Mathematical modeling of circadian rhythms: gene expression, membrane excitability, and jet lag

Circadian (~24-hour) rhythms offer one of the clearest examples of the interplay between different levels of nervous system organization, with dynamic changes in 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). Our 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. In this seminar, I will attempt to provide a mathematical understanding of these daily transitions in SCN electrical state and the role they play in regulating gene expression. The circadian clock also influences multiple intracellular processes within cardiomyocytes and has recently been linked to ventricular arrhythmias in mice. I will describe how we are using mathematical modeling to understand the relationship between circadian rhythms and the dynamical mechanisms underlying early afterdepolarizations, which are secondary oscillations during the repolarization phase of the action potential that have been associated with sudden cardiac death. Finally, I will discuss entrainment maps, a new mathematical tool we have developed to understand properties of circadian oscillators. I will use entrainment maps and a model of the human circadian pacemaker to explain several features of jet lag.