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1Centre National de la Recherche Scientifique-Neurophysique et Physiologie du Système Moteur-Université Paris René Descartes, 75270 Paris Cedex 06, France; and 2Volen Center, Brandeis University, Waltham, Massachusetts 02454
Submitted 6 December 2002; accepted in final form 11 February 2003
When the local field potential of a cortical network displays coherent fast
oscillations (
40-Hz gamma or 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 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).
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