Abstract
Avalanches of electrochemical activity in brain networks have been empirically reported to obey scale-invariant behavior --characterized by power-law distributions up to some upper cut-off-- both in vitro and in vivo. Elucidating whether such scaling laws stem from the underlying neural dynamics operating at the edge of a phase transition is a fascinating possibility, as systems poised at criticality have been argued to exhibit a number of important functional advantages. Here we employ a well-known model for neural dynamics with synaptic plasticity, to elucidate an alternative scenario in which neuronal avalanches can coexist, overlapping in time, but still remaining scale-free. Remarkably their scale-invariance does not stem from underlying criticality nor self-organization at the edge of a continuous phase transition. Instead, it emerges from the fact that perturbations to the system exhibit a neutral drift --guided by demographic fluctuations-- with respect to endogenous spontaneous activity. Such a neutral dynamics --similar to the one in neutral theories of population genetics-- implies marginal propagation of activity, characterized by power-law distributed causal avalanches. Importantly, our results underline the importance of considering causal information --on which neuron triggers the firing of which-- to properly estimate the statistics of avalanches of neural activity. We discuss the implications of these findings both in modeling and to elucidate experimental observations, as well as its possible consequences for actual neural dynamics and information processing in actual neural networks.
Highlights
The introduction by Kimura in 1968 of the neutral theory—hypothesizing that most evolutionary change is the result of genetic drift acting on neutral alleles [1]— caused much debate and a revolution in the way population genetics and molecular evolution were understood
We explore the possibility and discuss the potential benefit that empirically observed neural avalanches could be scale-free as a result of an underlying neutral dynamics—i.e., that each single event of activity is indistinguishable from others and can potentially propagate through the network in a marginal way, i.e., without an intrinsic tendency to either expand or contract— alternatively to being self-organized to the edge of a phase transition
Given that critical dynamics emerge at continuous phase transitions, the presence of scale-invariant avalanches within the up state in the absence of any such transition in this model is unusual
Summary
The introduction by Kimura in 1968 of the neutral theory—hypothesizing that most evolutionary change is the result of genetic drift acting on neutral alleles [1]— caused much debate and a revolution in the way population genetics and molecular evolution were understood. The introduction of a novel species within an established population triggers a random cascade of changes, or “avalanche,” which—as a result of the implicit neutrality—does not have an inherent net tendency to either shrink or expand at the expenses of others This marginal-propagation process generates scalefree avalanches, which resemble critical ones even if the system is not necessarily posed at the edge of a phase transition [3,4]. We explore the possibility and discuss the potential benefit that empirically observed neural avalanches could be scale-free as a result of an underlying neutral dynamics—i.e., that each single event of activity is indistinguishable from others and can potentially propagate through the network in a marginal way, i.e., without an intrinsic tendency to either expand or contract— alternatively to being self-organized to the edge of a phase transition. We propose that the diversity encountered for causal avalanches with respect to their size, duration, as well as spatial and temporal realization provides a rich reservoir that the real neural systems could exploit for efficient coding, optimal transmission of information, and, for memory and learning [43]
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