Department of Mathematical Sciences
April 12, 2016
Understanding entrainment properties of circadian oscillator models using a one-dimensional map
Various circadian oscillators that arise across different species are subject to periodic external light-dark forcing. A central question to address is whether the oscillator entrains to the external forcing, and if so, what determines the phase of entrainment. A typical way to asses phase locking is to use the phase response curve (PRC) to measure the change in phase of an oscillator due to an external perturbation as a function of the phase of the perturbation. PRC based methods work well when the perturbations are weak and brief. To consider longer and stronger external inputs, we have developed a new tool called an entrainment map. This is a one-dimensional map that can be determined analytically by understanding the phase space structure of the underlying, unperturbed circadian oscillator. It can easily be computed numerically. Using the map, we are able to determine conditions for existence and stability of phase locked solutions as well as how these solutions depend on parameters such as light intensity and photoperiod. We show that the entrainment map yields more accurate predictions for phase locking than the PRC. We demonstrate our method on a two-dimensional model of a molecular clock in Drosophila as well as a three-dimensional model of human circadian rhythm. This is joint work with Casey Diekman.