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The Critically Tuned Cortex
Neuron
Previews The Critically Tuned Cortex John M. Beggs1,* 1Indiana University Department of Physics, 727 East 3rd Street, Bloomington, IN 47405-7105, USA *Correspondence: [email protected] https://doi.org/10.1016/j.neuron.2019.10.039
The criticality hypothesis predicts that cortex operates near a critical point for optimum information processing. In this issue of Neuron, Ma et al. (2019) find evidence consistent with a mechanism that tunes cortex to criticality, even in the face of a strong perturbation over several days. For over 20 years, evidence has steadily accumulated to suggest that the cortex operates near a critical point where activity is poised in a narrow region between damping and amplification. At this critical point, activity in one neuron on average leads to activity in only one other neuron. By contrast, activity in the damped, or subcritical, phase quickly dies out. And activity in the amplified, or supercritical, phase quickly expands. One of the reasons this research has sparked interest is because being critical is thought to be tightly linked to optimal information processing (Cocchi et al., 2017). For example, computational simulations predicted that dynamic range would be maximal at the critical point (Kinouchi and Copelli, 2006). Physiological studies in vitro prompted by this work demonstrated that this was indeed the case (Shew et al., 2009). Since then, in vivo experiments with whisker stimulation in rats have confirmed that dynamic range is maximized at the critical point (Gautam et al., 2015). Other computational work has predicted that information storage and computational power also would be maximized at the critical point. Overall, this has produced a consistent picture that having a critical cortex can have benefits. So how can one know, experimentally, if the cortex is operating near the critical point? Perhaps the simplest thing to measure is the branching ratio, which is just the average number of neurons activated by one active neuron. As stated above, this ratio should be one at the critical point, less than one in the subcritical phase, and greater than one in the supercritical phase (Figure 1A). Recent advancements now allow the branching ratio to be measured with great accuracy, even if only one or a few neu-
rons are sampled (Wilting and Priesemann, 2018). Another indicator of criticality can be found in the statistics of neuronal avalanches. Here, avalanche size can be defined as the number of spikes across an electrode array during a period of continuous activity that is bracketed by periods of silence. Avalanche duration can be given by the number of consecutive time bins during which there is activity. When the distributions of avalanche sizes or avalanche durations are plotted on a log-log scale, they should produce straight lines, indicating power laws (Beggs and Plenz, 2003). This strongly suggests, but does not prove, that the system is critical. To really show criticality, it is important to demonstrate that the slopes of these power laws are related to each other by a simple equation called an exponent relation (Friedman et al., 2012). Even the most ardent skeptics of criticality admit that an exponent relation is a convincing sign that a system is operating near the critical point (Touboul and Destexhe, 2017). Using these tools, various groups all over the world have looked for signatures of criticality in diverse systems. To date, there is evidence suggesting that humans, macaques, rats, turtles, and even zebrafish operate near the critical point. Yet many important questions remain. If being near this narrow critical point is beneficial for information processing, one would expect the brain to have mechanisms for maintaining criticality, just as the body regulates blood pressure, heart rate, and temperature within a range for healthy operation. Is there any evidence for such tuning toward the critical point? If so, what are the mechanisms? In this issue of Neuron, Ma et al. (2019) report their results after pursuing
these questions. They placed 16-channel microwire arrays in both left and right primary visual cortices of rats, recording spiking neuronal ensembles day and night for about 200 h. Using the measures described above, they confirmed that neuronal activity showed signatures of criticality. Next, they sutured one eye shut, causing the contralateral visual cortex to be deprived of visual inputs for several days. As expected, firing rates in the deprived cortex significantly declined after about 24 h and rose back to pre-suture levels about 60 h later. These results have been previously reported and are understood through the well-established framework of firing-rate homeostasis (Hengen et al., 2013). What had not been seen before, though, was what happened to the measures of criticality. They showed a departure from criticality immediately after suture and recovery to criticality about 48 h later (Figure 1B). Two features are noteworthy about these findings. First, they show evidence, for the first time, that is consistent with some homeostatic mechanism working to restore the cortex to criticality after a large perturbation lasting several days. Second, they show that this mechanism, whatever it is, does not follow the same time course as firingrate homeostasis observed from the extracellular electrodes. Recall that the departure from criticality was immediate, 24 h before firing rates showed a significant drop, and that recovery to criticality occurred more than 30 h before firing rates were restored. This naturally prompted another question: if firing rate homeostasis is not driving the restoration to criticality, then what is? Here, Ma and colleagues undertook a computational modeling study to
