Abstract
Bistability within a small neural circuit can arise through an appropriate strength of excitatory recurrent feedback. The stability of a state of neural activity, measured by the mean dwelling time before a noise-induced transition to another state, depends on the neural firing-rate curves, the net strength of excitatory feedback, the statistics of spike times, and increases exponentially with the number of equivalent neurons in the
circuit. Here, we show that such stability is greatly enhanced by synaptic facilitation and reduced by synaptic depression. We take into account the alteration in times of synaptic vesicle release, by calculating distributions of inter-release intervals of a
synapse, which differ from the distribution of its incoming interspike intervals when the synapse is dynamic. In particular, release intervals produced by a Poisson spike train have a coefficient of variation greater than one when synapses are probabilistic and facilitating, whereas the coefficient of variation is less than one when synapses are depressing. However, in spite of the increased variability in postsynaptic input producedby facilitating synapses, their dominant effect is reduced synaptic efficacy at low input rates compared to high rates, which increases the curvature of neural input-output
functions, leading to wider regions of bistability in parameter space and enhanced lifetimes of memory states. Our results are based on analytic methods with approximate formulae and bolstered by simulations of both Poisson processes and of circuits of noisy spiking model neurons.