Neuro-physiological experiments on monkeys [1] have reported highly irregular persistent activity during the performance of an oculomotor delayed-response task. These experiments show that during the delay period the ISI's coefficient of variation (CV) of prefrontal neurons is above 1, on average, and larger than during the fixation period.

Previous models [2-3] of spontaneous and selective persistent activity in the cortex based on excitatory synaptic feedback do not reproduce this feature because the excitatory feedback during persistent activity brings neurons in a region of the f-I curve in which the firing is relatively independent from fluctuations and hence the CV is small.

We show that this feature of irregularity can be reproduced in a network in which persistent activity is induced by excitatory feedback, provided that (i) the post-spike reset is close enough to threshold , (ii) synaptic efficacies are a non-linear function of the pre-synaptic firing rate. Non-linearity between pre-synaptic rate and effective synaptic strength is implemented by a standard short-term depression mechanism (STD) [4].

First, we consider the simplest possible network with excitatory feedback: a fully connected homogeneous network of excitatory leaky integrate-and-fire neurons, both with numerical simulations and analytical techniques. The results are then confirmed in a network with selective excitatory neurons and inhibition. In both cases there is a large range of values of the synaptic efficacies for which the statistics of firing of single cells is similar to experimental data.

[1] Compte A, Constantinidis J T, Raghavachari S, Chafee M V, Goldman-Rakic P s, 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] Amit D J and Brunel N, Model of global spontaneous activity and local structured activity during delay periods in the cerebral cortex. Cerebral Cortex 7: 237-252 (1997b).
[3] Brunel N, Persistent activity and the single-cell frequency-current curve in a cortical network model. Comput. Neural. Syst. 11: 1-20 (2000).
[4] Romani S, Amit D J, Mongillo G, Mean-field analysis of selective persitent activity in presence of short-term synaptic depression. J. Comp. Neurosci. 20 : 201-217 (2006).