Modeling Formalisms in Systems Biology of Apoptosis

Chapter
First Online:

Abstract

Apoptosis is a form of cellular suicide central to various aspects in biology including tissue homeostasis, embryonic development, carcinogenesis, and neurodegenerative disorders. Quantitative modeling approaches provided valuable insights into the digital and irreversible nature of apoptosis initiation. In this chapter, we summarize the mathematical formalisms used in systems biology of apoptosis. In addition, we give an overview of apoptosis-related research questions that can be addressed by modeling. Moreover, we review top-down and bottom-up modeling approaches applied to apoptosis, and particularly focus on ordinary differential equation (ODE) modeling. Basic concepts such as bistability and sensitivity analysis are introduced, and a review of apoptosis-related ODE models is provided. We describe bistability, temporal switching, crosstalk between death and survival, and also discuss approaches to model cell-to-cell variability.

Keywords

Mitochondrial Outer Membrane Permeabilization Ordinary Differential Equation Model Unstable Steady State Extrinsic Noise Apoptosis Initiation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, log in to check access.

References

  1. Albeck JG, Burke JM, Aldridge BB et al (2008a) Quantitative analysis of pathways controlling extrinsic apoptosis in single cells. Mol Cell 30:11–25. doi: 10.1016/j.molcel.2008.02.012 PubMedCrossRefGoogle Scholar
  2. Albeck JG, Burke JM, Spencer SL et al (2008b) Modeling a snap-action, variable-delay switch controlling extrinsic cell death. PLoS Biol 6:2831–2852. doi: 10.1371/journal.pbio.0060299 PubMedCrossRefGoogle Scholar
  3. Aldridge BB, Haller G, Sorger PK, Lauffenburger DA (2006) Direct Lyapunov exponent analysis enables parametric study of transient signalling governing cell behaviour. Syst Biol 153:425–432CrossRefGoogle Scholar
  4. Bagci EZ, Vodovotz Y, Billiar TR et al (2006) Bistability in apoptosis: roles of bax, bcl-2, and mitochondrial permeability transition pores. Biophys J 90:1546–1559. doi: 10.1529/biophysj.105.068122 PubMedCrossRefGoogle Scholar
  5. Bagci EZ, Vodovotz Y, Billiar TR et al (2008) Computational insights on the competing effects of nitric oxide in regulating apoptosis. PLoS One 3:e2249. doi: 10.1371/journal.pone.0002249 PubMedCrossRefGoogle Scholar
  6. Bentele M, Lavrik I, Ulrich M et al (2004) Mathematical modeling reveals threshold mechanism in CD95-induced apoptosis. J Cell Biol 166:839–851. doi: 10.1083/jcb.200404158 PubMedCrossRefGoogle Scholar
  7. Breiman L, Friedman J, Stone CJ, Olshen RA (1984) Classification and regression trees (new edition). CRC, Boca RatonGoogle Scholar
  8. Brunelle JK, Letai A (2009) Control of mitochondrial apoptosis by the Bcl-2 family. J Cell Sci 122:437–441. doi: 10.1242/jcs.031682 PubMedCrossRefGoogle Scholar
  9. Calzone L, Tournier L, Fourquet S et al (2010) Mathematical modelling of cell-fate decision in response to death receptor engagement. PLoS Comput Biol 6:e1000702. doi: 10.1371/journal.pcbi.1000702 PubMedCrossRefGoogle Scholar
