25 May 2007
Daniel Forger
Department of Mathematics
University of Michigan
Biological clocks time many events in nature including sleep patterns, developmental events, and hormone release. Recent experimental work has shown that these clocks consist of feedback networks of interacting genes and proteins within cells. By analyzing mathematical models (ordinary differential equations), we derive strict requirements for when oscillations emerge in genetic feedback networks. We show how a bistable clock can be built, where external signals can start or stop rhythmicity, and discuss recent experimental work to build synthetic clocks. Amazingly, the period of these clocks depends only on how quickly molecules are removed, and whether rhythms are close to sinusoidal. From this general theory, more accurate mammalian models of circadian (~24-hour) rhythms will be considered, and we will explain why a family in Utah always wakes up early.