Coexistence of fast and slow gamma oscillations in one population of inhibitory spiking neurons

Oscillations are a hallmark of neural population activity in various brain regions with a spectrum covering a wide range of frequencies. Within this spectrum γ oscillations have received particular attention due to their ubiquitous nature and their correlation with higher brain functions. Recently, it has been reported that γ oscillations in the hippocampus of behaving rodents are segregated in two distinct frequency bands: slow and fast. These two γ rhythms correspond to different states of the network, but their origin has been not yet clarified. Here we show theoretically and numerically that a single inhibitory population can give rise to coexisting slow and fast γ rhythms corresponding to collective oscillations of a balanced spiking network. The slow and fast γ rhythms are generated via two different mechanisms: the fast one being driven by the coordinated tonic neural firing and the slow one by endogenous fluctuations due to irregular neural activity. We show that almost instantaneous stimulations can switch the collective γ oscillations from slow to fast and vice versa. Furthermore, to draw a connection with the experimental observations, we consider the modulation of the γ rhythms induced by a slower (θ) rhythm driving the network dynamics. In this context, depending on the strength of the forcing and the noise amplitude, we observe phase-amplitude and phase-phase coupling between the fast and slow γ oscillations and the θ forcing. Phase-phase coupling reveals on average different θ-phase preferences for the two coexisting γ rhythms joined to a wide cycle-to-cycle variability.