  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.
