A design principle for neuronal firing with up-down oscillation through Na⁺ dynamics

Nonrapid eye movement sleep is characterized by high-amplitude and low-frequency electroencephalography signals. These signals are thought to be produced by the synchronized activity of cortical neurons, demonstrating the alternating bursting (up) and resting (down) states. Here, such an activity is referred to as up-down oscillation (UDO). Previously, we discussed the importance of the Ca²⁺-dependent hyperpolarization pathway in the generation of UDO by simulating neuronal activity based on the Hodgkin-Huxley-type model. We herein focus on intracellular Na⁺ dynamics. The Na⁺-centered model indicates that the activation of voltage-gated Na⁺ channels leads to intracellular Na⁺ accumulation, which in turn activates Na⁺-dependent K⁺ (KNa) channels or Na⁺/K⁺ ATPases, resulting in the down state. Activation kinetics of voltage-gated Na⁺ channels are important in shaping the UDO firing. Therefore, our model demonstrates that voltage-gated Na⁺ and KNa channels or Na⁺/K⁺ ATPases are candidate pathways for UDO induction.