Isochron-based phase response analysis of circadian rhythms

Circadian rhythms possess the ability to robustly entrain to the environmental cycles. This ability relies on the phase synchronization of circadian rhythm gene regulation to different environmental cues, of which light is the most obvious and important. The elucidation of the mechanism of circadian entrainment requires an understanding of circadian phase behavior. This article presents two phase analyses of oscillatory systems for infinitesimal and finite perturbations based on isochrons as a phase metric of a limit cycle. The phase response curve of circadian rhythm can be computed from the results of the analyses. The application to a mechanistic Drosophila circadian rhythm model gives experimentally testable hypotheses for the control mechanisms of circadian phase responses and evidence for the role of phase and period modulations in circadian photic entrainment.