  10. Certo M, Del Gaizo MV, Nishino M et al (2006) Mitochondria primed by death signals determine cellular addiction to antiapoptotic BCL-2 family members. Cancer Cell 9:351–365. doi: 10.1016/j.ccr.2006.03.027 PubMedCrossRefGoogle Scholar
  11. Chaves M, Eissing T, Allgöwer F (2008) Bistable biological systems: a characterization through local compact input-to-state stability. IEEE Trans Automat Contr 53:87–100CrossRefGoogle Scholar
  12. Chen C, Cui J, Lu H et al (2007a) Modeling of the role of a Bax-activation switch in the mitochondrial apoptosis decision. Biophys J 92:4304–4315. doi: 10.1529/biophysj.106.099606 PubMedCrossRefGoogle Scholar
  13. Chen C, Cui J, Zhang W, Shen P (2007b) Robustness analysis identifies the plausible model of the Bcl-2 apoptotic switch. FEBS Lett 581:5143–5150. doi: 10.1016/j.febslet.2007.09.063 PubMedCrossRefGoogle Scholar
  14. Chonghaile TN, Letai A (2008) Mimicking the BH3 domain to kill cancer cells. Oncogene 27(Suppl 1):S149–S157. doi: 10.1038/onc.2009.52 CrossRefGoogle Scholar
  15. Cui J, Chen C, Lu H et al (2008) Two independent positive feedbacks and bistability in the Bcl-2 apoptotic switch. PLoS One 3:e1469. doi: 10.1371/journal.pone.0001469 PubMedCrossRefGoogle Scholar
  16. Deng J, Carlson N, Takeyama K et al (2007) BH3 profiling identifies three distinct classes of apoptotic blocks to predict response to ABT-737 and conventional chemotherapeutic agents. Cancer Cell 12:171–185. doi: 10.1016/j.ccr.2007.07.001 PubMedCrossRefGoogle Scholar
  17. Dumitru CA, Gulbins E (2006) TRAIL activates acid sphingomyelinase via a redox mechanism and releases ceramide to trigger apoptosis. Oncogene 25:5612–5625. doi: 10.1038/sj.onc.1209568 PubMedCrossRefGoogle Scholar
  18. Düssmann H, Rehm M, Concannon CG et al (2010) Single-cell quantification of Bax activation and mathematical modelling suggest pore formation on minimal mitochondrial Bax accumulation. Cell Death Differ 17:278–290. doi: 10.1038/cdd.2009.123 PubMedCrossRefGoogle Scholar
  19. Eissing T, Conzelmann H, Gilles ED et al (2004) Bistability analyses of a caspase activation model for receptor-induced apoptosis. J Biol Chem 279:36892–36897. doi: 10.1074/jbc.M404893200 PubMedCrossRefGoogle Scholar
  20. Ferrell JE Jr (1996) Tripping the switch fantastic: how a protein kinase cascade can convert graded inputs into switch-like outputs. Trends Biochem Sci 21:460–466PubMedCrossRefGoogle Scholar
  21. Fischer SF, Vier J, Kirschnek S et al (2004) Chlamydia inhibit host cell apoptosis by degradation of proapoptotic BH3-only proteins. J Exp Med 200:905–916. doi: 10.1084/jem.20040402 PubMedCrossRefGoogle Scholar
  22. Fricker N, Beaudouin J, Richter P et al (2010) Model-based dissection of CD95 signaling dynamics reveals both a pro- and antiapoptotic role of c-FLIPL. J Cell Biol 190:377–389. doi: 10.1083/jcb.201002060 PubMedCrossRefGoogle Scholar
  23. Fussenegger M, Bailey JE, Varner J (2000) A mathematical model of caspase function in apoptosis. Nat Biotechnol 18:768–774. doi: 10.1038/77589 PubMedCrossRefGoogle Scholar
  24. Goldstein JC, Waterhouse NJ, Juin P et al (2000) The coordinate release of cytochrome c during apoptosis is rapid, complete and kinetically invariant. Nat Cell Biol 2:156–162. doi: 10.1038/35004029 PubMedCrossRefGoogle Scholar
