Dietmar Plenz

Neuronal Avalanches in Neocortical Circuits

Networks of living neurons exhibit diverse patterns of activity, including oscillations, synchrony, and waves. Recent work in physics has shown yet another mode of activity in systems composed of many nonlinear units interacting locally. For example, avalanches, earthquakes, and forest fires all propagate in systems organized into a critical state in which event sizes show no characteristic scale and are described by power laws. We hypothesized that a similar mode of activity with complex emergent properties could exist in networks of cortical neurons. We investigated this issue in mature organotypic cultures and acute slices of rat cortex by recording spontaneous local field potentials continuously using a 60 channel multielectrode array. Here, we show that propagation of spontaneous activity in cortical networks is described by equations that govern avalanches. As predicted by theory for a critical branching process, the propagation obeys a power law with an exponent of -3/2 for event sizes, with a branching parameter close to the critical value of 1. Simulations show that a branching parameter at this value optimizes information transmission in feedforward networks, while preventing runaway network excitation. Our findings suggest that “neuronal avalanches” may be a generic property of cortical networks, and represent a mode of activity that differs profoundly from oscillatory, synchronized, or wave-like network states. In the critical state, the network may satisfy the competing demands of information transmission and network stability.

Neuronal Avalanches Are Diverse and Precise Activity Patterns That Are Stable for Many Hours in Cortical Slice Cultures

A major goal of neuroscience is to elucidate mechanisms of cortical information processing and storage. Previous work from our laboratory (Beggs and Plenz, 2003) revealed that propagation of local field potentials (LFPs) in cortical circuits could be described by the same equations that govern avalanches. Whereas modeling studies suggested that these “neuronal avalanches” were optimal for information transmission, it was not clear what role they could play in information storage. Work from numerous other laboratories has shown that cortical structures can generate reproducible spatiotemporal patterns of activity that could be used as a substrate for memory. Here, we show that although neuronal avalanches lasted only a few milliseconds, their spatiotemporal patterns were also stable and significantly repeatable even many hours later. To investigate these issues, we cultured coronal slices of rat cortex for 4 weeks on 60-channel microelectrode arrays and recorded spontaneous extracellular LFPs continuously for 10 hr. Using correlation-based clustering and a global contrast function, we found that each cortical culture spontaneously produced 4736 ± 2769 (mean ± SD) neuronal avalanches per hour that clustered into 30 ± 14 statistically significant families of spatiotemporal patterns. In 10 hr of recording, over 98% of the mutual information shared by these avalanche patterns were retained. Additionally, jittering analysis revealed that the correlations between avalanches were temporally precise to within ±4 msec. The long-term stability, diversity, and temporal precision of these avalanches indicate that they fulfill many of the requirements expected of a substrate for memory and suggest that they play a central role in both information transmission and storage within cortical networks.

Spontaneous cortical activity in awake monkeys composed of neuronal avalanches

Spontaneous neuronal activity is an important property of the cerebral cortex but its spatiotemporal organization and dynamical framework remain poorly understood. Studies in reduced systems—tissue cultures, acute slices, and anesthetized rats—show that spontaneous activity forms characteristic clusters in space and time, called neuronal avalanches. Modeling studies suggest that networks with this property are poised at a critical state that optimizes input processing, information storage, and transfer, but the relevance of avalanches for fully functional cerebral systems has been controversial. Here we show that ongoing cortical synchronization in awake rhesus monkeys carries the signature of neuronal avalanches. Negative LFP deflections (nLFPs) correlate with neuronal spiking and increase in amplitude with increases in local population spike rate and synchrony. These nLFPs form neuronal avalanches that are scale-invariant in space and time and with respect to the threshold of nLFP detection. This dimension, threshold invariance, describes a fractal organization: smaller nLFPs are embedded in clusters of larger ones without destroying the spatial and temporal scale-invariance of the dynamics. These findings suggest an organization of ongoing cortical synchronization that is scale-invariant in its three fundamental dimensions—time, space, and local neuronal group size. Such scale-invariance has ontogenetic and phylogenetic implications because it allows large increases in network capacity without a fundamental reorganization of the system.

