T. W. Fawcett and A. D. Higginson, Heavy use of equations impedes communication among biologists, Proceedings of the National Academy of Sciences, vol.77, issue.5659, pp.11735-11739, 2012.
DOI : 10.2307/2265753

URL : http://www.pnas.org/content/109/29/11735.full.pdf

A. R. Carvunis, E. Gomez, N. Thierry-mieg, L. Trilling, and M. Vidal, Systems biology : from yesterday's concepts to tomorrow's discoveries, Med Sci, pp.25-31, 2009.

A. D. Sheftel, D. R. Richardson, J. Prchal, and P. Ponka, Mitochondrial Iron Metabolism and Sideroblastic Anemia, Acta Haematologica, vol.122, issue.2-3, pp.120-133, 2009.
DOI : 10.1159/000243796

M. W. Hentze, M. U. Muckenthaler, and N. C. Andrews, Balancing Acts, Cell, vol.117, issue.3, pp.285-297, 2004.
DOI : 10.1016/S0092-8674(04)00343-5

M. A. Schaub, T. A. Henzinger, and J. Fisher, Qualitative networks : a symbolic approach to analyze biological signaling networks, BMC Syst Biol, vol.1, issue.4, 2007.

Z. P. Gerdtzen, Modeling Metabolic Networks for Mammalian Cell Systems: General Considerations, Modeling Strategies, and Available Tools, Genomics and Systems Biology of Mammalian Cell Culture, pp.71-108, 2012.
DOI : 10.1007/10_2011_120

R. Thomas, Logical Description, Analysis, and Synthesis of Biological and Other Networks Comprising Feedback Loops, Adv. Chem. Phys, vol.55, pp.247-282, 1983.
DOI : 10.1002/9780470142790.ch20

R. Thomas and R. , Biological Feedback, 1990.
URL : https://hal.archives-ouvertes.fr/hal-00087681

R. Thomas and M. Kaufman, Multistationarity, the basis of cell differentiation and memory. II. Logical analysis of regulatory networks in terms of feedback circuits, Chaos: An Interdisciplinary Journal of Nonlinear Science, vol.94, issue.1, pp.180-195, 2001.
DOI : 10.1007/978-3-642-49321-8_11

J. Demongeot, R. Thomas, and M. Thellier, A mathematical model for storage and recall functions in plants, Comptes Rendus de l'Acad??mie des Sciences - Series III - Sciences de la Vie, vol.323, issue.1, pp.93-97, 2000.
DOI : 10.1016/S0764-4469(00)00103-7

M. Kaufman, F. Andris, and O. Leo, A logical analysis of T cell activation and anergy, Proceedings of the National Academy of Sciences, vol.160, issue.1, pp.3894-3899, 1999.
DOI : 10.1084/jem.185.3.405

F. Corblin, S. Tripodi, É. Fanchon, D. Ropers, and L. Trilling, A declarative constraint-based method for analyzing discrete genetic regulatory networks, Biosystems, vol.98, issue.2, pp.91-104, 2009.
DOI : 10.1016/j.biosystems.2009.07.007

URL : https://hal.archives-ouvertes.fr/hal-00793012

F. Corblin, É. Fanchon, and L. Trilling, Applications of a formal approach to decipher discrete genetic networks, BMC Bioinformatics, vol.11, issue.1, 2010.
DOI : 10.1186/1471-2105-11-385

F. Achcar, J. Camadro, and D. Mestivier, A Boolean probabilistic model of metabolic adaptation to oxygen in relation to iron homeostasis and oxidative stress, BMC Systems Biology, vol.5, issue.1, 2011.
DOI : full_text

URL : https://hal.archives-ouvertes.fr/hal-00624203

A. Sackmann, D. Formanowicz, P. Formanowicz, and J. Blazewicz, New insights into the human body iron metabolism analyzed by a Petri net based approach, Biosystems, vol.96, issue.1, pp.104-113, 2009.
DOI : 10.1016/j.biosystems.2008.12.003

E. H. Snoussi, Qualitative dynamics of piecewise-linear differential equations: a discrete mapping approach, Dynamics and Stability of Systems, vol.54, issue.3-4, pp.565-583, 1989.
DOI : 10.1016/S0006-3495(71)86192-1

H. De-jong, J. L. Gouze, C. Hernandez, M. Page, T. Sari et al., Qualitative simulation of genetic regulatory networks using piecewise-linear models, Bulletin of Mathematical Biology, vol.66, issue.2, pp.301-340, 2004.
DOI : 10.1016/j.bulm.2003.08.010

URL : https://hal.archives-ouvertes.fr/hal-00173849

D. Ropers, H. De-jong, M. Page, D. Schneider, and J. Geiselmann, Qualitative simulation of the carbon starvation response in Escherichia coli, Biosystems, vol.84, issue.2, pp.124-152, 2006.
DOI : 10.1016/j.biosystems.2005.10.005

URL : https://hal.archives-ouvertes.fr/hal-00171698

D. Ropers, V. Baldazzi, H. De, and J. , Model Reduction Using Piecewise-Linear Approximations Preserves Dynamic Properties of the Carbon Starvation Response in Escherichia coli, IEEE/ACM Transactions on Computational Biology and Bioinformatics, vol.8, issue.1, pp.166-181, 2011.
DOI : 10.1109/TCBB.2009.49

URL : https://hal.archives-ouvertes.fr/hal-00793034

J. Ahmad, G. Bernot, J. Comet, D. Lime, and O. Roux, Hybrid Modelling and Dynamical Analysis of Gene Regulatory Networks with Delays, Complexus, vol.3, issue.4, pp.231-251, 2006.
DOI : 10.1159/000110010

URL : https://hal.archives-ouvertes.fr/hal-00415810

J. Comet, J. Fromentin, G. Bernot, and O. Roux, A Formal Model for Gene Regulatory Networks with Time Delays, 1st International Conference on Computational Systems-Biology and Bioinformatics, pp.1-13, 2010.
DOI : 10.3166/tsi.26.73-98

