Abstract
Strategically located between the thalamus and the cortex, the inhibitory thalamic reticular nucleus (TRN) is a hub to regulate selective attention during wakefulness and control the thalamic and cortical oscillations during sleep. A salient feature of TRN neurons contributing to these functions is their characteristic firing patterns, ranging in a continuum from tonic spiking to bursting spiking. However, the dynamical mechanism under these firing behaviors is not well understood. In this study, by applying a reduction method to a full conductance-based neuron model, we construct a reduced three-variable model to investigate the dynamics of TRN neurons. We show that the reduced model can effectively reproduce the spiking patterns of TRN neurons as observed in vivo and in vitro experiments, and meanwhile allow us to perform bifurcation analysis of the spiking dynamics. Specifically, we demonstrate that the rebound bursting of a TRN neuron is a type of "fold/homo-clinic" bifurcation, and the tonic spiking is the fold cycle bifurcation. Further one-parameter bifurcation analysis reveals that the transition between these discharge patterns can be controlled by the external current. We expect that this reduced neuron model will help us to further study the complicated dynamics and functions of the TRN network.