Lyapunov Exponents and Phase Diagrams Reveal Multi-Factorial Control over TRAIL-Induced Apoptosis
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CitationAldridge, Bree B., Suzanne Gaudet, Douglas A. Lauffenburger, and Peter K. Sorger. 2011. Lyapunov exponents and phase diagrams reveal multi-factorial control over TRAIL-induced apoptosis. Molecular Systems Biology 7:553.
AbstractReceptor-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.
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