/. (. +9-*-uwuxa-*-5d and *. , +9*7, ($S*IgSLH*"8.'*(00(57*.'*D(.+0/D5()*%-*&*0(()%&5Z*+9*5&'6&'($^*Ig^LH*M00(57/D*5&'6&'('*5,(&E(* (''(+7.&,*'7D4574D&,*6D/7(.+'A*.+8.%.7&57.E(*'.7(*FSaG*&+)*6D/B/7('*.7'*)(9D&)&7./+*E.&*4%.Q4.7.+&7./+*FS?GH*3+*&)).7./+*7/*78(*).D(57* &57.E&7.('H** !"#$%&'()*&+&,-'.'*/0*"123#$.+)45()*&65&7./+*** ??* * 11*<=*>, pp.78-9787

O. 94d and *. +. , @:hc32X* [g"??^* 5(, 78&7* &D(* 6D( 78&+* (N6(D.B(+7&, pp.778785-778791

!. &%, D7-* @* I*?:;( '8'"#1266)@A2%*B 2&#!8' + 2, <B)' #(07e* 78(* E&,4(* /0* XD7./+()*.+*78, p.5

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!. &+, 3#' :=&' %2-&' 2, 3B)' I2L* !"#* &+)* Y#M* ).&9D&B'* '8/R.+9* XD/6(D7-* @* E&

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*. R&, 0.()*%-*'(77, 3+* 787H* 2'* &* D('4,7A* 6&D&B4+)* 78&7* D(6&D&B(7D.V&7, pp.78-84
URL : https://hal.archives-ouvertes.fr/in2p3-00169733

*. Gonzalvez, F. Ashkenazi, and A. , New insights into apoptosis signaling by Apo2L/TRAIL, Oncogene, vol.173, issue.34, pp.4752-4765, 2010.
DOI : 10.1038/onc.2010.221

S. Spencer and P. Sorger, Measuring and Modeling Apoptosis in Single Cells, Cell, vol.144, issue.6, pp.926-939, 2011.
DOI : 10.1016/j.cell.2011.03.002

P. Jost, S. Grabow, D. Gray, M. Mckenzie, and U. Nachbur, XIAP discriminates between type I and type II FAS-induced apoptosis, Nature, vol.139, issue.7258, pp.1035-1039, 2009.
DOI : 10.1038/nature08229

URL : http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2956120

C. Scaffidi, S. Fulda, A. Srinivasan, C. Friesen, and F. Li, Two CD95 (APO-1/Fas) signaling pathways, The EMBO Journal, vol.17, issue.6, pp.1675-1687, 1998.
DOI : 10.1093/emboj/17.6.1675

URL : http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1170515

B. Aldridge, S. Gaudet, D. Lauffenburger, and P. Sorger, Lyapunov exponents and phase diagrams reveal multi-factorial control over TRAIL-induced apoptosis, Molecular Systems Biology, vol.52, issue.1, p.553, 2011.
DOI : 10.1126/science.288.5467.874

URL : http://doi.org/10.1038/msb.2011.85

P. Bhola and S. Simon, Determinism and divergence of apoptosis susceptibility in mammalian cells, Journal of Cell Science, vol.122, issue.23, pp.4296-4302, 2009.
DOI : 10.1242/jcs.055590

M. Rehm, H. Huber, C. Hellwig, S. Anguissola, and H. Dussmann, Dynamics of outer mitochondrial membrane permeabilization during apoptosis, Cell Death and Differentiation, vol.60, issue.4, pp.613-623, 2009.
DOI : 10.1371/journal.pone.0002844

B. Barnhart, E. Alappat, and M. Peter, The CD95 Type I/Type II model, Seminars in Immunology, vol.15, issue.3, pp.185-193, 2003.
DOI : 10.1016/S1044-5323(03)00031-9

T. Eissing, H. Conzelmann, E. Gilles, F. Allgöwer, and E. Bullinger, Bistability Analyses of a Caspase Activation Model for Receptor-induced Apoptosis, Journal of Biological Chemistry, vol.279, issue.35, pp.36892-36897, 2004.
DOI : 10.1074/jbc.M404893200

E. Klipp, W. Liebermeister, C. Wierling, A. Kowald, and H. Lehrach, Systems Biology: A Textbook, 2009.

A. Hoffmann, A. Levchenko, M. Scott, and D. Baltimore, The Ikappa B-NF-kappa B Signaling Module: Temporal Control and Selective Gene Activation, Science, vol.298, issue.5596, pp.1241-1245, 2002.
DOI : 10.1126/science.1071914

