Contributions of Intrinsic Membrane Dynamics to Fast Network Oscillations With Irregular Neuronal Discharges

TLDR

Fast LFP oscillations (40–200 Hz) involve irregular neuronal firing far below the oscillation frequency, and computational models have linked these rhythms to intrinsic membrane dynamics described by leaky and exponential integrate‑and‑fire neurons. The study extends the leaky‑integrate‑and‑fire framework to populations of more realistic Hodgkin–Huxley conductance‑based neurons. In a randomly connected, sparsely synapsed GABAergic network driven by noisy sinusoidal input, coherent oscillations arise whose frequency is analytically predicted from synaptic time constants and the single‑cell preferred discharge phase. The model shows that 200‑Hz oscillations emerge when single‑cell input conductance is high, and that in a two‑population network recurrent excitation can either raise or lower the rhythm depending on the relative timing of excitatory and inhibitory currents, underscoring the strong influence of detailed single‑cell properties on emergent network oscillations.

Abstract

During fast oscillations in the local field potential (40–100 Hz gamma, 100–200 Hz sharp-wave ripples) single cortical neurons typically fire irregularly at rates that are much lower than the oscillation frequency. Recent computational studies have provided a mathematical description of such fast oscillations, using the leaky integrate-and-fire (LIF) neuron model. Here, we extend this theoretical framework to populations of more realistic Hodgkin–Huxley-type conductance-based neurons. In a noisy network of GABAergic neurons that are connected randomly and sparsely by chemical synapses, coherent oscillations emerge with a frequency that depends sensitively on the single cell's membrane dynamics. The population frequency can be predicted analytically from the synaptic time constants and the preferred phase of discharge during the oscillatory cycle of a single cell subjected to noisy sinusoidal input. The latter depends significantly on the single cell's membrane properties and can be understood in the context of the simplified exponential integrate-and-fire (EIF) neuron. We find that 200-Hz oscillations can be generated, provided the effective input conductance of single cells is large, so that the single neuron's phase shift is sufficiently small. In a two-population network of excitatory pyramidal cells and inhibitory neurons, recurrent excitation can either decrease or increase the population rhythmic frequency, depending on whether in a neuron the excitatory synaptic current follows or precedes the inhibitory synaptic current in an oscillatory cycle. Detailed single-cell properties have a substantial impact on population oscillations, even though rhythmicity does not originate from pacemaker neurons and is an emergent network phenomenon.