Subthreshold-level activities in neurons play a crucial role in neuronal oscillations. These small-amplitude oscillations have been suggested to be involved in synaptic plasticity and in determining the frequency of network oscillations. Subthreshold membrane oscillations (STOs) and subthreshold resonance oscillations (SROs) are the main constituents of subthreshold-level activities in neurons. In this study, a general theoretical framework for analyzing the mechanisms underlying STOs and SROs in neurons is presented. Results showed that the resting membrane potential and the hyperpolarization-activated potassium channel (h-channel) affect the subthreshold-level activities in stellate cells. The contribution of h-channel on resonance is attributed to its large time constant, which produces the time lag between Ih and the membrane potential. Conversely, the persistent sodium channels (Nap-channels) only play an amplifying role in these neurons.
Subthreshold oscillations in combination with large-amplitude oscillations generate mixed-mode oscillations (MMOs), which mediate various spatial and temporal cognition and memory processes and behavioral motor tasks. Although many studies have shown that canard theory is a reliable method to investigate the properties underlying the MMOs phenomena, the relationship between the results obtained by applying canard theory and conductance-based models of neurons and their electrophysiological mechanisms are still not well understood. The goal of this study was to apply canard theory to the conductance-based model of pyramidal neurons in layer V of the Entorhinal Cortex to investigate the properties of MMOs under antiepileptic drug conditions (i.e., when persistent sodium current is inhibited). We investigated not only the mathematical properties of MMOs in these neurons, but also the electrophysiological mechanisms that shape spike clustering. Our results show that pyramidal neurons can display two types of MMOs and the magnitude of the slow potassium current determines whether MMOs of type I or type II would emerge. Our results also indicate that slow potassium currents with large time constant have significant impact on generating the MMOs, as opposed to fast inward currents. Our results provide complete characterization of the subthreshold activities in MMOs in pyramidal neurons and provide explanation to experimental studies that showed MMOs of type I or type II in pyramidal neurons under antiepileptic drug conditions.