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A mathematical model of caspase function in apoptosis

Nature Biotechnology volume 18, pages 768–774 (2000)Cite this article

A Corrigendum to this article was published on 01 February 2001

Abstract

Caspases (cysteine-containing aspartate-specific proteases) are at the core of the cell's suicide machinery. These enzymes, once activated, dismantle the cell by selectively cleaving key proteins after aspartate residues. The events culminating in caspase activation are the subject of intense study because of their role in cancer, and neurodegenerative and autoimmune disorders. Here we present a mechanistic mathematical model, formulated on the basis of newly emerging information, describing key elements of receptor-mediated and stress-induced caspase activation. We have used mass-conservation principles in conjunction with kinetic rate laws to formulate ordinary differential equations that describe the temporal evolution of caspase activation. Qualitative strategies for the prevention of caspase activation are simulated and compared with experimental data. We show that model predictions are consistent with available information. Thus, the model could aid in better understanding caspase activation and identifying therapeutic approaches promoting or retarding apoptotic cell death.

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Figure 1: Executioner caspase activation cascade.
Figure 2: Receptor mediated caspase activation.
Figure 3: Stress induced caspase activation.
Figure 4: Deactivating stress induced caspase activation.
Figure 5: The effect of decoy proteins and IAPs.

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References

  1. Evan, G. & Littlewood, T. A matter of life and cell death . Science 281, 1317–1722 (1998).

    Article  CAS  Google Scholar 

  2. Thompson, C.B. Apoptosis in the pathogenesis and treatment of disease. Science 267, 1456–1462 ( 1995).

    Article  CAS  Google Scholar 

  3. Haass, C. Apoptosis. Dead end for neurodegeneration? Nature 399 , 204–207 (1999).

    Article  CAS  Google Scholar 

  4. Ashkenazi, A. & Dixit, V.M. Death receptors: signaling and modulation . Science 281, 1305–1308 (1998).

    Article  CAS  Google Scholar 

  5. Adams, J.M. & Cory, S. The Bcl-2 protein family: arbiters of cell survival. Science 281, 1322– 1326 (1998).

    Article  CAS  Google Scholar 

  6. Thornberry, N.A. & Lazebnik, Y. Caspases: enemies within. Science 281, 1312– 1316 (1998).

    Article  CAS  Google Scholar 

  7. Green, D.R. & Reed, J.C. Mitochondria and apoptosis. Science 281, 1309–1312 (1998).

    Article  CAS  Google Scholar 

  8. Smith, C.A., Farrah, T. & Goodwin, R.G. The TNF receptor superfamily of cellular and viral proteins: activation, costimulation, and death. Cell 76, 959–962 (1994).

    Article  CAS  Google Scholar 

  9. Tartaglia, L.A., Ayres, T.M., Wong, G.H. & Goeddel, D.V. A novel domain within the 55 kd TNF receptor signals cell death. Cell 74, 845–853 (1993).

    Article  CAS  Google Scholar 

  10. Nagata, S. Apoptosis by death factor. Cell 88, 355– 365 (1997).

    Article  CAS  Google Scholar 

  11. Huang, B., Eberstadt, M., Olejniczak, E.T., Meadows, R.P. & Fesik, S.W. NMR structure and mutagenesis of the Fas (APO-1/CD95) death domain. Nature 384, 638–641 (1996).

    Article  CAS  Google Scholar 

  12. Chinnaiyan, A.M., O'Rourke, K., Tewari, M. & Dixit, V.M. FADD, a novel death domain-containing protein, interacts with the death domain of Fas and initiates apoptosis. Cell 81, 505– 512 (1995).

    Article  CAS  Google Scholar 

  13. Boldin, M.P. et al. A novel protein that interacts with the death domain of Fas/APO1 contains a sequence motif related to the death domain. J. Biol. Chem. 270, 7795–7798 ( 1995).

    Article  CAS  Google Scholar 

  14. Boldin, M.P. et al. Self-association of the “death domains” of the p55 tumor necrosis factor (TNF) receptor and Fas/APO1 prompts signaling for TNF and Fas/APO1 effects. J. Biol. Chem. 270, 387–391 (1995).

    Article  CAS  Google Scholar 

  15. Muzio, M., Stockwell, B.R., Stennicke, H.R., Salvesen, G.S. & Dixit, V.M. An induced proximity model for caspase-8 activation. J. Biol. Chem. 273, 2926– 2930 (1998).

    Article  CAS  Google Scholar 

  16. Salvesen, G.S. & Dixit, V.M. Caspase activation: the induced-proximity model. Proc. Natl. Acad. Sci. USA 96, 10964–10967 (1999).

    Article  CAS  Google Scholar 

  17. Li, P. et al. Cytochrome c and dATP-dependent formation of Apaf-1/caspase-9 complex initiates an apoptotic protease cascade. Cell 91, 479–489 (1997).

    Article  CAS  Google Scholar 

  18. Yang, J. et al. Prevention of apoptosis by Bcl-2: release of cytochrome c from mitochondria blocked. Science 275, 1129– 1132 (1997).

    Article  CAS  Google Scholar 

  19. Kluck, R.M., Bossy-Wetzel, E., Green, D.R. & Newmeyer, D.D. The release of cytochrome c from mitochondria: a primary site for Bcl-2 regulation of apoptosis. Science 275, 1132– 1136 (1997).

