The brain's circadian clock controls daily rhythms in hormone production and sleep/wake behavior. Disruptions of these rhythms, due to jet lag or night-shift work for example, have health implications for millions of Americans. The primary goal of this project is to gain a mathematical understanding of the role that the clock's electrical activity plays in circadian timekeeping, in particular the way the clock responds to the external light/dark cycle. This project will contribute to the BRAIN Initiative by discovering principles about the flow of information between the cell membrane and genes. These newly discovered principles will aid in the development of mathematical models of brain processes such as long-term memory formation and the control of neuronal survival and death. This project will also impact areas of mathematical biology beyond circadian rhythms through its development of computer simulation methods that are capable of handling widely disparate time scales. Through this project, the investigator will mentor graduate and undergraduate students in interdisciplinary research at the interface of mathematics and neuroscience, and will participate in educational outreach to under-served urban communities in collaboration with the Urban Scholar Society.
The primary goal of this project is to create a mathematical framework for understanding how dynamic changes in gene expression affect the electrical properties of neurons and ultimately animal behavior. Circadian rhythms offer one of the clearest examples of the interplay between these different levels of organization, with rhythmic gene expression leading to daily rhythms in neural activity, physiology, and behavior. The main output signal of the master circadian clock in mammals has long been believed to be a simple day/night difference in the firing rate of neurons within the suprachiasmatic nucleus (SCN). Recent findings challenge this theory, and demonstrate that a substantial portion of SCN neurons exhibit a more complex and counterintuitive set of electrical state transitions throughout the day/night cycle. Through data-driven mathematical modeling, simulation, and dynamical systems analysis of the key cell types within the clock nucleus, this project will develop an understanding of the daily transitions in the SCN's electrical state and the functional roles they play in the mammalian circadian clock. In addition, this project will determine whether the activity patterns of two distinct classes of SCN neurons originate at the cellular or the circuit level by deriving conductance-based mathematical models of membrane excitability for both cell types and their synapses. The transitions in SCN activity patterns that occur throughout the day/night cycle will be explained by developing a multi-scale model of circadian timekeeping that links detailed models of the molecular clocks inside SCN neurons to these models of membrane excitability.
