Phase sensitivity analysis for biological oscillatory systems

Oscillation is one of the most important nonlinear behaviors which is widely observed in living cells. There has been a growing experimental and computational evidence of oscillations in biological systems, which brings an increasing interest in understanding how such oscillations occur and what are the main factors in controlling these oscillations. Sensitivity analysis is a powerful tool in investigating the impact of parameter variations on the change of oscillation behaviors quantitatively. For an oscillatory system, the phase sensitivity analysis is a challenging problem in formulation and computation. In this work, a systematic phase sensitivity analysis method is proposed by analyzing the relationship between the phase sensitivity and the state sensitivity. A new concept of basal state sensitivity is proposed based on which the phase sensitivity can be derived. The proposed algorithm is easy to implement and interpret for limit cycle oscillatory systems. It is applied to a circadian rhythm mathematical model. The simulation result shows the efficiency of this approach and also highlights the importance of investigating sensitivity analysis using different features of a limit cycle.