Robust stability analysis for cyclic gene regulatory networks with uncertainty

This paper investigates robustness properties of gene regulatory networks with cyclic interconnections. In particular, we treat the heterogeneity of the gene's dynamics using a framework of robustness analysis, and derive necessary and sufficient conditions for robust stability. To this end, we first present a mathematical formulation of the gene regulatory network where dynamics of gene expression has a certain degree of uncertainty. Then, graphical and analytic criteria for robust stability are derived based on a robustness analysis scheme for large-scale multi-agent systems. These conditions are easily applicable to large-scale gene regulatory networks, which involve many components. Finally, the results are interpreted from a biological viewpoint, and they are verified by numerical simulations.