What Determines the Frequency of Fast Network Oscillations With Irregular Neural Discharges? I. Synaptic Dynamics and Excitation-Inhibition Balance

TLDR

Fast cortical oscillations (≈40 Hz gamma or ≈200 Hz ripples) coexist with irregular, sparse neuronal spikes, posing a challenge to coupled‑oscillator theories; prior work showed noise and strong inhibition can generate coherent rhythms, but used overly simplified synaptic kinetics. The study aims to quantitatively derive the coherent oscillation frequency in a randomly connected leaky integrate‑and‑fire network using realistic synaptic parameters. Rhythmogenesis arises from a compromise between a fast interneuronal mechanism and a slower excitatory‑inhibitory feedback loop, depending on the relative time scales of excitatory and inhibitory currents and the balance of recurrent excitation and inhibition. In noise‑dominated interneuronal networks, oscillation frequency is governed mainly by the shortest synaptic time constants, while in mixed networks the rhythm is set by the ratio of excitatory to inhibitory time scales and the E/I balance; a higher excitation/inhibition ratio shifts the rhythm toward slower gamma frequencies.

Abstract

When the local field potential of a cortical network displays coherent fast oscillations ( approximately 40-Hz gamma or approximately 200-Hz sharp-wave ripples), the spike trains of constituent neurons are typically irregular and sparse. The dichotomy between rhythmic local field and stochastic spike trains presents a challenge to the theory of brain rhythms in the framework of coupled oscillators. Previous studies have shown that when noise is large and recurrent inhibition is strong, a coherent network rhythm can be generated while single neurons fire intermittently at low rates compared to the frequency of the oscillation. However, these studies used too simplified synaptic kinetics to allow quantitative predictions of the population rhythmic frequency. Here we show how to derive quantitatively the coherent oscillation frequency for a randomly connected network of leaky integrate-and-fire neurons with realistic synaptic parameters. In a noise-dominated interneuronal network, the oscillation frequency depends much more on the shortest synaptic time constants (delay and rise time) than on the longer synaptic decay time, and approximately 200-Hz frequency can be realized with synaptic time constants taken from slice data. In a network composed of both interneurons and excitatory cells, the rhythmogenesis is a compromise between two scenarios: the fast purely interneuronal mechanism, and the slower feedback mechanism (relying on the excitatory-inhibitory loop). The properties of the rhythm are determined essentially by the ratio of time scales of excitatory and inhibitory currents and by the balance between the mean recurrent excitation and inhibition. Faster excitation than inhibition, or a higher excitation/inhibition ratio, favors the feedback loop and a much slower oscillation (typically in the gamma range).