M. Adimy, F. Crauste, and S. Ruan, A Mathematical Study of the Hematopoiesis Process with Applications to Chronic Myelogenous Leukemia, SIAM Journal on Applied Mathematics, vol.65, issue.4, pp.1328-1352, 2005.
DOI : 10.1137/040604698
URL : https://hal.archives-ouvertes.fr/hal-00375977

R. Anderson, Geometric and probabilistic stability criteria for delay systems, Mathematical Biosciences, vol.105, issue.1, pp.81-96, 1991.
DOI : 10.1016/0025-5564(91)90049-O

R. Anderson, Intrinsic parameters and stability of differential-delay equations, Journal of Mathematical Analysis and Applications, vol.163, issue.1, pp.184-199, 1992.
DOI : 10.1016/0022-247X(92)90287-N
URL : http://doi.org/10.1016/0022-247x(92)90287-n

R. Apostu and M. Mackey, Understanding cyclical thrombocytopenia: A mathematical modeling approach, Journal of Theoretical Biology, vol.251, issue.2, pp.297-316, 2008.
DOI : 10.1016/j.jtbi.2007.11.029
URL : http://digitool.Library.McGill.CA:80/webclient/DeliveryManager?pid=101834&custom_att_2=direct

F. Atay, Distributed Delays Facilitate Amplitude Death of Coupled Oscillators, Physical Review Letters, vol.1, issue.9, p.94101, 2003.
DOI : 10.2307/2967482

F. Atay, Delayed feedback control near Hopf bifurcation, Discrete Contin, Dynam. Systems Ser. S, vol.1, pp.197-205, 2008.
DOI : 10.3934/dcdss.2008.1.197
URL : http://arxiv.org/abs/0812.4687

S. Basu, A. Dunn, A. Ward, and G. , Function and modes of action, Int. J. Mol. Med, vol.10, pp.3-10, 2002.

J. Bélair, M. C. Mackey, and J. M. Mahaffy, Age-structured and two-delay models for erythropoiesis, Mathematical Biosciences, vol.128, issue.1-2, pp.317-346, 1995.
DOI : 10.1016/0025-5564(94)00078-E

R. Bellman and K. Cooke, Differential-Difference Equations, Academic press, 1963.

E. Beretta and Y. Kuang, Geometric Stability Switch Criteria in Delay Differential Systems with Delay Dependent Parameters, SIAM Journal on Mathematical Analysis, vol.33, issue.5, pp.1144-1165, 2002.
DOI : 10.1137/S0036141000376086

L. Berezansky and E. Braverman, Stability of linear differential equations with a distributed delay, Comm. Pure Appl. Math, vol.10, pp.1361-1375, 2011.

L. Berezansky and E. Braverman, Stability of equations with a distributed delay, monotone production and nonlinear mortality, Nonlinearity, vol.26, issue.10, pp.26-2833, 2013.
DOI : 10.1088/0951-7715/26/10/2833

S. Bernard, J. Bélair, and M. C. Mackey, Sufficient conditions for stability of linear differential equations with distributed delay, Discrete Contin, Dynam. Systems Ser. B, vol.1, pp.233-256, 2001.

S. Bernard, J. Belair, and M. C. Mackey, Oscillations in cyclical neutropenia: new evidence based on mathematical modeling, Journal of Theoretical Biology, vol.223, issue.3, pp.283-298, 2003.
DOI : 10.1016/S0022-5193(03)00090-0

]. S. Bernard, B. Cajavec, L. Pujo-menjouet, M. Mackey, and H. Herzel, Modelling transcriptional feedback loops: The role of Gro
URL : https://hal.archives-ouvertes.fr/hal-00372717

F. Boese, The stability chart for the linearized Cushing equation with a discrete delay and with gamma-distributed delays, Journal of Mathematical Analysis and Applications, vol.140, issue.2, pp.510-536, 1989.
DOI : 10.1016/0022-247X(89)90081-4

S. Campbell, Time delays in neural systems, in Handbook of Brain Connectivity, pp.65-90, 2007.

S. Campbell and R. Jessop, Approximating the Stability Region for a Differential Equation with a Distributed Delay, Mathematical Modelling of Natural Phenomena, vol.4, issue.2, pp.1-27, 2009.
DOI : 10.1051/mmnp/20094201

C. Colijn and M. Mackey, A mathematical model of hematopoiesis???I. Periodic chronic myelogenous leukemia, Journal of Theoretical Biology, vol.237, issue.2, pp.117-132, 2005.
DOI : 10.1016/j.jtbi.2005.03.033

C. Colijn and M. Mackey, A mathematical model of hematopoiesis: II. Cyclical neutropenia, Journal of Theoretical Biology, vol.237, issue.2, pp.133-146, 2005.
DOI : 10.1016/j.jtbi.2005.03.034

C. Colijn and M. Mackey, Bifurcation and Bistability in a Model of Hematopoietic Regulation, SIAM Journal on Applied Dynamical Systems, vol.6, issue.2, pp.378-394, 2007.
DOI : 10.1137/050640072

K. L. Cooke and Z. Grossman, Discrete delay, distributed delay and stability switches, Journal of Mathematical Analysis and Applications, vol.86, issue.2, pp.592-627, 1982.
DOI : 10.1016/0022-247X(82)90243-8
URL : http://doi.org/10.1016/0022-247x(82)90243-8

F. Crauste, Stability and Hopf bifurcation for a first-order delay differential equation with distributed delay, in Complex Time-Delay Systems, pp.263-296, 2010.

T. Erneux, Applied Delay Differential Equations, 2009.

C. Eurich, A. Thiel, and L. Fahse, Distributed Delays Stabilize Ecological Feedback Systems, Physical Review Letters, vol.33, issue.15, p.158104, 2005.
DOI : 10.1038/35012234

J. Hale, Functional differential equations with infinite delays, Journal of Mathematical Analysis and Applications, vol.48, issue.1, pp.276-283, 1974.
DOI : 10.1016/0022-247X(74)90233-9
URL : http://doi.org/10.1016/0022-247x(74)90233-9

J. Hale and J. Kato, Phase space for retarded equations with infinite delay, Funkcial. Ekvac, vol.21, pp.11-41, 1978.

J. Hale, S. Verduyn, and . Lunel, Introduction to Functional Differential Equations, 1993.
DOI : 10.1007/978-1-4612-4342-7

N. Hayes, Roots of the Transcendental Equation Associated with a Certain Difference-Differential Equation, Journal of the London Mathematical Society, vol.1, issue.3, pp.226-232, 1950.
DOI : 10.1112/jlms/s1-25.3.226

C. Huang and S. Vandewalle, An Analysis of Delay-Dependent Stability for Ordinary and Partial Differential Equations with Fixed and Distributed Delays, SIAM Journal on Scientific Computing, vol.25, issue.5, pp.1608-1632, 2004.
DOI : 10.1137/S1064827502409717

G. Hutchinson, CIRCULAR CAUSAL SYSTEMS IN ECOLOGY, Annals of the New York Academy of Sciences, vol.2, issue.36, pp.221-246, 1948.
DOI : 10.1111/j.1469-8137.1943.tb04982.x

K. Kaushansky, The molecular mechanisms that control thrombopoiesis, Journal of Clinical Investigation, vol.115, issue.12, pp.3339-3347, 2005.
DOI : 10.1172/JCI26674
URL : http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1297257

G. Kiss and B. Krauskopf, Stability implications of delay distribution for first-order and second-order systems, Discrete and Continuous Dynamical Systems - Series B, vol.13, issue.2, pp.327-345, 2010.
DOI : 10.3934/dcdsb.2010.13.327

M. Koury and M. Bondurant, Erythropoietin retards DNA breakdown and prevents programmed death in erythroid progenitor cells, Science, vol.248, issue.4953, pp.248-378, 1990.
DOI : 10.1126/science.2326648

T. Krisztin, Stability for functional-differential equations and some variational problems, Tohoku Mathematical Journal, vol.42, issue.3, pp.42-407, 1990.
DOI : 10.2748/tmj/1178227618

Y. Kuang, Delay Differential Equations: With Applications in Population Dynamics, 1993.

Y. Kuang, Nonoccurrence of stability switching in systems of differential equations with distributed delays, Quarterly of Applied Mathematics, vol.52, issue.3, pp.569-578, 1994.
DOI : 10.1090/qam/1292206

J. Lei and M. Mackey, Multistability in an age-structured model of hematopoiesis: Cyclical neutropenia, Journal of Theoretical Biology, vol.270, issue.1, pp.143-153, 2011.
DOI : 10.1016/j.jtbi.2010.11.024

N. Macdonald, Biological Delay Systems: Linear Stability Theory, Cambridge Studies in Mathematical Biology, vol.8, 1989.

M. C. Mackey, Unified hypothesis of the origin of aplastic anaemia and periodic hematopoiesis, Blood, pp.51-941, 1978.

M. C. Mackey and L. Glass, Oscillation and chaos in physiological control systems, Science, vol.197, issue.4300, pp.197-287, 1977.
DOI : 10.1126/science.267326

U. Meyer, J. Shao, S. Chakrabarty, S. Brandt, H. Luksch et al., Distributed delays stabilize neural feedback systems, Distributed delays stabilize neural feedback systems, pp.79-87, 2008.
DOI : 10.1515/REVNEURO.2003.14.1-2.85
URL : http://arxiv.org/pdf/0712.0036

R. Miyazaki, Characteristic equation and asymptotic behavior of delay-differential equation, Funkcial. Ekvac, vol.40, pp.471-481, 1997.

