The dynamic structure underlying subthreshold oscillatory activity and the onset of spikes in a model of medial entorhinal cortex stellate cells

Medial entorhinal cortex layer II stellate cells display subthreshold oscillations (STOs). We study a single compartment biophysical model of such cells which qualitatively reproduces these STOs. We argue that in the subthreshold interval (STI) the seven-dimensional model can be reduced to a three-dimensional system of equations with well differentiated times scales. Using dynamical systems arguments we provide a mechanism for generations of STOs. This mechanism is based on the "canard structure," in which relevant trajectories stay close to repelling manifolds for a significant interval of time. We also show that the transition from subthreshold oscillatory activity to spiking ("canard explosion") is controlled in the STI by the same structure. A similar mechanism is invoked to explain why noise increases the robustness of the STO regime. Taking advantage of the reduction of the dimensionality of the full stellate cell system, we propose a nonlinear artificially spiking (NAS) model in which the STI reduced system is supplemented with a threshold for spiking and a reset voltage. We show that the synchronization properties in networks made up of the NAS cells are similar to those of networks using the full stellate cell models.