Free Access
Math. Model. Nat. Phenom.
Volume 4, Number 3, 2009
Cancer modelling (Part 2)
Page(s) 12 - 67
Published online 05 June 2009
  1. M. Adimy, F. Crauste. Global stability of a partial differential equation with distributed delay due to cellular replication. Nonlinear Analysis, 54 (2003), No. 8,1469–1491.
  2. M. Adimy, F. Crauste, S. Ruan. A mathematical study of the hematopoiesis process with applications to chronic myelogenous leukemia. SIAM J. Appl. Math., 65 (2005), No. 4,1328–1352.
  3. M. Adimy, F. Crauste, A. El Abdllaoui. Discrete maturity-structured model of cell differentiation with applications to acute myelogenous leukemia. J. Biological Systems, 16 (2008), No. 3, 395–424. [CrossRef]
  4. B.D. Aguda. Modeling the cell division cycle. In A. Friedman (Ed.) Tutorials in Mathematical Biosciences III: Cell Cycle, Proliferation, and Cancer, pp. 1–22. Springer, New York, 2005.
  5. Z. Agur. Mathematical modelling of cancer chemotherapy: Investigation of the resonance phenomenon. In: O. Arino et al. (Ed.). Advances in mathematical population dynamics -molecules, cells and man. Papers from the 4th international conference, Rice Univ., Houston, TX, USA, May 23–27, 1995, Ser. Math. Biol. Med. 6 (1997), pp. 571–578, World Scientific, Singapore.
  6. T. Alarcón, H.M. Byrne, P.K. Maini. Towards whole-organ modelling of tumour growth. Prog. Biophys. Mol. Biol., 85 (2004), No. 2-3, 451–72. [CrossRef] [PubMed]
  7. L. Alberghina, H.W. Westerhoff (Eds.). Systems Biology. Definitions and Perspectives. Springer, Berlin, 2005.
  8. B.B. Aldridge, J.M. Burke, D.A. Lauffenburger, P.K. Sorger. Physicochemical modelling of cell signalling. Nature Rev. Mol. Cell Biol., 8 (2006), No. 11, 1195–1203.
  9. A. Altinok, F. Lévi, A. Goldbeter. Identifying mechanisms of chronotolerance and chronoefficacy for the anticancer drugs 5-fluorouracil and oxaliplatin by computational modeling. Eur. J. Pharm. Sci., 36 (2009), No. 1, 20–38. [CrossRef] [PubMed]
  10. J.C. Ameisen. La sculpture du vivant. Stock, Paris, 1999.
  11. A.R.A. Anderson, M.A. Chaplain. Chap 10 in L. Preziosi (Ed.). Cancer modelling and simulation, Chapman and Hall, London, 2003.
  12. A.R.A. Anderson, A.M. Weaver, P.T. Cummings, V. Quaranta. Tumor morphology and phenotypic evolution driven by selective pressure from the microenvironment. Cell, 127 (2006), No. 5, 905–915.
  13. A. Aouba, F. Péquignot, A. Le Toullec, E. Jougla. Les causes médicales de décès en France en 2004 et leur évolution / Medical causes of death in France in 2004 and trends 1980-2004 (English abstract). Bulletin épidémiologique hebdomadaire de l'INVS,18 septembre 2007, 35–36. Available on line from
  14. O. Arino. A survey of structured cell population dynamics. Acta Biotheor., 43 (1995), No. 1-2, 3–25. [CrossRef] [PubMed]
  15. O. Arino, M. Kimmel. Comparison of approaches to modeling of cell population dynamics. SIAM J. Appl. Math., 53 (1993), No. 5, 1480–1504. [CrossRef] [MathSciNet]
  16. O. Arino, E. Sanchez. A survey of cell population dynamics. J. Theor. Med., 1 (1997), No. 1, 35–51. [CrossRef]
  17. H. Barbason, B. Bouzahzah, C. Herens, J. Marchandise, J. Sulon, J. van Cantfort. Circadian synchronization of liver regeneration in adult rats: the role played by adrenal hormones. Cell Prolif., 22 (1989), No. 6, 451–460. [CrossRef]
