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This study presents a novel mathematical modeling framework that is uniquely suited to investigating the structure and dynamics of the sleep-wake regulatory network in the brain stem and hypothalamus. It is based on a population firing rate model formalism that is modified to explicitly include concentration levels of neurotransmitters released to postsynaptic populations. Using this framework, interactions among primary brain stem and hypothalamic neuronal nuclei involved in rat sleep-wake regulation are modeled. The model network captures realistic rat polyphasic sleep-wake behavior consisting of wake, rapid eye movement (REM) sleep, and non-REM (NREM) sleep states. Network dynamics include a cyclic pattern of NREM sleep, REM sleep, and wake states that is disrupted by simulated variability of neurotransmitter release and external noise to the network. Explicit modeling of neurotransmitter concentrations allows for simulations of microinjections of neurotransmitter agonists and antagonists into a key wake-promoting population, the locus coeruleus (LC). Effects of these simulated microinjections on sleep-wake states are tracked and compared with experimental observations. Agonist/antagonist pairs, which are presumed to have opposing effects on LC activity, do not generally induce opposing effects on sleep-wake patterning because of multiple mechanisms for LC activation in the network. Also, different agents, which are presumed to have parallel effects on LC activity, do not induce parallel effects on sleep-wake patterning because of differences in the state dependence or independence of agonist and antagonist action. These simulation results highlight the utility of formal mathematical modeling for constraining conceptual models of the sleep-wake regulatory network.

Simulating Microinjection Experiments in a Novel Model of the Rat Sleep-Wake Regulatory Network