Robust stability analysis of gene-protein regulatory networks with cyclic activation-inhibition interconnections

This paper studies analytic robust stability criteria for large-scale cyclic gene-protein regulatory network systems with unstructured or parametric uncertainties. We first consider a class of gene expressions, which is described as uncertain Linear Transcription-Translation Models (LTTMs) with not only feedback loops from translation products to transcription but also degradation properties of proteins and mRNAs. We then show that such uncertain models belong to a class of large-scale dynamical linear network systems with a generalized frequency variable, and then propose considerably simple analytic robust stability analysis methods. The developed schemes require less computational burden, and hence can be readily applied to large-scale genetic regulatory networks.