  18. J. Barnes. The Presocratic philosophers. Paperback edition,1 vol., Routledge, London, 1982.
  19. M.-A. Barrat-Petit, C. Naulin-Ifi, P. Mahler, G. Milano. Dihydropyrimidine déshydrogénase (DPD) : rythme et conséquences. (in French, English summary). Pathol.-Biol., 53 (2005), No. 5, 261–264. [CrossRef] [PubMed]
  20. C. Basdevant, J. Clairambault, F. Lévi. Optimisation of time-scheduled regimen for anti-cancer drug infusion. Mathematical Modelling and Numerical Analysis, 39 (2006), No. 6, 1069–1086. [CrossRef] [EDP Sciences] [MathSciNet]
  21. B. Basse, B.C. Baguley, E.S. Marshall, W.R. Joseph, B. van Brunt, G. Wake, D.J.N. Wall. A mathematical model for analysis of the cell cycle in cell lines derived from human tumors. J. Math. Biol., 47 (2003), No. 4, 295–312. [CrossRef] [MathSciNet] [PubMed]
  22. F. Bekkal Brikci, J. Clairambault, B. Perthame. Analysis of a molecular structured population model with polynomial growth for the cell cycle. Mathematical and Computer Modelling, 47 (2008), No. 7-8, 699–713. [CrossRef] [MathSciNet]
  23. F. Bekkal Brikci, J. Clairambault, B. Ribba, B. Perthame. An age-and-cyclin-structured cell population model for healthy and tumoral tissues. J. Math. Biol., 57(2008), No. 1, 91–110.
  24. N. Bellomo (Ed.). Selected Topics in Cancer Modeling: Genesis, Evolution, Immune Competition, and Therapy. Birkhäuser, Boston, 2008.
  25. N. Bellomo, M. Delitala. From the mathematical kinetic, and stochastic game theory to modelling mutations, onset, progression and immune competition of cancer cells. Physics of Life Reviews, 5 (2008), No. 4, 183–206. [CrossRef]
  26. Y. Ben-Neriah, G.Q. Daley, A.M. Mes-Masso, O.N. Witte, D. Baltimore. The chronic myelogenous leukemia-specific p210 protein is the product of the BCR/ABL hybrid gene. Science, 233 (1986), No. 4760 , 212–214.
  27. S. Bernard, HP. Herzel. Why do cells cycle with a 24 h period? Genome Informatics, 17 (2006), No. 1, 72–79.
  28. S. Bernard, J. Bélair, M.C. Mackey. Oscillations in cyclical neutropenia: New evidence based on mathematical modeling. J. Theor. Biol., 223 (2003), No. 3, 283–298. [CrossRef] [PubMed]
  29. N. Bessonov, A. Ducrot, V. Volpert. Modeling of leukemia development in the bone marrow. Proc. of the annual Symposium on Mathematics applied in Biology and Biophysics, Tome XLVIII (2005), vol. 2, 79–88.
  30. N. Bessonov, I. Demin, L. Pujo-Menjouet, V. Volpert. A multi-agent model describing self-renewal of differentiation effects on the blood cell population. Mathematical and computer modelling, 49 (2009), No. 11-12, 2116–2127. [CrossRef] [MathSciNet]
  31. M. Bizzarri, A. Cucina, F. Conti, F. D'Anselmi. Beyond the Oncogene Paradigm: Understanding the Complexity in Cancerogenesis. Acta Biotheor., 56 (2008), No. 3, 173–196. [CrossRef] [PubMed]
  32. G.A. Bjarnason, R.C.K. Jordan, R.C.K., R.B. Sothern. Circadian variation in the expression of cell-cycle proteins in the human oral epithelium. Am. J. Pathol., 154 (1999), No. 2, 613–622. [CrossRef] [PubMed]
  33. M.V. Blagosklonny, A. Pardee. The restriction point of the cell cycle. Cell Cycle, 1 (1974), No. 2, 103–110.
  34. J.L. Boldrini, M.I.S. Costa. Therapy burden, drug resistance, and optimal treatment regimen for cancer therapy. IMA J. Math. Appl. Med. Biology, 17 (2000), No. 1, 33–51. [CrossRef]
  35. N.A. Boughattas, F. Lévi, et al. Circadian Rhythm in Toxicities and Tissue Uptake of 1,2-diamminocyclohexane(trans-1)oxaloplatinum(II) in Mice. Cancer Research, 49 (1989), No. 12, 3362–3368. [PubMed]
  36. K. Boushaba, H.A. Levine, M. Nilsen-Hamilton. A mathematical model for the regulation of tumor dormancy based on enzyme kinetics. Bull. Math. Biol., 68 (2006), No. 7, 1495–1526. [CrossRef] [MathSciNet] [PubMed]
  37. L. Bourgey. Observation et expérience chez Aristote. Vrin, coll. Bibliothèque d'Histoire de la Philosophie, Paris, 1955.
