Neuronal avalanches in spontaneous activity in vivo

Abstract

Many complex systems give rise to events that are clustered in space and time, thereby establishing a correlation structure that is governed by power law statistics. In the cortex, such clusters of activity, called "neuronal avalanches," were recently found in local field potentials (LFPs) of spontaneous activity in acute cortex slices, slice cultures, the developing cortex of the anesthetized rat, and premotor and motor cortex of awake monkeys. At present, it is unclear whether neuronal avalanches also exist in the spontaneous LFPs and spike activity in vivo in sensory areas of the mature brain. To address this question, we recorded spontaneous LFPs and extracellular spiking activity with multiple 4 × 4 microelectrode arrays (Michigan Probes) in area 17 of adult cats under anesthesia. A cluster of events was defined as a consecutive sequence of time bins Δt (1-32 ms), each containing at least one LFP event or spike anywhere on the array. LFP cluster sizes consistently distributed according to a power law with a slope largely above -1.5. In two thirds of the corresponding experiments, spike clusters also displayed a power law that displayed a slightly steeper slope of -1.8 and was destroyed by subsampling operations. The power law in spike clusters was accompanied with stronger temporal correlations between spiking activities of neurons that spanned longer time periods compared with spike clusters lacking power law statistics. The results suggest that spontaneous activity of the visual cortex under anesthesia has the properties of neuronal avalanches.

Fig. 1.

Recording of extracellular unit activity and definition of spatiotemporal spike clusters in cat visual cortex. Top: spontaneous spiking activity for 72 neurons shown in the form of a raster plot for the duration of 500 ms (single 4 × 4 Michigan probe inserted in area 17). Bottom: 3 spatiotemporal spike clusters at higher temporal resolution (zoom). In this example, continuous time is discretized into time bins of width Δt = 5 ms. A spike cluster is bracketed by at least 1 bin with no activity (blank bin) and consists of a continuous sequence of bins with at least 1 spike in each (active bins). In this example, all 3 spike clusters have the same lifetime of 10 ms.

Fig. 2.

The organization of spontaneous local field potential (LFP) events into spatiotemporal clusters shows the statistical features of neuronal avalanches. A: the probability distribution of LFP cluster sizes for 6 different bin sizes, Δt. The size is defined as the number of active electrodes in an LFP event cluster. Note the linear decay of the distribution shown in log-log coordinates and the cut-off point of size = 16 electrodes, which is the total number of electrodes of the array. B: dependence of the exponent α on the bin size, Δt, for 7 different arrays with a power law distribution. C: probability distributions of lifetimes plotted in log-log coordinates for 7 different arrays (bin size = 1 ms). D: lifetime distributions of 1 array computed for 6 different bin sizes in log-log coordinates.

Fig. 3.

Spike cluster sizes in vivo show power law statistic similar to that of neuronal avalanches. A: probability to observe a spike cluster of a given size s is plotted in log-log coordinates for 4 different bin sizes Δt. Spike cluster size is calculated as the number of spikes for the duration of the cluster and is shown for values between 2 and 100. B: comparison of quality with which power law and exponential functions fitted cluster size distributions in different recordings. The order of the recordings on the abscissa was organized according to the quality of the exponential fit. Error bars: SD. C: same as in A but calculated for 5 different recordings and only 1 Δt. Four of the recordings are plotted with Δt = 3 ms and 1 with Δt = 9 ms.

Fig. 4.

The slope of the power law. A: change in the slope, α, shown as a function of bin size, Δt, for the 4 arrays with power law statistics in the depicted range of Δt. B: interspike interval (ISI)_array distribution for the recordings shown in Fig. 3A plotted in log-log coordinates (black, left ordinate) and the running average of this distribution, avgΔt, computed as a function of the ISIs (red, right ordinate). The dashed line represents the value of avgΔt (2.3 ms in this case), which was used in the analysis in C. C: distributions of spike cluster sizes calculated at corresponding avgΔt for 5 different arrays. The slopes α for each recording are indicated in the plot.

Fig. 5.

Example recording in which a power law was not detected consistently across different bin sizes. A: spike cluster size distribution shown as a function of bin size. The notation and the analyses are the same as in Fig. 3A. B: ISI_unit distribution for 8 different recordings. C: ISI_array distributions calculated for recordings that exhibited a power law in the cluster size distributions. D: same as in C for datasets without a power law in the cluster size distribution.

Fig. 6.

Lifetime distributions of spike clusters. A: distribution of cluster lifetimes computed for all recordings. Star: the 3 recordings whose size distributions did not follow a power law in the size distribution. B: example lifetime distributions for 1 recording in area 17 calculated for different values of Δt.

Fig. 7.

Examples of cross-correlation (CCH) and auto-correlation histograms (ACH) averaged across all spikes trains or pairs of spike trains recorded from an array and obtained in recordings that either did or did not exhibit a power law in the event size distributions.

Fig. 8.

Subsampling analysis. A: distributions of spikes clusters for a fully sampled dataset and 3 different degrees of subsampling. B: comparison of power law and exponential fit for 4 different sample sizes averaged across all datasets with previously established power law. Each pair of fits was obtained by subsampling 10× the original recordings at the indicated level and at different Δts (4 datasets: 2–8 ms, 1 dataset: 6–16 ms) and averaging the obtained values across all Δts and all recordings in which a power law was detected before. Error bars: SD.