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

M. Davidich and S. Bornholdt, The transition from differential equations to Boolean networks: A case study in simplifying a regulatory network model, Journal of Theoretical Biology, vol.255, issue.3, pp.269-277, 2008.
DOI : 10.1016/j.jtbi.2008.07.020

G. Kervizic and L. Corcos, Dynamical modeling of the cholesterol regulatory pathway with Boolean networks, BMC Systems Biology, vol.2, issue.1, p.99, 2008.
DOI : 10.1186/1752-0509-2-99

J. Aracena, É. Fanchon, M. Montalva, and M. Noual, Combinatorics on update digraphs in Boolean networks, Discrete Applied Mathematics, vol.159, issue.6, pp.401-409, 2011.
DOI : 10.1016/j.dam.2010.10.010

J. J. Hopfield, Neural networks and physical systems with emergent collective computational abilities., Proceedings of the National Academy of Sciences, vol.79, issue.8, pp.2554-2558, 1982.
DOI : 10.1073/pnas.79.8.2554

T. Hervé, J. M. Dolmazon, and J. Demongeot, Random field and neural information., Proceedings of the National Academy of Sciences, pp.806-810, 1990.
DOI : 10.1073/pnas.87.2.806

J. Aracena, S. B. Lamine, M. A. Mermet, O. Cohen, and J. Demongeot, Mathematical modeling in genetic networks: relationships between the genetic expression and both chromosomic breakage and positive circuits, IEEE Transactions on Systems, Man and Cybernetics, Part B (Cybernetics), vol.33, issue.5, pp.825-834, 2003.
DOI : 10.1109/TSMCB.2003.816928

J. Aracena, J. Demongeot, and E. Goles, Positive and Negative Circuits in Discrete Neural Networks, IEEE Transactions on Neural Networks, vol.15, issue.1, pp.77-83, 2004.
DOI : 10.1109/TNN.2003.821555

H. B. Amor, F. Corblin, É. Fanchon, A. Elena, L. Trilling et al., Formal Methods for Hopfield-Like Networks, Acta Biotheoretica, vol.9, issue.2, pp.21-39, 2013.
DOI : 10.1007/978-3-642-81703-8_24

URL : https://hal.archives-ouvertes.fr/hal-00834160

J. Demongeot32-]-r, H. David, and . Alla, Discrete, Continuous, and Hybrid Petri Nets Quantitative modeling of stochastic systems in molecular biology by using stochastic Petri nets, Random automata networks Automata networks in computer science : theory and applications, pp.47-57, 1987.

Á. M. Halász, H. J. Lai, M. Mccabe-pryor, K. Radhakrishnan, and J. S. Edwards, Analytical Solution of Steady-State Equations for Chemical Reaction Networks with Bilinear Rate Laws, IEEE/ACM Transactions on Computational Biology and Bioinformatics, vol.10, issue.4, pp.957-969, 2013.
DOI : 10.1109/TCBB.2013.41

E. Asarin, T. Dang, and A. Girard, Hybridization methods for the analysis of nonlinear systems, Acta Informatica, vol.12, issue.2, pp.451-476, 2007.
DOI : 10.1007/978-1-4612-0017-8

URL : https://hal.archives-ouvertes.fr/hal-00157475

M. B. Sass, A. N. Lorenz, R. L. Green, and R. A. Coleman, A pragmatic approach to biochemical systems theory applied to an ??-synuclein-based model of Parkinson's disease, Journal of Neuroscience Methods, vol.178, issue.2, pp.366-377, 2009.
DOI : 10.1016/j.jneumeth.2008.12.014

M. W. Covert, C. H. Schilling, and B. Palsson, Regulation of Gene Expression in Flux Balance Models of Metabolism, Journal of Theoretical Biology, vol.213, issue.1, pp.73-88, 2001.
DOI : 10.1006/jtbi.2001.2405

O. Maler and D. Nickovic, Monitoring Temporal Properties of Continuous Signals, Lecture Notes in Computer Science, vol.3253, pp.152-166, 2004.
DOI : 10.1007/978-3-540-30206-3_12

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=

A. Donzé, É. Fanchon, L. M. 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

S. Stoma, A. Donzé, F. Bertaux, O. Maler, and G. Batt, STL-based Analysis of TRAIL-induced Apoptosis Challenges the Notion of Type I/Type II Cell Line Classification, PLoS Computational Biology, vol.102, issue.5, p.1003056, 2013.
DOI : 10.1371/journal.pcbi.1003056.s010

URL : https://hal.archives-ouvertes.fr/hal-00750063

J. J. Tyson, K. C. Chen, and B. Novak, Sniffers, buzzers, toggles and blinkers: dynamics of regulatory and signaling pathways in the cell, Current Opinion in Cell Biology, vol.15, issue.2, pp.221-231, 2003.
DOI : 10.1016/S0955-0674(03)00017-6

H. Kitano, Biological robustness, Nature Reviews Genetics, vol.37, issue.11, pp.826-837, 2004.
DOI : 10.1038/scientificamerican1179-98

K. Csillery, M. G. Blum, O. E. Gaggiotti, and O. Francois, Approximate Bayesian Computation (ABC) in practice, Trends in Ecology & Evolution, vol.25, issue.7, pp.25410-418, 2010.
DOI : 10.1016/j.tree.2010.04.001

URL : https://hal.archives-ouvertes.fr/hal-00553810

A. Georgoulas, A. Clark, A. Ocone, S. Gilmore, and G. Sanguinetti, A subsystems approach for parameter estimation of ODE models of hybrid systems, Electronic Proceedings in Theoretical Computer Science, pp.30-41, 2012.
DOI : 10.4204/EPTCS.92.3