  38. M. Breccia, G. Alimena. Resistance to imatinib in chronic myeloid leukemia and therapeutic approaches to circumvent the problem. Cardiovasc. Hematol. Disord. Drug Targets, 9 (2009), No. 1, 21–28. [CrossRef] [PubMed]
  39. N.F. Britton. Reaction-diffusion equations and their applications to biology. Academic Press, London, 1986
  40. M.P. Brynildsen, J.J. Collins. Systems biology makes it personal. Mol. Cell, 34 (2009), No. 1, 137–138. [CrossRef] [PubMed]
  41. F.J. Burns, I.F. Tannock. On the existence of a G0 phase in the cell cycle. Cell Tissue Kinet., 19 (1970), No. 4, 321–334.
  42. H.M. Byrne, D. Drasdo. Individual-based and continuum models of growing cell populations: a comparison. J. Math. Biol., 58 (2009), No. 4-5, 657–87. [CrossRef] [MathSciNet] [PubMed]
  43. L. Calzone, S. Soliman. Coupling the cell cycle and the circadian cycle. INRIA internal research report #5835 (2006). Available online from
  44. A. Cappuccio, M.A. Herrero, L. Nunez. Biological optimization of tumor radiosurgery. Med Phys., 36 (2009), No. 1, 98–104. [CrossRef] [PubMed]
  45. N. Champagnat, R. Ferrière, S. Méléard. Unifying evolutionary dynamics: From individual stochastic processes to macroscopic models. Theoretical Population Biology, 69 (2006), No. 3, 297–321. [CrossRef] [PubMed]
  46. S.G. Chaney, S.L. Campbell, E. Bassett, Y.B. Wu. Recognition and processing of cisplatin- and oxaliplatin-DNA adducts. Clin. Rev. Oncol. Hematol., 53 (2003), No. 1, 3–11. [CrossRef]
  47. J.T. Chang, C. Carvalho, S. Mori S, A.H. Bild, M.L. Gatza, Q. Wang Q, J.E. Lucas JE, A. Potti, P.G. Febbo, M. West, J.R. Nevins. A genomic strategy to elucidate modules of oncogenic pathway signaling networks. Mol. Cell, 34 (2009), No.1, 104–14. [CrossRef] [PubMed]
  48. G. Chiorino, J.A.J. Metz, D. Tomasoni, P. Ubezio. Desynchronization rate in cell populations: mathematical modeling and experimental data. J. Theor. Biol., 208 (2001), No.2, 185–199. [CrossRef] [PubMed]
  49. A. Ciliberto, M.J. Petrus, J.J. Tyson, J.C. Sible. A kinetic model of the cyclin E/Cdk2 developmental timer in Xenopus laevis embryos. Biophys. Chem., 104 (2003), No. 3, 573–89. [CrossRef] [PubMed]
  50. A. Ciliberto, B. Novak, J.J. Tyson. Steady states and oscillations in the p53/Mdm2 network. Cell Cycle, 4 (2005), No. 3, 488–493. [CrossRef] [PubMed]
  51. J. Clairambault. A step toward optimization of cancer therapeutics. Physiologically based modelling of circadian control on cell proliferation. IEEE-EMB Magazine, 27 (2008), No.1, 20–24. [CrossRef]
  52. J. Clairambault, S. Gaubert, B. Perthame. An inequality for the Perron and Floquet eigenvalues of monotone differential systems and age structured equations. C. R. Acad. Sci. (Paris) Ser. I Mathématique, 345 (2007), No. 10, 549-554.
  53. J. Clairambault. Modelling oxaliplatin drug delivery to circadian rhythm in drug metabolism and host tolerance. Advanced Drug Delivery Reviews (ADDR), 59 (2007), No. 9-10, 1054–1068. [CrossRef] [PubMed]
  54. J. Clairambault, P. Michel, B. Perthame. A model of the cell cycle and its circadian control. In: Mathematical Modeling of Biological Systems, Volume I: Cellular Biophysics, Regulatory Networks, Development, Biomedicine, and Data Analysis, Deutsch, A., Brusch, L., Byrne, H., de Vries, G., Herzel, H. (Eds.), Birkhäuser, Boston, pp. 239-251, 2007.
