Waking and sleep states are regulated by the coordinated activity of a number of neuronal population in the brainstem and hypothalamus whose synaptic interactions compose a sleep-wake regulatory network. Physiologically based mathematical models of the sleep-wake regulatory network contain mechanisms operating on multiple time scales including relatively fast synaptic-based interations between neuronal populations, and much slower homeostatic and circadian processes that modulate sleep-wake temporal patterning. In this study, we exploit the naturally arising slow time scale of the homeostatic sleep drive in a reduced sleep-wake regulatory network model to utilize fast-slow analysis to investigate the dynamics of rapid eye movement (REM) sleep regulation. The network model consists of a reduced number of wake-, non-REM (NREM) sleep-, and REM sleep-promoting neuronal populations with the synaptic interactions reflecting the mutually inhibitory flip-flop conceptual model for sleep-wake regulation and the reciprocal interaction model for REM sleep regulation. Network dynamics regularly alternate between wake and sleep states as goverend by the slow homeostatic sleep drive. By varying a parameter associated with the activation of the REM-promoting population, we cause REM dynamics during sleep episodes to vary from supression to single activations to regular REM-NREM cycling, corresponding to changes in REM patterning induced by circadian modulation and observed in different mammalian species. We also utilize fast-slow analysis to explain complex effects on sleep-wake patterning of simulated experiments in which agonists and antagonists of different neurotransmitters are microinjected into specific neuronal populations participating in the sleep-wake regulatory network.
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Diniz Behn, Cecilia and V. Booth. “A Fast-Slow Analysis of the Dynamics of REM Sleep.” SIAM Journal of Applied Dynamical System 11.1 (2012): 212-242.