  25. Golks A, Brenner D, Fritsch C et al (2005) c-FLIPR, a new regulator of death receptor-induced apoptosis. J Biol Chem 280:14507–14513. doi: 10.1074/jbc.M414425200 PubMedCrossRefGoogle Scholar
  26. Gómez-Benito M, Marzo I, Anel A, Naval J (2005) Farnesyltransferase inhibitor BMS-214662 induces apoptosis in myeloma cells through PUMA up-regulation, Bax and Bak activation, and Mcl-1 elimination. Mol Pharmacol 67:1991–1998. doi: 10.1124/mol.104.007021 PubMedCrossRefGoogle Scholar
  27. Harrington HA, Ho KL, Ghosh S, Tung KC (2008) Construction and analysis of a modular model of caspase activation in apoptosis. Theor Biol Med Model 5:26. doi: 10.1186/1742-4682-5-26 PubMedCrossRefGoogle Scholar
  28. Hasenauer J, Waldherr S, Doszczak M et al (2011) Identification of models of heterogeneous cell populations from population snapshot data. BMC Bioinformatics 12:125. doi: 10.1186/1471-2105-12-125 PubMedCrossRefGoogle Scholar
  29. Ho KL, Harrington HA (2010) Bistability in apoptosis by receptor clustering. PLoS Comput Biol 6:e1000956. doi: 10.1371/journal.pcbi.1000956 PubMedCrossRefGoogle Scholar
  30. Hoffmann JC, Pappa A, Krammer PH, Lavrik IN (2009) A new C-terminal cleavage product of procaspase-8, p30, defines an alternative pathway of procaspase-8 activation. Mol Cell Biol 29:4431–4440. doi: 10.1128/MCB.02261-07 PubMedCrossRefGoogle Scholar
  31. Hu T-M, Hayton WL, Mallery SR (2006) Kinetic modeling of nitric-oxide-associated reaction network. Pharm Res 23:1702–1711. doi: 10.1007/s11095-006-9031-4 PubMedCrossRefGoogle Scholar
  32. Hua F, Cornejo MG, Cardone MH et al (2005) Effects of Bcl-2 levels on Fas signaling-induced caspase-3 activation: molecular genetic tests of computational model predictions. J Immunol 175:985–995PubMedGoogle Scholar
  33. Hua F, Hautaniemi S, Yokoo R, Lauffenburger DA (2006) Integrated mechanistic and data-driven modelling for multivariate analysis of signalling pathways. J R Soc Interface 3:515–526. doi: 10.1098/rsif.2005.0109 PubMedCrossRefGoogle Scholar
  34. Hughes MA, Harper N, Butterworth M et al (2009) Reconstitution of the death-inducing signaling complex reveals a substrate switch that determines CD95-mediated death or survival. Mol Cell 35:265–279. doi: 10.1016/j.molcel.2009.06.012 PubMedCrossRefGoogle Scholar
  35. Janes KA, Albeck JG, Gaudet S et al (2005) A systems model of signaling identifies a molecular basis set for cytokine-induced apoptosis. Science 310:1646–1653. doi: 10.1126/science.1116598 PubMedCrossRefGoogle Scholar
  36. Janes KA, Gaudet S, Albeck JG et al (2006) The response of human epithelial cells to TNF involves an inducible autocrine cascade. Cell 124:1225–1239. doi: 10.1016/j.cell.2006.01.041 PubMedCrossRefGoogle Scholar
  37. Krueger A, Schmitz I, Baumann S et al (2001) Cellular FLICE-inhibitory protein splice variants inhibit different steps of caspase-8 activation at the CD95 death-inducing signaling complex. J Biol Chem 276:20633–20640. doi: 10.1074/jbc.M101780200 PubMedCrossRefGoogle Scholar
