An integrate-and-fire mathematical model of sleep-wake neuronal networks in the developing mammal

Abstract

Sleep behavior is present in nearly all animals, and is a vital part of growth, development, and overall health. Infant mammals cycle randomly between short bouts of sleep and wake, and the lengths of these bouts both follow an exponential distribution. As mammals mature into adulthood, the mean sleep and wake bout lengths increase, and we also observe a change in the distribution of wake bout lengths from exponential to power law. Focusing on three regions of the brainstem that are involved in sleep-wake regulation, we develop a novel integrate-and-fire neuronal network model to expand upon previous mathematical models of sleep-wake regulation in mammals, focusing on rats. This model allows fine control over neuronal connectivity while simultaneously increasing the size and complexity of the modeled system to make it more representative of reality. We establish a relationship between neuronal network structure and function that could explain the different sleep-wake behaviors observed in rats as they progress through development. We explore the relationship between three different neuronal populations as well as the overall network behavior of the system. We find that increasing synaptic connectivity strength between the wake-promoting region and the wake-active region accounts for the observed changes in mammalian sleep-wake patterns. This dynamic neuronal connectivity is a possible mechanism that accurately accounts for sleep-wake pattern changes observed during mammalian development.