M. Bentele, I. Lavrik, M. Ulrich, S. Stösser, and D. Heermann, Mathematical modeling reveals threshold mechanism in CD95-induced apoptosis, The Journal of Cell Biology, vol.15, issue.6, pp.839-851, 2004.
DOI : 10.1038/sj.bjc.6601330

F. Hua, M. Cornejo, M. Cardone, C. Stokes, and D. Lauffenburger, Effects of Bcl-2 Levels on Fas Signaling-Induced Caspase-3 Activation: Molecular Genetic Tests of Computational Model Predictions, The Journal of Immunology, vol.175, issue.2, pp.985-995, 2005.
DOI : 10.4049/jimmunol.175.2.985

E. Bagci, Y. Vodovotz, T. Billiar, G. Ermentrout, and I. Bahar, Bistability in Apoptosis: Roles of Bax, Bcl-2, and Mitochondrial Permeability Transition Pores, Biophysical Journal, vol.90, issue.5, pp.1546-1559, 2006.
DOI : 10.1529/biophysj.105.068122

S. Legewie, N. Blüthgen, and H. Herzel, Mathematical Modeling Identifies Inhibitors of Apoptosis as Mediators of Positive Feedback and Bistability, PLoS Computational Biology, vol.22, issue.9, p.120, 2006.
DOI : 10.1371/journal.pcbi.0020120.sd007

M. Rehm, H. Huber, H. Dussmann, and J. Prehn, Systems analysis of effector caspase activation and its control by X-linked inhibitor of apoptosis protein, The EMBO Journal, vol.6, issue.18, pp.4338-4349, 2006.
DOI : 10.1074/jbc.M204783200

C. Chen, J. Cui, H. Lu, R. Wang, and S. Zhang, Modeling of the Role of a Bax-Activation Switch in the Mitochondrial Apoptosis Decision, Biophysical Journal, vol.92, issue.12, pp.4304-4315, 2007.
DOI : 10.1529/biophysj.106.099606

J. Albeck, J. Burke, S. Spencer, D. Lauffenburger, and P. Sorger, Modeling a snapaction , variable-delay switch controlling extrinsic cell death, PLoS Biology, vol.6, pp.2831-2852, 2008.

S. Spencer, S. Gaudet, J. Albeck, J. Burke, and P. Sorger, Non-genetic origins of cell-to-cell variability in TRAIL-induced apoptosis, Nature, vol.382, issue.7245, pp.428-432, 2009.
DOI : 10.1038/nature08012

Z. Mai and H. Liu, Boolean network-based analysis of the apoptosis network: Irreversible apoptosis and stable surviving, Journal of Theoretical Biology, vol.259, issue.4, pp.760-769, 2009.
DOI : 10.1016/j.jtbi.2009.04.024

L. Calzone, L. Tournier, S. Fourquet, D. Thieffry, and B. Zhivotovsky, Mathematical Modelling of Cell-Fate Decision in Response to Death Receptor Engagement, PLoS Computational Biology, vol.2006, issue.3, p.1000702, 2010.
DOI : 10.1371/journal.pcbi.1000702.s008

URL : https://hal.archives-ouvertes.fr/inserm-00704979

J. Saez-rodriguez, L. Alexopoulos, M. Zhang, M. Morris, and D. Lauffenburger, Comparing Signaling Networks between Normal and Transformed Hepatocytes Using Discrete Logical Models, Cancer Research, vol.71, issue.16, pp.5400-5411, 2011.
DOI : 10.1158/0008-5472.CAN-10-4453

URL : http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3207250

R. Schlatter, K. Schmich, A. Vizcarra, I. Scheurich, P. Sauter et al., ON/OFF and Beyond - A Boolean Model of Apoptosis, PLoS Computational Biology, vol.122, issue.12, p.1000595, 2009.
DOI : 10.1371/journal.pcbi.1000595.s007

B. Aldridge and G. Haller, Direct Lyapunov exponent analysis enables parametric study of transient signalling governing cell behaviour, IEE Proceedings - Systems Biology, vol.153, issue.6, pp.425-432, 2006.
DOI : 10.1049/ip-syb:20050065

A. Algeciras-schimnich, E. Pietras, B. Barnhart, P. Legembre, and S. Vijayan, Two CD95 tumor classes with different sensitivities to antitumor drugs, Proceedings of the National Academy of Sciences, vol.100, issue.20, pp.11445-11450, 2003.
DOI : 10.1073/pnas.2034995100

