A mathematical model of network dynamics governing sleep-wake patterns in mice

This work comprises a mathematical modeling approach to the elucidation of mechanisms governing mouse sleep-wake behavior. Behavioral states of wake, rapid eye movement sleep, and non-REM sleep and transitions among them are regulated by a network of neurons in the brainstem and hypothalamus. State-dependent activity in specific neuronal populations creates clearly defined bouts of each state.; We analyze experimental data to characterize the form and structure of mouse sleep-wake behavior. Our characterization is based on time spent in each state, frequency and duration of bouts, and organization of states as quantified by transition probabilities. An important feature arising from these analyses is a qualitative difference between brief and sustained wake bouts. We hypothesize that different mechanisms underlie each type of wake bout and consider them to be distinct states.; We model the activity of each population in the sleep-wake network using Morris-Lecar type relaxation oscillators; connectivity between populations is modeled as coupling between oscillators. The fast-slow nature of these equations allows us to describe network behavior on multiple time scales. Transitions between states occur quickly, and minimal time is spent in intermediate states. External factors, such as homeostatic sleep drives, affect network properties on slower time scales.; In addition to studying baseline mouse behavior, we consider fragmented sleep-wake behavior observed in orexin knockout mice. Anomalies in the orexin system have been linked to narcolepsy, a sleep disorder characterized by behavioral state instability; orexin knockout mice exhibit similar behavior. Orexinergic neurons are known to interact with the sleep-wake network, but the bases for their stabilizing effects are not understood. By varying model parameters consistent with orexinergic sites of action, we identify possible mechanisms by which orexin stabilizes sleep-wake network dynamics.; To analyze the dynamics of the model network, we derive a sequence of reduced models in which salient network changes can be tracked in two or three dimensions. Model dimension is reduced using both fast-slow and dominant scale techniques. By identifying key variables in each transition, dynamics of the full network are reduced to local bifurcations in low-dimensional systems. This analysis provides insight into transition mechanisms in the mouse sleep-wake network.