Abstract
Adenosine is a nucleoside with a hypothesized role in sleep because its concentration in the brain oscillates in sync with the human circadian rhythm. A majority of the research looks at adenosine's effects on individual receptors. However, there is much less research about the network of neurons associated with these receptors, and how it works with adenosine to regulate sleep. Using the Wilson Cowan Model and actual biological data, a mathematical model was developed to give more insight into this network's behavior. Of particular significance was the existence of a system of three neuron populations, consisting of sleep-promoting neurons, inhibitory interneurons, and excitatory interneurons, that has these saturation thresholds. Reaching this threshold in adenosine causes the firing behavior of the inhibitory interneurons and the sleep-promoting neurons to change from one of their steady states to the other. Additionally, using this three-population network, a fourth population of wake-promoting neurons, or the locus coeruleus, was incorporated into this system to demonstrate the effects of the homeostatic process of sleep, one analogous to a sleep pressure. Furthermore, through the addition of a periodic adenosine signal as input, the model was able to demonstrate the effects of the circadian process of sleep, one that governs the changes between periods of high and low sleep propensity.