N. Monk, Oscillatory Expression of Hes1, p53, and NF-??B Driven by Transcriptional Time Delays, Current Biology, vol.13, issue.16, pp.1409-1413, 2003.
DOI : 10.1016/S0960-9822(03)00494-9
URL : http://doi.org/10.1016/s0960-9822(03)00494-9

H. Ozbay, C. Bonnet, and J. Clairambault, Stability analysis of systems with distributed delays and application to hematopoietic cell maturation dynamics, 2008 47th IEEE Conference on Decision and Control, pp.2050-2055, 2008.
DOI : 10.1109/CDC.2008.4738654

K. Rateitschak and O. Wolkenhauer, Intracellular delay limits cyclic changes in gene expression, Mathematical Biosciences, vol.205, issue.2, pp.163-179, 2007.
DOI : 10.1016/j.mbs.2006.08.010
URL : http://arxiv.org/abs/q-bio/0602009

O. Solomon and E. Fridman, New stability conditions for systems with distributed delays, Automatica, vol.49, issue.11, pp.3467-3475, 2013.
DOI : 10.1016/j.automatica.2013.08.025

G. Stépán, Retarded Dynamical Systems: Stability and Characteristic Functions, 1989.

T. Stiehl and A. Marciniak-czochra, Characterization of stem cells using mathematical models of multistage cell lineages, Mathematical and Computer Modelling, vol.53, issue.7-8, pp.1505-1517, 2011.
DOI : 10.1016/j.mcm.2010.03.057

X. Tang, Asymptotic behavior of a differential equation with distributed delays, Journal of Mathematical Analysis and Applications, vol.301, issue.2, pp.313-335, 2005.
DOI : 10.1016/j.jmaa.2004.07.023

D. L. Motola, Identification of Ligands for DAF-12 that Govern Dauer Formation and Reproduction in C. elegans, Cell, vol.124, issue.6, p.1209, 2006.
DOI : 10.1016/j.cell.2006.01.037

R. C. Lee, R. L. Feinbaum, and V. Ambros, The C. elegans heterochronic gene lin-4 encodes small RNAs with antisense complementarity to lin-14, Cell, vol.75, issue.5, p.843, 1993.
DOI : 10.1016/0092-8674(93)90529-Y
URL : https://hal.archives-ouvertes.fr/in2p3-00597159

M. Chalfie, H. R. Horvitz, and J. E. Sulston, Mutations that lead to reiterations in the cell lineages of C. elegans, Cell, vol.24, issue.1, p.59, 1981.
DOI : 10.1016/0092-8674(81)90501-8

A. Esquela-kerscher, families in the hypodermis and the reproductive system, Developmental Dynamics, vol.13, issue.4, p.868, 2005.
DOI : 10.1002/dvdy.20572

B. Gerisch, C. Weitzel, C. Kober-eisermann, V. Rottiers, and A. Antebi, A Hormonal Signaling Pathway Influencing C. elegans Metabolism, Reproductive Development, and Life Span, Developmental Cell, vol.1, issue.6, p.841, 2001.
DOI : 10.1016/S1534-5807(01)00085-5
URL : http://doi.org/10.1016/s1534-5807(01)00085-5

A. H. Ludewig, A novel nuclear receptor/coregulator complex controls C. elegans lipid metabolism, larval development, and aging, Genes & Development, vol.18, issue.17, p.2120, 2004.
DOI : 10.1101/gad.312604

M. Li, M. W. Jones-rhoades, N. C. Lau, D. P. Bartel, and A. E. Rougvie, Regulatory Mutations of mir-48, a C. elegans let-7 Family MicroRNA, Cause Developmental Timing Defects, Developmental Cell, vol.9, issue.3, p.415, 2005.
DOI : 10.1016/j.devcel.2005.08.002

H. Grosshans, T. Johnson, K. L. Reinert, M. Gerstein, and F. J. Slack, The Temporal Patterning MicroRNA let-7 Regulates Several Transcription Factors at the Larval to Adult Transition in C. elegans, Developmental Cell, vol.8, issue.3, p.321, 2005.
DOI : 10.1016/j.devcel.2004.12.019

J. Varghese and S. M. Cohen, microRNA miR-14 acts to modulate a positive autoregulatory loop controlling steroid hormone signaling in Drosophila, Genes & Development, vol.21, issue.18, p.2277, 2007.
DOI : 10.1101/gad.439807

J. J. Repa, Regulation of Absorption and ABC1-Mediated Efflux of Cholesterol by RXR Heterodimers, Science, vol.289, issue.5484, p.1524, 2000.
DOI : 10.1126/science.289.5484.1524

G. Hayes, V. Ruvkun, and A. Ambros, Rougvie for strains; N. Timchenko for gel shift support; and D. Magner, S. Greene, and F. Schroeder for manuscript comments, This work was supported by NIH grant GM077201 and the Ellison Medical Foundation (A.A.), and the Howard Hughes Medical Institute and the Robert A. Welch Foundation (D.J.M.)

R. Passier, L. W. Van-laake, and C. L. Mummery, Stem-cell-based therapy and lessons from the heart, Nature, vol.100, issue.7193, p.322, 2008.
DOI : 10.1161/01.CIR.103.14.1920

M. A. Laflamme and C. E. Murry, Regenerating the heart, Nature Biotechnology, vol.100, issue.7, p.845, 2005.
DOI : 10.1126/science.307.5712.1028b

S. Martin-puig, Z. Wang, and K. R. Chien, Lives of a Heart Cell: Tracing the Origins of Cardiac Progenitors, Cell Stem Cell, vol.2, issue.4, p.320, 2008.
DOI : 10.1016/j.stem.2008.03.010

S. M. Wu, K. R. Chien, and C. Mummery, Origins and Fates of Cardiovascular Progenitor Cells, Cell, vol.132, issue.4, p.537, 2008.
DOI : 10.1016/j.cell.2008.02.002
URL : http://doi.org/10.1016/j.cell.2008.02.002

M. H. Soonpaa and L. J. Field, Survey of Studies Examining Mammalian Cardiomyocyte DNA Synthesis, Circulation Research, vol.83, issue.1, p.15, 1998.
DOI : 10.1161/01.RES.83.1.15
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.511.8799

R. D. Bhardwaj, Neocortical neurogenesis in humans is restricted to development, Proceedings of the National Academy of Sciences, vol.16, issue.3, p.12564, 2006.
DOI : 10.1017/S0033822200003672

K. Spalding, R. D. Bhardwaj, B. Buchholz, H. Druid, and J. Frisén, Retrospective Birth Dating of Cells in Humans, Cell, vol.122, issue.1, p.133, 2005.
DOI : 10.1016/j.cell.2005.04.028

R. Nydal and K. Lovseth, Distribution of Radiocarbon from Nuclear Tests, Nature, vol.5, issue.4988, p.1029, 1965.
DOI : 10.1269/jrr.5.124

I. Levin and B. Kromer, The Tropospheric 14CO2 Level in Mid-Latitudes of the Northern Hemisphere (1959???2003), Radiocarbon, vol.16, issue.03, p.1261, 2004.
DOI : 10.1038/298001a0

K. L. Spalding, B. A. Buchholz, L. Bergman, H. Druid, and J. Frisén, Forensics: Age written in teeth by nuclear tests, Nature, vol.437, issue.7057, p.333, 2005.
DOI : 10.1038/437333a

W. F. Libby, R. Berger, J. F. Mead, G. V. Alexander, and J. F. Ross, Replacement Rates for Human Tissue from Atmospheric Radiocarbon, Science, vol.146, issue.3648, p.1170, 1964.
DOI : 10.1126/science.146.3648.1170

E. M. Wild, 14C dating with the bomb peak: An application to forensic medicine, Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms, vol.172, issue.1-4, p.944, 2000.
DOI : 10.1016/S0168-583X(00)00227-5

M. Rubart and L. J. Field, CARDIAC REGENERATION: Repopulating the Heart, Annual Review of Physiology, vol.68, issue.1, p.29, 2006.
DOI : 10.1146/annurev.physiol.68.040104.124530

