in the 1980s, when Danish physicist Per Bak and his collaborators suggested that a range of natural phenomena display what they called “self-organised criticality”. The archetypal example is a heap of sand. Add more grains to it, and the peak grows until it reaches a critical point at which it suddenly collapses. These avalanches occur spontaneously again and again: the grains in the heap constantly reorganise themselves by collapsing only to return to a critical state.
One defining characteristic of these avalanches is that they are “scale invariant” – they occur at all sizes and the distribution of sizes follows a power law, meaning smaller avalanches occur more frequently than bigger ones, according to a strict ratio. Bak pointed to other natural systems that experience avalanche-like convulsions with a power-law scaling, including mass extinctions, earthquakes, and the spread of forest fires. There were even hints of this behaviour in living systems. Was Bak on to something?
Unfortunately, says William Bialek, a theoretical physicist at Princeton University, this grand theory didn’t deliver when it was applied to biology. Despite claims that self-organised criticality should not only be widespread but beneficial to life, he points out that there has been no strong evidence that either scenario is true.
Now, though, ever-faster computers and low-cost sensors have allowed researchers to collect vast swathes of data and run huge statistical analyses and simulations that would have been impossible a decade ago. And with this, Bialek and his Princeton colleague Thierry Mora have been able to uncover persuasive evidence that criticality does indeed play a role in living creatures.
Rather than self-organised criticality, Mora and Bialek have turned to an older notion: the critical phase transition, in which a system of many interacting components switches suddenly from one state to another. Probably the best known example is the magnetic transition or critical point of iron. At temperatures below the transition, the magnetic poles of all the atoms are aligned. But heated close to the transition, the orientation of these poles fluctuates, creating a shifting patchwork of magnetised domains of different sizes. At the critical point itself, fluctuations are sufficient to totally scramble the ordering: the metal loses its magnetism.
Magnetic alignment below the phase transition occurs because each atom interacts with its neighbours, allowing them to come to a kind of collective decision about their orientation. Phase transitions of this kind occur in all manner of physical systems, from superconductors to polymer mixtures. Why not in living things too?
While Mora and Bialek were developing their ideas, Andrea Cavagna and his team at the Institute for Complex Systems in Rome, Italy, were finding evidence that backed them up. The team fixed three video cameras on top of the city’s , which overlooks a major winter roosting site for starlings. Then they filmed the birds at dusk during their flocking displays and used machine vision software to extract the movements of every bird in 3D – no mean feat given that each flock can have several thousand members.
Video: Neighbourly birds help coordinate a flock
The data allowed Cavagna to figure out the flock’s average speed and direction, as well as how each bird deviated from these at each moment. From this they calculated the correlations between birds: how closely the deviations of any two birds were matched as the distance between pairs increased. The results were surprising. “We found that the correlation was very strong,” Cavagna says. The birds seem to be tuned in to variations in one another’s movements even when they are too far away to see each other. One bird can influence others far away through “neighbour-to-neighbour” interactions, just as fluctuations in the orientation of iron atoms close to the critical point are transmitted through the material.
Beauty of flocking
Analogies between magnetism and flocking in animals are not new, but Cavagna’s study was the first to show that real flocks of birds exhibit magnet-like critical behaviour, says Bialek. Although Cavagna does not know exactly how the starlings achieve this, he suspects it is beneficial to them. If, as it seems, the flock is close to a critical point, the birds avoid two extremes: they are neither in a disordered state where interactions between individuals are ineffective, nor in an ordered one in which interactions are so strong that it is locked into regimented group motion. At criticality, the flock remains coordinated but highly responsive to external disturbances. If any bird spots a predator, the others get wind of it almost immediately and can head for safety. Flocking, says Cavagna, gives the .
“At criticality, the flock remains coordinated but responsive to danger”
Since then, Cavagna and colleagues have switched their attention to midges. These insects form small swarms to mate, and the prevailing view was that swarming midges buzz around independently. Cavagna expected his observations to confirm this, but when his team filmed the insects around Rome’s parks, they concluded that there are . Just like starlings, midges seem to live close to a critical phase transition.
Cavagna’s starlings are one of the largest groups of collectively moving creatures ever analysed, yet this is nothing compared to unpicking the workings of the human brain. Somehow, several billion neurons act together so that we can learn, store memories and sense the world around us. And here too, elaborate experiments have begun to reveal intriguing evidence of criticality.
In 2003, a team at Indiana University in Bloomington used a large array of micro-electrodes to monitor neuron activity in thin slices of the brain cortex of rats. They found that avalanches of electrical activity are scale invariant. Other experiments show these avalanches travel repeatedly along particular chains of neurons over periods of hours. The researchers suspect that avalanches may help us to make and store memories.
Computer simulations seem to confirm this picture. When Bialek and his colleagues created a simple computer model of how individual neurons work and how they are wired up, they found that long-range correlations between the firing of neurons emerged spontaneously. Since their behaviour is linked in this way, the state of each neuron is to some degree “encoded” in the rest of the network, says Bialek. He describes this as a mechanism for error correction and recovery of lost information – perhaps a safeguard against forgetting, he suggests.