T. Toni, D. Welch, N. Strelkowa, A. Ipsen, and M. P. Stumpf, Approximate Bayesian computation scheme for parameter inference and model selection in dynamical systems, Journal of The Royal Society Interface, vol.24, issue.6, pp.187-202, 2009.
DOI : 10.1093/bioinformatics/btm607

URL : http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2658655

T. J. Hickey and D. K. Wittenberg, Rigorous Modeling of Hybrid Systems Using Interval Arithmetic Constraints, Hybrid Systems : Computation and Control, pp.402-416, 2004.
DOI : 10.1007/978-3-540-24743-2_27

A. Donzé, Breach, A Toolbox for Verification and Parameter Synthesis of Hybrid Systems, CAV, pp.167-170, 2010.
DOI : 10.1007/978-3-642-14295-6_17

A. C. Hindmarsh, P. N. Brown, K. E. Grant, S. L. Lee, R. Serban et al., SUNDIALS, ACM Transactions on Mathematical Software, vol.31, issue.3, pp.31363-396, 2005.
DOI : 10.1145/1089014.1089020

J. Wang and K. Pantopoulos, Regulation of cellular iron metabolism, Biochemical Journal, vol.18, issue.3, pp.365-381, 2011.
DOI : 10.1126/science.283.5402.676

Y. Yu, Z. Kovacevic, and D. R. Richardson, Tuning Cell Cycle Regulation with an Iron Key, Cell Cycle, vol.6, issue.16, pp.1982-1994, 2007.
DOI : 10.4161/cc.6.16.4603

G. Cairo and S. Recalcati, Iron-regulatory proteins : molecular biology and pathophysiological implications Expert reviews in molecular medicine, pp.1-13, 2007.

M. P. Yeager and R. A. Coleman, In silico evidence for glutathione- and iron-related pathogeneses in Parkinson's disease, Journal of Neuroscience Methods, vol.188, issue.1, pp.151-164, 2010.
DOI : 10.1016/j.jneumeth.2010.01.034

V. Hower, P. Mendes, F. M. Torti, R. Laubenbacher, S. Akman et al., A general map of iron metabolism and tissue-specific subnetworks, Molecular BioSystems, vol.65, issue.6, pp.422-443, 2009.
DOI : 10.1177/002215549704500306

K. Pantopoulos, S. K. Porwal, A. Tartakoff, and L. Devireddy, Mechanisms of Mammalian Iron Homeostasis, Biochemistry, vol.51, issue.29, pp.5705-5724, 2012.
DOI : 10.1021/bi300752r

URL : http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3572738

A. Funahashi, M. Morohashi, H. Kitano, and N. Tanimura, CellDesigner: a process diagram editor for gene-regulatory and biochemical networks, BIOSILICO, vol.1, issue.5, pp.159-162, 2003.
DOI : 10.1016/S1478-5382(03)02370-9

F. Samaniego, J. Chin, K. Iwai, T. A. Rouault, and R. D. Klausner, Molecular characterization of a second iron-responsive element binding protein, iron regulatory protein 2. Structure, function, and post-translational regulation, J. Biol. Chem, vol.269, issue.49, pp.30904-30910, 1994.

B. R. Henderson and L. C. Kuhn, Differential Modulation of the RNA-binding Proteins IRP-1 and IRP-2 in Response to Iron, Journal of Biological Chemistry, vol.267, issue.35, pp.20509-20515, 1995.
DOI : 10.1073/pnas.85.24.9503

N. K. Gray and M. W. Hentze, Iron regulatory protein prevents binding of the 43S translation pre-initiation complex to ferritin and eALAS mRNAs, EMBO J, vol.13, issue.16, pp.3882-3891, 1994.

A. A. Vashisht, K. B. Zumbrennen, X. Huang, D. N. Powers, A. Durazo et al., Control of Iron Homeostasis by an Iron-Regulated Ubiquitin Ligase, Science, vol.33, issue.suppl_2, pp.326718-721, 2009.
DOI : 10.1093/nar/gki408

B. J. Iacopetta and E. H. Morgan, The kinetics of transferrin endocytosis and iron uptake from transferrin in rabbit reticulocytes, J. Biol. Chem, vol.258, issue.15, pp.9108-9115, 1983.

A. D. Sheftel, A. S. Zhang, C. Brown, O. S. Shirihai, and P. Ponka, Direct interorganellar transfer of iron from endosome to mitochondrion, Blood, vol.110, issue.1, pp.125-132, 2007.
DOI : 10.1182/blood-2007-01-068148

C. Seiser, M. Posch, N. Thompson, and L. C. Kuhn, Effect of Transcription Inhibitors on the Iron-dependent Degradation of Transferrin Receptor mRNA, Journal of Biological Chemistry, vol.261, issue.49, pp.29400-29406, 1995.
DOI : 10.1128/MCB.9.5.1996

R. Erlitzki, J. C. Long, and E. C. , Multiple, Conserved Iron-responsive Elements in the 3???-Untranslated Region of Transferrin Receptor mRNA Enhance Binding of Iron Regulatory Protein 2, Journal of Biological Chemistry, vol.46, issue.45, pp.42579-42587, 2002.
DOI : 10.1074/jbc.M203276200

N. Hubert and M. W. Hentze, Previously uncharacterized isoforms of divalent metal transporter (DMT)-1: Implications for regulation and cellular function, Proceedings of the National Academy of Sciences, vol.363, issue.Pt 3, pp.12345-12350, 2002.
DOI : 10.1042/0264-6021:3630449

A. P. West, M. J. Bennett, V. M. Sellers, N. C. Andrews, C. A. Enns et al., Comparison of the Interactions of Transferrin Receptor and Transferrin Receptor 2 with Transferrin and the Hereditary Hemochromatosis Protein HFE, Journal of Biological Chemistry, vol.94, issue.49, pp.27538135-38138, 2000.
DOI : 10.1073/pnas.93.1.13

B. J. Iacopetta, E. H. Morgan, and G. C. Yeoh, Transferrin receptors and iron uptake during erythroid cell development, Biochimica et Biophysica Acta (BBA) - Biomembranes, vol.687, issue.2, pp.204-210, 1982.
DOI : 10.1016/0005-2736(82)90547-8

