Collaborative Research: Nonsmooth Maps, Coupled Oscillators and Seasonal Variation of Sleep and Circadian Rhythms

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This project will develop and analyze mathematical models for circadian clock signaling and its control of sleep-wake regulation to determine how seasonality is encoded in the neural activity of the clock. Circadian (~24 hour) rhythms in behavior and physiology, including sleep-wake rhythms, are entrained by the sun's daily light cycle and affect physical and mental health. These rhythms are driven by the brain's master circadian clock, which receives light information from the eyes and coordinates biological rhythms throughout the body. In modern life, exposure to artificial light can erode the crucial tie between internal physiological rhythms and environmental light timing. The proposed mathematical modeling and data analysis projects focus on understanding how information and uncertainty in light signals are processed and stored in the master circadian clock and propagated downstream to sleep-wake networks through neural signaling. In collaboration with a clinical researcher, the mathematical models will be applied to data describing light exposure and sleep in elementary school-aged children during the school year and summer to understand summer vacation-induced disruptions to sleep and circadian rhythms. An additional collaborator at a primarily undergraduate and Hispanic-serving institution will contribute to modeling the clock and developing a mathematical modeling mini-course for undergraduate students. Undergraduate, graduate and postdoctoral trainees will be involved in the research. This project is funded jointly by the Division of Mathematical Sciences Mathematical Biology Program and the Division of Integrative Organismal Systems Neural Systems Cluster.Behavioral states of waking, sleep, and rapid eye movement (REM) sleep are governed by networks of brainstem and hypothalamic neuronal populations, and mathematical modeling of these networks provides insights into the dynamics of their interactions. The master circadian clock in the suprachiasmatic nucleus (SCN) controls the timing of behavior across the 24 hour day and involves a hierarchy of physiological processes from the intracellular molecular "circadian clock," to clock-driven variations in the electrophysiological responses of SCN neurons, to the collective signaling of the SCN neural network and its dynamic role modulating sleep-wake behavior. Using an innovative combination of mathematical modeling and analysis, key aspects of light-dependent circadian modulation of sleep-wake behavior will be explored at multiple spatial and temporal scales. Return maps will be used to reduce dimensionality and formally classify the relationship between circadian signaling and bifurcations in sleep-wake patterning. Effects of coherence of SCN activity on sleep-wake behavior will be established theoretically, and these results will be applied to understand experimentally observed changes in phase relationships between dorsal and ventral SCN regions in rodents under seasonal light variation. SCN and sleep-wake network models will be combined to investigate the role of dorsal-ventral interactions in gating light effects on SCN activity; to quantify sensitivity of the human clock to erratic light schedules; and to examine mechanisms underlying summer vacation-induced changes in sleep-wake behavior in data collected in elementary school-aged children. Project results will identify potential targets for interventions to alleviate summer vacation-induced disruptions to sleep and circadian rhythms.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.