The spike patterns of prefrontal cortex neurons are highly irregular (CV close to 1) during the delay period of a spatial working memory task. 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 . 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 . 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  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  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 . 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
Acknowledgments: K.H. is supported by JSPS Research Fellowship.
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