I. De-domenico, D. M. Ward, G. Musci, and J. Kaplan, Evidence for the multimeric structure of ferroportin, Blood, vol.109, issue.5, pp.2205-2209, 2007.
DOI : 10.1182/blood-2006-06-032516

D. L. Zhang, R. M. Hughes, H. Ollivierre-wilson, M. C. Ghosh, and T. A. Rouault, A Ferroportin Transcript that Lacks an Iron-Responsive Element Enables Duodenal and Erythroid Precursor Cells to Evade Translational Repression, Cell Metabolism, vol.9, issue.5, pp.461-473, 2009.
DOI : 10.1016/j.cmet.2009.03.006

D. M. Ward and J. Kaplan, Ferroportin-mediated iron transport: Expression and regulation, Biochimica et Biophysica Acta (BBA) - Molecular Cell Research, vol.1823, issue.9, pp.1426-1433, 2012.
DOI : 10.1016/j.bbamcr.2012.03.004

URL : http://doi.org/10.1016/j.bbamcr.2012.03.004

L. Cianetti, P. Segnalini, A. Calzolari, O. Morsilli, F. Felicetti et al., Expression of alternative transcripts of ferroportin-1 during human erythroid differentiation, Haematologica, issue.12, pp.901595-1606, 2005.

L. Cianetti, M. Gabbianelli, and N. M. Sposi, Ferroportin and Erythroid Cells: An Update, Advances in Hematology, vol.34, issue.1, 2010.
DOI : 10.1042/BST0340007

URL : http://doi.org/10.1155/2010/404173

P. M. Harrison and P. Arosio, The ferritins: molecular properties, iron storage function and cellular regulation, Biochimica et Biophysica Acta (BBA) - Bioenergetics, vol.1275, issue.3, pp.1275161-203, 1996.
DOI : 10.1016/0005-2728(96)00022-9

URL : http://doi.org/10.1016/0005-2728(96)00022-9

N. D. Chasteen and P. M. Harrison, Mineralization in Ferritin: An Efficient Means of Iron Storage, Journal of Structural Biology, vol.126, issue.3, pp.182-194, 1999.
DOI : 10.1006/jsbi.1999.4118

D. M. Lawson, A. Treffry, P. J. Artymiuk, P. M. Harrison, S. J. Yewdall et al., Identification of the ferroxidase centre in ferritin, FEBS Letters, vol.27, issue.1-2, pp.207-210, 1989.
DOI : 10.1016/0162-0134(86)80068-X

H. Shi, K. Z. Bencze, T. L. Stemmler, and C. C. Philpott, A Cytosolic Iron Chaperone That Delivers Iron to Ferritin, Science, vol.2, issue.7, pp.1207-1210, 2008.
DOI : 10.1038/nchembio797

URL : http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2505357

I. De-domenico, M. B. Vaughn, L. Li, D. Bagley, G. Musci et al., Ferroportin-mediated mobilization of ferritin iron precedes ferritin degradation by the proteasome, The EMBO Journal, vol.278, issue.22, pp.5396-5404, 2006.
DOI : 10.1083/jcb.110.4.1013

M. W. Hentze, T. A. Rouault, S. W. Caughman, A. Dancis, J. B. Harford et al., A cis-acting element is necessary and sufficient for translational regulation of human ferritin expression in response to iron., Proceedings of the National Academy of Sciences, vol.84, issue.19, pp.6730-6734, 1987.
DOI : 10.1073/pnas.84.19.6730

N. Aziz and H. N. Munro, Iron regulates ferritin mRNA translation through a segment of its 5' untranslated region., Proceedings of the National Academy of Sciences, vol.84, issue.23, pp.8478-8482, 1987.
DOI : 10.1073/pnas.84.23.8478

E. Pourcelot, M. Lénon, N. Mobilia, J. Y. Cahn, J. Arnaud et al., Iron for proliferation of cell lines and hematopoietic progenitors: Nailing down the intracellular functional iron concentration, Biochimica et Biophysica Acta (BBA) - Molecular Cell Research, vol.1853, issue.7, pp.18531596-1605, 2015.
DOI : 10.1016/j.bbamcr.2015.03.009

M. Shvartsman, E. Fibach, and Z. I. Cabantchik, Transferrin-iron routing to the cytosol and mitochondria as studied by live and real-time fluorescence, Biochemical Journal, vol.258, issue.1, pp.185-193, 2010.
DOI : 10.1111/j.1365-2141.1978.tb03662.x

D. R. Richardson, D. J. Lane, E. M. Becker, M. L. Huang, M. Whitnall et al., Mitochondrial iron trafficking and the integration of iron metabolism between the mitochondrion and cytosol, Proceedings of the National Academy of Sciences, vol.74, issue.6, pp.10775-10782, 2010.
DOI : 10.1086/421530

G. C. Ferreira and J. Gong, 5-Aminolevulinate synthase and the first step of heme biosynthesis, Journal of Bioenergetics and Biomembranes, vol.135, issue.2, pp.151-159, 1995.
DOI : 10.1042/bj1350257

D. B. Mirel, K. Marder, J. Graziano, G. Freyer, Q. Zhao et al., Characterization of the human mitochondrial aconitase gene (ACO2), Gene, vol.213, issue.1-2, pp.205-218, 1998.
DOI : 10.1016/S0378-1119(98)00188-7

T. C. Cox, M. J. Bawden, A. Martin, and B. K. May, Human erythroid 5-aminolevulinate synthase : promoter analysis and identification of an iron-responsive element in the mRNA, EMBO J, vol.10, issue.7, pp.1891-1902, 1991.