N. Ozören and W. El-deiry, Defining Characteristics of Types I and II Apoptotic Cells in Response to TRAIL, Neoplasia, vol.4, issue.6, pp.551-557, 2002.
DOI : 10.1038/sj.neo.7900270

A. Donzé, Breach, A Toolbox for Verification and Parameter Synthesis of Hybrid Systems, Proceedings of the 22nd International Conference on Computer Aided Verification, pp.167-170, 2010.
DOI : 10.1007/978-3-642-14295-6_17

M. Peter and P. Krammer, The CD95(APO-1/Fas) DISC and beyond, Cell Death and Differentiation, vol.10, issue.1, pp.26-35, 2003.
DOI : 10.1038/sj.cdd.4401186

Y. Huang, Y. Park, R. Rich, D. Segal, and D. Myszka, Structural Basis of Caspase Inhibition by XIAP Differential Roles of the Linker versus the BIR Domain, Cell, vol.104, issue.5, pp.781-790, 2001.
DOI : 10.1016/S0092-8674(02)02075-5

L. Chen, L. Smith, Z. Wang, and J. Smith, Preservation of Caspase-3 Subunits from Degradation Contributes to Apoptosis Evoked by Lactacystin: Any Single Lysine or Lysine Pair of the Small Subunit Is Sufficient for Ubiquitination, Molecular Pharmacology, vol.64, issue.2, pp.334-345, 2003.
DOI : 10.1124/mol.64.2.334

X. Luo, I. Budihardjo, H. Zou, C. Slaughter, and X. Wang, Bid, a Bcl2 Interacting Protein, Mediates Cytochrome c Release from Mitochondria in Response to Activation of Cell Surface Death Receptors, Cell, vol.94, issue.4, pp.481-490, 1998.
DOI : 10.1016/S0092-8674(00)81589-5

H. Kim, M. Rafiuddin-shah, H. Tu, J. Jeffers, and G. Zambetti, Hierarchical regulation of mitochondrion-dependent apoptosis by BCL-2 subfamilies, Nature Cell Biology, vol.14, issue.12, pp.1348-1358, 2006.
DOI : 10.1073/pnas.0406837101

C. Du, M. Fang, Y. Li, L. Li, and X. Wang, Smac, a Mitochondrial Protein that Promotes Cytochrome c???Dependent Caspase Activation by Eliminating IAP Inhibition, Cell, vol.102, issue.1, pp.33-42, 2000.
DOI : 10.1016/S0092-8674(00)00008-8

O. Maler and D. Nickovic, Monitoring Temporal Properties of Continuous Signals Proceedings of Formal Techniques, Modelling and Analysis in Real-Time and Fault-Tolerant Systems Conference, pp.152-166, 2004.

A. Donzé, E. Fanchon, L. Gattepaille, O. Maler, and P. Tracqui, Robustness Analysis and Behavior Discrimination in Enzymatic Reaction Networks, PLoS ONE, vol.7, issue.9, p.24246, 2011.
DOI : 10.1371/journal.pone.0024246.s002

M. Rehm, H. Dussmann, R. Janicke, J. Tavare, and D. Kogel, Single-cell Fluorescence Resonance Energy Transfer Analysis Demonstrates That Caspase Activation during Apoptosis Is a Rapid Process: ROLE OF CASPASE-3, Journal of Biological Chemistry, vol.277, issue.27, pp.24506-24514, 2002.
DOI : 10.1074/jbc.M110789200

J. Barnat, L. Brim, I. Cerna, S. Drasan, and D. Safranek, Parallel Model Checking Large-Scale Genetic Regulatory Networks with DiVinE, Electronic Notes in Theoretical Computer Science, vol.194, issue.3, pp.35-50, 2008.
DOI : 10.1016/j.entcs.2007.12.001

G. Batt, B. Yordanov, R. Weiss, and C. Belta, Robustness analysis and tuning of synthetic gene networks, Bioinformatics, vol.23, issue.18, pp.2415-2422, 2007.
DOI : 10.1093/bioinformatics/btm362

G. Batt, M. Page, I. Cantone, G. Goessler, and P. Monteiro, Efficient parameter search for qualitative models of regulatory networks using symbolic model checking, Bioinformatics, vol.26, issue.18, pp.603-613, 2010.
DOI : 10.1093/bioinformatics/btq387

URL : https://hal.archives-ouvertes.fr/inria-00482569

G. Bernot, J. Comet, A. Richard, and J. Guespin, Application of formal methods to biological regulatory networks: extending Thomas??? asynchronous logical approach with temporal logic, Journal of Theoretical Biology, vol.229, issue.3, pp.339-347, 2004.
DOI : 10.1016/j.jtbi.2004.04.003

