Stable, highly irregular persistent activity induced by colored noise
Kosuke Hamaguchi1,2 and Nicolas Brunel2
1RIKEN BSI, Japan, 2UMR 8119 CNRS-Universite Rene Descartes, France

The spike patterns of prefrontal cortex neurons are highly irregular (CV close to 1) during the delay period of a spatial working memory task[1]. During this task, some neurons switch from a background state to an active firing state when spatial cue is presented and maintain their active states during delay period [1]. Thus, the prefrontal neuron network has multi-stable states with high spike irregularity.

One robust mechanism to obtain high spike irregularity is to balance excitation and inhibition in recurrent connections [2]. However, self-sustained activity typically relies on strong recurrent excitation. In an excitation-dominated network, CV of spike trains typically decreases as the firing rate increases. Therefore, it is unclear how to obtain both high CVs and bistability.

Here we propose a model that can reconcile this apparent contradictions. Recent analysis of sparsely connected recurrent network with spiking neurons [3] indicates the existence of fluctuation-driven bistability. More recent study shows that it requires relatively wide distributed delay of synapses to stabilize the fluctuation-driven bistable states [4] if the synapses are instantaneous (delta-function). We found that the instability occurs due to a Hopf-bifurcation. Here we use exponential-decay synapses with realistic time constants to alleviate the oscillatory instability. The system is now driven by colored noise. We calculate the firing rate of colored noise driven Leaky Integrate-and-Fire (LIF) neuron by using numerical calculations of 2D Fokker-Planck equation and analytically calculated firing rate with first order correction in small synaptic time constant limit [5]. We confirm that the fluctuation-driven bistability also exists in colored noise driven LIF neuron network both from the self-consistent analysis and simulations. These results indicate that prefrontal cortex would be operating in the regime of balanced/inhibition-dominated network.
Acknowledgments: K.H. is supported by JSPS Research Fellowship.

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