A theoretic control approach in signal-controlled metabolic pathways - Ramesh Garimella; Uma Garimella; Weijiu Liu (Mathematical Biosciences and Engineering)
Cells use a signal transduction mechanism to regulate certainmetabolic pathways. In this paper, the regulatory mechanism isanalyzed mathematically. For this analysis, a mathematical modelfor the pathways is first established using a system of differentialequations. Then the linear stability, controllability, andobservability of the system are investigated. We show that thelinearized system is controllable and observable, and that the realparts of all eigenvalues of the linearized system are nonpositiveusing Routh's stability criterion. Controllability and observabilityare structural properties of a dynamical system. Thus our resultsmay explain why the metabolic pathways can be controlled andregulated. Finally observer-based and proportional output feedbackcontrollers are designed to regulate the end product to its desired level. Applications to the regulation of blood glucose levels are discussed.