M. S. Parmacek and R. J. Solaro, Biology of the troponin complex in cardiac myocytes, Progress in Cardiovascular Diseases, vol.47, issue.3, p.159, 2004.
DOI : 10.1016/j.pcad.2004.07.003

G. Olivetti, M. Melissari, J. M. Capasso, and P. Anversa, Cardiomyopathy of the aging human heart. Myocyte loss and reactive cellular hypertrophy, Circulation Research, vol.68, issue.6, p.1560, 1991.
DOI : 10.1161/01.RES.68.6.1560

G. Olivetti, Aging, Cardiac Hypertrophy and Ischemic Cardiomyopathy Do Not Affect the Proportion of Mononucleated and Multinucleated Myocytes in the Human Heart, Journal of Molecular and Cellular Cardiology, vol.28, issue.7, p.1463, 1996.
DOI : 10.1006/jmcc.1996.0137

C. P. Adler, The Development and Regenerative Potential of Cardiac Muscle, pp.227-252, 1991.

M. A. Laflamme, D. Myerson, J. E. Saffitz, and C. E. Murry, Evidence for Cardiomyocyte Repopulation by Extracardiac Progenitors in Transplanted Human Hearts, Circulation Research, vol.90, issue.6, p.634, 2002.
DOI : 10.1161/01.RES.0000014822.62629.EB

S. Reppert and D. Weaver, Coordination of circadian timing in mammals, Nature, vol.109, issue.6901, pp.935-941, 2002.
DOI : 10.1080/14639230050058301

S. Aton and E. Herzog, Come Together, Right???Now: Synchronization of Rhythms in a Mammalian Circadian Clock, Neuron, vol.48, issue.4, pp.531-534, 2005.
DOI : 10.1016/j.neuron.2005.11.001

M. Antle and R. Silver, Orchestrating time: arrangements of the brain circadian clock, Trends in Neurosciences, vol.28, issue.3, pp.145-151, 2005.
DOI : 10.1016/j.tins.2005.01.003

D. Welsh, D. Logothetis, M. Meister, S. Reppert, A. Burchert et al., Individual References 1, 1995.

J. Guilhot, F. X. Mahon, and C. Schütz, Frequency of CTLA-4 Receptor Ligand (CD86, B7.2)-Positive Plasmacytoid Dendritic Cells Predicts Risk of Disease Recurrence after Tyrosine-Kinase Inhibitor Discontinuation in Chronic Myeloid Leukemia: Results from a Prospective Substudy of the Euroski Trial, Blood, issue.23, p.126599, 2015.

S. Chu, T. Mcdonald, A. Lin, S. Chakraborty, Q. Huang et al., Persistence of leukemia stem cells in chronic myelogenous leukemia patients in prolonged remission with imatinib treatment, Blood, vol.118, issue.20, pp.1185565-5572, 2011.
DOI : 10.1182/blood-2010-12-327437

G. D. Clapp, Applying Mathematical Models to Study the Role of the Immune System in Chronic Myelogenous Leukemia, 2016.

G. D. Clapp and D. Levy, A Review of Mathematical Models for Lymphoma and Leukemia. Drug Discovery Today: Disease Models, pp.1-6, 2015.

G. D. Clapp, T. Lepoutre, N. Nicolini, and D. Levy, BCR-ABL transcript variations in chronic phase chronic myelogenous leukemia patients on imatinib first-line: Possible role of the autologous immune system, OncoImmunology, vol.86, issue.5, p.1122159, 2016.
DOI : 10.1158/0008-5472.CAN-15-0611

G. D. Clapp, T. Lepoutre, R. Cheikh, S. Bernard, J. Ruby et al., Implication of the Autologous Immune System in BCR-ABL Transcript Variations in Chronic Myelogenous Leukemia Patients Treated with Imatinib, Cancer Research, vol.75, issue.19, pp.754053-4062, 2015.
DOI : 10.1158/0008-5472.CAN-15-0611
URL : https://hal.archives-ouvertes.fr/hal-01251396

M. W. Deininger, J. M. Goldman, and J. Melo, The molecular biology of chronic myeloid leukemia Blood, pp.3343-3356, 2000.

J. H. Falkenburg, A. R. Wafelman, P. Joosten, W. M. Smit, C. A. Van-bergen et al., Complete remission of accelerated phase chronic myeloid leukemia by treatment with leukemia-reactive cytotoxic T lymphocytes Blood, pp.1201-1209, 1999.

S. M. Graham, H. G. Jørgensen, E. Allan, C. Pearson, M. J. Alcorn et al., Primitive, quiescent, Philadelphia-positive stem cells from patients with chronic myeloid leukemia are insensitive to STI571 in vitro, Blood, vol.99, issue.1, pp.319-325, 2008.
DOI : 10.1182/blood.V99.1.319

M. Ilander, A. Kreutzman, and S. Mustjoki, IFN? induces prolonged remissions modeling curative immunologic responses in chronic myeloid leukemia Oncoimmunology, 2014.
DOI : 10.4161/onci.28781
URL : http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4063137

P. S. Kim, P. P. Lee, and D. Levy, A PDE model for imatinib-treated chronic myelogenous leukemia Bulletin of mathematical biology, pp.1994-2016, 2008.

P. S. Kim, P. P. Lee, and D. Levy, Dynamics and potential impact of the immune response to chronic myelogenous leukemia PLoS computational biology, p.1000095, 2008.

N. Komarova and D. Wodarz, Effect of cellular quiescence on the success of targeted CML therapy PloS one, p.990, 2007.

F. Mahon, D. Réa, J. Guilhot, F. Guilhot, F. Huguet et al., Discontinuation of imatinib in patients with chronic myeloid leukaemia who have maintained complete molecular remission for at least 2 years: the prospective, multicentre Stop Imatinib (STIM) trial, The Lancet Oncology, vol.11, issue.11, pp.111029-111064, 2010.
DOI : 10.1016/S1470-2045(10)70233-3

F. Michor, T. P. Hughes, Y. Iwasa, S. Branford, N. P. Shah et al., Dynamics of chronic myeloid leukaemia, Nature, vol.81, issue.7046, pp.4351267-70, 2005.
DOI : 10.1126/science.1099480

O. 'brien, S. G. Guilhot, F. Larson, R. A. Gathmann, I. Baccarani et al., Imatinib compared with interferon and low-dose cytarabine for newly diagnosed chronic-phase chronic myeloid leukemia, pp.348994-1004, 2003.

A. Delmer, P. Rousselot, L. Legros, M. Berger, S. Corm et al., Imatinib plus peginterferon alfa-2a in chronic myeloid leukemia, The New England journal of medicine, issue.26, pp.3632511-3632532, 2010.

I. Roeder, M. Horn, I. Glauche, A. Hochhaus, M. Mueller et al., Dynamic modeling of imatinib-treated chronic myeloid leukemia: functional insights and clinical implications, Nature Medicine, vol.13, issue.10, pp.1181-1185, 2006.
DOI : 10.1038/nm1487

D. M. Ross, S. Branford, J. F. Seymour, A. P. Schwarer, C. Arthur et al., Patients with chronic myeloid leukemia who maintain a complete molecular response after stopping imatinib treatment have evidence of persistent leukemia by DNA PCR, Leukemia, vol.5, issue.10, pp.241719-1724, 2010.
DOI : 10.1111/j.1365-2141.1995.tb03392.x

P. Rousselot, F. Huguet, D. Rea, L. Legros, J. M. Cayuela et al., Imatinib mesylate discontinuation in patients with chronic myelogenous leukemia in complete molecular remission for more than 2 years Blood, pp.58-61, 2007.

