Dynamics of synaptically coupled integrate-and-fire-or-burst neurons

The minimal integrate-and-fire-or-burst (IFB) neuron model reproduces the salient features of experimentally observed thalamocortical (TC) relay neuron response properties, including the tem- poral tuning of both tonic spiking (i.e., conventional action potentials) and post-inhibitory rebound bursting mediated by a low-threshold calcium current. In this paper we consider networks of IFB neurons with slow synaptic interactions and show how the dynamics may be described with a smooth firing rate model. When the firing rate of the IFB model is dominated by a refractory process the equations of motion simplify and may be solved exactly. Numerical simulations are used to show that a pair of reciprocally interacting inhibitory spiking IFB TC neurons supports an alternating rhythm of the type predicted from the firing rate theory. A change in a single parameter of the IFB neuron allows it to fire a burst of spikes in response to a depolarizing signal, so that it mimics the behavior of a reticular (RE) cell. Within a continuum model we show that a network of RE cells with on-center excitation can support a fast traveling pulse. In contrast a network of inhibitory TC cells is found to support a slowly propagating lurching pulse.