053

Title:

Entrainment dynamics of forced, hierarchichal circadian systems

Discipline: Mathematics

Presenter:

Guangyuan Liao

Abstract:

The ability of a circadian system to entrain to the twenty four hour light dark cycle is one its most important properties. A new tool, called the entrainment map, was recently introduced to study the this process for a single oscillator. Here we generalize the map to study the effects of light-dark forcing in a hierarchical system consisting of a central circadian oscillator that drives a peripheral circadian oscillator. We develop techniques to reduced the higher dimensional phase space of the coupled system to derive a generalized 2-D entrainment map. Deteriming the nature of various fixed points, together with an understanding of their stable and unstable manifolds, leads to conditions for existence and stability of periodic orbits of the circadian system. We use the map to investigage how various properties of solutions depend on parameters and intitial conditions including the time to and direction of entrainment. We show that the concepts of phase advance and phase delay need to be carefully assessed in considering hierarchichal systems.

Author(s):

Guangyuan Liao, Casey Diekman, Amitabha Bose

Funding Acknowledgements:

None