Dynamical analysis of the programmed cell death pathway

The biochemical processes that lead to the programmed death of the cell (apoptosis) have been studied since a long time. Recently several mathematical models have been proposed, that try to describe the essential features of the pathway. In this paper we consider one of such models and compare two possible scenarios of activation of the apoptotic process: an instantaneous perturbation or a persistent stress, represented respectively by an appropriate initial state or a constant input to the system. The new results here reported are i) the proof that the system with constant input has at least one equilibrium state; ii) the characterization of equilibrium and stability patterns in the presence of the constant input; iii) the analysis of the sensitivity of the dynamic time response both to the intensity of an initial perturbation, and to the level and duration of a persistent stress. Finally, the effect of modulating the level of expression of genes involved in the pathway is analyzed, with the aim of exploring the control mechanism of this crucial process.