Death and rebirth of neural activity in sparse inhibitory networks

Abstract

In this paper, we clarify the mechanisms underlying a general phenomenon present in pulse-coupled heterogeneous inhibitory networks: inhibition can induce not only suppression of the neural activity, as expected, but it can also promote neural reactivation. In particular, for globally coupled systems, the number of firing neurons monotonically reduces upon increasing the strength of inhibition (neurons' death). However, the random pruning of the connections is able to reverse the action of inhibition, i.e. in a sparse network a sufficiently strong synaptic strength can surprisingly promote, rather than depress, the activity of the neurons (neurons' rebirth). Thus the number of firing neurons reveals a minimum at some intermediate synaptic strength. We show that this minimum signals a transition from a regime dominated by the neurons with higher firing activity to a phase where all neurons are effectively sub-threshold and their irregular firing is driven by current fluctuations. We explain the origin of the transition by deriving an analytic mean field formulation of the problem able to provide the fraction of active neurons as well as the first two moments of their firing statistics. The introduction of a synaptic time scale does not modify the main aspects of the reported phenomenon. However, for sufficiently slow synapses the transition becomes dramatic, the system passes from a perfectly regular evolution to an irregular bursting dynamics. In this latter regime the model provides predictions consistent with experimental findings for a specific class of neurons, namely the medium spiny neurons in the striatum.

19 pages, 10 figures, submitted to NJP

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Cited by in corpus (12)

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• Coexistence of fast and slow gamma oscillations in one population of inhibitory spiking neurons
• Coherent oscillations in balanced neural networks driven by endogenous fluctuations
• Collective irregular dynamics in balanced networks of leaky integrate-and-fire neurons
• Exact firing time statistics of neurons driven by discrete inhibitory noise
• Noise-induced Extreme Events in Hodgkin-Huxley Neural Networks
• Neural Activity of Heterogeneous Inhibitory Spiking Networks with Delay
• Fourier analysis of a delayed Rulkov neuron network
• Synaptic shot-noise triggers fast and slow global oscillations in balanced neural networks
• Discontinuous transition to chaos in a canonical random neural network
• Dynamics and computation in mixed networks containing neurons that accelerate towards spiking
• Less is different: why sparse networks with inhibition differ from complete graphs