An E-I Firing Rate Model for Gamma Oscillations

Abstract

Firing rate models for describing the mean-field activities of neuronal ensembles can be used effectively to study network function and dynamics, including synchronization and rhythmicity of excitatory-inhibitory populations. However, traditional Wilson-Cowan-like models, being amenable to mathematical analysis, are found unable to capture some dynamics such as Interneuronal Network Gamma oscillations (ING) although use of an explicit delay can help. We resolve this issue by introducing a mean-voltage variable (v) that considers the subthreshold integration of inputs and works as an effective delay in the negative feedback loop between firing rate (r) and synaptic gating of inhibition (s). Here we describe a three-variable r-s-v firing rate model for I-I networks, which is biophysically interpretable and capable of generating INGlike oscillations. Linear stability analysis, numerical branch-tracking and simulations show that the rate model captures many of the common features of spiking network models for ING. We also propose an alternative r-u-s model for ING which considers an implicit delay by a presynaptic variable u. Furthermore, we extend the framework to E-I networks. With our sixvariable r-s-v model, we describe for the first time in firing rate models the transition from Pyramidal-Interneuronal Network Gamma (PING) to ING by increasing the external drive to the inhibitory population without adjusting synaptic weights. Having PING and ING available in a single network, without invoking synaptic blockers, is plausible and natural for explaining the emergence and transition of two different types of gamma oscillations.

Rodents’ visual gamma as a biomarker of pathological neural conditions

“…A recent computational study (Lu & Rinzel, 2023) indeed detailed how the same network can transition from PING to ING by increasing the external drive to the inhibitory population without adjusting synaptic weights. Gamma rhythmogenesis has also been further complicated by the different GABAergic interneuron types in the neocortex (Campagnola et al, 2022).…”