Mean-field analysis of selective persistent activity in presence of short-term synaptic depression

Mean-Field theory is extended to recurrent networks of spiking neurons endowed with short-term depression (STD) of synaptic transmission. The extension involves the use of the distribution of interspike intervals of an integrate-and-fire neuron receiving a Gaussian current, with a given mean and variance, in input. This, in turn, is used to obtain an accurate estimate of the resulting postsynaptic current in presence of STD. The stationary states of the network are obtained requiring self-consistency for the currents-those driving the emission processes and those generated by the emitted spikes. The model network stores in the distribution of two-state efficacies of excitatory-to-excitatory synapses, a randomly composed set of external stimuli. The resulting synaptic structure allows the network to exhibit selective persistent activity for each stimulus in the set. Theory predicts the onset of selective persistent, or working memory (WM) activity upon varying the constitutive parameters (e.g. potentiated/depressed long-term efficacy ratio, parameters associated with STD), and provides the average emission rates in the various steady states. Theoretical estimates are in remarkably good agreement with data 'recorded' in computer simulations of the microscopic model.