  55. J. Clairambault, P. Michel, B. Perthame. Circadian rhythm and tumour growth. C. R. Acad. Sci. (Paris) Mathématique (Équations aux dérivées partielles), 342 (2006), No. 1, 17–22.
  56. L. Cojocaru, Z. Agur. A theoretical analysis of interval drug dosing for cell-cycle-phase-specific drugs. Math. BioSci., 109 (1992), No 1, 85–97.
  57. C. Colijn, M.C. Mackey. A mathematical model of hematopoiesis: I. Periodic chronic myelogenous leukemia. J. Theor. Biol., 237 (2005), No. 2, 117–132. [CrossRef] [PubMed]
  58. M.I.S Costa, J.L. Boldrini. Chemotherapeutic treatments: a study of the interplay among drug resistance, toxicity and recuperation from side effects. Bull. Math. Biol., 59 (1997), No. 2, 205–232. [CrossRef] [PubMed]
  59. M.I.S. Costa, J.L. Boldrini. Conflicting objectives in chemotherapy with drug resistance. Bull. Math. Biol., 59 (1997), No. 4, 707–724. [CrossRef] [PubMed]
  60. C. Csajka, D. Verotta. Pharmacokinetic-pharmacodynamic modelling: history and perspectives. J. Pharmacokinet. Pharmacodyn., 33 (2006), No. 3, 227–79. [CrossRef] [PubMed]
  61. A. Csikasz Nagy, D. Battogtokh, K.C. Chen, B. Novak, J.J. Tyson. Analysis of a generic model of eukaryotic cell-cycle regulation. Biophys J., 90 (2006), No. 12, 4361–79. [CrossRef] [PubMed]
  62. R. Dautray, J.-L. Lions. Mathematical analysis and numerical methods for sciences and technology. Ch. VIII, 187–199, Springer, Berlin,1990.
  63. T. David-Pfeuty. The flexible evolutionary anchorage-dependent Pardee's restriction point of mammalian cells: how its deregulation may lead to cancer. Biochim Biophys Acta., 1765 (2006), No. 1, 38–66. [PubMed]
  64. B.F. Dibrov, A.M. Zhabotinsky, Yu.A. Neyfakh, M.P. Orlova, L.I. Churikova. Optimal scheduling for cell synchronization by cycle-phase-specific blockers. Math. BioSci., 66 (1983), No. 2, 167–185. [CrossRef]
  65. B.F. Dibrov, A.M. Zhabotinsky, Yu.A. Neyfakh, M.P. Orlova, L.I. Churikova. Mathematical model of cancer chemotherapy. Periodic schedules of phase-specific cytotoxic-agent administration increasing the selectivity of therapy. Math. BioSci., 73 (1985), No. 1, 1–31. [CrossRef] [MathSciNet]
  66. O. Diekmann, P.E. Jabin, S. Mischler, B. Perthame. The dynamics of adaptation: an illuminating example and a Hamilton-Jacobi approach. Theoretical Population Biology, 67 (2005), No. 4, 257–271. [CrossRef] [PubMed]
  67. L. Dimitrio. Irinotecan: Modelling intracellular pharmacokinetics and pharmacodynamics, M2 master thesis (in French, English summary). University Pierre-et-Marie-Curie and INRIA internal report, June 2007.
  68. D. Dingli, A. Traulsen, J.M. Pacheco. Stochastic dynamics of hematopoietic tumor stem cells. Cell Cycle, 6 (2007), No. 4, 461–466. [CrossRef] [PubMed]
  69. D. Dingli, A. Traulsen, F. Michor. (A)symmetric stem cell replication and cancer. PLoS Comput. Biol., 2007, Mar 16;3(3):e53. [doi:10.1371/journal.pcbi.0030053].
  70. D. Dingli, A. Traulsen, J.M. Pacheco. Compartmental architecture and dynamics of hematopoiesis. PLoS One, 2007, Apr. 4, 2(4): e345. [doi:10.1371/journal.pone.0000345].
