Isochron-based phase sensitivity analysis of oscillatory biological systems

Circadian rhythms possess the ability to entrain their internal phase to that of the environment. This ability relies on the phase response of circadian gene regulation to different environmental cues, of which light is the most obvious and important. Analyzing phase response of oscillatory systems requires the development of methods specific for these systems' attributes, such as the period and phase. This article presents two phase analyses of oscillatory systems for infinitesimal and finite perturbations, based on the isochron as a phase measure. In addition, phase response curves can be computed from the results of the analyses. Finally, the application to investigate the phase behavior of Drosophila circadian rhythm gives experimentally testable predictions for the control mechanisms of circadian phase and period responses.