  38. Legewie S, Blüthgen N, Herzel H (2006) Mathematical modeling identifies inhibitors of apoptosis as mediators of positive feedback and bistability. PLoS Comput Biol 2:e120. doi: 10.1371/journal.pcbi.0020120 PubMedCrossRefGoogle Scholar
  39. Levenberg K (1944) A method for the solution of certain problems in least squares. Quart Appl Math 2:164–168Google Scholar
  40. Li B, Dou QP (2000) Bax degradation by the ubiquitin/proteasome-dependent pathway: involvement in tumor survival and progression. Proc Natl Acad Sci USA 97:3850–3855. doi: 10.1073/pnas.070047997 PubMedCrossRefGoogle Scholar
  41. Li P, Nijhawan D, Budihardjo I et al (1997) Cytochrome c and dATP-dependent formation of Apaf-1/caspase-9 complex initiates an apoptotic protease cascade. Cell 91:479–489PubMedCrossRefGoogle Scholar
  42. Mai Z, Liu H (2009) Boolean network-based analysis of the apoptosis network: irreversible apoptosis and stable surviving. J Theor Biol 259:760–769. doi: 10.1016/j.jtbi.2009.04.024 PubMedCrossRefGoogle Scholar
  43. Mannick JB, Hausladen A, Liu L et al (1999) Fas-induced caspase denitrosylation. Science 284:651–654PubMedCrossRefGoogle Scholar
  44. Marquardt D (1963) An algorithm for least-squares estimation of nonlinear parameters. SIAM J Appl Math 11:431–441CrossRefGoogle Scholar
  45. McDonald ER 3rd, El-Deiry WS (2004) Suppression of caspase-8- and -10-associated RING proteins results in sensitization to death ligands and inhibition of tumor cell growth. Proc Natl Acad Sci USA 101:6170–6175. doi: 10.1073/pnas.0307459101 PubMedCrossRefGoogle Scholar
  46. Nair VD, Yuen T, Olanow CW, Sealfon SC (2004) Early single cell bifurcation of pro- and antiapoptotic states during oxidative stress. J Biol Chem 279:27494–27501. doi: 10.1074/jbc.M312135200 PubMedCrossRefGoogle Scholar
  47. Neumann L, Pforr C, Beaudouin J et al (2010) Dynamics within the CD95 death-inducing signaling complex decide life and death of cells. Mol Syst Biol 6:352. doi: 10.1038/msb.2010.6 PubMedCrossRefGoogle Scholar
  48. Okazaki N, Asano R, Kinoshita T, Chuman H (2008) Simple computational models of type I/type II cells in Fas signaling-induced apoptosis. J Theor Biol 250:621–633. doi: 10.1016/j.jtbi.2007.10.030 PubMedCrossRefGoogle Scholar
  49. Pace V, Bellizzi D, Giordano F et al (2010) Experimental testing of a mathematical model relevant to the extrinsic pathway of apoptosis. Cell Stress Chaperones 15:13–23. doi: 10.1007/s12192-009-0118-9 PubMedCrossRefGoogle Scholar
  50. Pfeuty B, David-Pfeuty T, Kaneko K (2008) Underlying principles of cell fate determination during G1 phase of the mammalian cell cycle. Cell Cycle 7:3246–3257PubMedCrossRefGoogle Scholar
  51. Philippi N, Walter D, Schlatter R et al (2009) Modeling system states in liver cells: survival, apoptosis and their modifications in response to viral infection. BMC Syst Biol 3:97. doi: 10.1186/1752-0509-3-97 PubMedCrossRefGoogle Scholar
  52. Pop C, Fitzgerald P, Green DR, Salvesen GS (2007) Role of proteolysis in caspase-8 activation and stabilization. Biochemistry 46:4398–4407. doi: 10.1021/bi602623b PubMedCrossRefGoogle Scholar
  53. Press WH, Vetterling WT, Teukolsky SA, Flannery BP (1992) Modeling of data, chap 15, 2nd edn, Numerical recipes in C. Cambridge University Press, New York, pp 662–666Google Scholar
