On the asymptotic behavior of a cyclic biochemical system with delay

The study of the effects of feedback in biochemical circuits is central to the understanding of complex molecular processes such as signal transduction. In this paper, a simple cyclic system with delay is considered, whose nonlinearities are assumed to have a form common in the theory of mass action kinetics. Two possible consequences of this assumption are then discussed, namely either the global convergence to equilibrium, or the existence of periodic solutions for large delay. The work on monotone controlled systems by Sontag and Angeli is central to this discussion, as is the application of Schwarzian derivatives to Michaelis-Menten and Hill nonlinearities