Sensitivity analysis of oscillatory biological systems with a SVD-based algorithm

There has been a growing body of 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. Model-based sensitivity analysis can help to investigate the impact of parameter variations on the change of oscillation behaviors quantitatively. To perform sensitivity analysis for systems with limit cycles, a modified method based on singular value decomposition (SVD) is proposed to obtain period sensitivity. The links between the SVD terms and the components of the state sensitivity matrix are thoroughly investigated, based on which the period sensitivity can be readily derived from the largest SVD term with an analytical solution. The improved algorithm keeps the advantages of the former SVD-based method in good convergence and it is easy to implement. A circadian rhythm model is used to present computations of period sensitivity and amplitude sensitivity. The simulation result indicates the efficiency of the method.