R. Aguda, B. D. Tang, and Y. , The kinetic origins of the restriction point in the mammalian cell cycle, Cell Proliferation, vol.82, issue.5, p.321, 1999.
DOI : 10.1016/0955-0674(95)80067-0

V. Amador, S. Ge, P. G. Santamaria, D. Guardavaccaro, and M. Pagano, APC/CCdc20 Controls the Ubiquitin-Mediated Degradation of p21 in Prometaphase, Molecular Cell, vol.27, issue.3, p.462, 2007.
DOI : 10.1016/j.molcel.2007.06.013

T. Bashir, N. V. Dorrello, V. Amador, D. Guardavaccaro, and M. Pagano, Control of the SCFSkp2???Cks1 ubiquitin ligase by the APC/CCdh1 ubiquitin ligase, Nature, vol.428, issue.6979, p.190, 2004.
DOI : 10.1038/nature02330

A. Chauhan, Regulation of mammalian cell cycle progression in the regenerating liver, Journal of Theoretical Biology, vol.283, issue.1, pp.103-112, 2011.
DOI : 10.1016/j.jtbi.2011.05.026
URL : https://hal.archives-ouvertes.fr/hal-00719488

A. Blindenbacher, X. Wang, I. Langer, R. Savino, L. Terracciano et al., Interleukin 6 is important for survival after partial hepatectomy in mice, Hepatology, vol.36, issue.3, p.674, 2003.
DOI : 10.1053/jhep.2003.50378

A. Chauhan, S. Legewie, P. O. Westermark, S. Lorenzen, and H. Herzel, A mesoscale model of G1/S phase transition in liver regeneration, Journal of Theoretical Biology, vol.252, issue.3, p.465, 2008.
DOI : 10.1016/j.jtbi.2008.01.020

H. Chen, S. Tsai, and G. Leone, Emerging roles of E2Fs in cancer: an exit from cell cycle control, Nature Reviews Cancer, vol.94, issue.11, p.785, 2009.
DOI : 10.3171/jns.2001.94.5.0799

K. C. Chen, L. Calzone, A. Csikasz-nagy, F. R. Cross, B. Novak et al., Integrative Analysis of Cell Cycle Control in Budding Yeast, Molecular Biology of the Cell, vol.15, issue.8, p.3841, 2004.
DOI : 10.1091/mbc.E03-11-0794

S. Dangi, F. M. Chen, and P. Shapiro, Activation of extracellular signal-regulated kinase (ERK) in G2 phase delays mitotic entry through p21CIP1, Cell Proliferation, vol.12, issue.1, p.261, 2006.
DOI : 10.1074/jbc.273.37.24108

M. Deguchi, K. Shiraki, H. Inoue, H. Okano, T. Ito et al., Expression of survivin during liver regeneration, Biochemical and Biophysical Research Communications, vol.297, issue.1, p.59, 2002.
DOI : 10.1016/S0006-291X(02)02128-9

A. W. Duncan, M. H. Taylor, R. D. Hickey, H. Newell, A. E. Lenzi et al., The ploidy conveyor of mature hepatocytes as a source of genetic variation, Nature, vol.6, issue.7316, p.707, 2010.
DOI : 10.1038/nature09414

J. I. Fabrikant, THE KINETICS OF CELLULAR PROLIFERATION IN REGENERATING LIVER, The Journal of Cell Biology, vol.36, issue.3, p.551, 1968.
DOI : 10.1083/jcb.36.3.551

I. Garcia-higuera, E. Manchado, P. Dubus, M. Canamero, J. Mendez et al., Genomic stability and tumour suppression by the APC/C cofactor Cdh1, Nature Cell Biology, vol.96, issue.7, p.802, 2008.
DOI : 10.1038/nprot.2006.205

A. L. Gartel and A. L. Tyner, Transcriptional Regulation of the p21(WAF1/CIP1)Gene, Experimental Cell Research, vol.246, issue.2, p.280, 1999.
DOI : 10.1006/excr.1998.4319

J. W. Harper, S. J. Elledge, K. Keyomarsi, B. Dynlacht, L. H. Tsai et al., Inhibition of cyclin-dependent kinases by p21., Molecular Biology of the Cell, vol.6, issue.4, p.387, 1995.
DOI : 10.1091/mbc.6.4.387
URL : https://www.ncbi.nlm.nih.gov/pmc/articles/PMC301199/pdf

E. Hayashi, A. Yasui, K. Oda, M. Nagino, Y. Nimura et al., Loss of p27Kip1 accelerates DNA replication after partial hepatectomy in mice, Journal of Surgical Research, vol.111, issue.2, p.196, 2003.
DOI : 10.1016/S0022-4804(03)00052-0

J. E. Holt, J. Weaver, and K. T. Jones, Spatial regulation of APCCdh1-induced cyclin B1 degradation maintains G2 arrest in mouse oocytes, Development, vol.137, issue.8, p.1297, 2010.
DOI : 10.1242/dev.047555

S. M. Jones and A. Kazlauskas, Growth factor-dependent signaling and cell cycle progression, FEBS Letters, vol.76, issue.3, p.110, 2001.
DOI : 10.1073/pnas.76.3.1279

R. Kasili, J. D. Walker, L. A. Simmons, J. Zhou, L. De-veylder et al., SIAMESE Cooperates With the CDH1-like Protein CCS52A1 to Establish Endoreplication in Arabidopsis thaliana Trichomes, Genetics, vol.185, issue.1, p.257, 2010.
DOI : 10.1534/genetics.109.113274

A. S. Lundberg and R. A. Weinberg, Functional Inactivation of the Retinoblastoma Protein Requires Sequential Modification by at Least Two Distinct Cyclin-cdk Complexes, Molecular and Cellular Biology, vol.18, issue.2, p.753, 1998.
DOI : 10.1128/MCB.18.2.753

R. Y. Ma, T. H. Tong, A. M. Cheung, A. C. Tsang, W. Y. Leung et al., Raf/MEK/MAPK signaling stimulates the nuclear translocation and transactivating activity of FOXM1c, Journal of Cell Science, vol.118, issue.4, p.795, 2005.
DOI : 10.1242/jcs.01657

T. Matsuo, S. Yamaguchi, S. Mitsui, A. Emi, F. Shimoda et al., Control Mechanism of the Circadian Clock for Timing of Cell Division in Vivo, Science, vol.302, issue.5643, p.255, 2003.
DOI : 10.1126/science.1086271

D. O. Morgan, The Cell Cycle: Principles of Control, 2007.

K. I. Nakayama and K. Nakayama, Regulation of the cell cycle by SCF-type ubiquitin ligases, Seminars in Cell & Developmental Biology, vol.16, issue.3, p.323, 2005.
DOI : 10.1016/j.semcdb.2005.02.010

H. Nam, S. Kim, M. Lee, B. Lee, T. Hara et al., The ERK-RSK1 activation by growth factors at G2 phase delays cell cycle progression and reduces mitotic aberrations, Cellular Signalling, vol.20, issue.7, p.1349, 2008.
DOI : 10.1016/j.cellsig.2008.03.008

Y. A. Nevzorova, D. Tschaharganeh, N. Gassler, Y. Geng, R. Weiskirchen et al., Aberrant Cell Cycle Progression and Endoreplication in Regenerating Livers of Mice That Lack a Single E-Type Cyclin, Gastroenterology, vol.137, issue.2, p.691, 2009.
DOI : 10.1053/j.gastro.2009.05.003

B. Novak and J. J. Tyson, A model for restriction point control of the mammalian cell cycle, Journal of Theoretical Biology, vol.230, issue.4, p.563, 2004.
DOI : 10.1016/j.jtbi.2004.04.039

Y. Y. Park, H. Nam, and J. Lee, Hepatocyte growth factor at S phase induces G2 delay through sustained ERK activation, Biochemical and Biophysical Research Communications, vol.356, issue.1, p.300, 2007.
DOI : 10.1016/j.bbrc.2007.02.123

J. R. Pomerening, S. Y. Kim, and J. E. Ferrell, Systems-Level Dissection of the Cell-Cycle Oscillator: Bypassing Positive Feedback Produces Damped Oscillations, Cell, vol.122, issue.4, p.565, 2005.
DOI : 10.1016/j.cell.2005.06.016

J. R. Pomerening, E. D. Sontag, and J. E. Ferrell, Building a cell cycle oscillator: hysteresis and bistability in the activation of Cdc2, Nature Cell Biology, vol.5, issue.4, p.346, 2003.
DOI : 10.1038/ncb954

T. A. Potapova, J. R. Daum, K. S. Byrd, and G. J. Gorbsky, Fine Tuning the Cell Cycle: Activation of the Cdk1 Inhibitory Phosphorylation Pathway during Mitotic Exit, Molecular Biology of the Cell, vol.20, issue.6, p.1737, 2009.
DOI : 10.1091/mbc.E08-07-0771

Z. Qu, W. R. Maclellan, and J. N. Weiss, Dynamics of the Cell Cycle: Checkpoints, Sizers, and Timers, Biophysical Journal, vol.85, issue.6, p.3600, 2003.
DOI : 10.1016/S0006-3495(03)74778-X

Z. Qu, J. N. Weiss, and W. R. Maclellan, Regulation of the mammalian cell cycle: a model of the G1-to-S transition, AJP: Cell Physiology, vol.284, issue.2, p.349, 2003.
DOI : 10.1152/ajpcell.00066.2002

S. M. Reppert and D. R. Weaver, Coordination of circadian timing in mammals, Nature, vol.109, issue.6901, p.935, 2002.
DOI : 10.1080/14639230050058301

S. J. Sigrist and C. F. Lehner, Drosophila fizzy-related Down-Regulates Mitotic Cyclins and Is Required for Cell Proliferation Arrest and Entry into Endocycles, Cell, vol.90, issue.4, p.671, 1997.
DOI : 10.1016/S0092-8674(00)80528-0
URL : http://doi.org/10.1016/s0092-8674(00)80528-0

