Computational Study of Desynchronization of Fast‐Spiking Interneurons at Macroscopic Gamma Oscillations

Abstract

There are typically two distinct types of single‐neuron dynamics, known as Class I and Class II. Fast‐spiking (FS) neurons are a type of Class II neuron, which tend to exhibit periodic spikes in the gamma frequency. Although the population dynamics of Class I neurons are well elucidated with the Fokker‐Planck equation (FPE), much remains unknown about the population dynamics of Class II neurons. This is because the population model of Class II neurons typically leads to a high‐dimensional FPE that is hard to analyze. The modified theta (MT) model is one of the simplest mathematical models of Class I neurons, which possesses voltage‐dependent dynamics and has advantages in the analysis of population dynamics. In this study, we propose two approximation methods to derive a one‐dimensional FPE for FS interneurons using the framework of MT transformation. One method is mean‐field approximation of the variable related to adaptation; the other is semi‐adiabatic approximation of the variable. We confirm the firing characteristics of a single neuron in these approximated models match well to that of the original model proposed by Izhikevich. For the populational dynamics of the gamma oscillation, FPEs with these approximations make it possible to identify the region where Class II neuron firings synchronize. Bifurcation analyses of two FPEs show that semi‐adiabatic approximation fits better to the numerical results than mean‐field approximation. FPE with semi‐adiabatic approximation better illustrates the fact that a population of FS interneurons has a narrower region of gamma oscillation than that of Class I neurons. Moreover, analysis with semi‐adiabatic approximation of a population composed of both Class I and FS interneurons has a narrower region of synchronization with an increase in the FS interneuron ratio. © 2020 Institute of Electrical Engineers of Japan. Published by Wiley Periodicals LLC.