Towards modeling local sleep phenomena: a toy model of a smallest sleep unit

Recent research in sleep physiology demonstrates that sleep state does not necessarily involve the entire brain. To explain these new findings, the concept of “local sleep” has been proposed. This research focuses on mathematical modeling of minimal “sleep unit”. The proposed model shows transition to a state equivalent to local sleep at the level of the neuro-glia-vascular unit. In particular, a sufficiently strong stimulus can put the model into a state with low both activity and sensitivity to external stimuli. We show that this behavior persists for small ensemble of model units, as well as if we replace the action of neighbors with a positive feedback loop that returns to model unit its own signal with some delay. We conclude that our minimalistic model demonstrates those features that are necessary for further model studies of the spatiotemporal dynamics of sleep.