Complex systems operate in ways that are hard to predict from their parts alone, because their behavior is influenced by how their parts interact. As the famous saying goes, more is not just more; “more is different.” Brain researchers are increasingly turning to the idea that complex systems support many of the brain’s functions, from spatial navigation to memory function. Likewise, they are beginning to realize that many types of brain dysfunction reflect a complex system gone awry, such as when the epileptic brain enters a seizure.
Creating a seizure in a computer simulation is trivial; it’s what generally happens when you incorporate excitatory feedback loops with no inhibitory force to counter them. It’s vastly more challenging, however, to create a model that approaches the complexity of the brain that isn’t seizing. Something akin to this delicate balance is thought to stabilize a number of brain systems, including those that maintain sanity (versus psychosis) and mood stability (versus mania or depression). Indeed, that the brain somehow exists in an exquisite equilibrium the vast majority of the time seems like nothing short of a miracle — given that it relies on numerous giant amplifying feedback loops, offering many avenues to disruption.
Beyond the brain, many other complex systems live in a similarly delicate balance. Ecosystems can break into toxic blooms. Snow packs can break into avalanches. Weather can break into hurricanes and tornadoes. These systems, however, are not just complex but chaotic, meaning that they are subject to the butterfly effect, by which even tiny perturbations can sometimes push the system out of whack. (The phenomenon gets its name from the way that Edward Lorenz first described it: as if a butterfly flapping its wings over Brazil could cause a tornado in Texas.)
The butterfly effect explains why weather forecasts are much more accurate for the next few days than for the next few weeks. We can measure current conditions with only a certain degree of accuracy, and those small errors in our measurements of what’s happening now turn into big errors in our model predictions later.
For the same reason, chaotic systems are exceedingly hard to control, which naturally leads to a question: If the brain is chaotic like the weather — if seizures, depression and psychosis are the analogs of hurricanes — is there any hope of bringing it back to a healthy state via a brain-based intervention, such as a drug or brain stimulation? Or are our efforts to control the brain’s complex systems doomed from the outset? In this essay, I contemplate that question. I also asked 14 experts in complex systems to chime in.
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reakthroughs in weather research date back to the early 1900s, when researchers began to formulate the types of weather forecasting models that we use today. Often forgotten is that the explicit goal of early weather research was not just to predict the weather but also control it — both to head off disasters and to weaponize it. Indeed, weather control was the explicit goal behind “the Meteorology Project,” organized by Princeton University mathematician John von Neumann and industrial researcher Vladimir Zworykin, the latter of whom contributed to developing the television. As the Second World War began to ramp down in the mid-1940s, the pair approached government officials in Washington, D.C., to request funding for their two-step plan to create a new computing infrastructure to predict the weather (the outcome of which is reflected in today’s computers as the von Neumann architecture) and to control the weather using those predictions. As described in their proposal, “Only with exact scientific weather knowledge will effective weather control be possible.”
Over the next few decades, other researchers around the globe sought to control the weather. In the United States, a government effort called Project Cirrus, for example, focused on disabling hurricanes. In 1947, the team attempted to dissipate a hurricane, conveniently forecast to remain at sea, by dropping 80 kilograms of dry ice on it from a B-17 bomber. The intent was to disrupt the hurricane’s internal structure, but instead the worst possible thing happened: The hurricane’s trajectory shifted 130 degrees, and it landed in Georgia. Project Stormfury resuscitated the idea in 1962 and lasted a few decades but never achieved any success. In short, 75 years after the Meteorology Project, we’ve achieved von Neumann and Zworykin’s first goal, forecasting, but weather control hasn’t really panned out. Today, weather control happens in subtle ways, such as when China precipitated rain during the 2008 Olympics to ensure that it did not happen at an inopportune time. But because of chaos, we still cannot influence the paths of hurricanes in any predictable way.
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The chaos in our brain is a feature we can control and not a maladaptive ‘bug’ we need to quell.
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Kanaka Rajan
Kanaka Rajan
For brain researchers, the history of weather control should give us pause. In our own attempts at controlling the brain, how likely is it that we’ll face the same difficulties that foiled weather researchers? The answer depends greatly on what type of thing the brain is, and that’s still a bit difficult to say. One theory suggests that the brain exists on the knife edge between order and disorder, in a state called “criticality.”
