Mammalian Circadian Rhythms: Mathematical Models of the SCN Network and Cell Synchronization

"Mammalian Circadian Rhythms: Mathematical Models of the SCN Network and Cell Synchronization"Joseph Miller, PhD, Dept. of Cell and Neurobiology, USC Keck School of Medicine, and Wijesuriya Dayawansa, PhD, Dept. of Mathematics and Statistics, Texas Tech UniversityVirtually all species on earth exhibit near-24 hr (circadian) rhythms in nearly every physiological and behavioral variable, including activity, sleep-wake cycling, body temperature and hormone release. The mammalian circadian clock is localized in the suprachiasmatic nucleus (SCN) of the hypothalamus and is both necessary and sufficient for circadian rhythm generation and maintenance. It comprises about 16,000 neurons, each of which is an autonomous cellular oscillator with a period of approximately 24 hr. The molecular substrates of the clock have recently been elucidated and some eight genes and gene products have been identified as components of a self-sustaining molecular feedback loop which constitutes the clock hardware. Mathematical modeling of the SCN cell oscillators largely originated from the work of Kronauer. Recently there have been several studies in which low dimensional dynamical models have been extracted from complicated biochemical interaction models to represent oscillatory responses in SCN cells. We will review some of the recent work on this topic. It has proven more difficult to determine the means by which these 16,000 clock neurons remain synchronized. Our main interest is in how such a network of SCN neurons can produce a synchronized oscillatory output. We model network connections in a probabilistic manner, and discuss the relevance of the first and second eigenvalues of a random graph to interpret observed synchronization times. We will discuss how to relate quantitative physiological parameters of the clock such as time to synchronize, resistance to lesion, temperature compensation and phase response curves to certain hypotheses regarding the SCN connectivity network. We argue that a small world topology is far more appropriate than the classical nearest neighbor interaction model.

Location: Olin Hall of Engineering (OHE) - 132

Audiences: Graduate

Contact: Wyatt Adam