  71. D. Dingli, J.M. Pacheco. Some dynamic aspects of hematopoietic stem cells. Stem Cell Rev., 4 (2008), No. 1, 57–64. [CrossRef] [PubMed]
  72. D. Dingli, T. Antal, A. Traulsen, J.M. Pacheco. Progenitor self-renewal and cyclical neutropenia. Cell Prolif., 42 (2009), No. 3, 330–338. [CrossRef] [PubMed]
  73. M. Doumic-Jauffret. Analysis of a population model structured by the cells molecular content. Mathematical Modelling of Natural Phenomena, 2 (2007), No. 3, 121–15. [CrossRef] [EDP Sciences] [MathSciNet]
  74. D. Drasdo, S. Höhme, M. Block. On the Role of Physics in the Growth and Pattern Formation of Multi-Cellular Systems: What can we Learn from Individual-Cell Based Models? J. Stat. Phys.,128 (2007), No. 1-2, 287–345.
  75. B.J. Druker, et al. Effects of a selective inhibitor of the Abl tyrosine kinase activity on the growth of BCR-ABL positive cells. Nature Med., 2 (1996), No. 5, 561–566. [CrossRef]
  76. B.J. Druker, et al. Efficacy and safety of a specific inhibitor of the BCR-ABL tyrosine kinase in chronic myeloid leukemia. N. Engl. J. Med., 344 (2001), No. 14, 1031–1037. [CrossRef] [PubMed]
  77. A. Ducrot, V. Volpert. On a model of leukemia development with a spatial cell distribution. Mathematical Modelling of Natural Phenomena, 2 (2007), No. 3, 101–120. [CrossRef] [EDP Sciences] [MathSciNet]
  78. M. Eisen. Mathematical models in cell biology and cancer chemotherapy. Lectures Notes in Biomathematics 30, Springer, Berlin, 1979.
  79. M. Elshaikh, M. Ljungman, R. Ten Haken, A.S. Lichter. Advances in Radiation Oncology. Annu. Rev. Med., 57 (2006),19–31.
  80. S. Faivre, D. Chan, R. Salinas, B. Woynarowska, J.M. Woynarowski. DNA strand breaks and apoptosis induced by oxaliplatin in cancer cells. Biochemical pharmacology, 66 (2003), No. 2, 225–237. [CrossRef] [PubMed]
  81. E. Fearon, B. Vogelstein. A genetic model for colorectal tumorigenesis. Cell, 61 (1990), No. 5, 759–67. [CrossRef] [PubMed]
  82. J.E. Ferrell Jr. Tripping the switch fantastic: how a protein kinase cascade can convert graded inputs into switch-like outputs. Trends Biochem. Sci., 21 (1996), No. 12, 460–466. [CrossRef] [PubMed]
  83. J.E. Ferrell Jr. How responses get more switch-like as you move down a protein kinase cascade. Trends Biochem. Sci., 22 (1997), No. 8, 288–289.
  84. E. Filipski, V.M. King, X.M. Li, T.G. Granda, F. Lévi. Host circadian clock as a control point in tumor progression. J. Natl. Cancer Inst., 94 (2002), No. 9, 690–697. [CrossRef] [PubMed]
  85. E. Filipski, P.F. Innominato, M.W. Wu, X.M. Li, S. Iacobelli, L.J. Xian, F. Lévi. Effect of light and food schedules on liver and tumor molecular clocks in mice. J. Natl. Cancer Inst., 97 (2005), No. 7, 507–517. [CrossRef] [PubMed]
  86. G. Finak, N. Bertos, F. Pepin, S. Sadekova, M. Souleimanova, H. Zhao, H. Chen, G. Omeroglu, S. Meterissian, A. Omeroglu, M. Hallett, M. Park. Stromal gene expression predicts clinical outcome in breast cancer. Nature Med., 14 (2008), No. 5, 518–527. [CrossRef] [PubMed]
  87. B. Finkenstädt, E.A. Heron, M. Komorowski, K. Edwards, S. Tang, C.V. Harper CV, J.R. Davis, M.R. White, A.J. Millar, D.A. Rand. Reconstruction of transcriptional dynamics from gene reporter data using differential equations. Bioinformatics, 24 (2008), No. 24, 2901–2907. [CrossRef] [PubMed]
  88. K.R. Fister, J.C. Panetta. Optimal control applied to cell-cycle-specific cancer chemotherapy. SIAM J. Appl. Math., 60 (2000), No. 3, 1059–1072.