Neuron 104, November 20, 2019 ª 2019 Elsevier Inc. 623
Neuron
Previews
seek answers. Their model was more broadly accepted and A populated with excitatory and seen as relevant for cortical sub-critical m<1 inhibitory neurons and confunction. tained three known mechanisms for self-organization in REFERENCES m=1 critical cortical circuits: spike-timing Beggs, J.M., and Plenz, D. (2003). dependent plasticity, firing-rate Neuronal avalanches in neocortical cirhomeostasis, and synaptic cuits. J. Neurosci. 23, 11167–11177. scaling. After a very broad super-critical m > 1 Cocchi, L., Gollo, L.L., Zalesky, A., and parameter search including Breakspear, M. (2017). Criticality in the over 400 models, they found brain: A synthesis of neurobiology, models and cognition. Prog. Neurobiol. that only a small fraction of 158, 132–152. parameter combinations reproB Friedman, N., Ito, S., Brinkman, B.A., duced the data. Interestingly, Shimono, M., DeVille, R.E., Dahmen, these successful models all K.A., Beggs, J.M., and Butler, T.C. pointed to the connectivity and (2012). Universal critical dynamics in high resolution neuronal plasticity of inhibitory neurons avalanche data. Phys. Rev. Lett. 108, as the most plausible candidate 208102. for maintaining criticality. Gautam, S.H., Hoang, T.T., Like most good research, McClanahan, K., Grady, S.K., and this work both answers old Shew, W.L. (2015). Maximizing sensory firing rate dynamic range by tuning the cortical questions and raises new state to criticality. PLoS Comput. Biol. ones. Future studies will need 11, e1004576. to record from more neurons Hengen, K.B., Lambo, M.E., Van (the microwire arrays captured branching ratio (m) Hooser, S.D., Katz, D.B., and activity from 4–16 neurons per Turrigiano, G.G. (2013). Firing rate homeostasis in visual cortex of freely cortex), so that substantial days behaving rodents. Neuron 80, numbers of both excitatory 335–342. and inhibitory neurons can be Figure 1. Homeostasis of Criticality Kinouchi, O., and Copelli, M. (2006). identified by spike waveform (A) Three possible phases of activity. Top, activity is subcritical, where Optimal dynamical range of excitable shapes. It will be interesting one spike in a neuron leads to, on average, less than one spike in another networks at criticality. Nat. Phys. 2, 348–351. neuron. Here, the branching ratio is less than one (m < 1). Middle, activity to see if the change in inhibiis critically balanced, where one spike in a neuron usually leads to one tory firing rates precedes that Ma, Z., Turrigiano, G.G., Wessel, R., spike in another neuron (m = 1). Bottom, activity is supercritical, where of the excitatory firing rates, and Hengen, K.B. (2019). Cortical one spike in a neuron leads to many spikes in other neurons (m > 1). Circuit Dynamics Are as predicted by the successful (B) Schematic of recovery to criticality. Top, time course of firing rate in Homeostatically Tuned to Criticality visual cortex before and after eye suture. Black arrow indicates drop models. In Vivo. Neuron 104, this issue, and white arrow indicates recovery. Bottom, time course of branching 655–664. It also will be crucial to ratio, m, which measures closeness to criticality. Note that m drops check if the purported homeoimmediately after suture and recovers before firing rate. Shew, W.L., Yang, H., Petermann, T., static mechanism can restore Roy, R., and Plenz, D. (2009). cortex to criticality after a Neuronal avalanches imply maximum positive perturbation (for example, impossible to test visual performance dynamic range in cortical networks at criticality. an increase in excitatory input to while the eye is sutured, but perhaps J. Neurosci. 29, 15595–15600. visual cortex); so far only recovery under a positive perturbation one could Touboul, J., and Destexhe, A. (2017). Power-law from a negative perturbation has been test if, say, visual recognition was statistics and universal scaling in the absence of restored at the same time as recovery criticality. Phys. Rev. E 95, 012413. demonstrated. Another issue of interest will be to to criticality. This is exactly the type Wilting, J., and Priesemann, V. (2018). see how the recovery to criticality influ- of experiment that will be needed if Inferring collective dynamical states from widely ences behavioral performance. It seems the concept of criticality is to become unobserved systems. Nat. Commun. 9, 2325.
