S. Harris and A. Levine, The p53 pathway: positive and negative feedback loops, Oncogene, vol.12, issue.17, pp.2899-2908, 2005.
DOI : 10.1038/sj.onc.1208615

K. Vousden and D. Lane, p53 in health and disease, Nature Reviews Molecular Cell Biology, vol.331, issue.4, pp.275-283, 2007.
DOI : 10.1038/nrm2147

F. Murray-zmijewski, E. Slee, and X. Lu, A complex barcode underlies the heterogeneous response of p53 to stress, Nature Reviews Molecular Cell Biology, vol.443, issue.9, pp.702-712, 2008.
DOI : 10.1038/nrm2451

L. Segel and M. Slemrod, The Quasi-Steady-State Assumption: A Case Study in Perturbation, SIAM Review, vol.31, issue.3, pp.446-477, 1989.
DOI : 10.1137/1031091

J. Keener and J. Sneyd, Mathematical Physiology I: Cellular Physiology, 2009.

B. Goodwin, Oscillatory behavior in enzymatic control processes Advances in enzyme regulation, pp.425-438, 1965.

B. Aronson, K. Johnson, and J. Dunlap, The circadian clock locus frequency: a single ORF defines period length and temperature compensation, Proc. Nat. Acad. Sci. U S A 91, pp.7683-7687, 1994.

E. Batchelor, S. Mock, I. Bhan, A. Loewer, and G. Lahav, Recurrent Initiation: A Mechanism for Triggering p53 Pulses in Response to DNA Damage, Molecular Cell, vol.30, issue.3, pp.277-289, 2008.
DOI : 10.1016/j.molcel.2008.03.016

A. Ciliberto, B. Novak, and J. Tyson, Steady States and Oscillations in the p53/Mdm2 Network, Cell Cycle, vol.4, issue.3, pp.488-493, 2005.
DOI : 10.4161/cc.4.3.1548

L. Dimitrio, J. Clairambault, and R. Natalini, A spatial physiological model for p53 intracellular dynamics, Journal of Theoretical Biology, vol.316, pp.9-24, 2013.
DOI : 10.1016/j.jtbi.2012.08.035
URL : https://hal.archives-ouvertes.fr/hal-00726014

N. Geva-zatorsky, N. Rosenfeld, S. Itzkovitz, R. Milo, and A. Sigal, Oscillations and variability in the p53 system, Molecular Systems Biology, vol.101, pp.1-13, 2006.
DOI : 10.1038/msb4100068

J. Kim and T. Jackson, Mechanisms That Enhance Sustainability of p53 Pulses, PLoS ONE, vol.97, issue.6, 2013.
DOI : 10.1371/journal.pone.0065242.s006

L. Ma, J. Wagner, J. Rice, W. Hu, and A. Levine, A plausible model for the digital response of p53 to DNA damage, Proceedings of the National Academy of Sciences, vol.102, issue.40, pp.14266-14271, 2005.
DOI : 10.1073/pnas.0501352102

K. Puszy´nskipuszy´nski, B. Hat, and T. Lipniacki, Oscillations and bistability in the stochastic model of p53 regulation, Journal of Theoretical Biology, vol.254, issue.2, pp.452-465, 2008.
DOI : 10.1016/j.jtbi.2008.05.039

J. Wagner, L. Ma, J. Rice, W. Hu, and A. Levine, p53???Mdm2 loop controlled by a balance of its feedback strength and effective dampening using ATM and delayed feedback, IEE Proceedings - Systems Biology, vol.152, issue.3, pp.109-118, 2005.
DOI : 10.1049/ip-syb:20050025

T. Zhang, P. Brazhnik, and J. Tyson, Exploring Mechanisms of the DNA-Damage Response: p53 Pulses and their Possible Relevance to Apoptosis, Cell Cycle, vol.6, issue.1, pp.85-94, 2007.
DOI : 10.4161/cc.6.1.3705

X. Zhang, F. Liu, and W. Wang, Two-phase dynamics of p53 in the DNA damage response, Proceedings of the National Academy of Sciences, vol.108, issue.22, pp.8990-8995, 2011.
DOI : 10.1073/pnas.1100600108