  54. Raue A, Kreutz C, Maiwald T et al (2009) Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood. Bioinformatics 25:1923–1929. doi: 10.1093/bioinformatics/btp358 PubMedCrossRefGoogle Scholar
  55. Raue A, Becker V, Klingmüller U, Timmer J (2010) Identifiability and observability analysis for experimental design in nonlinear dynamical models. Chaos 20:045105. doi: 10.1063/1.3528102 PubMedCrossRefGoogle Scholar
  56. Reed JC (1999) Dysregulation of apoptosis in cancer. J Clin Oncol 17:2941–2953PubMedGoogle Scholar
  57. Reed JC, Miyashita T, Takayama S et al (1996) BCL-2 family proteins: regulators of cell death involved in the pathogenesis of cancer and resistance to therapy. J Cell Biochem 60:23–32. doi:10.1002/(SICI)1097-4644(19960101)60:1<23::AID-JCB5>3.0.CO;2-5PubMedCrossRefGoogle Scholar
  58. Rehm M, Dussmann H, Janicke RU et al (2002) Single-cell fluorescence resonance energy transfer analysis demonstrates that caspase activation during apoptosis is a rapid process. Role of caspase-3. J Biol Chem 277:24506–24514. doi: 10.1074/jbc.M110789200 PubMedCrossRefGoogle Scholar
  59. Rehm M, Huber HJ, Dussmann H, Prehn JHM (2006) Systems analysis of effector caspase activation and its control by X-linked inhibitor of apoptosis protein. EMBO J 25:4338–4349. doi: 10.1038/sj.emboj.7601295 PubMedCrossRefGoogle Scholar
  60. Rehm M, Huber HJ, Hellwig CT et al (2009) Dynamics of outer mitochondrial membrane permeabilization during apoptosis. Cell Death Differ 16:613–623. doi: 10.1038/cdd.2008.187 PubMedCrossRefGoogle Scholar
  61. Rössig L, Fichtlscherer B, Breitschopf K et al (1999) Nitric oxide inhibits caspase-3 by S-nitrosation in vivo. J Biol Chem 274:6823–6826PubMedCrossRefGoogle Scholar
  62. Scaffidi C, Schmitz I, Krammer PH, Peter ME (1999) The role of c-FLIP in modulation of CD95-induced apoptosis. J Biol Chem 274:1541–1548PubMedCrossRefGoogle Scholar
  63. Schimmer AD (2004) Inhibitor of apoptosis proteins: translating basic knowledge into clinical practice. Cancer Res 64:7183–7190. doi: 10.1158/0008-5472.CAN-04-1918 PubMedCrossRefGoogle Scholar
  64. Schlatter R, Schmich K, Avalos Vizcarra I et al (2009) ON/OFF and beyond–a boolean model of apoptosis. PLoS Comput Biol 5:e1000595. doi: 10.1371/journal.pcbi.1000595 PubMedCrossRefGoogle Scholar
  65. Schorr K, Li M, Krajewski S et al (1999) Bcl-2 gene family and related proteins in mammary gland involution and breast cancer. J Mammary Gland Biol Neoplasia 4:153–164PubMedCrossRefGoogle Scholar
  66. Scott FL, Stec B, Pop C et al (2009) The Fas-FADD death domain complex structure unravels signalling by receptor clustering. Nature 457:1019–1022. doi: 10.1038/nature07606 PubMedCrossRefGoogle Scholar
  67. Siehs C, Oberbauer R, Mayer G et al (2002) Discrete simulation of regulatory homo- and heterodimerization in the apoptosis effector phase. Bioinformatics 18:67–76PubMedCrossRefGoogle Scholar
  68. Song Z, Yao X, Wu M (2003) Direct interaction between survivin and Smac/DIABLO is essential for the anti-apoptotic activity of survivin during taxol-induced apoptosis. J Biol Chem 278:23130–23140. doi: 10.1074/jbc.M300957200 PubMedCrossRefGoogle Scholar
