Modeling fast and slow gamma oscillations with interneurons of different subtype

Abstract

Experimental and theoretical studies demonstrate that neuronal gamma oscillations crucially depend on interneurons, but current models do not consider the diversity of known interneuron subtypes. Moreover, in CA1 of the hippocampus, experimental evidence indicates the presence of multiple gamma oscillators, two of which may be coordinated by differing interneuron populations. In this article, we show that models of networks with competing interneuron populations with different postsynaptic effects are sufficient to generate, within CA1, distinct oscillatory regimes. We find that strong mutual inhibition between the interneuron populations permits distinct fast and slow gamma states, whereas weak mutual inhibition generates mixed gamma states. We develop idealized firing rate models to illuminate dynamic properties of these competitive gamma networks, and reinforce these concepts with basic spiking models. The models make several explicit predictions about gamma oscillators in CA1. Specifically, interneurons of different subtype phase-lock to different gamma states, and one population of interneurons is silenced and the other active during fast and slow gamma events. Finally, mutual inhibition between interneuron populations is necessary to generate distinct gamma states. Previous experimental studies indicate that fast and slow gamma oscillations reflect different information processing modes, although it is unclear whether these rhythms are intrinsic or imposed. The models outlined demonstrate that basic architectures can locally generate these oscillations, as well as capture other features of fast and slow gamma, including theta-phase preference and spontaneous transitions between gamma states. These models may extend to describe general dynamics in networks with diverse interneuron populations. The oscillatory coordination of neural signals is crucial to healthy brain function. We have developed an idealized neuronal model that generates distinct fast and slow gamma oscillations, a known feature of the rodent hippocampus. Our work provides a mechanism of this phenomenon, as well as a theoretical framework for future experiments concerning hippocampal gamma. It moreover offers a tractable model of competitive gamma oscillations that is generalizable across the nervous system.

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

“…These two ingredients usually characterize real brain networks, where our prediction that slow (fast) γ oscillations are associated with more (less) irregular neuronal dynamics can be experimentally tested, e.g., by measuring the coefficient of variation associated with these two states. Furthermore, previous theoretical analysis of γ oscillations based on two interacting Wilson-Cowan rate models with different synaptic times revealed only the possible coexistence of two stable limit cycles, both corresponding to tonic collective firing, i.e., mean-driven COs [54].…”

“…Furthermore, there is experimental evidence that γ rhythms can be generated locally in vitro in the CA1, as well as in the CA3 and mEC, due to optogenetic stimulations [39,48,49] or pharmacological manipulations, but at lower γ frequencies with respect to optogenetics [50][51][52][53]. A recent theoretical work has analyzed the emergence of γ oscillations in a neural circuit composed of two populations of interneurons with fast and slow synaptic timescales [54]. Based on the results of this idealized rate model and on the analysis of experimental data sets for the CA1, the authors showed that multiple γ bands can arise locally without being the reflection of feedforward inputs.…”

Dynamics of a large system of spiking neurons with synaptic delay

“…Then, to investigate the existence of a fully synchronized state, we can drop the index j in Eq. (12). Note that, in the absence of coupling, Eq.…”

Firing rate equations require a spike synchrony mechanism to correctly describe fast oscillations in inhibitory networks

“…where R represents the mean firing rate in the population, S is the synaptic activation, and the time constants τ m and τ d are the neuronal and synaptic time constants respectively [39,43]…”