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This article is part of the supplement: Eighteenth Annual Computational Neuroscience Meeting: CNS*2009

Open Access Poster presentation

Slow population rhythms emerge in noisy inhibitory network models

Ernest CY Ho12*, Liang Zhang13 and Frances K Skinner1234

Author Affiliations

1 Toronto Western Research Institute, University Health Network, Toronto, Ontario, Canada

2 Departments of Physiology, University of Toronto, Toronto, Ontario, Canada

3 Departments of Medicine (Neurology), University of Toronto, Toronto, Ontario, Canada

4 Institute of Biomaterials and Biomedical Engineering, University of Toronto, Toronto, Ontario, Canada

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BMC Neuroscience 2009, 10(Suppl 1):P156  doi:10.1186/1471-2202-10-S1-P156

The electronic version of this article is the complete one and can be found online at: http://www.biomedcentral.com/1471-2202/10/S1/P156


Published:13 July 2009

© 2009 Ho et al; licensee BioMed Central Ltd.

Poster presentation

Inhibitory, interneuronal networks are known to underlie high-frequency (gamma, 40–80 Hz) population oscillations, and they are also known to underlie low-frequency rhythms. For example, spontaneous, slow (0.5–4 Hz) rhythms occur in rodent hippocampus [1]. However, it is unclear whether an inhibitory network can generate population oscillations much slower than the intrinsic firing frequencies of its consitutent neurons. Here we show that an inhibitory network model in the absence of any slow processes is able to produce low-frequency rhythms. To obtain this, we bridge our network model simulations with a dynamical mean-field (DMA) model [2] to approximate the location of relevant parameter regimes.

The individual interneuron model is a two-dimensional conductance-based model and the network is formed with fast, inhibitory GABAA type synapses. The DMA model representing a large all-to-all coupled system consists of 30 equations that include equations describing synaptic noises. Bifurcation analysis is used to explore the DMA model, in particular, to identify parameter regimes for which bursting activities occur. These parameters are used in network simulations. The network model consists of an all-to-all coupled network of 20 interneurons. Each interneuron is described by: CdV/dt = Iapp + bη-gL(V-EL)-gNam(V-ENa)-gKn(V-EK)-gsyn(V-Esynisi; m(V) = 1/(1+exp(-4/3-V/15)); dn/dt = 1/(1+exp(-5-V/5))-n; dsi/dt=a(1-si)/(1+exp(-Vi/2))-si/τ, where Σisi sums the (inhibitory) synaptic gating variables from other interneurons in the network, η represents white noise of unit strength and b represents the strength of the noise. Figure 1 shows a raster plot from a 30 second network simulation (left) with the corresponding average summated synaptic activities (right). The parameters used are taken from identified bursting regimes in the DMA model analysis. Parameters values: Iapp= 4.8 μA/cm2; b= 0.08 ms1/2mA/cm2; gL= 8 mS/cm2; gK= 10 mS/cm2; gNa= 20 mS/cm2; gsyn= 0.0263 mS/cm2; EL= -80 mV; EK= -90 mV; ENa= 60 mV; Esyn= -85 mV; τ = 10 ms; C = 1 μF/cm2. The intrinsic firing frequency at Iapp = 4.8 μA/cm2 for these neurons (with zero noise) is 52 Hz. Slow population rhythms (approx 0.5 Hz), or bursts of synaptic activities, can be seen to emerge due to a "switching" between sparsely firing and coherently firing network states.

thumbnailFigure 1. Slow Network Rhythm.

A DMA model analysis has been used to find parameter regimes that allow slow rhythms to be expressed by inhibitory network models. These regimes are identified by bursting activities in a simpler mean-field model. Given the bridging used between the DMA model and the network simulations, we expect that this slow pattern should also occur in much larger network models. We have previously obtained values for synaptic "noise" parameters underlying slow hippocampal rhythms [3]. It will be interesting to determine whether bursting in the DMA models, and thus slow population rhythms in large network simulations, occur using these experimentally-based synaptic noise parameter values. If so, this would suggest a novel way in which slow rhythms could emerge in biological, inhibitory networks.

Acknowledgements

NSERC of Canada.

References

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