The organizing principles of neuronal avalanches: cell assemblies in the cortex?

Neuronal avalanches are spatiotemporal patterns of neuronal activity that occur spontaneously in superficial layers of the mammalian cortex under various experimental conditions. These patterns reflect fast propagation of local synchrony, display a rich spatiotemporal diversity and recur over several hours. The statistical organization of pattern sizes is invariant to the choice of spatial scale, demonstrating that the functional linking of cortical sites into avalanches occurs on all spatial scales with a fractal organization. These features suggest an underlying network of neuronal interactions that balances diverse representations with predictable recurrence, similar to what has been theorized for cell assembly formation. We propose that avalanches reflect the transient formation of cell assemblies in the cortex and discuss various models that provide mechanistic insights into the underlying dynamics, suggesting that they arise in a critical regime.

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.

When inhibition goes incognito: feedback interaction between spiny projection neurons in striatal function

Theories about basal ganglia function have always been driven by our knowledge about the spiny projection neurons of the striatum. At the core of these theories lies the question of how, precisely, spiny projection neurons process cortical inputs. Most recently, studies demonstrating the role of spiny projection neurons in local synaptic GABA transmission have provided several new avenues for exploring striatal dynamics. They have also suggested new experimental directives for examining the specific ways in which spiny projection neurons both compete and cooperate through their local axon collaterals during cortical input processing.

Powerlaw: a Python package for analysis of heavy-tailed distributions.

Power laws are theoretically interesting probability distributions that are also frequently used to describe empirical data. In recent years, effective statistical methods for fitting power laws have been developed, but appropriate use of these techniques requires significant programming and statistical insight. In order to greatly decrease the barriers to using good statistical methods for fitting power law distributions, we developed the powerlaw Python package. This software package provides easy commands for basic fitting and statistical analysis of distributions. Notably, it also seeks to support a variety of user needs by being exhaustive in the options available to the user. The source code is publicly available and easily extensible.

Neuronal avalanches organize as nested theta- and beta/gamma-oscillations during development of cortical layer 2/3

Maturation of the cerebral cortex involves the spontaneous emergence of distinct patterns of neuronal synchronization, which regulate neuronal differentiation, synapse formation, and serve as a substrate for information processing. The intrinsic activity patterns that characterize the maturation of cortical layer 2/3 are poorly understood. By using microelectrode array recordings in vivo and in vitro, we show that this development is marked by the emergence of nested θ- and β/γ-oscillations that require NMDA- and GABAA-mediated synaptic transmission. The oscillations organized as neuronal avalanches, i.e., they were synchronized across cortical sites forming diverse and millisecond-precise spatiotemporal patterns that distributed in sizes according to a power law with a slope of −1.5. The correspondence between nested oscillations and neuronal avalanches required activation of the dopamine D1 receptor. We suggest that the repetitive formation of neuronal avalanches provides an intrinsic template for the selective linking of external inputs to developing superficial layers.

Fast synaptic transmission between striatal spiny projection neurons.

Striatal inhibition plays an important role in models of cortex-basal ganglia function and is altered in many basal ganglia diseases. The γ-aminobutyric acid ergic spiny projection neuron comprises >95% of striatal neurons, but despite strong anatomical evidence, the electrophysiological properties and functions of their local axon collaterals are unknown. We simultaneously recorded from adjacent spiny projection neurons (<5–10 μm) in whole-cell patch mode and demonstrated a fast synaptic connection between 26/69 pairs in cortex-striatum-substantia nigra organotypic cultures and 5/38 pairs in acute striatal slices. The synapse, which was blocked by γ-aminobutyric acid type A antagonists, displayed a wide range of failure rates, was depolarizing at rest, and reversed above −60 mV. Presynaptic bursts of action potentials were highly correlated with total postsynaptic depolarization at rest. Synaptic transmission was optimized for burst discharge >14 Hz and showed considerable short-term plasticity, including paired-pulse depression at intervals <25 ms, intraburst facilitation, and interburst augmentation. This activity-dependent collateral interaction provides the basis for a new class of basal ganglia models in which striatal neurons cooperate as well as compete during processing of cortical inputs.