624 Neuron 104, November 20, 2019
Previews The Critically Tuned Cortex John M. Beggs1,* 1Indiana University Department of Physics, 727 East 3rd Street, Bloomington, IN 47405-7105, USA *Correspondence: [email protected] https://doi.org/10.1016/j.neuron.2019.10.039
The criticality hypothesis predicts that cortex operates near a critical point for optimum information processing. In this issue of Neuron, Ma et al. (2019) find evidence consistent with a mechanism that tunes cortex to criticality, even in the face of a strong perturbation over several days. For over 20 years, evidence has steadily accumulated to suggest that the cortex operates near a critical point where activity is poised in a narrow region between damping and amplification. At this critical point, activity in one neuron on average leads to activity in only one other neuron. By contrast, activity in the damped, or subcritical, phase quickly dies out. And activity in the amplified, or supercritical, phase quickly expands. One of the reasons this research has sparked interest is because being critical is thought to be tightly linked to optimal information processing (Cocchi et al., 2017). For example, computational simulations predicted that dynamic range would be maximal at the critical point (Kinouchi and Copelli, 2006). Physiological studies in vitro prompted by this work demonstrated that this was indeed the case (Shew et al., 2009). Since then, in vivo experiments with whisker stimulation in rats have confirmed that dynamic range is maximized at the critical point (Gautam et al., 2015). Other computational work has predicted that information storage and computational power also would be maximized at the critical point. Overall, this has produced a consistent picture that having a critical cortex can have benefits. So how can one know, experimentally, if the cortex is operating near the critical point? Perhaps the simplest thing to measure is the branching ratio, which is just the average number of neurons activated by one active neuron. As stated above, this ratio should be one at the critical point, less than one in the subcritical phase, and greater than one in the supercritical phase (Figure 1A). Recent advancements now allow the branching ratio to be measured with great accuracy, even if only one or a few neu-
rons are sampled (Wilting and Priesemann, 2018). Another indicator of criticality can be found in the statistics of neuronal avalanches. Here, avalanche size can be defined as the number of spikes across an electrode array during a period of continuous activity that is bracketed by periods of silence. Avalanche duration can be given by the number of consecutive time bins during which there is activity. When the distributions of avalanche sizes or avalanche durations are plotted on a log-log scale, they should produce straight lines, indicating power laws (Beggs and Plenz, 2003). This strongly suggests, but does not prove, that the system is critical. To really show criticality, it is important to demonstrate that the slopes of these power laws are related to each other by a simple equation called an exponent relation (Friedman et al., 2012). Even the most ardent skeptics of criticality admit that an exponent relation is a convincing sign that a system is operating near the critical point (Touboul and Destexhe, 2017). Using these tools, various groups all over the world have looked for signatures of criticality in diverse systems. To date, there is evidence suggesting that humans, macaques, rats, turtles, and even zebrafish operate near the critical point. Yet many important questions remain. If being near this narrow critical point is beneficial for information processing, one would expect the brain to have mechanisms for maintaining criticality, just as the body regulates blood pressure, heart rate, and temperature within a range for healthy operation. Is there any evidence for such tuning toward the critical point? If so, what are the mechanisms? In this issue of Neuron, Ma et al. (2019) report their results after pursuing
these questions. They placed 16-channel microwire arrays in both left and right primary visual cortices of rats, recording spiking neuronal ensembles day and night for about 200 h. Using the measures described above, they confirmed that neuronal activity showed signatures of criticality. Next, they sutured one eye shut, causing the contralateral visual cortex to be deprived of visual inputs for several days. As expected, firing rates in the deprived cortex significantly declined after about 24 h and rose back to pre-suture levels about 60 h later. These results have been previously reported and are understood through the well-established framework of firing-rate homeostasis (Hengen et al., 2013). What had not been seen before, though, was what happened to the measures of criticality. They showed a departure from criticality immediately after suture and recovery to criticality about 48 h later (Figure 1B). Two features are noteworthy about these findings. First, they show evidence, for the first time, that is consistent with some homeostatic mechanism working to restore the cortex to criticality after a large perturbation lasting several days. Second, they show that this mechanism, whatever it is, does not follow the same time course as firingrate homeostasis observed from the extracellular electrodes. Recall that the departure from criticality was immediate, 24 h before firing rates showed a significant drop, and that recovery to criticality occurred more than 30 h before firing rates were restored. This naturally prompted another question: if firing rate homeostasis is not driving the restoration to criticality, then what is? Here, Ma and colleagues undertook a computational modeling study to
