A design principle of spindle oscillations in mammalian sleep.

Neural oscillations are mainly regulated by molecular mechanisms and network connectivity of neurons. Large-scale simulations of neuronal networks have driven the population-level understanding of neural oscillations. However, cell-intrinsic mechanisms, especially a design principle, of neural oscillations remain largely elusive. Herein, we developed a minimal, Hodgkin-Huxley-type model of groups of neurons to investigate molecular mechanisms underlying spindle oscillation, which is synchronized oscillatory activity predominantly observed during mammalian sleep. We discovered that slowly inactivating potassium channels played an essential role in characterizing the firing pattern. The detailed analysis of the minimal model revealed that leak sodium and potassium channels, which controlled passive properties of the fast variable (i.e., membrane potential), competitively regulated the base value and time constant of the slow variable (i.e., cytosolic calcium concentration). Consequently, we propose a theoretical design principle of spindle oscillations that may explain intracellular mechanisms behind the flexible control over oscillation density and calcium setpoint.