System identification and robustness analysis of the circadian regulatory network via microarray data in Arabidopsis thaliana

The circadian regulatory network is one of the main topics of plant investigations. The intracellular interactions among genes in response to the environmental stimuli of light are related to the foundation of functional genomics in plant. However, the sensitivity analysis of the circadian system has not analyzed by perturbed stochastic dynamic model via microarray data in plant. In this study, the circadian network is constructed for Arabidopsis thaliana using a stochastic dynamic model with sigmoid interaction, activation delay, and regulation of input light taken into consideration. The describing function method in nonlinear control theory about nonlinear limit cycle (oscillation) is employed to interpret the oscillations of the circadian regulatory networks from the viewpoint that nonlinear network will continue to oscillate if its feedback loop gain is equal to 1 to support the oscillation of circadian network. Based on the dynamic model via microarray data, the system sensitivity analysis is performed to assess the robustness of circadian regulatory network via biological perturbations. We found that the circadian network is more sensitive to the perturbation of the trans-expression threshold, is more sensitive to the activation level of steady state, rather than the trans-sensitivity rate.