C. K. Wu, H. A. Dailey, J. P. Rose, A. Burden, V. M. Sellers et al., The 2.0 A structure of human ferrochelatase, the terminal enzyme of heme biosynthesis, Nature Structural Biology, vol.8, issue.2, pp.156-160, 2001.
DOI : 10.1038/84152

URL : https://hal.archives-ouvertes.fr/in2p3-00857363

D. R. Crooks, M. C. Ghosh, R. G. Haller, W. H. Tong, and T. A. Rouault, Posttranslational stability of the heme biosynthetic enzyme ferrochelatase is dependent on iron availability and intact iron-sulfur cluster assembly machinery, Blood, vol.115, issue.4, pp.860-869, 2010.
DOI : 10.1182/blood-2009-09-243105

D. Krell, M. Assoku, M. Galloway, P. Mulholland, I. Tomlinson et al., Screen for IDH1, IDH2, IDH3, D2HGDH and L2HGDH Mutations in Glioblastoma, PLoS ONE, vol.16, issue.5, p.19868, 2011.
DOI : 10.1371/journal.pone.0019868.g002

URL : http://doi.org/10.1371/journal.pone.0019868

L. Oliveira and J. C. Drapier, Down-regulation of iron regulatory protein 1 gene expression by nitric oxide, Proceedings of the National Academy of Sciences, vol.179, issue.1, pp.6550-6555, 2000.
DOI : 10.1016/S0378-1119(96)00329-0

F. Zhang, W. Wang, Y. Tsuji, S. V. Torti, and F. M. Torti, Post-transcriptional Modulation of Iron Homeostasis during p53-dependent Growth Arrest, Journal of Biological Chemistry, vol.12, issue.49, pp.33911-33918, 2008.
DOI : 10.1038/nrm2147

M. W. Hentze and L. C. Kuhn, Molecular control of vertebrate iron metabolism: mRNA-based regulatory circuits operated by iron, nitric oxide, and oxidative stress., Proceedings of the National Academy of Sciences, vol.93, issue.16, pp.8175-8182, 1996.
DOI : 10.1073/pnas.93.16.8175

M. Castoldi and M. U. Muckenthaler, Regulation of iron homeostasis by microRNAs, Cellular and Molecular Life Sciences, vol.10, issue.23, pp.3945-3952, 2012.
DOI : 10.1016/j.bbagen.2010.02.005

C. Sangokoya, J. F. Doss, and J. T. Chi, Iron-Responsive miR-485-3p Regulates Cellular Iron Homeostasis by Targeting Ferroportin, PLoS Genetics, vol.116, issue.4, p.1003408, 2013.
DOI : 10.1371/journal.pgen.1003408.s005

URL : http://doi.org/10.1371/journal.pgen.1003408

E. Nemeth and T. Ganz, Regulation of Iron Metabolism by Hepcidin, Annual Review of Nutrition, vol.26, issue.1, pp.323-342, 2006.
DOI : 10.1146/annurev.nutr.26.061505.111303

URL : https://hal.archives-ouvertes.fr/inserm-00864080

E. Nemeth, M. S. Tuttle, J. Powelson, M. B. Vaughn, A. Donovan et al., Hepcidin Regulates Cellular Iron Efflux by Binding to Ferroportin and Inducing Its Internalization, Science, vol.306, issue.5704, pp.3062090-2093, 2004.
DOI : 10.1126/science.1104742

J. A. Borghans, R. J. De-boer, and L. A. Segel, Extending the quasi-steady state approximation by changing variables, Bulletin of Mathematical Biology, vol.26, issue.1, pp.43-63, 1996.
DOI : 10.1007/BF02458281

S. W. Omholt, X. Kefang, Ø. Andersen, and E. Plahte, Description and Analysis of Switchlike Regulatory Networks Exemplified by a Model of Cellular Iron Homeostasis, Journal of Theoretical Biology, vol.195, issue.3, pp.339-350, 1998.
DOI : 10.1006/jtbi.1998.0800

E. H. Flach and S. Schnell, Use and abuse of the quasi-steady-state approximation, IEE Proceedings - Systems Biology, vol.153, issue.4, pp.187-191, 2006.
DOI : 10.1049/ip-syb:20050104

C. J. Doherty and S. A. Kay, Circadian Control of Global Gene Expression Patterns, Annual Review of Genetics, vol.44, issue.1, pp.419-444, 2010.
DOI : 10.1146/annurev-genet-102209-163432

URL : http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4251774

E. Buckingham, On Physically Similar Systems; Illustrations of the Use of Dimensional Equations, Physical Review, vol.4, issue.4, pp.345-376, 1914.
DOI : 10.1103/PhysRev.4.345

W. G. Xu and Q. S. Li, The dimensionlessness of chemical kinetic equation, Journal of Mathematical Chemistry, vol.31, issue.3, pp.237-250, 2002.
DOI : 10.1023/A:1020720920578

S. H. Lam and D. A. Goussis, The CSP method for simplifying kinetics, International Journal of Chemical Kinetics, vol.79, issue.4, pp.461-486, 1994.
DOI : 10.1007/978-1-4684-4298-4_1

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=

W. A. Stein, The Sage Development Team, Sage Mathematics Software, 2014.

J. Chifman, A. Kniss, P. Neupane, I. Williams, B. Leung et al., The core control system of intracellular iron homeostasis: A mathematical model, Journal of Theoretical Biology, vol.300, pp.91-99, 2012.
DOI : 10.1016/j.jtbi.2012.01.024

S. Mitchell and P. Mendes, A Computational Model of Liver Iron Metabolism, PLoS Computational Biology, vol.142, issue.11, p.1003299, 2013.
DOI : 10.1371/journal.pcbi.1003299.s002

T. Dang and T. Dreossi, Falsifying Oscillation Properties of Parametric Biological Models, Proceedings Second International Workshop on Hybrid Systems and Biology, HSB 2013, pp.53-67, 2013.
DOI : 10.4204/EPTCS.125.4

L. Granvilliers and F. Benhamou, Algorithm 852, ACM Transactions on Mathematical Software, vol.32, issue.1, pp.138-156, 2006.
DOI : 10.1145/1132973.1132980

