Woodrow L. Shew

Neuronal avalanches imply maximum dynamic range in cortical networks at criticality.

Spontaneous neuronal activity is a ubiquitous feature of cortex. Its spatiotemporal organization reflects past input and modulates future network output. Here we study whether a particular type of spontaneous activity is generated by a network that is optimized for input processing. Neuronal avalanches are a type of spontaneous activity observed in superficial cortical layers in vitro and in vivo with statistical properties expected from a network operating at “criticality.” Theory predicts that criticality and, therefore, neuronal avalanches are optimal for input processing, but until now, this has not been tested in experiments. Here, we use cortex slice cultures grown on planar microelectrode arrays to demonstrate that cortical networks that generate neuronal avalanches benefit from a maximized dynamic range, i.e., the ability to respond to the greatest range of stimuli. By changing the ratio of excitation and inhibition in the cultures, we derive a network tuning curve for stimulus processing as a function of distance from criticality in agreement with predictions from our simulations. Our findings suggest that in the cortex, (1) balanced excitation and inhibition establishes criticality, which maximizes the range of inputs that can be processed, and (2) spontaneous activity and input processing are unified in the context of critical phenomena.

Information Capacity and Transmission Are Maximized in Balanced Cortical Networks with Neuronal Avalanches

The repertoire of neural activity patterns that a cortical network can produce constrains the ability of the network to transfer and process information. Here, we measured activity patterns obtained from multisite local field potential recordings in cortex cultures, urethane-anesthetized rats, and awake macaque monkeys. First, we quantified the information capacity of the pattern repertoire of ongoing and stimulus-evoked activity using Shannon entropy. Next, we quantified the efficacy of information transmission between stimulus and response using mutual information. By systematically changing the ratio of excitation/inhibition (E/I) in vitro and in a network model, we discovered that both information capacity and information transmission are maximized at a particular intermediate E/I, at which ongoing activity emerges as neuronal avalanches. Next, we used our in vitro and model results to correctly predict in vivo information capacity and interactions between neuronal groups during ongoing activity. Close agreement between our experiments and model suggest that neuronal avalanches and peak information capacity arise because of criticality and are general properties of cortical networks with balanced E/I.

The Functional Benefits of Criticality in the Cortex

Rapidly growing empirical evidence supports the hypothesis that the cortex operates near criticality. Although the confirmation of this hypothesis would mark a significant advance in fundamental understanding of cortical physiology, a natural question arises: What functional benefits are endowed to cortical circuits that operate at criticality? In this review, we first describe an introductory-level thought experiment to provide the reader with an intuitive understanding of criticality. Second, we discuss some practical approaches for investigating criticality. Finally, we review quantitative evidence that three functional properties of the cortex are optimized at criticality: 1) dynamic range, 2) information transmission, and 3) information capacity. We focus on recently reported experimental evidence and briefly discuss the theory and history of these ideas.

Maximal Variability of Phase Synchrony in Cortical Networks with Neuronal Avalanches

Ongoing interactions among cortical neurons often manifest as network-level synchrony. Understanding the spatiotemporal dynamics of such spontaneous synchrony is important because it may (1) influence network response to input, (2) shape activity-dependent microcircuit structure, and (3) reveal fundamental network properties, such as an imbalance of excitation (E) and inhibition (I). Here we delineate the spatiotemporal character of spontaneous synchrony in rat cortex slice cultures and a computational model over a range of different E–I conditions including disfacilitated (antagonized AMPA, NMDA receptors), unperturbed, and disinhibited (antagonized GABAA receptors). Local field potential was recorded with multielectrode arrays during spontaneous burst activity. Synchrony among neuronal groups was quantified based on phase-locking among recording sites. As network excitability was increased from low to high, we discovered three phenomena at an intermediate excitability level: (1) onset of synchrony, (2) maximized variability of synchrony, and (3) neuronal avalanches. Our computational model predicted that these three features occur when the network operates near a unique balanced E–I condition called “criticality.” These results were invariant to changes in the measurement spatial extent, spatial resolution, and frequency bands. Our findings indicate that moderate average synchrony, which is required to avoid pathology, occurs over a limited range of E–I conditions and emerges together with maximally variable synchrony. If variable synchrony is detrimental to cortical function, this is a cost paid for moderate average synchrony. However, if variable synchrony is beneficial, then by operating near criticality the cortex may doubly benefit from moderate mean and maximized variability of synchrony.

Predicting criticality and dynamic range in complex networks: effects of topology.

The collective dynamics of a network of coupled excitable systems in response to an external stimulus depends on the topology of the connections in the network. Here we develop a general theoretical approach to study the effects of network topology on dynamic range, which quantifies the range of stimulus intensities resulting in distinguishable network responses. We find that the largest eigenvalue of the weighted network adjacency matrix governs the network dynamic range. When the largest eigenvalue is exactly one, the system is in a critical state and its dynamic range is maximized. Further, we examine higher order behavior of the steady state system, which predicts that networks with more homogeneous degree distributions should have higher dynamic range. Our analysis, confirmed by numerical simulations, generalizes previous studies in terms of the largest eigenvalue of the adjacency matrix.