Could criticality even play a role in organising behaviour in the brain? Last year a team led by Dante Chialvo from the University of California, Los Angeles, used simulations to show that if large clusters of interconnected neurons operate close to a critical transition, they reproduce “resting state networks”. These patterns of collective activity, seen in brain scans, are associated with functions such as cognition and sensing. So criticality seems to help .
What is so surprising, says Sethna, is that this kind of behaviour can arise not through specialised interactions between cells, but via a fundamental characteristic of any system with many interacting components. Intriguingly, he and his colleagues are seeing signs that this occurs not just between cells but also within them.
Some biological membranes are patchworks in which different types of lipid molecules are segregated like immiscible droplets of oil and water. Insoluble lipid “rafts” have a , rather like the domains of a near-critical magnet, leading Sethna’s team to argue that they are close to a critical phase transition at which the molecules become fully miscible. Could these fluctuations serve a purpose?
Sethna believes so, pointing to an obscure phenomenon originating in the 1980s, when researchers predicted a “” between surfaces immersed in a mix of two immiscible liquids. Analogous to the quantum Casimir force that pulls together two closely spaced metal plates in a vacuum, it arises close to the critical temperature at which the liquids cease to be immiscible and just mingle intimately. Near this critical temperature the liquids form rapidly fluctuating blobs of different sizes. By confining the mixture between two surfaces, the larger fluctuations are squeezed out, and this creates a pressure that pushes the surfaces together. Experiments show that the critical Casimir force can extend over tens of nanometres, and Sethna and others suggest it could play a key role in cell signalling by helping proteins to clump together. Protein clusters that form in the cell membrane are known to be part of “signalling cascades” which transmit information into the cell. When immune cells detect an allergen, for example, receptor proteins cluster in their membrane and trigger the release of histamines. In effect, Sethna says, proteins at the membrane surface may be communicating via size fluctuations in the lipid rafts that they sit in.
This could explain the way some cells behave. For example, cells lacking cholesterol, a lipid, don’t work properly, perhaps because its absence shifts the membrane’s state away from the critical point, disrupting signalling. Ben Machta, a colleague of Bialek’s in the physics department at Princeton, suggests that criticality may also help explain the anaesthetic effects of a broad range of molecules, from noble gases to complex organics. His work suggests that rather than binding to specific receptors in membranes, these anaesthetics alter the lipid membrane’s critical point and thus the functioning of key proteins called ion channels.
Controlling proteins is one thing. Could criticality even guide the growth and development of whole organisms? Bialek and colleagues recently reported critical behaviour in a gene regulatory network – a set of genes with the ability to switch each other on or off. The network they studied has just two genes, and is involved in the spatial patterning of the fruit fly embryo. The team was able to measure how expression of the two genes varied along the embryo’s body. Bialek predicted that if the strength of the interaction between the two genes is close to a critical point, it would show up as four specific patterns in their expression. Sure enough, the measurements revealed these signatures, including correlations in expression in well-separated parts of the embryo, where either one or the other gene was switched off at any given point. Criticality may have evolved this role to maximise the signal-to-noise ratio in the flow of information between genes and proteins, says Bialek. This would allow even small concentrations of proteins to reliably regulate the behaviour of genes: the sensitivity of a critical state means even small control signals can have big effects.
A physical law
Evolution might not just use critical phase transitions – it could actually be one. That is certainly Eigen’s view. He argues that in a system of self-replicating, information-bearing entities – like genes – when the rates of replication and mutation reach certain threshold values. In other words, natural selection is not just something that simply “happens” in reproducing systems, but is a physical law, an .
“Evolution might not just use critical phase transitions – it could actually be one”
Eigen’s theory also suggests an important role for neutral selection – in which mutations may persist even though they convey no adaptive benefit. He shows that such mutations are akin to fluctuations that occur near a critical point. These are essential, he suggests, because they stop natural selection getting stuck in minor valleys of the evolutionary landscape that are not optimal. This fits with a suggestion by evolutionary biologist John Tyler Bonner, at Princeton, that the random fluctuations of neutral evolution could account for the immense variety of forms found in organisms such as diatoms.
Most biologists have yet to embrace these ideas, preferring to focus on unpicking the details rather than searching for overarching principles. “There’s a big difference in culture,” says Sethna. “Biologists tend to be sceptical of anything involving a lot of math.”
Bialek is only too aware of the challenges ahead. To tackle them, he has helped establish an interdisciplinary centre called the at the City University of New York, where he is director. Here physicists can exchange ideas with neuroscientists, ecologists and other biologists. Cavagna became a visiting professor at the centre last year, and is collaborating with Bialek and Mora to refine our understanding of flocking behaviour. This mix of cultures offers the best opportunity to show that, as Sethna puts it, cells, animals and entire ecosystems “do a lot of interesting physics”.
This article appeared in print under the headline “The borders of order”
