Ortiz promptly identified one of the knottier problems with the hypothesis: It’s very difficult to maintain a perfect tipping point in a messy biological system like the brain. The puzzle compelled him to join forces with Beggs to investigate further.
Ortiz’s criticism has beleaguered the theory ever since the late Danish physicist Per Bak proposed it in 1992. Bak suggested that the brain exhibits “self-organized criticality,” tuning to its critical point automatically. Its exquisitely ordered complexity and thinking ability arise spontaneously, he contended, from the disordered electrical activity of neurons.
Bak’s canonical example of a self-organized critical system is a simple sandpile. If you drop individual grains of sand on top of a sandpile one by one, each grain has a chance of causing an avalanche. Bak and colleagues showed that those avalanches will follow a “power law,” with smaller avalanches occurring proportionally more frequently than larger ones. So if there are 100 small avalanches in which 10 grains slide down the side of the sandpile during a given period, there will be 10 larger avalanches involving 100 grains in the same period, and just one large avalanche involving 1,000 grains. When a huge avalanche collapses the whole pile, the base widens, and the sand begins to pile up again until it returns to its critical point, where, again, avalanches of any size may occur. The sandpile is incredibly complex, with millions or billions of tiny elements, yet it maintains an overall stability.
The brain’s tens of billions of neurons form a highly complex, interconnected network. Bak hypothesized that, like a sandpile, the network balances at its critical point, with electrical activity following a power law. So when a neuron fires, this can trigger an “avalanche” of firing by connected neurons, and smaller avalanches occur more frequently than larger ones. In hundreds of papers over the past three decades advancing the idea, researchers have argued that operating at criticality would optimize the brain’s performance by maximizing information transfer and processing. The mystery is how such a noisy system as the brain can maintain such a finely tuned critical state, since another feature of criticality is that the system is most sensitive to any input that could cause it to alter its activity.
For Ortiz, as he listened to Beggs talk about the theory in a physics department conference room at Indiana, “it was obviously a fine-tuning problem,” he said. Criticality “is not something in nature you would find very easily. As soon as there is any perturbation that moves the system away from that fine-tuning, it’s not going to be critical.” Another strike against the critical brain hypothesis is that the textbook definition of criticality in statistical physics requires a system of infinite size. “So the fact that the brain is finite means true criticality is off the table,” said Beggs, who is a professor of biophysics at Indiana.
Yet compelling, if inconclusive, experimental evidence suggests that the brain’s neuronal activity does exhibit hallmarks of criticality. This has led several scientists to propose variations on Bak’s original theory. Ortiz and Beggs, along with graduate students Rashid Williams-García (now a postdoc at the University of Pittsburgh) and Mark Moore, have argued that perhaps the brain inhabits a “quasicritical state.” That is, rather than sitting at a precise critical point, it migrates around a broader but well-defined region, “a volume in phase space where the system can adapt to work efficiently and optimally,” Ortiz said.
Viola Priesemann of the Max Planck Institute for Dynamics and Self-Organization in Göttingen, Germany, has proposed a similar concept. She reasons that the brain could operate in the so-called “subcritical” regime, just below the tipping point. In both scenarios, the brain operates near the critical point, rather than being precariously poised there. This arrangement offers much-needed stability while still enabling highly efficient information transfer and processing.
The new proposals please one of the field’s earliest experimental pioneers, Dietmar Plenz of the National Institute of Mental Health, who has found evidence of power laws in the neuron firing patterns of monkeys. Whereas 15 years ago, criticality was not yet deemed a serious possibility, “now I think criticality is on the map,” Plenz said. “I think we are seeing that there’s a regime of cortical dynamics that is close to criticality. This is huge progress, because now we are not talking anymore about whether or not the brain is critical, but about in what specific aspect is it critical.”
Not Quite Critical
Scientists often use the same model for criticality as they do for nuclear chain reactions. In nuclear fission, a fission event gives off two particles, and they each give off two more, and so on, yielding a branching ratio (the expected number of descendants from a single event) of two. Such a system goes “supercritical” to produce an atomic bomb. Meanwhile in a “subcritical” system, the branching ratio is less than one, and so the chain reaction fizzles out. In a critical system, the branching ratio will be exactly one, setting off a sustained nuclear reaction capable (for example) of running a power plant indefinitely. Similarly, if the brain is truly critical, there will be a power-law distribution of avalanche sizes, but one neuron should, on average, activate one other neuron.