This critical brain hypothesis builds on work from physics focused on how phase transitions happen, such as when water changes to steam at a high temperature or carbon changes to diamond at high pressure. In these cases, the large-scale collective property of the system changes when a single parameter, such as temperature or pressure, crosses a critical point. But in other cases, this is not quite the right way to think about it — control derives not from an external parameter such as temperature, but rather from within the system itself. Grains of sand dropped onto a sandpile, for example, elicit avalanches that are just large enough to keep it at the boundary between piling and flattening. Birds in a flock move collectively, but individuals can affect the group’s behavior, which is crucial for responding to predators. The system organizes itself in a way that maintains it at that critical boundary of a phase transition.
The critical brain hypothesis accounts for a similar boundary. The gist is that if the brain is too disordered, it can’t do anything very useful, akin to being sedated. If it’s too ordered, it also can’t do anything, akin to being in a seizure. But at the edge of order and disorder, it’s optimally positioned to do all the many things it needs to do. The idea follows from studies of criticality in artificial recurrent neural networks, which perform optimally when positioned at the critical boundary. In such networks, the strength of recurrent interactions between model neurons controls where on the spectrum the network sits. If neurons are too interconnected, a small input will trigger every neuron to fire; if neurons aren’t connected enough, even a giant input will peter out before it makes its way through the network. But if neurons are connected by just the right amount, an input can and will be processed in a sensible way by a subset of model neurons.
Maintaining the brain at the critical boundary between order and disorder requires some type of exquisite regulation. In artificial neural networks, the balance of excitatory and inhibitory connections maintains criticality — the same may be true in the brain. Along time scales of hours and days, plasticity and other forms of homeostatic regulation, which refers to neurons’ capacity to regulate their own excitability relative to total network activity, could help maintain this balance. Along time scales of seconds to minutes, firing-rate adaptation could play this role. Conversely, anything that upsets these mechanisms, including mutated ion channels, broken plasticity mechanisms or aberrant neurotransmission, could throw the brain into a perpetually or partially disordered state.
Although it is a compelling idea, it has been very difficult to test hypotheses of brain criticality. Ideally, we would do things like study how the brain evolves after it is reset to similar initial conditions, and that’s just not possible. Instead, most attempts seek to identify the types of signatures typical of systems in a critical state. Phenomena akin to avalanches have been observed in neurons’ spiking patterns, for example: bursts of activity in cell cultures that occur with a power law distribution, where small bursts are much more likely than large ones. Another measure relies on the reverberation expected to be triggered in a system, which creates long-range correlations across time. To date, the evidence supports the critical brain hypothesis, but it’s far from definitive. We just don’t yet know.
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hould the brain prove to be chaotic — or close to the critical boundary — what are the implications? Does it mean all hope of control, and therefore treatment, is lost, as is the case for the weather? Or is that the wrong way to think about it? We might consider a few possibilities.
First, some haven’t given up on the idea that chaotic systems can in fact be controlled with targeted perturbations. Researchers have figured out ways to control chaotic systems, in theory, via approaches such as the continuous injection of a signal, based on model predictions, as well as perturbations among attractor states. (Attractor states are patterns of activity that a network relaxes into, a bit like a ball rolling into a valley.) But for such an approach to be helpful, researchers would first have to create very extremely precise models of the brain. They would also have to develop ways to control the human brain with much more precision than is typically available today. Under the assumption that this approach would take the form of manipulating either genetic expression or brain activity, it would likely require the control of many genes or stimulation sites.
Second, insofar as disordered states such as seizures are signs of the brain entering subcritical or supercritical states, the brain appears to have internal mechanisms for restoring normal function. Under severe conditions, seizures can continue for hours — illustrating that the brain is physically capable of it — but typically last just minutes. Likewise, people often enter depressive and psychotic episodes and then exit them days or weeks later. Unfortunately, we don’t really understand the mechanisms by which the brain self-organizes and renormalizes. A better understanding of those mechanisms could lead to better treatments or preventions, akin to the fences used to prevent avalanches.
Of course, the answer may be the one we wish were not true: It may be that in some cases, we simply cannot control the brain — at least not in the ways we would need to treat some types of dysfunction, such as epilepsy, psychosis and depression.