Neuron 104, November 20, 2019 ª 2019 Elsevier Inc. 623
Neuron
Previews
seek answers. Their model was more broadly accepted and A populated with excitatory and seen as relevant for cortical sub-critical m<1 inhibitory neurons and confunction. tained three known mechanisms for self-organization in REFERENCES m=1 critical cortical circuits: spike-timing Beggs, J.M., and Plenz, D. (2003). dependent plasticity, firing-rate Neuronal avalanches in neocortical cirhomeostasis, and synaptic cuits. J. Neurosci. 23, 11167–11177. scaling. After a very broad super-critical m > 1 Cocchi, L., Gollo, L.L., Zalesky, A., and parameter search including Breakspear, M. (2017). Criticality in the over 400 models, they found brain: A synthesis of neurobiology, models and cognition. Prog. Neurobiol. that only a small fraction of 158, 132–152. parameter combinations reproB Friedman, N., Ito, S., Brinkman, B.A., duced the data. Interestingly, Shimono, M., DeVille, R.E., Dahmen, these successful models all K.A., Beggs, J.M., and Butler, T.C. pointed to the connectivity and (2012). Universal critical dynamics in high resolution neuronal plasticity of inhibitory neurons avalanche data. Phys. Rev. Lett. 108, as the most plausible candidate 208102. for maintaining criticality. Gautam, S.H., Hoang, T.T., Like most good research, McClanahan, K., Grady, S.K., and this work both answers old Shew, W.L. (2015). Maximizing sensory firing rate dynamic range by tuning the cortical questions and raises new state to criticality. PLoS Comput. Biol. ones. Future studies will need 11, e1004576. to record from more neurons Hengen, K.B., Lambo, M.E., Van (the microwire arrays captured branching ratio (m) Hooser, S.D., Katz, D.B., and activity from 4–16 neurons per Turrigiano, G.G. (2013). Firing rate homeostasis in visual cortex of freely cortex), so that substantial days behaving rodents. Neuron 80, numbers of both excitatory 335–342. and inhibitory neurons can be Figure 1. Homeostasis of Criticality Kinouchi, O., and Copelli, M. (2006). identified by spike waveform (A) Three possible phases of activity. Top, activity is subcritical, where Optimal dynamical range of excitable shapes. It will be interesting one spike in a neuron leads to, on average, less than one spike in another networks at criticality. Nat. Phys. 2, 348–351. neuron. Here, the branching ratio is less than one (m < 1). Middle, activity to see if the change in inhibiis critically balanced, where one spike in a neuron usually leads to one tory firing rates precedes that Ma, Z., Turrigiano, G.G., Wessel, R., spike in another neuron (m = 1). Bottom, activity is supercritical, where of the excitatory firing rates, and Hengen, K.B. (2019). Cortical one spike in a neuron leads to many spikes in other neurons (m > 1). Circuit Dynamics Are as predicted by the successful (B) Schematic of recovery to criticality. Top, time course of firing rate in Homeostatically Tuned to Criticality visual cortex before and after eye suture. Black arrow indicates drop models. In Vivo. Neuron 104, this issue, and white arrow indicates recovery. Bottom, time course of branching 655–664. It also will be crucial to ratio, m, which measures closeness to criticality. Note that m drops check if the purported homeoimmediately after suture and recovers before firing rate. Shew, W.L., Yang, H., Petermann, T., static mechanism can restore Roy, R., and Plenz, D. (2009). cortex to criticality after a Neuronal avalanches imply maximum positive perturbation (for example, impossible to test visual performance dynamic range in cortical networks at criticality. an increase in excitatory input to while the eye is sutured, but perhaps J. Neurosci. 29, 15595–15600. visual cortex); so far only recovery under a positive perturbation one could Touboul, J., and Destexhe, A. (2017). Power-law from a negative perturbation has been test if, say, visual recognition was statistics and universal scaling in the absence of restored at the same time as recovery criticality. Phys. Rev. E 95, 012413. demonstrated. Another issue of interest will be to to criticality. This is exactly the type Wilting, J., and Priesemann, V. (2018). see how the recovery to criticality influ- of experiment that will be needed if Inferring collective dynamical states from widely ences behavioral performance. It seems the concept of criticality is to become unobserved systems. Nat. Commun. 9, 2325.
624 Neuron 104, November 20, 2019