Intrinsically-generated fluctuating activity in excitatory-inhibitory networks

Recurrent networks of non-linear units display a variety of dynamical regimes depending on the structure of their synaptic connectivity. A particularly remarkable phenomenon is the appearance of strongly fluctuating, chaotic activity in networks of deterministic, but randomly connected rate units. How this type of intrinsically generated fluctuations appears in more realistic networks of spiking neurons has been a long standing question. To ease the comparison between rate and spiking networks, recent works investigated the dynamical regimes of randomly-connected rate networks with segregated excitatory and inhibitory populations, and firing rates constrained to be positive. These works derived general dynamical mean field (DMF) equations describing the fluctuating dynamics, but solved these equations only in the case of purely inhibitory networks. Using a simplified excitatory-inhibitory architecture in which DMF equations are more easily tractable, here we show that the presence of excitation qualitatively modifies the fluctuating activity compared to purely inhibitory networks. In presence of excitation, intrinsically generated fluctuations induce a strong increase in mean firing rates, a phenomenon that is much weaker in purely inhibitory networks. Excitation moreover induces two different fluctuating regimes: for moderate overall coupling, recurrent inhibition is sufficient to stabilize fluctuations; for strong coupling, firing rates are stabilized solely by the upper bound imposed on activity, even if inhibition is stronger than excitation. These results extend to more general network architectures, and to rate networks receiving noisy inputs mimicking spiking activity. Finally, we show that signatures of the second dynamical regime appear in networks of integrate-and-fire neurons.Author summary: Electrophysiological recordings from cortical circuits reveal strongly irregular and highly complex temporal patterns of in-vivo neural activity. In the last decades, a large number of theoretical studies have speculated on the possible sources of fluctuations in neural assemblies, pointing out the possibility of self-sustained irregularity, intrinsically generated by network mechanisms. In particular, a seminal study showed that purely deterministic, but randomly connected rate networks intrinsically develop chaotic fluctuations due to the recurrent feedback. In the simple and highly symmetric class of models considered in classical works, the transition from stationary activity to chaos is characterized by the behavior of the auto-correlation function and the critical slowing down of fluctuations. Following up on recent works, here we combine analytical and numerical tools to investigate the macroscopic dynamics generated by more realistic models of excitatory and inhibitory rate units. We show that the presence of excitation leads to a strong signature of the onset of chaos in the first-order statistics of the network activity, and that this effect is highly robust with respect to spiking noise. We moreover find that excitation leads to two different types of fluctuating activity at moderate and strong synaptic coupling, even when inhibition dominates. Finally, we test the appearance of analogous dynamical regimes in networks of integrate-and-fire neurons.