C. S. Sorensen, C. Lukas, E. R. Kramer, J. M. Peters, J. Bartek et al., Nonperiodic Activity of the Human Anaphase-Promoting Complex-Cdh1 Ubiquitin Ligase Results in Continuous DNA Synthesis Uncoupled from Mitosis, Molecular and Cellular Biology, vol.20, issue.20, p.7613, 2000.
DOI : 10.1128/MCB.20.20.7613-7623.2000

M. Swat, A. Kel, and H. Herzel, Bifurcation analysis of the regulatory modules of the mammalian G1/S transition, Bioinformatics, vol.20, issue.10, p.1506, 2004.
DOI : 10.1093/bioinformatics/bth110

R. Taub, Liver regeneration: from myth to mechanism, Nature Reviews Molecular Cell Biology, vol.135, issue.10, p.836, 2004.
DOI : 10.1073/pnas.220430497

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, p.221, 2003.
DOI : 10.1016/S0955-0674(03)00017-6

W. Wei, N. G. Ayad, Y. Wan, G. Zhang, M. W. Kirschner et al., Degradation of the SCF component Skp2 in cell-cycle phase G1 by the anaphase-promoting complex, Nature, vol.428, issue.6979, p.194, 2004.
DOI : 10.1038/nature02381

M. Akashi, A. Okamoto, Y. Tsuchiya, T. Todo, E. Nishida et al., A Positive Role for PERIOD in Mammalian Circadian Gene Expression, Cell Reports, vol.7, issue.4, pp.1056-1064, 2014.
DOI : 10.1016/j.celrep.2014.03.072

A. Altinok, D. Gonze, F. Lévi, and A. Goldbeter, An automaton model for the cell cycle, Interface Focus, vol.47, issue.3, pp.36-47, 2011.
DOI : 10.1146/annurev.pharmtox.47.120505.105208
URL : http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3262245

S. Becker-weimann, J. Wolf, H. Herzel, and A. Kramer, Modeling Feedback Loops of the Mammalian Circadian Oscillator, Biophysical Journal, vol.87, issue.5, pp.3023-3034, 2004.
DOI : 10.1529/biophysj.104.040824

S. Bernard and H. Herzel, Why do cells cycle with a 24 hour period? Genome Inf, pp.72-79, 2006.

S. Bernard, B. C. Bernad, F. Lévi, and H. Herzel, Tumor Growth Rate Determines the Timing of Optimal Chronomodulated Treatment Schedules, PLoS Computational Biology, vol.350, issue.3, p.1000712, 2010.
DOI : 10.1371/journal.pcbi.1000712.s004
URL : https://hal.archives-ouvertes.fr/hal-00470302

F. Brikci, J. Clairambault, B. Ribba, and B. Perthame, An age-and-cyclin-structured cell population model for healthy and tumoral tissues, Journal of Mathematical Biology, vol.16, issue.6, pp.91-110, 2007.
DOI : 10.1128/MCB.16.6.2554
URL : https://hal.archives-ouvertes.fr/inria-00081301

F. Brikci, J. Clairambault, and B. Perthame, Analysis of a molecular structured population model with possible polynomial growth for the cell division cycle, Mathematical and Computer Modelling, vol.47, issue.7-8, pp.699-713, 2008.
DOI : 10.1016/j.mcm.2007.06.008

L. Cardone, J. Hirayama, F. Giordanao, T. Tamaru, J. Palvino et al., Circadian Clock Control by SUMOylation of BMAL1, Science, vol.309, issue.5739, pp.1390-1394, 2005.
DOI : 10.1126/science.1110689
URL : https://hal.archives-ouvertes.fr/hal-00187478

A. Chauhan, S. Lorenzen, H. Herzel, and S. Bernard, Regulation of mammalian cell cycle progression in the regenerating liver, Journal of Theoretical Biology, vol.283, issue.1, pp.103-112, 2011.
DOI : 10.1016/j.jtbi.2011.05.026
URL : https://hal.archives-ouvertes.fr/hal-00719488

Z. Chen and S. Mcknight, A Conserved DNA Damage Response Pathway Responsible for Coupling the Cell Division Cycle to the Circadian and Metabolic Cycles, Cell Cycle, vol.6, issue.23, pp.2906-2912, 2007.
DOI : 10.4161/cc.6.23.5041

J. Clairambault, S. Gaubert, and T. Lepoutre, Comparison of Perron and Floquet Eigenvalues in Age Structured Cell Division Cycle Models, Mathematical Modelling of Natural Phenomena, vol.4, issue.3, pp.183-209, 2009.
DOI : 10.1051/mmnp/20094308
URL : https://hal.archives-ouvertes.fr/hal-00344039

J. Clairambault, S. Gaubert, and T. Lepoutre, Circadian rhythm and cell population growth, Mathematical and Computer Modelling, vol.53, issue.7-8, pp.1558-1567, 2011.
DOI : 10.1016/j.mcm.2010.05.034
URL : https://hal.archives-ouvertes.fr/hal-00492983

M. Doumic, Analysis of a Population Model Structured by the Cells Molecular Content, Mathematical Modelling of Natural Phenomena, vol.2, issue.3, pp.121-152, 2007.
DOI : 10.1051/mmnp:2007006
URL : https://hal.archives-ouvertes.fr/hal-00327131

J. Edmunds, LN, Cellular and Molecular Bases of Biological Clocks: Models and Mechanisms for Circadian Timekeeping, 1988.

J. E. Eide, M. F. Woolf, H. Kang, W. Hurst, and F. Camacho, Control of Mammalian Circadian Rhythm by CKI??-Regulated Proteasome-Mediated PER2 Degradation, Molecular and Cellular Biology, vol.25, issue.7, pp.2795-2807, 2005.
DOI : 10.1128/MCB.25.7.2795-2807.2005

C. Feillet, Phase locking and multiple oscillating attractors for the coupled mammalian clock and cell cycle, Proc. Natl. Acad. Sci, pp.9828-9833, 2014.
DOI : 10.1158/0008-5472.CAN-06-2086
URL : https://hal.archives-ouvertes.fr/hal-01421054

E. Filipski, F. Delaunay, V. King, M. Wu, B. Claustrat et al., Effects of Chronic Jet Lag on Tumor Progression in Mice, Cancer Research, vol.64, issue.21, pp.7879-7885, 2004.
DOI : 10.1158/0008-5472.CAN-04-0674

E. Filipski, P. Subramanian, J. Carriére, C. Guettier, H. Barbason et al., Circadian disruption accelerates liver carcinogenesis in mice, Mutation Research/Genetic Toxicology and Environmental Mutagenesis, vol.680, issue.1-2, pp.95-105, 2009.
DOI : 10.1016/j.mrgentox.2009.10.002

C. Focan, Circadian rhythms and cancer chemotherapy, Pharmacology & Therapeutics, vol.67, issue.1, pp.1-52, 1995.
DOI : 10.1016/0163-7258(95)00009-6

C. Focan, F. Lévi, and F. Kreutz, Continuous delivery of venous 5-fluorpuracil and arterial 5-fluorodeoxyuridine for hepatic metastases from colorectal cancer, Anti-Cancer Drugs, vol.10, issue.4, pp.385-392, 1999.
DOI : 10.1097/00001813-199904000-00006

C. Focan, F. Kreutz, D. Focan-henrard, and N. Moeneclaey, Chronotherapy with 5-fluorouracil, folinic acid and carboplatin for metastatic colorectal cancer; an interesting therapeutic index in a phase II trial, European Journal of Cancer, vol.36, issue.3, pp.341-347, 2000.
DOI : 10.1016/S0959-8049(99)00282-8

D. B. Forger and C. S. Peskin, A detailed predictive model of the mammalian circadian clock, Proc. Natl. Acad. Sci, pp.14806-14811, 2003.
DOI : 10.1101/gad.233702

L. Fu, H. Pelicano, J. Liu, P. Huang, and C. Lee, The circadian gene Period2 plays an important role in tumor suppression and DNA damage response in vivo, Cell, vol.11, pp.41-50, 2002.

A. T-e-r, 1 2 .E n t r a i n m e n toft h em a m m a l i a nc el lcy c l eb yt h ec i r ca d i a n clock: modeling two coupled cellular rhythms, PLoS Comput. Biol, vol.2, issue.85, p.1002516
URL : https://hal.archives-ouvertes.fr/in2p3-00122855

S. Gery, N. Komatsu, L. Baldjyan, A. Yu, D. Koo et al., The Circadian Gene Per1 Plays an Important Role in Cell Growth and DNA Damage Control in Human Cancer Cells, Molecular Cell, vol.22, issue.3, pp.375-382, 2006.
DOI : 10.1016/j.molcel.2006.03.038

D. Gonze, Abstract, Open Life Sciences, vol.35, issue.5, pp.699-711, 2011.
DOI : 10.1006/jtbi.1996.0067

A. Grèchez-cassiau, B. Rayet, F. Guillaumond, M. Teboul, and F. Delaunay, Expression and Hepatocyte Proliferation, Journal of Biological Chemistry, vol.285, issue.8, pp.4535-4542, 2008.
DOI : 10.1093/jnci/94.9.690

W. Hrushesky and G. Bjarnason, The application of circadian chronobiology to cancer chemotherapy, Cancer, pp.2666-2686, 1993.