J. Elia?, L. Dimitrio, J. Clairambault, and R. Natalini, The p53 protein and its molecular network: Modelling a missing link between DNA damage and cell fate, Biochimica et Biophysica Acta (BBA) - Proteins and Proteomics, vol.1844, issue.1, pp.232-247, 2014.
DOI : 10.1016/j.bbapap.2013.09.019

B. Jch and M. Kastan, DNA damage activates ATM through intermolecular autophosphorylation and dimer dissociation, Nature, vol.421, pp.499-506, 2003.

M. Fiscella, L. Zhang, S. Fan, K. Sakaguchi, and S. Shen, Wip1, a novel human protein phosphatase that is induced in response to ionizing radiation in a p53-dependent manner, Proc. Natl. Acad. Sci. USA 94, pp.6048-6053, 1997.
DOI : 10.1073/pnas.94.12.6048

B. Vogelstein, D. Lane, and A. Levine, Surfing the p53 network, Nature, vol.408, issue.6810, pp.307-310, 2000.
DOI : 10.1038/35042675

G. Lahav, N. Rosenfeld, A. Sigal, N. Geva-zatorsky, and A. Levine, Dynamics of the p53-Mdm2 feedback loop in individual cells, Nature Genetics, vol.36, issue.2, pp.147-150, 2004.
DOI : 10.1038/ng1293

T. Roubí?ek, Nonlinear Partial Differential Equations with Application, 2013.
DOI : 10.1007/978-3-0348-0513-1

L. Evans, Partial Differential Equations, 2010.

A. Serafini, Mathematical models for intracellular transport phenomena, Italy, 2007.

J. Elia?, L. Dimitrio, J. Clairambault, and R. Natalini, The dynamics of p53 in single cells: physiologically based ODE and reaction???diffusion PDE models, Physical Biology, vol.11, issue.4, 2014.
DOI : 10.1088/1478-3975/11/4/045001

P. Friedman, X. Chen, J. Bargonetti, and C. Prives, The p53 protein is an unusually shaped tetramer that binds directly to DNA, Proc. Natl. Acad. Sci. USA 90, pp.3319-3323, 1993.

R. Weinberg, D. Veprintsev, and A. Fersht, Cooperative Binding of Tetrameric p53 to DNA, Journal of Molecular Biology, vol.341, issue.5, pp.1145-1159, 2004.
DOI : 10.1016/j.jmb.2004.06.071

A. Hill, The possible effects of the aggregation of the molecules of haemoglobin on its dissociation curves, J. Physiol. (Lond.), vol.40, pp.4-7, 1910.

J. Murray, Mathematical Biology II: Spatial Models and Biomedical Applications, 2003.

N. Britton, Reaction-Diffusion Equations and Their Applications to Biology, 1986.

J. Leloup and A. Goldbeter, Incorporating the Formation of a Complex between the PER and TIM Proteins, Journal of Biological Rhythms, vol.380, issue.1, pp.70-87, 1998.
DOI : 10.1177/074873098128999934

D. Claude and J. Clairambault, MODEL OF PER PROTEIN OSCILLATIONS, Chronobiology International, vol.15, issue.9079, pp.1-14, 2000.
DOI : 10.1007/978-3-642-78734-8

A. Cangiani and R. Natalini, A spatial model of cellular molecular trafficking including active transport along microtubules, Journal of Theoretical Biology, vol.267, issue.4, pp.614-625, 2010.
DOI : 10.1016/j.jtbi.2010.08.017
URL : https://hal.archives-ouvertes.fr/hal-00637805

E. Nagy, Basic Equations of the Mass Transport through a Membrane Layer, 2012.

J. Dunlap, Molecular Bases for Circadian Clocks, Cell, vol.96, issue.2, pp.271-290, 1999.
DOI : 10.1016/S0092-8674(00)80566-8