What do researchers predict?
It seems plausible that important functions of the brain emerge from interactions among many neurons. The “more is different” idea then leads to many ways in which neural activity could be unpredictable or uncontrollable. In an ordinary magnet, we can push on the important collective modes of the system just by applying a magnetic field. But even in older, relatively simple models of neural networks, the analog of a magnetic field would be a complicated combination of inputs to each cell in the network, exciting some of the cells and inhibiting others. We don’t really have experimental tools that allow us to do this. So, even before we get to more controversial ideas such as criticality or chaos, we have serious problems.
Controlling a complex system such as the human brain is a formidable and challenging task. Evolutionary forces have done an extraordinary job of shaping the structure and dynamics of the brain: It self-organizes in response to internal and external perturbations through mechanisms that are still not fully understood. From a statistical physics perspective, unraveling how the brain — as well as other biological systems — is able to self-regulate its behavior while self-correcting for localized dysfunctions might open the door to a plethora of applications for systems biology and systems medicine in general, a perspective that makes the future rather exciting.
My intuition, and it is just an intuition, is that the brain will be controllable (by controllable I mean something like pushing the brain out of an epileptic state). The main reason for that is that it needs to be internally controllable — information from one area needs to be transferred to another, which can be thought of as one brain area controlling the state of another. Such forms of internal control and modulation are a core part of how I imagine brains work. If we could tap into something similar to these internal dials, we have a chance at controlling the brain. Our modes of access will be quite different, however. How to use that access will require a sophisticated understanding of how to influence complex systems, which we currently just don’t have. Moreover, more subtle control, such as correcting just the parts of the dynamics that changed as the result of neurodegeneration, for instance, similar to diverting but not scattering a hurricane, would require a deeper understanding still. The problem itself is not foreign to science — controlling dynamical systems is a rich field of engineering — but it tends to focus on more straightforward engineered systems, not the complex web of interactions among heterogenous units that is something like a brain. This is exactly the kind of challenge that I and many others are going to devote a few decades of our lives to understanding.
The brain differs from the weather in a way that may make it more amenable to control. The brain contains endless self-organizing, self-regulating loops, acting ceaselessly to tune it to a well-functioning state. This self-tuning property is common to all complex biological systems. Think about how your body maintains a nearly constant temperature over a broad range of ambient conditions. Similarly, the brain has mechanisms across all scales — from molecules to large-scale networks — for sensing deviations from the normal and steering itself back to the functional state. Many disease states result from a malfunction in one of the self-tuning mechanisms. Thus, if we could fix the self-tuning mechanism, restoring the production of a missing molecule, for example, this repaired mechanism would almost miraculously do all the hard work of steering the brain toward the functional state. Although this general idea sounds simple, it may be hard to realize in practice because the many self-tuning mechanisms are highly intertwined. The same molecule may be part of several self-tuning loops, and in trying to repair one, we could destroy another. In addition, the internal compensatory mechanisms may make a diseased brain different from a healthy one. For example, when one brain area is lesioned, another area can take over its function. Or an area deprived of inputs necessary to perform its function can take on a new function, such as when a visual area in a blind person responds to sound or touch. Given these kinds of alterations, the same self-tuning loop may produce different outcomes in a healthy versus a diseased brain. Technological advances enable us to interface with the brain with increasing spatial and temporal precision, but the problem of controlling the brain remains far from being solved.
I don’t think the brain is too complex to control to aid in the treatment of neuropathology. There are many examples showing that noninvasive electrical and magnetic perturbations to the human brain can help restore normal function. One area in which there has been particular advance is in the treatment of depression, where regular patterns of stimulation are improving symptoms by “renormalizing” circuit function. Single pulses of brain stimulation combined with electrophysiological recording of the brain’s response are also used to measure the complexity of the response in people in a coma, as a means to predict recovery. But our understanding of how these perturbations directly affect human brain circuits, and if and when they will have lasting effects, is limited. One approach to improving this understanding is by building detailed dynamical models of the biophysical elements that generate electromagnetic activity in cells and circuits, and simulating their response to various patterns of stimulation. With this approach, we can better understand the nature of the brain’s complexity and ultimately use it to our advantage to designe more efficacious stimulation paradigms.