T. Hunt and P. Sassone-corsi, Riding Tandem: Circadian Clocks and the Cell Cycle, Cell, vol.129, issue.3, pp.461-464, 2007.
DOI : 10.1016/j.cell.2007.04.015
URL : http://doi.org/10.1016/j.cell.2007.04.015

C. Johnson, Circadian clocks and cell division, Cell Cycle, vol.167, issue.19, pp.3864-3873, 2010.
DOI : 10.1126/science.167.3926.1730
URL : http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3047750

T. Kubo, K. Ozasa, K. Mikami, K. Wakai, Y. Fujino et al., Prospective Cohort Study of the Risk of Prostate Cancer among Rotating-Shift Workers: Findings from the Japan Collaborative Cohort Study, American Journal of Epidemiology, vol.164, issue.6, pp.549-555, 2006.
DOI : 10.1093/aje/kwj232

S. Langmesser, T. Tallone, A. Bordon, S. Rusconi, and U. Albrecht, Interaction of circadian clock proteins PER2 and CRY with BMAL1 and CLOCK, BMC Molecular Biology, vol.9, issue.1, pp.41-57, 2008.
DOI : 10.1186/1471-2199-9-41

C. Lee, J. Etchegaray, F. Cagampang, A. Loudon, and S. Reppert, Posttranslational Mechanisms Regulate the Mammalian Circadian Clock, Cell, vol.107, issue.7, pp.855-867, 2001.
DOI : 10.1016/S0092-8674(01)00610-9
URL : http://doi.org/10.1016/s0092-8674(01)00610-9

J. Leloup and A. Goldbeter, Modeling the mammalian circadian clock: Sensitivity analysis and multiplicity of oscillatory mechanisms, Journal of Theoretical Biology, vol.230, issue.4, pp.541-562, 2004.
DOI : 10.1016/j.jtbi.2004.04.040

F. Lévi, Therapeutic Implications of Circadian Rhythms in Cancer Patients, Novartis Found. Symp, vol.227, pp.136-142, 2000.
DOI : 10.1002/0470870796.ch8

T. Matsuo, S. Yamaguchi, S. Mitsui, A. Emi, F. Shimoda et al., Control Mechanism of the Circadian Clock for Timing of Cell Division in Vivo, Science, vol.302, issue.5643, pp.255-259, 2003.
DOI : 10.1126/science.1086271

. Milo, BioNumbers???the database of key numbers in molecular and cell biology, Nucleic Acids Research, vol.38, issue.suppl_1, pp.750-753, 2010.
DOI : 10.1093/nar/gkp889

H. Mirsky, A. Liu, D. Welsh, S. Kay, and F. Doyle, A model of the cell-autonomous mammalian circadian clock, Proc. Natl. Acad. Sci, pp.11107-11112, 2009.
DOI : 10.1016/S0092-8674(00)81014-4

D. Morgan, Principles of CDK regulation, Nature, vol.374, issue.6518, pp.131-134, 1995.
DOI : 10.1038/374131a0

D. Murray, M. Beckmann, and H. Kitano, Regulation of yeast oscillatory dynamics, Proc. Natl. Acad. Sci, pp.2241-2246, 2007.
DOI : 10.1101/gr.1239303
URL : http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1794218

E. Nagoshi, C. Saini, C. Bauer, T. Laroche, and F. Naef, Circadian Gene Expression in Individual Fibroblasts, Cell, vol.119, issue.5, pp.693-705, 2004.
DOI : 10.1016/j.cell.2004.11.015
URL : http://doi.org/10.1016/j.cell.2004.11.015

B. Novak, Z. Pataki, A. Ciliberto, and J. Tyson, Mathematical model of the cell division cycle of fission yeast, Chaos: An Interdisciplinary Journal of Nonlinear Science, vol.97, issue.1, pp.277-286, 2001.
DOI : 10.1091/mbc.11.2.543

H. Oster, A. Yasui, G. Van-der-horst, and U. Albrecht, Disruption of mCry2 restores circadian rhythmicity in mPer2 mutant mice, Genes & Development, vol.16, issue.20, pp.2633-2638, 2002.
DOI : 10.1101/gad.233702

B. Pando and A. Van-oudenaarden, Coupling cellular oscillators???circadian and cell division cycles in cyanobacteria, Current Opinion in Genetics & Development, vol.20, issue.6, pp.613-618, 2010.
DOI : 10.1016/j.gde.2010.09.001

C. Partch, K. Shields, C. Thompson, C. Selby, and A. Sancar, Posttranslational regulation of mammalian circadian clock by chryptochrome and protein phosphatase 5, Proc. Acad. Sci. USA 103, pp.10467-10472, 2006.

A. Pikovsky, M. Rosenblum, and J. Kurths, Synchronization, 2001.
URL : https://hal.archives-ouvertes.fr/hal-00349214

S. Reppert and D. Weaver, Coordination of circadian timing in mammals, Nature, vol.109, issue.6901, pp.935-941, 2002.
DOI : 10.1080/14639230050058301

T. Sato, R. Yamada, H. Ukai, J. Baggs, L. Miraglia et al., Feedback repression is required for mammalian circadian clock function, Nature Genetics, vol.41, issue.3, pp.212-219, 2006.
DOI : 10.1038/ng1745
URL : http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1994933

C. Savvidis and M. Koutsilieris, Circadian rhythm disruption in cancer biology, Mol. Med, vol.18, issue.1, pp.1249-1260, 2012.

L. Shearman, S. Sriram, D. Weaver, E. Maywood, I. Chaves et al., Interacting Molecular Loops in the Mammalian Circadian Clock, Science, vol.288, issue.5468, pp.1013-1019, 2000.
DOI : 10.1126/science.288.5468.1013

B. Tu, A. Kudlicki, M. Rowicka, and S. Mcknight, Logic of the Yeast Metabolic Cycle: Temporal Compartmentalization of Cellular Processes, Science, vol.310, issue.5751, pp.2-115, 2005.
DOI : 10.1126/science.1120499

C. Yang, F. Bernardo, G. Dong, S. Golden, and A. Van-oudenaarden, Circadian Gating of the Cell Cycle Revealed in Single Cyanobacterial Cells, Science, vol.95, issue.15, pp.1522-1526, 2010.
DOI : 10.1073/pnas.95.15.8660

W. Yu, M. Nomura, and M. Ikeda, Interacting feedback loops within the mammalian clock: BMAL1 is negatively autoregulated and upregulated by CRY1, CRY2, and PER2, Biochem. Biophys. Res. Commun, issue.3, pp.290-933, 2002.
DOI : 10.1006/bbrc.2001.6300

J. Zamborszky, A. Csikasz-nagy, and C. Hong, Computational Analysis of Mammalian Cell Division Gated by a Circadian Clock: Quantized Cell Cycles and Cell Size Control, Journal of Biological Rhythms, vol.302, issue.6, pp.542-553, 2007.
DOI : 10.1126/science.1089287

R. Cheikh, Modeling circadian clock???cell cycle interaction effects on cell population growth rates, Journal of Theoretical Biology, vol.363, pp.318-331, 2014.
DOI : 10.1016/j.jtbi.2014.08.008
URL : https://hal.archives-ouvertes.fr/hal-01055081

P. Altrock, L. Liu, and F. Michor, The mathematics of cancer: integrating quantitative models, CHAPTER 9. SELECTED PAPERS Bibliography, pp.730-745, 2015.
DOI : 10.1126/scitranslmed.3002356

B. Ananthasubramaniam and H. Herzel, Positive Feedback Promotes Oscillations in Negative Feedback Loops, PLoS ONE, vol.17, issue.8, pp.1-11, 2014.
DOI : 10.1371/journal.pone.0104761.s002
URL : http://doi.org/10.1371/journal.pone.0104761

M. Antle, D. Foley, N. Foley, and R. Silver, Gates and Oscillators: A Network Model of the Brain Clock, Journal of Biological Rhythms, vol.18, issue.4, pp.339-350, 2003.
DOI : 10.1046/j.1460-9568.2002.02224.x

M. Antle, N. Foley, D. Foley, and R. Silver, Gates and Oscillators II: Zeitgebers and the Network Model of the Brain Clock, Journal of Biological Rhythms, vol.94, issue.1, pp.14-25, 2007.
DOI : 10.1016/S0306-4522(99)00223-7