    Article  CAS  Google Scholar 

  20. Simpson, N.H., Singh, R.P., Perani, A., Goldenzon, C. & Al-Rubeai, M. In hybridoma cultures, deprivation of any single amino acid leads to apoptotic death, which is suppressed by the expression of the bcl-2 gene. Biotecnol. Bioeng. 59, 90– 98 (1998).

    Article  CAS  Google Scholar 

  21. Goswami, J., Sinskey, A.J., Steller, H., Stephanopoulos, G.N. & Wang, D.I. Apoptosis in batch cultures of Chinese hamster ovary cells. Biotechnol. Bioeng. 62, 632–640 (1999).

    Article  CAS  Google Scholar 

  22. Sanfeliu, A. & Stephanopoulos, G. Effect of glutamine limitation on the death of attached Chinese hamster ovary cells. Biotechnol. Bioeng. 64, 46–53 ( 1999).

    Article  CAS  Google Scholar 

  23. Deveraux, Q.L., Takahashi, R., Salvesen, G.S. & Reed, J.C. X-linked IAP is a direct inhibitor of cell-death proteases. Nature 388, 300–304 ( 1997).

    Article  CAS  Google Scholar 

  24. Deveraux, Q.L. et al. IAPs block apoptotic events induced by caspase-8 and cytochrome c by direct inhibition of distinct caspases. EMBO J. 17, 2215–2223 (1998).

    Article  CAS  Google Scholar 

  25. Seshagiri, S. & Miller, L.K. Baculovirus inhibitors of apoptosis (IAPs) block activation of Sf- caspase-1. Proc. Natl. Acad. Sci. USA 94, 13606–13611 ( 1997).

    Article  CAS  Google Scholar 

  26. Irmler, M. et al. Inhibition of death receptor signals by cellular FLIP. Nature 388, 125–126 ( 1997).

    Article  Google Scholar 

  27. Shu, H.B., Halpin, D.R. & Goeddel, D.V. Casper is a FADD- and caspase-related inducer of apoptosis . Immunity 6, 751–763 (1997).

    Article  CAS  Google Scholar 

  28. Koseki, T., Inohara, N., Chen, S. & Nunez, G. ARC, an inhibitor of apoptosis expressed in skeletal muscle and heart that interacts selectively with caspases. Proc. Natl. Acad. Sci. USA 95, 5156–5160 (1998).

    Article  CAS  Google Scholar 

  29. Amarante-Mendes, G.P. et al, Anti-apoptotic oncogenes prevent caspase-dependent and independent commitment for cell death. Cell Death Differ. 5, 298–306 (1998).

    Article  CAS  Google Scholar 

  30. Reed, J.C. Double identity for proteins of the Bcl-2 family. Nature 387, 773–776 (1997).

    Article  CAS  Google Scholar 

  31. Newton, K. & Strasser, A. The Bcl-2 family and cell death regulation. Curr. Opin. Genet. Dev. 8, 68 –75 (1998).

    Article  CAS  Google Scholar 

  32. Hsu, Y.T., Wolter, K.G. & Youle, R.J. Cytosol-to-membrane redistribution of Bax and Bcl-X(L) during apoptosis. Proc. Natl. Acad. Sci. USA 94, 3668–3672 (1997).

    Article  CAS  Google Scholar 

  33. Miyashita, T. & Reed, J.C. Tumor suppressor p53 is a direct transcriptional activator of the human bax gene. Cell 80, 293–299 (1995).

    Article  CAS  Google Scholar 

  34. Zhang, J., Cado, D., Chen, A., Kabra, N.H. & Winoto, A. Fas-mediated apoptosis and activation-induced T-cell proliferation are defective in mice lacking FADD/Mort1. Nature 392, 296–300 ( 1998).

    Article  CAS  Google Scholar 

  35. Yeh, W.C. et al. FADD: essential for embryo development and signaling from some, but not all, inducers of apoptosis. Science 279, 1954–1958 (1998).

    Article  CAS  Google Scholar 

  36. Ona, V.O. et al. Inhibition of caspase-1 slows disease progression in a mouse model of Huntington's disease. Nature 399, 263–267 (1999).

    Article  CAS  Google Scholar 

  37. Davidson, F.F. & Steller, H. Blocking apoptosis prevents blindness in Drosophila retinal degeneration mutants. Nature 391, 587–591 ( 1998).

    Article  CAS  Google Scholar 

Download references

Acknowledgements

This work was supported by the Swiss Priority Program in Biotechnology (SPP BioTech).

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  1. Jeffrey Varner

    Present address: Department of Chemical Engineering and Materials Science, University of Minnesota, 421 Washington Avenue SE, Minneapolis, MN, 55455-0132

Authors and Affiliations

  1. Institute of Biotechnology, ETH-Zurich, Zurich, CH-8093, Switzerland

    Martin Fussenegger & James E. Bailey

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  1. Martin Fussenegger
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Correspondence to Jeffrey Varner.

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Fussenegger, M., Bailey, J. & Varner, J. A mathematical model of caspase function in apoptosis. Nat Biotechnol 18, 768–774 (2000). https://doi.org/10.1038/77589

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