Developing objective sensitivity analysis of periodic systems: case studies of biological oscillators

Sensitivity analysis is a powerful tool in investigating the impact of parameter variations on the change of system behaviours quantitatively. For a periodic system, sensitivity analysis is a challenging problem since the standard sensitivity metrics grow unbounded when time tends to infinity. Objective sensitivity analyses using various oscillation features such as period, phase, amplitude, etc. are therefore needed to circumvent this problem. In this work, a new concept of basal state sensitivity is proposed based on which a phase sensitivity calculation is derived. The improved period sensitivity calculation following an existing algorithm using singular value decomposition (SVD) is also presented, which provides a simple calculation for the basal state sensitivity. These new sensitivity calculations are developed with the purpose to analyse biological oscillators since there is an increasing interest in understanding how oscillations occur and what the main controlling factors are following a growing experimental and computational evidence of oscillations in biological systems. The improved calculation of period sensitivity is shown to be consistent with the previous methods through a well studied circadian rhythm model. The calculation of new objective sensitivities are also testified by the same circadian rhythm model as well as an oscillatory signal transduction pathway model, which further illustrates the efficiency of this approach in handling complex biological oscillators in the presence of reaction conservations.