P. Arner, S. Bernard, M. Salehpour, G. Possnert, J. Liebl et al., Dynamics of human adipose lipid turnover in health and metabolic disease, Nature, vol.294, issue.7367, pp.110-113, 2011.
DOI : 10.1152/ajpregu.00396.2007
URL : https://hal.archives-ouvertes.fr/hal-00649210

N. Ashford, P. Bauman, H. Brown, R. Clapp, A. Finkel et al., Cancer risk: Role of environment, Science, vol.144, issue.5, pp.727-727, 2015.
DOI : 10.1016/j.cell.2011.02.013

S. Aton, C. Colwell, A. Harmar, J. Waschek, and E. Herzog, Vasoactive intestinal polypeptide mediates circadian rhythmicity and synchrony in mammalian clock neurons, Nature Neuroscience, vol.90, issue.4, pp.476-483, 2005.
DOI : 10.1016/0022-5193(78)90022-X
URL : http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1628303

D. Battogtokh and J. Tyson, Periodic forcing of a mathematical model of the eukaryotic cell cycle, Physical Review E, vol.15, issue.1, p.11910, 2006.
DOI : 10.1006/jtbi.1999.0952

J. Bélair, M. Mackey, and J. Mahaffy, Age-structured and two-delay models for erythropoiesis, Mathematical Biosciences, vol.128, issue.1-2, pp.317-346, 1995.
DOI : 10.1016/0025-5564(94)00078-E

O. Bergmann, R. Bhardwaj, S. Bernard, S. Zdunek, F. Barnabé-heider et al., Evidence for Cardiomyocyte Renewal in Humans, Science, vol.54, issue.5923, pp.98-102, 2009.
DOI : 10.1056/NEJM200106073442303
URL : https://hal.archives-ouvertes.fr/hal-00374382

O. Bergmann, J. Liebl, S. Bernard, K. Alkass, M. Yeung et al., The Age of Olfactory Bulb Neurons in Humans, Neuron, vol.74, issue.4, pp.634-639, 2012.
DOI : 10.1016/j.neuron.2012.03.030
URL : https://hal.archives-ouvertes.fr/hal-00755464

O. Bergmann, S. Zdunek, A. Felker, M. Salehpour, K. Alkass et al., Dynamics of Cell Generation and Turnover in the Human Heart, Cell, vol.161, issue.7, pp.1566-1575, 2015.
DOI : 10.1016/j.cell.2015.05.026
URL : https://hal.archives-ouvertes.fr/hal-01225091

S. Bernard, How to Build a Multiscale Model in Biology, Acta Biotheoretica, vol.58, issue.4, pp.291-303, 2013.
DOI : 10.1007/s00285-008-0211-1
URL : https://hal.archives-ouvertes.fr/hal-00867564

S. Bernard, Moving the Boundaries of Granulopoiesis Modelling, Bulletin of Mathematical Biology, vol.88, issue.6, pp.2358-2363, 2016.
DOI : 10.1093/annonc/mdq674
URL : https://hal.archives-ouvertes.fr/hal-01391393

S. Bernard and F. Crauste, Optimal linear stability condition for scalar differential equations with distributed delay, Discrete and Continuous Dynamical Systems - Series B, vol.20, issue.7, pp.1855-1876, 2015.
DOI : 10.3934/dcdsb.2015.20.1855
URL : https://hal.archives-ouvertes.fr/hal-00997528

S. Bernard and H. Herzel, Why do cells cycle with a 24 hour period?, Genome Info, vol.17, pp.72-79, 2006.
URL : https://hal.archives-ouvertes.fr/hal-00371755

S. Bernard, J. Bélair, and M. Mackey, Sufficient conditions for stability of linear differential equations with distributed delay, Discrete Contin Dynam Systems Ser B, vol.1, pp.233-256, 2001.

S. Bernard, B. ?ajavec, L. Pujo-menjouet, M. Mackey, and H. Herzel, Modelling transcriptional feedback loops: the role of Gro/TLE1 in Hes1 oscillations, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.5, issue.3, pp.1155-1170, 2006.
DOI : 10.1016/S1631-0691(01)01418-4
URL : https://hal.archives-ouvertes.fr/hal-00372717

S. Bernard, D. Gonze, B. ?ajavec, H. Herzel, and A. Kramer, Synchronization-Induced Rhythmicity of Circadian Oscillators in the Suprachiasmatic Nucleus, PLoS Computational Biology, vol.101, issue.4, p.68, 2007.
DOI : 10.1371/journal.pcbi.0030068.sv003
URL : https://hal.archives-ouvertes.fr/hal-00371737

S. Bernard, J. Frisén, and K. Spalding, A mathematical model for the interpretation of nuclear bomb test derived 14C incorporation in biological systems, Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms, vol.268, issue.7-8, pp.1295-1298, 2010.
DOI : 10.1016/j.nimb.2009.10.156
URL : https://hal.archives-ouvertes.fr/hal-00544517

A. Besse, G. Clapp, S. Bernard, F. Nicolini, D. Levy et al., Stability Analysis of a Model of Interaction Between the Immune System and Cancer Cells in Chronic Myelogenous Leukemia, Bulletin of Mathematical Biology, vol.109, issue.1, 2017.
DOI : 10.1182/blood-2006-03-011239
URL : https://hal.archives-ouvertes.fr/hal-01539364

K. Burnham and D. Anderson, Model selection and multimodel inference: a practical information-theoretic approach, 2003.
DOI : 10.1007/b97636

S. Campbell and I. Ncube, Stability in a scalar differential equation with multiple, distributed time delays, Journal of Mathematical Analysis and Applications, vol.450, issue.2, pp.1104-1122, 2017.
DOI : 10.1016/j.jmaa.2017.01.060

G. Clapp, T. Lepoutre, E. Cheikh, R. Bernard, S. Ruby et al., Implication of the Autologous Immune System in BCR-ABL Transcript Variations in Chronic Myelogenous Leukemia Patients Treated with Imatinib, Cancer Research, vol.75, issue.19, pp.4053-4062, 2015.
DOI : 10.1158/0008-5472.CAN-15-0611
URL : https://hal.archives-ouvertes.fr/hal-01251396

E. Cheikh, R. Bernard, S. , E. Khatib, and N. , Modeling circadian clock???cell cycle interaction effects on cell population growth rates, Journal of Theoretical Biology, vol.363, pp.318-331, 2014.
DOI : 10.1016/j.jtbi.2014.08.008
URL : https://hal.archives-ouvertes.fr/hal-01055081

J. Elser and K. Margulies, Hybrid Mathematical Model of Cardiomyocyte Turnover in the Adult Human Heart, PLoS ONE, vol.107, issue.12, p.51683, 2012.
DOI : 10.1371/journal.pone.0051683.s019

J. Enright, Mutual excitation of damped oscillators and self-sustainment of circadian rhythms Mathematical models of the circadian sleep-wake cycle, pp.1-17, 1984.

A. Ernst, K. Alkass, S. Bernard, M. Salehpour, S. Perl et al., Neurogenesis in the Striatum of the Adult Human Brain, Cell, vol.156, issue.5, pp.1072-1083, 2014.
DOI : 10.1016/j.cell.2014.01.044
URL : https://hal.archives-ouvertes.fr/hal-00952021

S. Friedman, A. Anderson, D. Bortz, A. Fletcher, H. Frieboes et al., Multicellds: a communitydeveloped standard for curating microenvironment-dependent multicellular data, p.90456, 2016.
DOI : 10.1101/090456

L. Fu, H. Pelicano, J. Liu, P. Huang, and C. Lee, The circadian gene Period2 plays an important role in tumor suppression and DNA damage response in vivo, pp.41-50, 2002.