I wouldn’t necessarily despair about unpredictability. The Lorenz system is a famous example of a chaotic attractor, developed as a model for atmospheric convection (to keep with your climate theme.) You can either change the 3D state (x, y, z) of the system or you can change the three quenched parameters (sigma, rho, beta) that govern how it evolves over time. The latter is indirect but much more powerful, even allowing you to eliminate chaos in the system entirely. Though I can’t tell you where the state of a Lorenz system will be far into the future, I can tell you that if you keep its quenched parameters fixed, its state will always lie within a tiny fraction of the total volume of 3D space. I believe this metaphor will hold for the brain: If we can create targeted interventions that speed, slow, amplify or suppress the flow of neural activity through particular brain regions, we can restrict the space of trajectories activity will take through those regions even without controlling said activity directly. This is what I think a lot of neuromodulators and neuropeptides are doing: reshaping the neural substrate to direct the flow of fast patterns of neural excitation and inhibition. Our challenge is that the brain has had millennia of evolution to make sure the right reshaping signals go to the right bits of substrate — we need to understand what it is they are doing there so we can hope to create interventions that mimic them with the same selectivity and specificity as the brain itself.
I think of these problems quite differently. Instead of focusing on the fact that diseased brains or normal brains that are faced with extreme perturbations “crash,” I would like to emphasize that the brain has many cellular and molecular mechanisms that promote stability. Just because it is possible to trigger brain dysfunction shouldn’t lead one to think that all brains are teetering on the edge of dysfunction. Rather, there are multiple sets of cell and circuit parameters that are consistent with “good enough” behavior, and this allows circuits to wander around in parameter space without losing function. And there are numerous and overlapping mechanisms that support cellular and neuronal stability. My lab studies the effects of temperature and other extreme perturbations on the crustacean stomatogastric nervous system. Although all animals will “crash” if you raise the temperature enough, they are resilient to the more than 20 degree Celsius temperature fluctuations that they usually experience. Many mechanisms play a role in this resilience, and likewise, many mechanisms also play roles in the resilience of healthy human brains.
Unlike a hurricane’s dynamics, those of the brain are subject to powerful regulatory mechanisms and are finely honed during development to perform specific functions. These compensatory forces ensure that most brains don’t erupt in seizures, and that relatively normal function can be maintained even in the presence of lesions or genetic mutations. I believe that a deeper understanding of the brain’s intrinsic regulatory mechanisms will be crucial to learning how to provide corrections when neural dynamics enter unhealthy states. Unfortunately, no two brains are alike, and I suspect that such an understanding will need to be tailored to individual brains, and that “precision medicine” approaches will be necessary to recapitulate the large degree of individual variability that accompanies almost every type of brain dysfunction. One hope, however, is that some of the key mechanisms will be best described in a “latent space,” abstracted away from the extraordinary complexity of neural circuits, and that such high-level descriptions will be more amenable to scientific inquiry and to treatments.
The brain’s initial processing, the sensory “shell” that takes in and processes input, may have the most to gain from being poised near criticality.
That gives the system exquisite responsiveness to changes in the external world. Whether that’s architected by the brain or a consequence of the structure of the driving input is up for debate, but the fact remains that signatures of criticality are observed in many sensing systems. Deeper in the brain, I’d expect neural populations to be, if anything, less critical — further from this kind of singularity. (Though, of course, hippocampal regions are the cradle of epileptic foci in humans.) What is clearly true is that the brain functions most of the time, in most organisms, in most individuals. This likely means that it’s not such a knife’s edge. As a theorist, I hope this feature of neural coding winds up being understandable and interpretable, not just a collection of patches that biology implemented over evolution’s punctuated trudge through functional space. Of course, biology doesn’t owe anything to a theorist. But I hope evolution also found some controllable knobs that we can discover.
My guess is that the brain is not as uncontrollable as the weather! In my view, the brain is a complex system that works in a highly distributed, heterarchical manner (i.e., lacking a clear hierarchy). Because it works in an integrated way with the body and environment, brain signals circulate in ways that are extremely hard to predict. But I wouldn’t go as far as viewing it as uncontrollable because of the inextricable link between brain and life. Brain and body systems are self-maintaining and in a continual process of homeostasis, which stabilizes their dynamics to remain within bounds that are compatible with life.
