### 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 and Casp9 by inhibitors of apoptosis 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, 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.
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 frequently inhibit consecutive intermediates in cellular signaling cascades, the feedback mechanism described in this paper is likely to be a widespread principle on how cells achieve ultrasensitivity, bistability, and irreversibility.
### introduction ###
Apoptosis, an evolutionary conserved form of cell suicide, allows multicellular organisms to eliminate damaged or excess cells in order to maintain tissue homeostasis.
Dysregulation of apoptosis is associated with various pathological conditions, including cancer and neurodegenerative disorders.
Aspartate-specific cysteine proteases, also known as caspases, are the central executioners of apoptosis.
In most cases, apoptotic stimuli activate initiator caspases, whose substrates, the effector caspases, ultimatively cause cellular demise by cleaving various cellular substrates CITATION .
Figure 1A schematically depicts the so-called extrinsic and intrinsic apoptotic pathways that elicit apoptosis by cleaving and thereby activating caspase-3, the major cellular effector caspase.
The extrinsic pathway is initiated by ligand-binding to death receptors, which then oligomerize and recruit various proteins, including pro-Casp8, into the so-called death-inducing signaling complex.
Formation of the death-inducing signaling complex leads to autoprocessing of pro-Casp8 into active Casp8, which then cleaves Casp3.
Cytotoxic stress or death-receptor stimulated Casp8 engage the intrinsic, or mitochondrial, apoptosis pathway by inducing the translocation of proapoptotic Bcl-2 family members such as Bax and Bid to mitochondria.
This event, which is negatively regulated by antiapoptotic Bcl-2 family members, results in the release of proapoptotic proteins from mitochondria into the cytosol.
Cytosolic cyto c then elicits the oligomerization of Apaf-1 into an active high-molecular-weight complex, the apoptosome, which recruits and stimulates Casp9, and thereby allows activation of effector caspases such as Casp3.
Smac and inhibitors of apoptosis such as X-linked IAP establish an additional layer of regulation in the intrinsic pathway: XIAP inhibits the catalytic activities of Casp9 and Casp3 through reversible binding, and cytosolic Smac relieves this inhibition by sequestering XIAP away from caspases CITATION .
Experimental studies revealed that the qualitative behaviour of caspase activation in the intrinsic pathway depends on the cellular context.
Cyto c added to cytosolic extracts activates Casp3 in an all-or-none fashion in some cells CITATION CITATION, while gradual activation was observed in other systems CITATION CITATION.
As cyto-c release from mitochondria can be a reversible event CITATION, which does not affect mitochondrial function CITATION CITATION, it has been suggested that downstream caspase activation irreversibly commits cells to apoptosis CITATION, CITATION.
Accordingly, cyto c induced Casp3 activation remained elevated even after a strong decline in cytosolic cyto c CITATION or after apo cyto c, an inhibitor of apoptosome formation, was added CITATION.
Furthermore, the time course of caspase activation via the intrinsic pathway equals that for irreversible commitment to apoptosis CITATION, CITATION, and caspase-inhibition allows for long-term cellular recovery and/or proliferation after removal of apoptotic stimuli CITATION, CITATION, CITATION CITATION.
Finally, Fas-treated Jurkat T cells, which enter apoptosis by the intrinsic pathway, escaped commitment to death as judged by maintenance of clonogenic potential if Casp3 was inhibited CITATION.
On the contrary, Casp3 activation was found to be a reversible event in glycochenodeoxycholate-treated hepatocytes CITATION .
These qualitative differences in caspase activation suggest that the intrinsic pathway is bistable in some cells, but monostable in others.
While simple monostable systems respond in a gradual and reversible manner, complex bistable systems exhibit true all-or-none responses and in some cases irreversibility.
Bistability is thought to require a positive circuit, which may be established either by positive feedback or by double-negative feedback.
Once a threshold stimulus is exceeded, such positive circuits allow bistable systems to switch from low activation levels to high activation levels in an all-or-none fashion.
Bistable systems display hysteresis, meaning that different stimulus-response curves are obtained depending upon whether the system began in its off or its on state.
In some cases, the on state is maintained indefinitely after the stimulus is removed, so that the system shows irreversible activation CITATION.
Experimental studies confirmed that bistability indeed occurs in natural and artificial biological networks CITATION CITATION .
Recent mathematical modeling demonstrated that bistability can arise from hidden, or implicit, feedback loops that are usually not explicitly drawn in biochemical reaction schemes CITATION, CITATION.
Similarily, we present a model showing that inhibition of Casp3 and Casp9 by IAPs results in an implicit positive feedback and in bistability.
As cellular inhibitory proteins frequently inhibit consecutive intermediates in cellular signaling cascades, the mechanism described in this paper is likely to be a widespread principle on how cells achieve ultrasensitivity, bistability, and irreversibility .