D. Gonze, S. Bernard, C. Waltermann, A. Kramer, and H. Herzel, Spontaneous Synchronization of Coupled Circadian Oscillators, Biophysical Journal, vol.89, issue.1, pp.120-129, 2005.
DOI : 10.1529/biophysj.104.058388
URL : https://hal.archives-ouvertes.fr/hal-00371748

B. Goodwin, Oscillatory behavior in enzymatic control processes Advances in enzyme regulation, pp.425-438, 1965.
DOI : 10.1016/0065-2571(65)90067-1

J. Hale and W. Huang, Global Geometry of the Stable Regions for Two Delay Differential Equations, Journal of Mathematical Analysis and Applications, vol.178, issue.2, pp.344-362, 1993.
DOI : 10.1006/jmaa.1993.1312

H. Huttner, O. Bergmann, M. Salehpour, A. Rácz, J. Tatarishvili et al., The age and genomic integrity of neurons after cortical stroke in humans, Nature Neuroscience, vol.10, issue.6, pp.801-803, 2014.
DOI : 10.1186/1471-2105-10-80
URL : https://hal.archives-ouvertes.fr/hal-01092159

J. Kajstura, M. Rota, D. Cappetta, B. Ogórek, C. Arranto et al., Cardiomyogenesis in the Aging and Failing Human Heart, Circulation, vol.126, issue.15, pp.1869-1881, 2012.
DOI : 10.1161/CIRCULATIONAHA.112.118380

C. Ko, Y. Yamada, D. Welsh, E. Buhr, A. Liu et al., Emergence of Noise-Induced Oscillations in the Central Circadian Pacemaker, PLoS Biology, vol.38, issue.10, p.1000513, 2010.
DOI : 10.1371/journal.pbio.1000513.s018

H. Kunz and P. Achermann, Simulation of circadian rhythm generation in the suprachiasmatic nucleus with locally coupled self-sustained oscillators, Journal of Theoretical Biology, vol.224, issue.1, pp.63-78, 2003.
DOI : 10.1016/S0022-5193(03)00141-3

V. Kuznetsov, I. Makalkin, M. Taylor, and A. Perelson, Nonlinear dynamics of immunogenic tumors: Parameter estimation and global bifurcation analysis, Bulletin of Mathematical Biology, vol.2, issue.2, pp.295-321, 1994.
DOI : 10.1007/978-1-4757-4067-7

J. Leloup and A. Goldbeter, Toward a detailed computational model for the mammalian circadian clock, Proceedings of the National Academy of Sciences, vol.197, issue.4300, pp.7051-7056, 2003.
DOI : 10.1126/science.267326

I. Levin, B. Kromer, and S. Hammer, Atmospheric ?14CO2 trend in western european background air from, Tellus B: Chemical and Physical Meteorology, vol.65, issue.1, 2000.
DOI : 10.3402/tellusb.v65i0.20092
URL : http://doi.org/10.3402/tellusb.v65i0.20092

A. Liu, D. Welsh, C. Ko, H. Tran, E. Zhang et al., Intercellular Coupling Confers Robustness against Mutations in the SCN Circadian Clock Network, Cell, vol.129, issue.3, pp.605-616, 2007.
DOI : 10.1016/j.cell.2007.02.047

J. Mahaffy, K. Joiner, and P. Zak, A GEOMETRIC ANALYSIS OF STABILITY REGIONS FOR A LINEAR DIFFERENTIAL EQUATION WITH TWO DELAYS, International Journal of Bifurcation and Chaos, vol.05, issue.03, pp.779-796, 1995.
DOI : 10.1142/S0218127495000570

E. Maywood, A. Reddy, G. Wong, O. Neill, J. et al., Synchronization and Maintenance of Timekeeping in Suprachiasmatic Circadian Clock Cells by Neuropeptidergic Signaling, Current Biology, vol.16, issue.6, pp.599-605, 2006.
DOI : 10.1016/j.cub.2006.02.023

N. Monk, Oscillatory Expression of Hes1, p53, and NF-??B Driven by Transcriptional Time Delays, Current Biology, vol.13, issue.16, pp.1409-1413, 2003.
DOI : 10.1016/S0960-9822(03)00494-9

E. Nagoshi, C. Saini, C. Bauer, T. Laroche, F. Naef et al., Circadian Gene Expression in Individual Fibroblasts, Cell, vol.119, issue.5, pp.693-705, 2004.
DOI : 10.1016/j.cell.2004.11.015
URL : http://doi.org/10.1016/j.cell.2004.11.015

H. Ohta, S. Yamazaki, and D. Mcmahon, Constant light desynchronizes mammalian clock neurons, Nature Neuroscience, vol.35, issue.3, pp.267-269, 2005.
DOI : 10.1016/j.cub.2004.11.057

J. Pett, A. Koren?i?, F. Wesener, A. Kramer, and H. Herzel, Feedback Loops of the Mammalian Circadian Clock Constitute Repressilator, PLOS Computational Biology, vol.9, issue.24, p.1005266, 2016.
DOI : 10.1371/journal.pcbi.1005266.s009

P. Reimer, M. Baillie, E. Bard, A. Bayliss, J. Beck et al., IntCal04 terrestrial radiocarbon age calibration, pp.0-26, 2004.
DOI : 10.1017/s0033822200032999
URL : http://researchcommons.waikato.ac.nz/bitstream/10289/3690/1/INTCAL04%20TERRESTRIAL%20RADIOCARBON%20AGE.pdf

S. Ruan and J. Wei, On the zeros of transcendental functions with applications to stability of delay differential equations with two delays. Dynamics of Continuous Discrete and Impulsive Systems Series A 10, pp.863-874, 2003.

P. Ruoff, M. Vinsjevik, C. Monnerjahn, and L. Rensing, The Goodwin Model: Simulating the Effect of Light Pulses on the Circadian Sporulation Rhythm of Neurospora Crassa, Journal of Theoretical Biology, vol.209, issue.1, pp.29-42, 2001.
DOI : 10.1006/jtbi.2000.2239

K. Spalding, E. Arner, P. Westermark, S. Bernard, B. Buchholz et al., Dynamics of fat cell turnover in humans, Nature, vol.19, issue.7196, pp.783-787, 2008.
DOI : 10.1017/S0033822200003672
URL : https://hal.archives-ouvertes.fr/hal-00372715

K. Spalding, O. Bergmann, K. Alkass, S. Bernard, M. Salehpour et al., Dynamics of Hippocampal Neurogenesis in Adult Humans, Cell, vol.153, issue.6, pp.1219-1227, 2013.
DOI : 10.1016/j.cell.2013.05.002
URL : https://hal.archives-ouvertes.fr/hal-00839513

K. Spalding, R. Bhardwaj, B. Buchholz, H. Druid, and J. Frisén, Retrospective Birth Dating of Cells in Humans, Cell, vol.122, issue.1, pp.133-143, 2005.
DOI : 10.1016/j.cell.2005.04.028

T. To, M. Henson, E. Herzog, and F. Doyle, A Molecular Model for Intercellular Synchronization in the Mammalian Circadian Clock, Biophysical Journal, vol.92, issue.11, pp.3792-3803, 2007.
DOI : 10.1529/biophysj.106.094086

C. Tomasetti and B. Vogelstein, Variation in cancer risk among tissues can be explained by the number of stem cell divisions, Science, vol.10, issue.4, pp.78-81, 2015.
DOI : 10.1038/ng0895-383

C. Tomasetti, L. Li, and B. Vogelstein, Stem cell divisions, somatic mutations, cancer etiology, and cancer prevention, Science, vol.62, issue.6331, pp.1330-1334, 2017.
DOI : 10.1158/0008-5472.CAN-09-0015

T. Tsai, Y. Choi, W. Ma, J. Pomerening, C. Tang et al., Robust, Tunable Biological Oscillations from Interlinked Positive and Negative Feedback Loops, Science, vol.289, issue.5476, pp.126-129, 2008.
DOI : 10.1126/science.289.5476.107
URL : http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2728800

A. Webb, N. Angelo, J. Huettner, and E. Herzog, Intrinsic, nondeterministic circadian rhythm generation in identified mammalian neurons, Proceedings of the National Academy of Sciences, vol.72, issue.1, pp.16493-16498, 2009.
DOI : 10.1016/0022-5193(78)90022-X
URL : http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2752526

J. Weiss, The hill equation revisited: uses and misuses, The FASEB Journal, vol.11, issue.11, p.835, 1997.

D. Welsh, D. Logothetis, M. Meister, and S. Reppert, Individual neurons dissociated from rat suprachiasmatic nucleus express independently phased circadian firing rhythms, Neuron, vol.14, issue.4, pp.697-706, 1995.
DOI : 10.1016/0896-6273(95)90214-7
URL : http://doi.org/10.1016/0896-6273(95)90214-7

C. Wild, P. Brennan, M. Plummer, F. Bray, K. Straif et al., Cancer risk: Role of chance overstated, Science, vol.8, issue.1, pp.728-728, 2015.
DOI : 10.1038/bjc.1954.1

S. Wu, S. Powers, W. Zhu, and Y. Hannun, Substantial contribution of extrinsic risk factors to cancer development, Nature, vol.112, issue.7584, pp.43-47, 2016.
DOI : 10.1073/pnas.1421839112

S. Yamaguchi, H. Isejima, T. Matsuo, R. Okura, K. Yagita et al., Synchronization of Cellular Clocks in the Suprachiasmatic Nucleus, Science, vol.302, issue.5649, pp.1408-1412, 2003.
DOI : 10.1126/science.1089287

M. Yeung, S. Zdunek, O. Bergmann, S. Bernard, M. Salehpour et al., Dynamics of Oligodendrocyte Generation and Myelination in the Human Brain, Cell, vol.159, issue.4, pp.766-774, 2014.
DOI : 10.1016/j.cell.2014.10.011
URL : https://hal.archives-ouvertes.fr/hal-01092151