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.

[1] Compte A, Constantinidis C, Raghavachari S Tegner J, Chafee MV, Goldman-Rakic PS, and Wang X-J., Temporally irregular mnemonic persistent activity in prefrontal neurons of monkeys during a delayed response task. J. Neurophysiol. 90:3441-3454 (2003).
[2] C van Vreeswijk and H Sompolinsky., Chaos in neuronal networks with balanced excitatory and inhibitory activity. Science 74(5293):1724-1726 (1996).
[3] Brunel N., Dynamics of sparsely connected networks of excitatory and inhibitory spiking neurons. J. Comp. Neurosci. 8(3):183-208 (2000).
[4] Renart A, Moreno-Bote R, Wang X-J, and Parga N., Mean-Driven and fluctuation-driven persistent activity in recurrent networks, Neural Computation 19: 1-46, (2007).
[5] Brunel N and Sergi S. Firing frequency of Leaky Integrate-and-Fire neurons with synaptic current dynamics, J. Theor. Biol. 195:87-95 (1998).