URL : https://hal.archives-ouvertes.fr/hal-00480813

N. C. Andrews, Forging a field: the golden age of iron biology, Blood, vol.112, issue.2, pp.219-230, 2008.
DOI : 10.1182/blood-2007-12-077388

D. Galaris and K. Pantopoulos, Oxidative Stress and Iron Homeostasis: Mechanistic and Health Aspects, Critical Reviews in Clinical Laboratory Sciences, vol.13, issue.1, pp.1-23, 2008.
DOI : 10.1038/nm1542

I. De-domenico, D. Mcvey, J. Ward, and . Kaplan, Regulation of iron acquisition and storage: consequences for iron-linked disorders, Nature Reviews Molecular Cell Biology, vol.39, issue.1, pp.72-81, 2008.
DOI : 10.1093/ajcp/96.2.215

R. C. Hider and X. Kong, Iron speciation in the cytosol: an overview, Dalton Trans., vol.30, issue.6, pp.3220-3229, 2013.
DOI : 10.1038/emboj.2011.105

P. Arosio and S. Levi, Cytosolic and mitochondrial ferritins in the regulation of cellular iron homeostasis and oxidative damage, Biochimica et Biophysica Acta (BBA) - General Subjects, vol.1800, issue.8, pp.1800783-792, 2010.
DOI : 10.1016/j.bbagen.2010.02.005

J. C. Salgado, A. Olivera-nappa, Z. P. Gerdtzen, V. Tapia, E. C. Theil et al., Mathematical modeling of the dynamic storage of iron in ferritin, BMC Systems Biology, vol.4, issue.1, p.147, 2010.
DOI : 10.1186/1752-0509-4-147

P. Aisen, Transferrin receptor 1, The International Journal of Biochemistry & Cell Biology, vol.36, issue.11, pp.2137-2143, 2004.
DOI : 10.1016/j.biocel.2004.02.007

R. Mayr, A. R. Janecke, M. Schranz, W. J. Griffiths, W. Vogel et al., Ferroportin disease: A systematic meta-analysis of clinical and molecular findings, Journal of Hepatology, vol.53, issue.5, pp.941-949, 2010.
DOI : 10.1016/j.jhep.2010.05.016

J. Gouzé, Positive and Negative Circuits in Dynamical Systems, Journal of Biological Systems, vol.06, issue.01, pp.11-15, 1998.
DOI : 10.1142/S0218339098000054

A. Donzé and O. Maler, Robust Satisfaction of Temporal Logic over Real-Valued Signals, FORMATS, pp.92-106, 2010.
DOI : 10.1007/978-3-642-15297-9_9

W. A. Stein, Version 6.2) The Sage Development Team, Sage Mathematics Software, 2014.

J. A. Nelder and R. Mead, A Simplex Method for Function Minimization, The Computer Journal, vol.7, issue.4, pp.308-313, 1965.
DOI : 10.1093/comjnl/7.4.308

E. Zamora-sillero, M. Hafner, A. Ibig, J. Stelling, and A. Wagner, Efficient characterization of high-dimensional parameter spaces for systems biology, BMC Systems Biology, vol.5, issue.1, p.142, 2011.
DOI : 10.1371/journal.pcbi.0030189

M. G. Kendall, A NEW MEASURE OF RANK CORRELATION, Biometrika, vol.30, issue.1-2, pp.81-93, 1938.
DOI : 10.1093/biomet/30.1-2.81

W. N. Venables and B. D. Ripley, Modern Applied Statistics with S, 2002.
DOI : 10.1007/978-0-387-21706-2

R. Development and C. Team, R : A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, 2011.

A. C. Cameron and P. K. Trivedi, Microeconometrics : methods and applications, 2005.
DOI : 10.1017/CBO9780511811241

H. R. Bengtsson and . Matlab, Read and write of MAT files together with R-to-MATLAB connectivity, 2014.

E. Pourcelot, N. Mobilia, A. Donzé, F. Louis, O. Maler et al., Cellular iron regulation in animals : need and use of suitable models, Nutzen- Risiko-Bewertung von Mineralstoffen und Spurenelemente : Biochemische, physiologische und toxikologische Aspekte, pp.73-89, 2013.

M. D. Knutson, M. Oukka, L. M. Koss, F. Aydemir, and M. Wessling-resnick, Iron release from macrophages after erythrophagocytosis is up-regulated by ferroportin 1 overexpression and down-regulated by hepcidin, Proceedings of the National Academy of Sciences, vol.29, issue.3, pp.1324-1328, 2005.
DOI : 10.1006/bcmd.2002.0572

URL : http://www.ncbi.nlm.nih.gov/pmc/articles/PMC547844

C. Dycke, P. Charbonnier, K. Pantopoulos, and J. M. Moulis, A role for lysosomes in the turnover of human iron regulatory protein 2, The International Journal of Biochemistry & Cell Biology, vol.40, issue.12, pp.2826-2832, 2008.
DOI : 10.1016/j.biocel.2008.05.015

URL : https://hal.archives-ouvertes.fr/hal-00382015

A. M. Weissman, R. D. Klausner, K. Rao, and J. B. Harford, Exposure of K562 cells to anti-receptor monoclonal antibody OKT9 results in rapid redistribution and enhanced degradation of the transferrin receptor, The Journal of Cell Biology, vol.102, issue.3, pp.951-958, 1986.
DOI : 10.1083/jcb.102.3.951

R. Moirand, A. M. Mortaji, O. Loréal, F. Paillard, P. Brissot et al., A new syndrome of liver iron overload with normal transferrin saturation. The Lancet, pp.95-97, 1997.

