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Legewie et al. (2006), Apoptosis

June 2008, model of the month by Melanie I. Stefan
Original model: BIOMD0000000102

Apoptosis, a form of programmed cell death, is crucial in development, as well as for maintaining homoeostasis in adult tissues [1]. There are several pathways resulting in apoptosis, all of which involve Cysteine Aspartyl-specific proteases (caspases) [1].

The extrinsic apoptotic pathway is triggered by ligand binding to cell-surface receptors, resulting in the recruitment of various proteins to form the death-inducing signalling complex (DISC). This complex promotes activation of caspase-8, which in turn activates caspase-3. Caspase-3 then induces the cellular changes that characterise apoptosis. The intrinsic pathway, in contrast, is triggered by cytotoxic stress, which induces the translocation of pro-apoptotic Bcl-2 family members, such as Bax, to the mitochondria. This leads to the release of mitochondrial cytochrome c into the cytosol, where it promotes the oligomerisation of the pro-apoptotic factor Apaf-1 into a complex called the "apoptosome". The aptoptosome recruits and activates caspase-9, which in turn promotes the activation of caspase-3. This process is further regulated by X-linked inhibitor of apoptosis (XIAP) protein, which inhibits the activity of both caspase-9 and caspase-3. Both extrinsic and intrinsic pathways have been reviewed in [2] and are shown in figure 1.

Extrinsic and intrinsic apoptosis pathways.

Figure 1: Extrinsic and intrinsic apoptosis pathways, figure taken from [2], modified. Direct positive feedback from caspase-3 on caspase-9 not shown.

The model by Legewie et al. ([3], BIOMD0000000102) focuses on the intrinsic apoptotic pathway. This pathway displays some properties that make it an interesting target for closer examination with mathematical methods: Depending on cellular context, cytochrome c induces caspase activation either gradually or in an all-or-none fashion. In addition, caspase activation is reversible in some cellular contexts, but irreversible in others. This suggests that the caspase activation pathway is monostable (characterised by a gradual response and reversibility) in some cells, but bistable (characterised by an all-or-none-response and sometimes irreversibility) in others. In order for bistability to occur, the existence of some form of positive (or double negative) feedback loop is a necessary, but not sufficient condition (reviewed in [4]).

Contribution of the indirect positive feedback loop to bistability.

Figure 2: Contribution of the indirect positive feedback loop to bistability. From [3].

According to the model by Legewie et al., there is one obvious feedback loop in that caspase-3 activates caspase-9, and thus promotes its own activation. But, more interestingly, there is also an additional indirect feedback loop caused by XIAP-mediated inhibition of both caspases: High levels of active caspase-3 will lead to XIAP being sequestered away from caspase-9, and thereby increase caspase-9 activity. The relevance of this additional feedback loop was demonstrated on a mutant model where direct activation of caspase-9 by caspase-3 was suppressed: The system could still display bistability. In the wildtype, both mechanisms interact (see figure 2). In this case, the nature of the system depends on the relative concentrations of caspase-3, caspase-9 and XIAP: If the concentration of XIAP exceeds that of caspase-3 and caspase-9 taken together, none of the feedback loops is employed and and caspase-3 is totally inhibited. If the concentration of caspase-9 is high compared to both caspase-3 and XIAP, XIAP will be sequestered away by excess caspase-9. In this case, only the direct feedback loop is employed and the system will display gradual activation of caspase-3. If both caspase-3 and caspase-9 are present at intermediate concentrations, both feedback loops work together to create bistability, and at even higher caspase concentrations, irreversibility. This provides a plausible explanation for qualitatively different behaviours of the intrinsic apoptotic pathway in different cellular contexts.

Although the interaction of caspase-3 and caspase-9 in the intrinsic apoptotic pathway was the starting point of their analysis, Legewie et al. suggest that the underlying mechanism might be widespread in systems displaying context-dependent ultrasensitivity, bistability and irreversibility. Indeed, a model for Bcl-2 including a direct and an indirect positive feedback loop has recently brought forward [5].

Bibliographic References

  1. D.W. Kufe, R.E. Pollock, R.R. Weichselbaum, R.C. Bast Jr., T.S. Gansler, J.F. Holland, and E. Frei III. Cancer Medicine. BC Decker Inc, 2003.
  2. G.S. Salvesen and C.S. Duckett. IAP proteins: blocking the road to death's door. Nat Rev Mol Cell Biol. 3(6):401-410, 2002. [SRS@EBI]
  3. S. Legewie, N. Blüthgen, H. Herzel. Mathematical modeling identifies inhibitors of apoptosis as mediators of positive feedback and bistability. PLoS Comput Biol. 2(9):e120, 2006. [SRS@EBI]
  4. J.E. Ferrell Jr. Self-perpetuating states in signal transduction: positive feedback, double-negative feedback and bistability. Curr Opin Cell Biol. 14(2):140-148, 2002. [SRS@EBI]
  5. J. Cui, C. Chen, H. Lu, T. Sun, P. Shen. Two independent positive feedbacks and bistability in the Bcl-2 apoptotic switch. PLoS ONE 3(1):e1469, 2008. [SRS@EBI]
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