Mathematical Modeling Identifies Inhibitors of Apoptosis as Mediators of Positive Feedback and Bistability

Abstract

The intrinsic, or mitochondrial, pathway of caspase activation is essential for apoptosis induction by various stimuli including cytotoxic stress. It depends on the cellular context, whether cytochrome c released from mitochondria induces caspase activation gradually or in an all-or-none fashion, and whether caspase activation irreversibly commits cells to apoptosis. By analyzing a quantitative kinetic model, we show that inhibition of caspase-3 (Casp3) and Casp9 by inhibitors of apoptosis (IAPs) results in an implicit positive feedback, since cleaved Casp3 augments its own activation by sequestering IAPs away from Casp9. We demonstrate that this positive feedback brings about bistability (i.e., all-or-none behaviour), and that it cooperates with Casp3-mediated feedback cleavage of Casp9 to generate irreversibility in caspase activation. Our calculations also unravel how cell-specific protein expression brings about the observed qualitative differences in caspase activation (gradual versus all-or-none and reversible versus irreversible). Finally, known regulators of the pathway are shown to efficiently shift the apoptotic threshold stimulus, suggesting that the bistable caspase cascade computes multiple inputs into an all-or-none caspase output. As cellular inhibitory proteins (e.g., IAPs) frequently inhibit consecutive intermediates in cellular signaling cascades (e.g., Casp3 and Casp9), the feedback mechanism described in this paper is likely to be a widespread principle on how cells achieve ultrasensitivity, bistability, and irreversibility. Multicellular organisms eliminate damaged or excess cells by programmed cell death, also known as apoptosis. By modelling the signaling pathways involved in the initiation of apoptosis, the authors provide insight into how cells prevent spontaneous apoptosis, but yet efficiently enter cell death, once proapoptotic signals exceed a threshold. The simulations also explain how cells accurately translate a complex set of pro- and anti-apoptotic signals into a life-or-death decision. Once apoptosis has been initiated, cellular demise must irreversibly proceed even if the initial trigger is removed, as partial cellular disintegration might lead to tissue inflammation or cellular deregulation. The authors explain how such irreversible commitment arises in the initiation pathways of apoptosis and provide experimentally testable predictions. Finally, the simulations reveal an unanticipated role for the inhibitor of apoptosis family of proteins, as these proteins are predicted to be involved in the amplification of death signals and not only in their suppression.