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Neurons in the intact brain receive a continuous and irregular synaptic bombardment from excitatory and inhibitory pre-synaptic neurons, which determines the firing activity of the stimulated neuron. In order to investigate the influence of inhibitory stimulation on the firing time statistics, we consider Leaky Integrate-and-Fire neurons subject to inhibitory instantaneous post-synaptic potentials. In particular, we report exact results for the firing rate, the coefficient of variation and the spike train spectrum for various synaptic weight distributions. Our results are not limited to stimulations of infinitesimal amplitude, but they apply as well to finite amplitude post-synaptic potentials, thus being able to capture the effect of rare and large spikes. The developed methods are able to reproduce also the average firing properties of heterogeneous neuronal populations., Comment: 20 pages, 8 Figures, submitted to Scientific Reports

Inhibition is a key aspect of neural dynamics playing a fundamental role for the emergence of neural rhythms and the implementation of various information coding strategies. Inhibitory populations are present in several brain structures and the comprehension of their dynamics is strategical for the understanding of neural processing. In this paper, we discuss a general mechanism 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). The introduction of a sparse connectivity in the network is able to reverse the action of inhibition, i.e. a sufficiently strong synaptic strength can surprisingly promote, rather than depress, the activity of the neurons (neurons? rebirth). Specifically, for small synaptic strengths, one observes an asynchronous activity of nearly independent supra-threshold neurons. By increasing the inhibition, a transition occurs towards a regime where the neurons are all effectively sub-threshold and their irregular firing is driven by current fluctuations. We explain this transition from a mean-driven to a fluctuation-driven regime by deriving an analytic mean field approach able to provide the fraction of active neurons together with the first two moments of the firing time distribution. We show that, by varying the synaptic time scale, the mechanism underlying the reported phenomenon remains unchanged. However, for sufficiently slow synapses the effect becomes dramatic. For small synaptic coupling the fraction of active neurons is frozen over long times and their firing activity is perfectly regular. For larger inhibition the active neurons display an irregular bursting behaviour induced by the emergence of correlations in the current fluctuations. In this latter regime the model gives predictions consistent with experimental findings for a specific class of neurons, namely the medium spiny neurons in the striatum.