Robust Stability Analysis and Design Under Consideration of Multiple Feedback Loops in the Tryptophan Regulatory Network of E. coli

The tryptophan operon of E. coli represents an important regulatory unit consisting of multiple feedback loops. The role of these loops is crucial to understand the dynamics of tryptophan biosynthesis. We analyze the robust stability of this system by splitting its state into fast (mRNA concentration) and slow (anthranilate synthase and tryptophan concentrations) variables, under consideration of nonlinear uncertainties. In addition, we analyze the role of these feedback loops as key design components, responsible for the physiological performance of this regulatory unit. The range of allowed parameter perturbations and the conditions that ensure the existence of asymptotically stable equilibria for the perturbed system are determined. We also analyze two important alternate regulatory designs for the tryptophan synthesis pathway and derive the corresponding stability conditions.