Abstract
Inhibitor of apoptosis proteins (IAPs) are best known for their roles as inhibitors of caspases and thereby inhibitors of the cell death process known as apoptosis. Legewie et al . developed a mathematical model of the core intrinsic apoptotic process involving Apaf-1, caspase 9, caspase 3, and X-linked IAP (XIAP). The input into the model is increased abundance of cytochrome c, which activates Apaf-1e, and the output is the concentration of active caspase 3. The model is based on 16 kinetic parameters and 13 differential equations. Three models were tested: a wild-type model in which XIAP competitively interacts with caspase 3 and caspase 9, a model in the presence of a mutant caspase 9 that cannot be cleaved and activated by caspase 3, and a noncompetitive model in which XIAP noncompetitively interacted with both caspase 3 and caspase 9. In the wild-type model, as active Apaf-1 concentration increased, the time course with which active caspase 3 was produced decreased as expected. When the activation of caspase 3 was plotted against the concentration of active Apaf-1, a bistable and irreversible state was observed both in the wild-type model and in the caspase 9 mutant model (although the total concentration of active caspase 3 was less in the caspase 9 mutant model). This suggested that the positive feedback between caspase 9 and caspase 3 was not the only contributor to bistability in the system. Further analysis suggested that XIAP contributed a positive feedback into caspase 3 activation. Caspase 3 was proposed to sequester XIAP away from caspase 9 under conditions of strong stimulation, thereby allowing caspase 9 to become further activated and ultimately allowing caspase 3 to be activated. The requirements were that the interactions between XIAP and caspase 3 and caspase 9 were competitive, caspase 3 abundance exceeded that of XIAP, and XIAP abundance exceeded that of caspase 9. The bistability and irreversibility of all three models depended on the concentrations of both caspase 3 and caspase 9, with only the wild-type model showing irreversibility in the physiological concentrations of each caspase, indicating that both caspase 3-mediated feedback and XIAP-mediated feedback contribute to irreversible bistability under physiological conditions. Their model accounts for experimentally observed differences in cellular responses to apoptotic stimuli by showing that the all-or-none threshold of the system is influenced by the abundance of caspase 3, caspase 9, and XIAP. The authors suggest wet-lab experiments that could be used to verify the model proposed. S. Legewie, N. Blüthgen, H. Herzel, Mathematical modeling identifies inhibitors of apoptosis as mediators of positive feedback and bistability. PLoS Comput. Biol. 2 , e120, 1061-1073 (2006). [PubMed]
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