Phase Sensitivity Analysis of a Circadian Rhythm Gene Network

Circadian rhythm synchronizes the daily activities of living organisms with the 24-hour earth rotation. The core of this clock is a transcriptional regulation of genes which produces an autonomous oscillation of 24-hour period. Despite the prevalence of oscillatory systems, sensitivity analysis of the key characteristics, such as period and phase, does not directly fit into the traditional framework for differential equations, which motivates the development of analyses aimed for these systems. This work focuses on the phase sensitivity analysis of circadian rhythm. Many of the concepts however can apply to oscillatory systems in general. Two examples of Drosophila circadian models illustrate the utilities of the developed analysis.