All cognition is dynamic, and the engine that produces cognition — the brain — is a complex dynamical system. Elegant theories based on the physics of large networks of idealized neurons, some of which I am proud to have written myself, have modeled the brain as a chaotic system. (Although, unlike the Lorenz attractor, which is a low-dimensional system described by three variables, neural activity in brains is thought to be more consistent with high-dimensional chaos.) In the face of all this chaotic activity produced internally by neural circuits in the brain, how do we manage to think or behave cogently? It turns out that neural circuits can actively turn down their intrinsically generated chaos when paying attention to even subtle sensory inputs. Interestingly, this mechanism — or phase transition — was theorized first and then verified experimentally through recordings from a number of brain areas. I think that this ability suppress intrinsic chaos is due to how we can think and behave, avoiding both hallucinatory oblivion and reflexive entrainment to our inputs or environment. This is just one of the ways by which the chaos in our brain is a feature we can control and not a maladaptive “bug” we need to quell.
The brain is an enormously complex system, and (like the weather) it may be impossible to exert precise control over it at scale. But is that level of control necessary? Extending the weather analogy a little further, we build houses with a locally controlled environment that keeps the temperature in a comfortable range. Clinically, we have multiple examples of neuromodulation approaches where targeted stimulation doesn’t “control” the brain precisely but still influences brain state enough to reduce tremor, seizure activity or depressive moods. Scientifically, approaches such as optogenetics have produced meaningful insight even in their basic form. Empirically, it seems we can make meaningful clinical and scientific progress without full control of the brain.
Is the brain the sort of system that is predictable or controllable? My answer would be: It depends on what you mean by “prediction” and “control.” There are certainly many examples of a specific perturbation having a predictable effect or outcome, and there has been strong emphasis in neuroscience on characterizing such cause-effect couplings. But the brain is more than that, a growing realization that requires a shift in thinking and perspective. I tend to approach the brain as a complex system consisting of a huge number of interconnected elements or neurons. When those elements become active, their individual states become entangled or mutually dependent, thus creating high-dimensional informational structures that we are just beginning to glimpse and understand. This collective action of many of the brain’s elements results in a continuous flow of activity that underpins cognition and behavior. The system has some level of predictability — consistent topography, patterns of synchrony and dimension reduction, for example. Brains are far from random, and this allows recognizable features to emerge. But, as for all truly complex systems, there’s a limit to prediction and control. For example, predicting specific brain states far in advance, similar to forecasting the weather over a period of weeks or months, is fundamentally impossible, as nonlinearities and chaotic fluctuations quickly take over. For those who want absolute control, this may seem an insurmountable challenge. But I see in it something far more comforting, even liberating. The brain’s complexity opens endless possibilities of creation and reconfiguration of patterns in space and time — and we have no way of predicting when and where they will occur.
As an ecologist and a wannabe neuroscientist, I think this is a super exciting area for dynamical systems thinking. Clearly the genie is out of the bottle with respect to prediction and understanding, and perhaps with regard to control as well: Witness recent results that try to figure out which of many possible brain-stimulating electrodes will cause the right effects in ways that circumvent the need to try them one by one. Here, researchers predicted the effects of targeted brain-area stimulation from resting activity using a nonlinear dynamical causality test (convergent cross-mapping). It’s a great step, and beyond it there’s so much untapped potential.
For instance, being chaotic (and thus nonlinear) means that you can’t really think of the individual parts of a dynamic system as being separate. This is what mathematicians would call “nonseparable,” meaning you can’t formally study one piece independently of others. Flipped around, this interdependence has huge advantages because with nonlinear dynamics and chaos in general, any one part of a dynamic system can have information about all of the other parts. This enables us to recreate a shadow version of the whole system from just one piece if it. In ecology, this has enabled us to predict future states of systems such as salmon populations, even when we don’t have access to measures of all the causal variables. Taking this a step further, because multiple shadow versions are possible, the same information can be represented simultaneously in factorially different ways, which is something one might imagine in how the brain works. I anticipate that this and other dynamical systems approaches will figure prominently in the quest to understand and treat the brain.
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