Abstract
In self-organized critical (SOC) systems avalanche size distributions follow power-laws. Power-laws have also been observed for neural activity, and so it has been proposed that SOC underlies brain organization as well. Surprisingly, for spiking activity in vivo, evidence for SOC is still lacking. Therefore, we analyzed highly parallel spike recordings from awake rats and monkeys, anesthetized cats, and also local field potentials from humans. We compared these to spiking activity from two established critical models: the Bak-Tang-Wiesenfeld model, and a stochastic branching model. We found fundamental differences between the neural and the model activity. These differences could be overcome for both models through a combination of three modifications: (1) subsampling, (2) increasing the input to the model (this way eliminating the separation of time scales, which is fundamental to SOC and its avalanche definition), and (3) making the model slightly sub-critical. The match between the neural activity and the modified models held not only for the classical avalanche size distributions and estimated branching parameters, but also for two novel measures (mean avalanche size, and frequency of single spikes), and for the dependence of all these measures on the temporal bin size. Our results suggest that neural activity in vivo shows a mélange of avalanches, and not temporally separated ones, and that their global activity propagation can be approximated by the principle that one spike on average triggers a little less than one spike in the next step. This implies that neural activity does not reflect a SOC state but a slightly sub-critical regime without a separation of time scales. Potential advantages of this regime may be faster information processing, and a safety margin from super-criticality, which has been linked to epilepsy.
Highlights
This implies that neural activity does not reflect a self-organized critical (SOC) state but a slightly sub-critical regime without a separation of time scales. Potential advantages of this regime may be faster information processing, and a safety margin from super-criticality, which has been linked to epilepsy
To understand which network dynamics between driven critical and Poissonian accounted best for the in vivo spike avalanches, we identified those measures in the model which depended most sensitively on α under subsampling: α had a prominent effect on the avalanche size distribution f(s), in particular how f(s) depended on the bin size
Our analysis of in vivo data indicated that the mammalian brain is not SOC because in vivo spiking activity differed fundamentally from activity expected for SOC
Summary
Avalanches, earthquakes, and forest fires are all cascades of activity in otherwise quiescent systems (Gutenberg and Richter, 1944; Bak et al, 1987; Drossel and Schwabl, 1992; Frette et al, 1996; Measures, variables, and abbreviations: α, connection strength or synaptic strength; β, scaling exponent (DFA); σ , branching parameter; σ ∗, estimated branching parameter; τ , critical exponent of the avalanche size distribution; bs, bin size; DFA, detrended fluctuation analysis; f(s), avalanche size distribution; f (s = 1, bs), frequency of avalanches of size s = 1 and their dependence on the bin size; h, rate of input spikes, called drive (Hz); , mean avalanche size; , average inter event interval; = 1/R; N, number of sampled (model) neurons; r, rate per unit (Hz); R, population rate (Hz); STS, separation of time scales. The size s of an avalanche is the number of units activated during a cascade, and interestingly, the distribution f(s) of avalanche sizes in the systems mentioned above precisely follows a power law: f (s) ∼ s−τ (1). Critical exponents determine the macroscopic behavior of a system, and indicate the system’s universality class (Wilson, 1975).
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