| Apoptosis, or programmed cell death, is a process of crucial importance for maintaining a homeostatic balance between cell proliferation and death. In the present study a new mathematical model is presented that draws attention to the possible occurrence of bistability in mitochondria-dependent apoptotic pathways, as well as a transition from bistable to monostable behavior---either apoptotic or cytoprotective, under well-defined conditions. Bistability is proposed to be conferred by positive feedback loops that enhance caspase-3 activation pathways through mitochondria and by kinetic cooperativity in the formation of an apoptosome complex. It essentially ensures that cells will not die in the presence of relatively small pro-apoptotic effects, but will undergo apoptosis when perturbing conditions or levels of pro-apoptotic agents exceed certain threshold values. The passage from bistable to monostable cytoprotective behavior i.e., resistance to apoptosis, may be induced by decreasing the levels of Bax, a pro-apoptotic enzyme, in agreement with experimental observations; while the opposite passage to a pro-apoptotic monostable state may be triggered by a change in the levels of mitochondrial permeability transition pore complexes (PTPCs). Further computations shed light on the origins of the experimentally observed dichotomous effects of nitric oxide (NO), demonstrating that the relative concentrations of anti- and pro-apoptotic reactive NO species, and the interplay of glutathione, dominate the cell fate at long times (of the order of hours). Transient apoptotic effects may be observed in the presence of high levels of intracellular non-heme iron, the duration of which may reach up to hours, despite the eventual convergence to an anti-apoptotic state. The computational results thus point to the importance of the precise timing of NO production and external stimulation in determining the eventual pro- or anti-apoptotic role of NO. The same mathematical model (network of interactions) applied with different model parameters to different cell types demonstrates that cells with high levels of intracellular non-heme iron are resistant to apoptosis while those subjected to high levels of superoxide undergo pathological death, consistent with experimental observations. |