S. Epsztejn, O. Kakhlon, H. Glickstein, W. Breuer, and I. Cabantchik, Fluorescence Analysis of the Labile Iron Pool of Mammalian Cells, Analytical Biochemistry, vol.248, issue.1, pp.31-40, 1997.
DOI : 10.1006/abio.1997.2126

O. S. Chen, K. P. Blemings, K. L. Schalinske, and R. S. Eisenstein, Dietary iron intake rapidly influences iron regulatory proteins, ferritin subunits and mitochondrial aconitase in rat liver, J. Nutr, vol.128, issue.3, pp.525-535, 1998.

R. C. Hunt and L. Marshall-carlson, Internalization and recycling of transferrin and its receptor. Effect of trifluoperazine on recycling in human erythroleukemic cells, J. Biol. Chem, vol.261, issue.8, pp.3681-3686, 1986.

J. Chifman, R. Laubenbacher, and S. V. Torti, A Systems Biology Approach to Iron Metabolism, Adv. Exp. Med. Biol, vol.844, pp.201-225, 2014.
DOI : 10.1007/978-1-4939-2095-2_10

URL : http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4464783

T. J. Lopes, T. Luganskaja, M. Vuji?-spasi?, M. W. Hentze, M. U. Muckenthaler et al., Systems analysis of iron metabolism: the network of iron pools and fluxes, BMC Systems Biology, vol.4, issue.1, 2010.
DOI : 10.1186/1752-0509-4-112

F. Achcar, Modélisations Booléennes probabilistes de l'homéostasie du fer pour l'exploration des liens entre stress oxydant et perturbations métaboliques : de la cellule à l'organisme, 2010.

D. Formanowicz, A. Sackmann, P. Formanowicz, and J. B?a?ewicz, Petri net based model of the body iron homeostasis, Journal of Biomedical Informatics, vol.40, issue.5, pp.476-485, 2007.
DOI : 10.1016/j.jbi.2006.12.001

J. Blazewicz, D. Formanowicz, P. Formanowicz, A. Sackmann, and M. Sajkowski, Modeling the process of human body iron homeostasis using a variant of timed Petri nets, Discrete Applied Mathematics, vol.157, issue.10, pp.2221-2231, 2009.
DOI : 10.1016/j.dam.2008.06.053

V. Becker, M. Schilling, J. Bachmann, U. Baumann, A. Raue et al., Covering a Broad Dynamic Range: Information Processing at the Erythropoietin Receptor, Science, vol.368, issue.9539, pp.3281404-1408, 2010.
DOI : 10.1016/S0140-6736(06)69120-4

W. Wang, X. Di, R. B. D-'agostino, S. V. Torti, and F. M. Torti, Excess Capacity of the Iron Regulatory Protein System, Journal of Biological Chemistry, vol.165, issue.34, pp.24650-24659, 2007.
DOI : 10.1074/jbc.M100941200

J. Ma, S. Haldar, M. A. Khan, S. D. Sharma, W. C. Merrick et al., Fe2+ binds iron responsive element-RNA, selectively changing protein-binding affinities and regulating mRNA repression and activation, Proceedings of the National Academy of Sciences, vol.276, issue.46, pp.8417-8422, 2012.
DOI : 10.1074/jbc.M104970200

URL : http://www.pnas.org/content/109/22/8417.full.pdf

J. B. Goforth, S. A. Anderson, C. P. Nizzi, and R. S. Eisenstein, Multiple determinants within iron-responsive elements dictate iron regulatory protein binding and regulatory hierarchy, RNA, vol.16, issue.1, pp.154-169, 2010.
DOI : 10.1261/rna.1857210

URL : http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2802025

R. M. Coulson and D. W. Cleveland, Ferritin synthesis is controlled by iron-dependent translational derepression and by changes in synthesis/transport of nuclear ferritin RNAs., Proceedings of the National Academy of Sciences, vol.90, issue.16, pp.7613-7617, 1993.
DOI : 10.1073/pnas.90.16.7613

L. V. Sharova, A. A. Sharov, T. Nedorezov, Y. Piao, N. Shaik et al., Database for mRNA Half-Life of 19 977 Genes Obtained by DNA Microarray Analysis of Pluripotent and Differentiating Mouse Embryonic Stem Cells, DNA Research, vol.16, issue.1, pp.45-58, 2009.
DOI : 10.1093/dnares/dsn030

S. Reuveni, I. Meilijson, M. Kupiec, E. Ruppin, and T. Tuller, Genome-Scale Analysis of Translation Elongation with a Ribosome Flow Model, PLoS Computational Biology, vol.455, issue.9, p.1002127, 2011.
DOI : 10.1371/journal.pcbi.1002127.s033

R. Y. Chan, C. Seiser, H. M. Schulman, L. C. Kühn, and P. Ponka, Regulation of transferrin receptor mRNA expression. Distinct regulatory features in erythroid cells, European Journal of Biochemistry, vol.17, issue.3, pp.683-692, 1994.
DOI : 10.1016/0014-4827(84)90180-0

E. Mattia, K. Rao, D. S. Shapiro, H. H. Sussman, and R. D. Klausner, Biosynthetic regulation of the human transferrin receptor by desferrioxamine in K562 cells, J. Biol. Chem, vol.259, issue.5, pp.2689-2692, 1984.

P. Shannon, A. Markiel, O. Ozier, N. S. Baliga, J. T. Wang et al., Cytoscape: A Software Environment for Integrated Models of Biomolecular Interaction Networks, Genome Research, vol.13, issue.11, pp.2498-2504, 2003.
DOI : 10.1101/gr.1239303

J. Demongeot, O. Cohen, and A. , Henrion-Caude. MicroRNAs and robustness in biological regulatory networks. a generic approach with applications at different levels : Physiologic, metabolic, and genetic, Systems Biology of Metabolic and Signaling Networks, pp.63-114, 2014.

T. Z. Kidane, E. Sauble, and M. C. Linder, Release of iron from ferritin requires lysosomal activity, AJP: Cell Physiology, vol.291, issue.3, pp.445-455, 2006.
DOI : 10.1152/ajpcell.00505.2005

K. Pantopoulos, N. K. Gray, and M. W. Hentze, Differential regulation of two related RNA-binding proteins, iron regulatory protein (IRP) and IRPB, RNA, vol.1, issue.2, pp.155-163, 1995.