R. Donaldson and D. Gilbert, A Model Checking Approach to the Parameter Estimation of Biochemical Pathways, Computational Methods in Systems Biology, pp.269-287, 2008.
DOI : 10.1007/978-3-540-88562-7_20

J. Fisher, N. Piterman, A. Hajnal, and T. Henzinger, Predictive Modeling of Signaling Crosstalk during C. elegans Vulval Development, PLoS Computational Biology, vol.77, issue.5, p.92, 2007.
DOI : 0016-6731(1974)077[0071:TGOCE]2.0.CO;2

S. Jha, E. Clarke, and C. Langmead, A Bayesian Approach to Model Checking Biological Systems, Computational Methods in Systems Biology, vol.204, issue.9, pp.218-234, 2009.
DOI : 10.1016/j.ic.2006.05.002

J. Heath, M. Kwiatkowska, G. Norman, D. Parker, and O. Tymchyshyn, Probabilistic model checking of complex biological pathways, Theoretical Computer Science, vol.391, issue.3, pp.239-257, 2008.
DOI : 10.1016/j.tcs.2007.11.013

A. Donzé and O. Maler, Robust satisfaction of temporal logic over real-valued signals. Formal Modeling and Analysis of Timed Systems, pp.92-106, 2010.

J. Albeck, J. Burke, B. Aldridge, M. Zhang, and D. Lauffenburger, Quantitative Analysis of Pathways Controlling Extrinsic Apoptosis in Single Cells, Molecular Cell, vol.30, issue.1, pp.11-25, 2008.
DOI : 10.1016/j.molcel.2008.02.012

N. Agard, S. Mahrus, J. Trinidad, A. Lynn, and A. Burlingame, Global kinetic analysis of proteolysis via quantitative targeted proteomics, Proceedings of the National Academy of Sciences, vol.109, issue.6, pp.1913-1918, 2012.
DOI : 10.1073/pnas.1117158109

C. Maas, I. Verbrugge, E. De-vries, G. Savich, and L. Van-de-kooij, Smac/DIABLO release from mitochondria and XIAP inhibition are essential to limit clonogenicity of Type I tumor cells after TRAIL receptor stimulation, Cell Death and Differentiation, vol.7, issue.10, pp.1613-1623, 2010.
DOI : 10.1158/0008-5472.CAN-07-5173

URL : https://hal.archives-ouvertes.fr/hal-00526840

M. Avriel, Nonlinear programming: analysis and methods, 2003.

N. Hansen and A. Ostermeier, Completely Derandomized Self-Adaptation in Evolution Strategies, Evolutionary Computation, vol.9, issue.2, pp.159-195, 2001.
DOI : 10.1016/0004-3702(95)00124-7

M. Kober-a, S. Legewie, C. Pforr, N. Fricker, and R. Eils, Caspase-8 activity has an essential role in CD95/Fas-mediated MAPK activation, Cell Death and Disease, vol.1115, issue.10, p.212, 2011.
DOI : 10.1038/cddis.2011.93

G. Fainekos and G. Pappas, Robustness of temporal logic specifications for continuous-time signals, Theoretical Computer Science, vol.410, issue.42, pp.4262-4291, 2009.
DOI : 10.1016/j.tcs.2009.06.021

A. Rizk, G. Batt, F. Fages, and S. Soliman, Continuous valuations of temporal logic specifications with applications to parameter optimization and robustness measures, Theoretical Computer Science, vol.412, issue.26, pp.2827-2839, 2011.
DOI : 10.1016/j.tcs.2010.05.008

URL : https://hal.archives-ouvertes.fr/hal-01431314

E. Klipp, R. Herwig, A. Kowald, C. Wierling, and H. Lehrach, Systems Biology in Practice. Concepts, Implementation and Application, 2005.

Z. Szallasi, J. Stelling, and V. Periwal, System Modeling in Cellular Biology: From Concepts to Nuts and Bolts, 2010.
DOI : 10.7551/mitpress/9780262195485.001.0001

S. Ghosh, Y. Matsuoka, Y. Asai, K. Hsin, and H. Kitano, Software for systems biology: from tools to integrated platforms, Nature Reviews Genetics, vol.19, pp.821-832, 2011.
DOI : 10.1038/nrg3096

R. Serban and A. Hindmarsh, CVODES: The Sensitivity-Enabled ODE Solver in SUNDIALS, Volume 6: 5th International Conference on Multibody Systems, Nonlinear Dynamics, and Control, Parts A, B, and C, 2005.
DOI : 10.1115/DETC2005-85597