N. Garceau, Y. Liu, J. Loros, and J. Dunlap, Alternative Initiation of Translation and Time-Specific Phosphorylation Yield Multiple Forms of the Essential Clock Protein FREQUENCY, Cell, vol.89, issue.3, pp.469-476, 1997.
DOI : 10.1016/S0092-8674(00)80227-5

Y. Yang, P. Cheng, and Y. Liu, Regulation of the Neurospora circadian clock by casein kinase II, Genes & Development, vol.16, issue.8, pp.994-1006, 2002.
DOI : 10.1101/gad.965102

M. Sturrock, A. Terry, D. Xirodimas, A. Thompson, and M. Chaplain, Spatio-temporal modelling of the Hes1 and p53-Mdm2 intracellular signalling pathways, Journal of Theoretical Biology, vol.273, issue.1, pp.15-31, 2011.
DOI : 10.1016/j.jtbi.2010.12.016
URL : https://hal.archives-ouvertes.fr/hal-00669200

C. Luo, J. Loros, and J. Dunlap, Nuclear localization is required for function of the essential clock protein FRQ, The EMBO Journal, vol.17, issue.5, pp.1228-1235, 1998.
DOI : 10.1093/emboj/17.5.1228

J. Braga, J. Mcnally, and M. Carmo-fonseca, A Reaction-Diffusion Model to Study RNA Motion by Quantitative Fluorescence Recovery after Photobleaching, Biophysical Journal, vol.92, issue.8, pp.2694-2703, 2007.
DOI : 10.1529/biophysj.106.096693

D. Vargas, R. A. Marras, S. Kramer, F. Tyagi, and S. , Mechanism of mRNA transport in the nucleus, Proceedings of the National Academy of Sciences, vol.102, issue.47, pp.17008-17013, 2005.
DOI : 10.1073/pnas.0505580102

L. Deanult, J. Loros, and J. Dunlap, WC-2 mediates WC-1-FRQ interaction within the PAS protein-linked circadian feedback loop of Neurospora, The EMBO Journal, vol.20, issue.1, pp.109-117, 2001.
DOI : 10.1093/emboj/20.1.109

K. Vousden and C. Prives, Blinded by the Light: The Growing Complexity of p53, Cell, vol.137, issue.3, pp.413-431, 2009.
DOI : 10.1016/j.cell.2009.04.037

S. Lain and D. Lane, Improving cancer therapy by non-genotoxic activation of p53, European Journal of Cancer, vol.39, issue.8, pp.1053-1060, 2003.
DOI : 10.1016/S0959-8049(03)00063-7

A. Joerger and A. Fersht, The Tumor Suppressor p53: From Structures to Drug Discovery, Cold Spring Harbor Perspectives in Biology, vol.2, issue.6, 2010.
DOI : 10.1101/cshperspect.a000919

S. Shreeram, O. Demidov, W. Hee, H. Yamaguchi, and N. Onishi, Wip1 Phosphatase Modulates ATM-Dependent Signaling Pathways, Molecular Cell, vol.23, issue.5, pp.757-764, 2006.
DOI : 10.1016/j.molcel.2006.07.010
URL : http://doi.org/10.1016/j.molcel.2006.07.010

S. Shreeram, W. Hee, O. Demidov, C. Kek, and H. Yamaguchi, Regulation of ATM/p53-dependent suppression of myc-induced lymphomas by Wip1 phosphatase, The Journal of Experimental Medicine, vol.2, issue.13, pp.2793-2799, 2006.
DOI : 10.1128/MCB.02240-05

E. Rothe, Zweidimensionale parabolische Randwertaufgaben als Grenzfall eindimensionaler Randwertaufgaben, Mathematische Annalen, vol.102, issue.1, pp.650-670, 1930.
DOI : 10.1007/BF01782368

Y. Liu, J. Loros, and J. Dunlap, Phosphorylation of the Neurospora clock protein FREQUENCY determines its degradation rate and strongly influences the period length of the circadian clock, Proceedings of the National Academy of Sciences, vol.97, issue.1, pp.234-239, 2000.
DOI : 10.1073/pnas.97.1.234