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J Neurophysiol (August 10, 2005). doi:10.1152/jn.00510.2004
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Submitted on May 14, 2004
Accepted on August 3, 2005

Contributions of intrinsic membrane dynamics to fast network oscillations with irregular neuronal discharges

Caroline Geisler1, Nicolas Brunel2, and Xiao-Jing Wang3*

1 Physics Department and Volen Center for Complex Systems, Brandeis University, Waltham, MA, USA; Center for Molecular and Behavioral Neuroscience, Rutgers University, Newark, NJ, USA
2 Laboratory of Neurophysics and Physiology, UMR 8119 CNRS-Universite Rene Descartes, 75270 Paris Cedex 06, France
3 Physics Department and Volen Center for Complex Systems, Brandeis University, Waltham, MA, USA

* To whom correspondence should be addressed. E-mail: xjwang{at}brandeis.edu.

During fast oscillations in the local field potential (40-100Hz gamma, 100-200Hz sharp wave ripples) single cortical neurons typically fire irregularly at rates that are much lower than the oscillation frequency. Recent computational studies have been devoted to provide 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 200Hz 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 large impact on population oscillations, even though rhythmicity does not originate from pacemaker neurons and is an emergent network phenomenon.




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