Time delays in metabolic control systems

In this work we use mathematical models with discrete and distributed time delays to analyse the stability of metabolic pathways controlled by end product. We assume the kinetics of the intermediates of the path to be unknown, and we cover the lack of information by using a time delay. We find that above a definite substrate value, there is a critical delay Tc in which a transition from stability to instability occurs. For discrete delays, we find that even if the interaction of the end product with the first (allosteric) enzyme is not cooperative, the pathway can potentially become unstable and oscillate. We then show that the existence of cooperative inhibition extends the parametric domain of instability. The introduction of distributed delays shows, when the kernels are not monotonically decreasing, that the dispersion increases the critical delay Tc. Finally, we comment on the possibility that metabolic oscillations are physiological signals useful for triggering adaptive strategies in cell behavior.