  69. Spencer SL, Gaudet S, Albeck JG et al (2009) Non-genetic origins of cell-to-cell variability in TRAIL-induced apoptosis. Nature 459:428–432. doi: 10.1038/nature08012 PubMedCrossRefGoogle Scholar
  70. Stennicke HR, Jürgensmeier JM, Shin H et al (1998) Pro-caspase-3 is a major physiologic target of caspase-8. J Biol Chem 273:27084–27090PubMedCrossRefGoogle Scholar
  71. Stucki JW, Simon H-U (2005) Mathematical modeling of the regulation of caspase-3 activation and degradation. J Theor Biol 234:123–131. doi: 10.1016/j.jtbi.2004.11.011 PubMedCrossRefGoogle Scholar
  72. Svingen PA, Loegering D, Rodriquez J et al (2004) Components of the cell death machine and drug sensitivity of the National Cancer Institute Cell Line Panel. Clin Cancer Res 10:6807–6820. doi: 10.1158/1078-0432.CCR-0778-02 PubMedCrossRefGoogle Scholar
  73. Timmer J, Müller T, Swameye I et al (2004) Modeling the nonlinear dynamics of cellular signal transduction. Int J Bifurcat Chaos 14:2069–2079CrossRefGoogle Scholar
  74. Toivonen HT, Meinander A, Asaoka T et al (2011) Modeling reveals that dynamic regulation of c-FLIP levels determines cell-to-cell distribution of CD95-mediated apoptosis. J Biol Chem 286:18375–18382. doi: 10.1074/jbc.M110.177097 PubMedCrossRefGoogle Scholar
  75. Tyas L, Brophy VA, Pope A et al (2000) Rapid caspase-3 activation during apoptosis revealed using fluorescence-resonance energy transfer. EMBO Rep 1:266–270. doi: 10.1093/embo-reports/kvd050 PubMedCrossRefGoogle Scholar
  76. Vieira HL, Belzacq AS, Haouzi D et al (2001) The adenine nucleotide translocator: a target of nitric oxide, peroxynitrite, and 4-hydroxynonenal. Oncogene 20:4305–4316PubMedCrossRefGoogle Scholar
  77. Vo T-T, Letai A (2010) BH3-only proteins and their effects on cancer. Adv Exp Med Biol 687:49–63PubMedCrossRefGoogle Scholar
  78. Willis SN, Chen L, Dewson G et al (2005) Proapoptotic Bak is sequestered by Mcl-1 and Bcl-xL, but not Bcl-2, until displaced by BH3-only proteins. Genes Dev 19:1294–1305. doi: 10.1101/gad.1304105 PubMedCrossRefGoogle Scholar
  79. Würstle ML, Laussmann MA, Rehm M (2010) The caspase-8 dimerization/dissociation balance is a highly potent regulator of caspase-8, -3, -6 signaling. J Biol Chem 285:33209–33218. doi: 10.1074/jbc.M110.113860 PubMedCrossRefGoogle Scholar
  80. Zhang H, Xu Q, Krajewski S et al (2000) BAR: an apoptosis regulator at the intersection of caspases and Bcl-2 family proteins. Proc Natl Acad Sci USA 97:2597–2602PubMedCrossRefGoogle Scholar
  81. Zhang R, Shah MV, Yang J et al (2008) Network model of survival signaling in large granular lymphocyte leukemia. Proc Natl Acad Sci USA 105:16308–16313. doi: 10.1073/pnas.0806447105 PubMedCrossRefGoogle Scholar
  82. Zhang T, Brazhnik P, Tyson JJ (2009) Computational analysis of dynamical responses to the intrinsic pathway of programmed cell death. Biophys J 97:415–434. doi: 10.1016/j.bpj.2009.04.053 PubMedCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2012

Authors and Affiliations

  1. 1.Division of Theoretical BioinformaticsDKFZ and BioQuantHeidelbergGermany
  2. 2.Institute of Molecular BiologyMainzGermany

Personalised recommendations