  89. C. Foley, S. Bernard, M.C. Mackey. Cost-effective G-CSF therapy strategies for cyclical neutropenia: Mathematical modelling based hypotheses. J. Theor. Biol., 238 (2006), No. 4, 754–763. [CrossRef] [PubMed]
  90. C. Foley, M.C. Mackey. Dynamic hematological disease: a review. J. Math. Biol., 58 (2009), No. 1-2, 285-322. [CrossRef] [MathSciNet] [PubMed]
  91. C. Foley, M.C. Mackey. Mathematical model for G-CSF administration after chemotherapy. J. Theor. Biol., 257 (2009), No. 1, 27–44. [CrossRef] [PubMed]
  92. D.B. Forger, M.E. Jewett, R.E. Kronauer. A simpler model of the human circadian pacemaker. J. Biol .Rhythms, 14 (1999), No. 6, 532–7.
  93. D.B. Forger, R.E. Kronauer. Reconciling mathematical models of biological clocks by averaging on approximate manifolds. SIAM J. Appl. Math., 62 (2002), No. 4, 1281–1296. [CrossRef] [MathSciNet]
  94. D.B. Forger, C.S. Peskin. A detailed predictive model of the mammalian circadian clock. Proc. Natl. Acad. Sci. USA, 100 (2003), No. 25, 14806–14811. [CrossRef]
  95. D.B. Forger, D.A. Dean 2nd, K. Gurdziel, J.-C. Leloup, C. Lee, C. Von Gall, J.P. Etchegaray, R.E. Kronauer, A. Goldbeter, C.S. Peskin, M.E. Jewett, D.R. Weaver. Development and validation of computational models for mammalian circadian oscillators. OMICS, 7 (2003), No. 4, 387–400. [CrossRef] [PubMed]
  96. S. A. Frank. Dynamics of Cancer. Incidence, Inheritance and evolution. Princeton university Press, Princeton, 2007.
  97. A. Friedman (Ed.). Cell Cycle, Proliferation, and Cancer. Tutorials in Mathematical Biosciences III, Lecture Notes in Mathematics 1872 / Mathematical Biosciences Subseries, Springer, New York, 2006.
  98. L. Fu, H. Pelicano, J. Liu, P. Huang, C.C. Lee. The circadian gene Per2 plays an important role in tumor suppression and DNA damage response in vivo. Cell, 111 (2002), No. 1, 41–50. [CrossRef] [PubMed]
  99. L. Fu, L., C.C. Lee. The circadian clock: pacemaker and tumor suppressor. Nature Rev. Cancer, 3 (2003), No. 5, 350–361. [CrossRef] [PubMed]
  100. J. Galle, G. Aust, G. Schaller, T. Beyer, D. Drasdo. Individual cell-based models of the spatio-temporal organisation of multicellular systems - achievements and limitations. Cytometry A, 69A (2006), No. 7, 704–710. [CrossRef]
  101. R.A. Gatenby, E.T. Gawlinski. A reaction-diffusion model of cancer invasion. Cancer Res., 56 (1996), No. 24, 745–53. [PubMed]
  102. R.A. Gatenby, E.T. Gawlinski. The glycolytic phenotype in carcinogenesis and tumor invasion: insights through mathematical models. Cancer Res., 63 (2003), No. 14, 3847–54. [PubMed]
  103. R.A. Gatenby, R.J. Gillies. A microenvironmental model of carcinogenesis. Nature Rev. Cancer, 8 (2008), No. 1, 56–61. [CrossRef]
  104. S. Génieys, V. Volpert, P. Auger. Adaptive dynamics: modelling Darwin's divergence principle. C. R. Acad. Sci. Paris Biologie, 329 (2006), No. 11, 876–879.
  105. S. Génieys, N. Bessonov, V. Volpert. Mathematical model of evolutionary branching. Mathematical and Computer Modelling, 49 (2009), No. 11-12, 2109–2115. [CrossRef] [MathSciNet]
  106. A. Gerisch, M.A. Chaplain. Mathematical modelling of cancer cell invasion of tissue: local and non-local models and the effect of adhesion. J. Theor. Biol., 250 (2008), No. 4, 684–704. [CrossRef] [MathSciNet] [PubMed]
  107. N. Geva-Zatorsky, N. Rosenfeld, S. Itzkovitz, R. Milo, A. Sigal, E. Dekel, T. Yarnitzky, Y. Liron, P. Polak, G. Lahav, U. Alon. Oscillations and variability in the p53 system. Mol. Syst. Biol., 2 (2006), 2:2006.0033. Epub 2006 Jun 13. [doi:10.1038/msb4100068].