E. Pourcelot, Homéostasie cellulaire du fer dans les cellules leucémiques myéloïdes, 2015.

T. Sun, W. Yang, J. Liu, and P. Shen, Modeling the Basal Dynamics of P53 System, PLoS ONE, vol.28, issue.11, p.27882, 2011.
DOI : 10.1371/journal.pone.0027882.s010

X. Brazzolotto, M. Andriollo, P. Guiraud, A. Favier, and J. M. Moulis, Interactions between doxorubicin and the human iron regulatory system, Biochimica et Biophysica Acta (BBA) - Molecular Cell Research, vol.1593, issue.2-3, pp.1593-1595, 2003.
DOI : 10.1016/S0167-4889(02)00391-9

URL : http://doi.org/10.1016/s0167-4889(02)00391-9

E. P. Testa, U. Testa, P. Samoggia, G. Salvo, A. Camagna et al., Expression of transferrin receptors in human erythroleukemic lines : regulation in the plateau and exponential phase of growth, Cancer Res, vol.46, issue.10, pp.5330-5334, 1986.

L. L. Chu and R. A. Fineberg, On the mechanism of iron-induced synthesis of apoferritin in HeLa cells, J. Biol. Chem, vol.244, issue.14, pp.3847-3854, 1969.

Y. Deville, M. Janssen, and P. Van-hentenryck, Consistency Techniques in Ordinary Differential Equations, Principles and Practice of Constraint Programming ? CP98, pp.162-176, 1998.
DOI : 10.1007/3-540-49481-2_13

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=

N. Mobilia, A. Rocca, S. Chorlton, L. Fanchon, and . Trilling, Logical Modeling and Analysis of Regulatory Genetic Networks in a Non Monotonic Framework, In Bioinformatics and Biomedical Engineering, vol.9043, pp.599-612, 2015.
DOI : 10.1007/978-3-319-16483-0_58

C. Baral, Knowledge Representation, Reasoning, and Declarative Problem Solving, 2003.
DOI : 10.1017/CBO9780511543357

M. Gebser, R. Kaminski, B. Kaufmann, M. Ostrowski, T. Schaub et al., A user's guide to gringo, clasp, clingo, and iclingo (version 3, 2010.

P. Besnard, An Introduction to Default Logic, 1989.
DOI : 10.1007/978-3-662-05689-9

G. Bossu and P. Siegel, Saturation, nonmonotonic reasoning and the closed-world assumption, Artificial Intelligence, vol.25, issue.1, pp.13-63, 1985.
DOI : 10.1016/0004-3702(85)90040-2

F. Corblin, L. Fanchon, C. Trilling, D. Chaouiya, and . Thieffry, Automatic inference of regulatory and dynamical properties from incomplete gene interaction and expression data [166] L. Sánchez and D. Thieffry. A logical analysis of the Drosophila Gap-gene system, Information Processing in Cells and Tissues, pp.25-30115, 2001.

J. Jaeger, M. Blagov, D. Kosman, K. N. Kozlov, E. Manu et al., Dynamical Analysis of Regulatory Interactions in the Gap Gene System of Drosophila melanogaster, Genetics, vol.167, issue.4, pp.1721-1737, 2004.
DOI : 10.1534/genetics.104.027334

F. Alves and R. Dilão, Modeling segmental patterning in Drosophila: Maternal and gap genes, Journal of Theoretical Biology, vol.241, issue.2, pp.342-359, 2006.
DOI : 10.1016/j.jtbi.2005.11.034

I. Cantone, L. Marucci, F. Iorio, M. A. Ricci, V. Belcastro et al., A Yeast Synthetic Network for In Vivo Assessment of Reverse-Engineering and Modeling Approaches, Cell, vol.137, issue.1, pp.172-181, 2009.
DOI : 10.1016/j.cell.2009.01.055

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

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

A. Rocca, N. Mobilia, É. Fanchon, T. Ribeiro, L. Trilling et al., ASP for Construction and Validation of Regulatory Biological Networks, pp.167-206, 2014.
DOI : 10.1063/1.1349893

S. Videla, C. Guziolowski, F. Eduati, S. Thiele, M. Gebser et al., Learning Boolean logic models of signaling networks with ASP, Theoretical Computer Science, vol.599, 2014.
DOI : 10.1016/j.tcs.2014.06.022

URL : https://hal.archives-ouvertes.fr/hal-01058610

T. Fayruzov, J. Janssen, D. Vermeir, C. Cornelis, and M. D. Cock, Modelling gene and protein regulatory networks with Answer Set Programming, International Journal of Data Mining and Bioinformatics, vol.5, issue.2, pp.209-229, 2011.
DOI : 10.1504/IJDMB.2011.039178

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=

M. Gelfond and V. Lifschitz, The stable model semantics for logic programming, Logic Programming, pp.1070-1080, 1988.

O. Sahin, H. Fröhlich, C. Löbke, U. Korf, S. Burmester et al., Modeling ERBB receptor-regulated G1/S transition to find novel targets for de novo trastuzumab resistance, BMC Systems Biology, vol.3, issue.1, 2009.
DOI : 10.1186/1752-0509-3-1

URL : http://doi.org/10.1186/1752-0509-3-1

Z. Khalis, J. Comet, A. Richard, and G. Bernot, The SMBioNet method for discovering models of gene regulatory networks, Genes, Genomes and Genomics, vol.3, issue.1, pp.15-22, 2009.

S. Klamt, J. Saez-rodriguez, J. A. Lindquist, L. Simeoni, and E. D. Gilles, A methodology for the structural and functional analysis of signaling and regulatory networks, BMC Bioinformatics, vol.7, issue.1, p.56, 2006.
DOI : 10.1186/1471-2105-7-56