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Data-driven mathematical models of sleep and circadian physiology in developmental and pharmacological contexts
Stowe, Shelby Rose
Stowe, Shelby Rose
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2024
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2025-11-26
Abstract
Circadian rhythms are the approximately 24-h biological cycles that regulate the timing of physiological and behavioral processes. This thesis centers on mathematical models of the circadian clock and applications of these models under different conditions. In the first project, we implement a phenomenological model of the circadian clock and analyze how different patterns of light exposure affect its properties. Our findings suggest that light patterns associated with habitually napping or non-napping children may be sufficient to explain observed differences in clock timing between these groups. In the second project, we apply a model of the sleep-wake regulatory network to describe the transition from habitually napping to non-napping patterns of sleep characterized by experimental and observational data from young children. Through a bifurcation analysis of the system, we show that changes in the dynamics of the homeostatic sleep drive and sensitivity to homeostatic pressure are sufficient to initiate the transition from habitually napping to consolidated sleep. In the third project, we integrate melatonin dynamics into a novel macroscopic model of the circadian clock. Model parameters are fit using data describing the relationship between exogenous melatonin dosage and plasma melatonin concentration, the illuminance-dependence of endogenous melatonin suppression, and the phase shifting effects of exogenous melatonin on the circadian clock. We analyze dynamical properties of the oscillator with the addition of forcing due to both endogenous melatonin synthesis and exogenous melatonin ingestion. This thesis showcases the utility of circadian oscillator models, provides insights into observed changes in sleep and circadian rhythms across early childhood development, and establishes a novel modeling framework to predict how interactions between melatonin and light affect the circadian clock.
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