Effective description of bistability and irreversibility in apoptosis

Apoptosis is a mechanism of programmed cell death in which cells engage in a controlled demolition and prepare to be digested without damaging their environment. In normal conditions apoptosis is repressed, until it is irreversibly induced by an appropriate signal. In adult organisms apoptosis is a natural way to dispose of damaged cells, and its disruption or excess is associated with cancer and autoimmune diseases. Apoptosis is regulated by a complex signaling network controlled by caspases, specialized enzymes that digest essential cellular components and promote the degradation of genomic DNA. In this work we propose an effective description of the signaling network focused on caspase-3 as a readout of cell fate. We integrate intermediate network interactions into a nonlinear feedback function acting on caspase-3 and introduce the effect of pro-apoptotic stimuli and regulatory elements as a saturating activation function. We find that the theory has a robust bistable regime where two possible states coexist, representing survival and cell death fates. For a broad range of parameters, strong stimuli can induce an irreversible switch to the death fate. We use the theory to explore dynamical stimulation conditions and determine how cell fate depends on different stimuli patterns. This analysis reveals a critical relation between transient stimuli intensity and duration to trigger irreversible apoptosis.