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

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.

The response of cortical neurons to in vivo-like input current: theory and experiment: II. Time-varying and spatially distributed inputs

“…Among these are the spatial distribution of inputs along dendrites as pioneered by Rall (1967), nonlinear dendritic interactions (for reviews see Koch andSegev 2000, Segev andLondon 2000), or the impact of high conductance states (Destexhe et al 2003;Geisler et al 2005).…”

Mechanisms of physiological and epileptic HFO generation

“…Regarding ripple oscillations, we should also quote several more theoretical studies showing (i) the contribution of intrinsic membrane dynamics to fast (200 Hz) network oscillations (Geisler et al, 2005), (ii) the influence of synaptic dynamics (excitation-inhibition balance) on the frequency of fast network (200 Hz) oscillations (Brunel and Wang, 2003) and iii) the influence of synaptic noise and physiological coupling in the generation of HFOs (100-200 Hz) (Stacey et al, 2009). …”

Frequency-domain order parameters for the burst and spike synchronization transitions of bursting neurons

“…Although the global potential X G is an important ensemble-averaged quantity to describe synchronization in computational neuroscience, it is practically difficult to directly get X G in real experiments. To overcome this difficulty, instead of X G , we use the IPFR which is an experimentally-obtainable population quantity used in both the experimental and the computational neuroscience (Brunel andHakim 1999, 2008;Brunel 2000;Brunel and Wang 2003;Geisler et al 2005;Brunel and Hansel 2006;Wang 2010). The IPFR is obtained from the raster plot of spikes which is a collection of spike trains of individual neurons.…”

“…Population synchronization may be well visualized in the raster plot of neural spikes which can be obtained in experiments. Instantaneous population firing rate (IPFR), RðtÞ, which is directly obtained from the raster plot of spikes, is a realistic population quantity describing collective behaviors in both the computational and the experimental neuroscience (Brunel andHakim 1999, 2008;Brunel 2000;Brunel and Wang 2003;Geisler et al 2005;Brunel and Hansel 2006;Wang 2010). This experimentally-obtainable RðtÞ is in contrast to the ensembleaveraged potential X G which is often used as a population quantity in the computational neuroscience, because to directly get X G in real experiments is very difficult.…”

“…In the field of neuroscience, power-spectral analysis of a time-series xðtÞ (e.g., neuronal membrane potential) is often made to examine how the variance of the data xðtÞ is distributed over the frequency components into which xðtÞ may be decomposed (Brunel andHakim 1999, 2008;Brunel 2000;Brunel and Wang 2003;Geisler et al 2005;Brunel and Hansel 2006). Following this conventional direction, we investigate the synchronization transitions of bursting neurons in the frequency domain.…”