Voltage Imaging of Waking Mouse Cortex Reveals Emergence of Critical Neuronal Dynamics

Complex cognitive processes require neuronal activity to be coordinated across multiple scales, ranging from local microcircuits to cortex-wide networks. However, multiscale cortical dynamics are not well understood because few experimental approaches have provided sufficient support for hypotheses involving multiscale interactions. To address these limitations, we used, in experiments involving mice, genetically encoded voltage indicator imaging, which measures cortex-wide electrical activity at high spatiotemporal resolution. Here we show that, as mice recovered from anesthesia, scale-invariant spatiotemporal patterns of neuronal activity gradually emerge. We show for the first time that this scale-invariant activity spans four orders of magnitude in awake mice. In contrast, we found that the cortical dynamics of anesthetized mice were not scale invariant. Our results bridge empirical evidence from disparate scales and support theoretical predictions that the awake cortex operates in a dynamical regime known as criticality. The criticality hypothesis predicts that small-scale cortical dynamics are governed by the same principles as those governing larger-scale dynamics. Importantly, these scale-invariant principles also optimize certain aspects of information processing. Our results suggest that during the emergence from anesthesia, criticality arises as information processing demands increase. We expect that, as measurement tools advance toward larger scales and greater resolution, the multiscale framework offered by criticality will continue to provide quantitative predictions and insight on how neurons, microcircuits, and large-scale networks are dynamically coordinated in the brain.

Lagrangian temperature, velocity and local heat flux measurement in Rayleigh-Benard convection

We have developed a small, neutrally buoyant, wireless temperature sensor. Using a camera for optical tracking, we obtain simultaneous measurements of position and temperature of the sensor as it is carried along by the flow in Rayleigh-Bénard convection, at Ra approximately 10;{10}. We report on statistics of temperature, velocity, and heat transport in turbulent thermal convection. The motion of the sensor particle exhibits dynamics close to that of Lagrangian tracers in hydrodynamic turbulence. We also quantify heat transport in plumes, revealing self-similarity and extreme variations from plume to plume.

Force measurements on rising bubbles

The dynamics of millimetre-sized air bubbles rising through still water are investigated using ultrasound velocimetry combined with high-speed video. From measurements of speed and three-dimensional trajectories we calculate time-resolved precise drag and lift forces on the bubble, which give rise to planar zigzag and three-dimensional spiralling motion. Temporal correlations of forces and the oscillatory bubble motions, particularly the lift force, emphasize the importance of the wake vortices found in previous studies.

Maximizing Sensory Dynamic Range by Tuning the Cortical State to Criticality.

Modulation of interactions among neurons can manifest as dramatic changes in the state of population dynamics in cerebral cortex. How such transitions in cortical state impact the information processing performed by cortical circuits is not clear. Here we performed experiments and computational modeling to determine how somatosensory dynamic range depends on cortical state. We used microelectrode arrays to record ongoing and whisker stimulus-evoked population spiking activity in somatosensory cortex of urethane anesthetized rats. We observed a continuum of different cortical states; at one extreme population activity exhibited small scale variability and was weakly correlated, the other extreme had large scale fluctuations and strong correlations. In experiments, shifts along the continuum often occurred naturally, without direct manipulation. In addition, in both the experiment and the model we directly tuned the cortical state by manipulating inhibitory synaptic interactions. Our principal finding was that somatosensory dynamic range was maximized in a specific cortical state, called criticality, near the tipping point midway between the ends of the continuum. The optimal cortical state was uniquely characterized by scale-free ongoing population dynamics and moderate correlations, in line with theoretical predictions about criticality. However, to reproduce our experimental findings, we found that existing theory required modifications which account for activity-dependent depression. In conclusion, our experiments indicate that in vivo sensory dynamic range is maximized near criticality and our model revealed an unanticipated role for activity-dependent depression in this basic principle of cortical function.

Cascades and Cognitive State: Focused Attention Incurs Subcritical Dynamics

The analysis of neuronal avalanches supports the hypothesis that the human cortex operates with critical neural dynamics. Here, we investigate the relationship between cascades of activity in electroencephalogram data, cognitive state, and reaction time in humans using a multimodal approach. We recruited 18 healthy volunteers for the acquisition of simultaneous electroencephalogram and functional magnetic resonance imaging during both rest and during a visuomotor cognitive task. We compared distributions of electroencephalogram-derived cascades to reference power laws for task and rest conditions. We then explored the large-scale spatial correspondence of these cascades in the simultaneously acquired functional magnetic resonance imaging data. Furthermore, we investigated whether individual variability in reaction times is associated with the amount of deviation from power law form. We found that while resting state cascades are associated with approximate power law form, the task state is associated with subcritical dynamics. Furthermore, we found that electroencephalogram cascades are related to blood oxygen level-dependent activation, predominantly in sensorimotor brain regions. Finally, we found that decreased reaction times during the task condition are associated with increased proximity to power law form of cascade distributions. These findings suggest that the resting state is associated with near-critical dynamics, in which a high dynamic range and a large repertoire of brain states may be advantageous. In contrast, a focused cognitive task induces subcritical dynamics, which is associated with a lower dynamic range, which in turn may reduce elements of interference affecting task performance.