Robust Stability Analysis for Cyclic Gene Regulatory Networks

Abstract

This paper investigates robust stability analysis for gene regulatory networks with cyclic interconnections where dynamics of each gene expression has a certain degree of uncertainty. By considering a class of perturbation, we treat the heterogeneity of gene's dynamics, and derive necessary and sufficient conditions for robust stability. To this end, we first show a graphical condition for robust stability based on a robustness analysis scheme for large-scale systems presented in a previous work. A key feature of the graphical condition is that robust stability is systematically confirmed by drawing elementary shapes that are determined by network structure, gene's dynamics and its uncertainty bounds. Moreover, it is shown that the criterion can be greatly simplified by using monotone properties of gene's dynamics. This reduction enables us to derive an analytic condition for robust stability, which is a main result of this paper. Finally, the results are interpreted from a biological viewpoint, and they are verified by numerical simulations.