Modeling & Analysis of Gene Expression as a Nonlinear Feedback Problem With State-Dependent Delay

This paper models the dynamics of gene expression as a nonlinear negative feedback system with a state-dependent delay. The delay accounts for the lag from the initiation of transcription until the appearance of the mature protein messenger RNA (mRNA). We do not consider this delay to be constant. Rather, we take this delay to be dependent on the instantaneous concentration of the protein. This gives rise to a nonlinear biological system with a state-dependent delay. We consider the degradation of mRNA and protein in the mathematical model. We give conditions for the asymptotic stability of the system. We also give examples and simulation results for which periodic (oscillatory) solutions/limit cycles are obtained. (C) 2017, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.