Lyapunov exponents and phase diagrams reveal multi-factorial control over TRAIL-induced apoptosis

Receptor‐mediated apoptosis proceeds via two pathways: one requiring only a cascade of initiator and effector caspases (type I behavior) and the second requiring an initiator–effector caspase cascade and mitochondrial outer membrane permeabilization (type II behavior). Here, we investigate factors controlling type I versus II phenotypes by performing Lyapunov exponent analysis of an ODE‐based model of cell death. The resulting phase diagrams predict that the ratio of XIAP to pro‐caspase‐3 concentrations plays a key regulatory role: type I behavior predominates when the ratio is low and type II behavior when the ratio is high. Cell‐to‐cell variability in phenotype is observed when the ratio is close to the type I versus II boundary. By positioning multiple tumor cell lines on the phase diagram we confirm these predictions. We also extend phase space analysis to mutations affecting the rate of caspase‐3 ubiquitylation by XIAP, predicting and showing that such mutations abolish all‐or‐none control over activation of effector caspases. Thus, phase diagrams derived from Lyapunov exponent analysis represent a means to study multi‐factorial control over a complex biochemical pathway.