Skip to main content

Advertisement

Slow population rhythms emerge in noisy inhibitory network models

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 + b η-g L (V-E L )-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; ds i /dt=a(1-s i )/(1+exp(-V i /2))-s i /τ, where Σ i s i 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; g L = 8 mS/cm2; gK= 10 mS/cm2; gNa= 20 mS/cm2; gsyn= 0.0263 mS/cm2; E L = -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.

Figure 1
figure1

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.

References

  1. 1.

    Wu C, Luk WP, Gillis J, Skinner F, Zhang L: Size does matter: Generation of intrinsic network rhythms in thick mouse hippocampal slices. J Neurophysiol. 2005, 93: 2302-2317. 10.1152/jn.00806.2004.

  2. 2.

    Hasegawa H: Dynamical mean-field theory of spiking neuron ensembles: Response to a single spike with independent noises. Phys Rev E. 2003, 67: 041903-10.1103/PhysRevE.67.041903.

  3. 3.

    Ho ECY, Zhang L, Skinner FK: Inhibition dominates in shaping spontaneous CA3 hippocampal network activities in vitro. Hippocampus. 2009, 19: 152-165. 10.1002/hipo.20493.

Download references

Acknowledgements

NSERC of Canada.

Author information

Correspondence to Ernest CY Ho.

Rights and permissions

Open Access This article is published under license to BioMed Central Ltd. This is an Open Access article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Reprints and Permissions

About this article

Keywords

  • Network Simulation
  • Parameter Regime
  • Inhibitory Network
  • Raster Plot
  • Population Oscillation