Abstract
Oscillations are a hallmark of neural population activity in various brain regions with a spectrum covering a wide range of frequencies. Within this spectrum gamma oscillations have received particular attention due to their ubiquitous nature and to their correlation with higher brain functions. Recently, it has been reported that gamma oscillations in the hippocampus of behaving rodents are segregated in two distinct frequency bands: slow and fast. These two gamma rhythms correspond to dfferent 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 gamma rhythms corresponding to collective oscillations of a balanced spiking network. The slow and fast gamma 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 gamma oscillations from slow to fast and vice versa. Furthermore, to make a closer contact with the experimental observations, we consider the modulation of the gamma rhythms induced by a slower (theta) rhythm driving the network dynamics. In this context, depending on the strength of the forcing, we observe phase-amplitude and phase-phase coupling between the fast and slow gamma oscillations and the theta forcing. Phase-phase coupling reveals different theta-phases preferences for the two coexisting gamma rhythms.
Highlights
The emergence of collective oscillations in complex system has been a subject largely studied in recent decades from an experimental as well as from a theoretical point of view
In the network the macroscopic focus turns out to be unstable towards microscopic fluctuations in the firing activity leading to the emergence of collective oscillations (COs) characterized by a frequency corresponding to that of the damped oscillations towards the MF focus
In proximity to the subcritical Hopf bifurcations, the coexistence of two COs with different origins is observable: slow γ oscillations being fluctuation driven. From our analysis it emerges that two ingredients are needed to observe coexisting slow and fast γ COs: the sparseness in the connections and the dynamical balance of the network activity
Summary
The emergence of collective oscillations in complex system has been a subject largely studied in recent decades from an experimental as well as from a theoretical point of view (for a recent review see [1]). The role of the synaptic mechanisms in promoting tonic synchronization in the γ range has been clarified in [17,22], while [23,24,25,26,27] have shown that fast network oscillations with irregular neural discharges can emerge when the neurons are operating in the so-called balanced state. This is a typical cortical state where the balance of excitation and inhibition allows for healthy activity in the brain. Appendix A is devoted to the analysis of coexisting γ oscillations in ErdosRényi networks and Appendix B discusses a general mechanism for the coexistence of noise-driven and tonic oscillations
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