Self-sustained activity in balanced networks with low firing-rate

The brain can display self-sustained activity (SSA), which is the persistent firing of neurons in the absence of external stimuli. This spontaneous activity shows low neuronal firing rates and is observed in diverse in vitro and in vivo situations. In this work, we study the influence of excitatory/inhibitory balance, connection density, and network size on the self-sustained activity of a neuronal network model. We build a random network of adaptive exponential integrate-and-fire (AdEx) neuron models connected through inhibitory and excitatory chemical synapses. The AdEx model mimics several behaviours of biological neurons, such as spike initiation, adaptation, and bursting patterns. In an excitation/inhibition balanced state, if the mean connection degree (K) is fixed, the firing rate does not depend on the network size (N), whereas for fixed N, the firing rate decreases when K increases. However, for large K, SSA states can appear only for large N. We show the existence of SSA states with similar behaviours to those observed in experimental recordings, such as very low and irregular neuronal firing rates, and spike-train power spectra with slow fluctuations, only for balanced networks of large size.