  108. D. Gholam, S. Giacchetti, C. Brézault-Bonnet, M. Bouchahda, D. Hauteville, R. Adam, B. Ducot, O. Ghémard, F. Kustlinger, C. Jasmin, F. Lévi. Chronomodulated irinotecan, oxaliplatin, and leucovorin-modulated 5-Fluorouracil as ambulatory salvage therapy in patients with irinotecan- and oxaliplatin-resistant metastatic colorectal cancer. Oncologist, 11 (2006), No. 10, 1072–80. [CrossRef] [PubMed]
  109. A. Goldbeter, D.E. Koshland Jr. An amplified sensitivity arising from covalent modification in biological systems. Proc. Natl. Acad. Sci. USA, 78 (1981), No. 11, 6840–4. [CrossRef]
  110. A. Goldbeter. A minimal cascade model for the mitotic oscillator involving cyclin and cdc2 kinase. Proc. Natl. Acad. Sci. USA, 88 (1991), No. 20, 9107–11. [CrossRef]
  111. A. Goldbeter. A model for circadian oscillations in the Drosophila period protein (PER). Proc Roy. Soc. B (Biol. Sci.) 261 (1995), No. 1362, 319–324.
  112. A. Goldbeter. Biochemical oscillations and cellular rhythms. Cambridge University Press, 1996.
  113. J.H. Goldie, A.J. Coldman. A mathematical model for relating the drug sensitivity of tumors to their spontaneous mutation rate. Canc. Treat. Rep., 63 (1979), No. 11-12, 1727–1733.
  114. J.H. Goldie, A.J. Coldman. Drug Resistance in Cancer: Mechanisms and Models. Cambridge University Press,1998.
  115. B.C. Goodwin. Temporal organization in cells: a dynamic theory of cellular control processes. Academic Press, New York, 1963.
  116. B.C. Goodwin. Oscillatory behavior in enzymatic control processes. In: Advances in enzyme regulation, vol. 3 (G. Weber, Ed.), pp. 425–438, Pergamon Press, Oxford, 1965.
  117. M.M. Gottesmann, T. Fojo, S.E. Bates. Multidrug resistance in cancer: Role of ABC transporters. Nature Rev. Cancer, 2 (2002), No. 1, 48–58. [CrossRef] [PubMed]
  118. T. Granda, X.H. Liu, R. Smaaland, N. Cermakian, E. Filipski, P. Sassone-Corsi, F. Lévi. Circadian regulation of cell cycle and apoptosis in mouse bone marrow and tumor. FASEB J., 19 (2005), No. 2, 304–306. [PubMed]
  119. M. Gyllenberg, G. Webb. Quiescence as an explanation of Gompertzian tumor growth. Growth Dev. Aging, 153 (1989), No. 1-2, 25–33.
  120. M. Gyllenberg, G. Webb. A nonlinear structured population model of tumor growth with quiescence. J. Math. Biol., 28 (1990), No. 6, 671–94. [CrossRef] [MathSciNet] [PubMed]
  121. T. Haferlach. Molecular genetic pathways as therapeutic targets in AML. In: Educational book, ASH 2008 meeting, pp. 400–411, 2008.
  122. D. Hanahan, R.A. Weinberg. The hallmarks of cancer. Cell, 100 (2000), No. 1, 57–70. [CrossRef] [PubMed]
  123. J.C. Harrison, J.E. Haber. Surviving the breakup; the DNA damage checkpoint. Annu. Rev. Genet., 40 (2006), 209–235.
  124. C. Haurie, D.C. Dale, M.C. Mackey. Cyclical neutropenia and other periodic hematological diseases: A review of mechanisms and mathematical models. Blood, 92 (1998), No. 8, 2629–2640. [PubMed]
  125. R. Heinrich, S. Schuster. The regulation of cellular systems. Chapman and Hall, New York, 1996.
  126. E.A. Heron, B. Finkenstädt, D.A. Rand. Bayesian inference for dynamic transcriptional regulation; the Hes1 system as a case study. Bioinformatics, 23 (2007), No. 19, 2596–603.
  127. P. Hinow, S.E. Wang, C.L. Arteaga, G.F. Webb. A mathematical model separates quantitatively the cytostatic and cytotoxic effects of a HER2 tyrosine kinase inhibitor. Theor. Biol. Med. Modelling, (2007). [doi:10.1186/1742-4682-4-14.]
  128. M. Hollstein, D. Sidransky, B. Vogelstein, C.C. Harris. p53 mutations in human cancers. Science, 253 (1991), No. 5015, 49–53. [CrossRef] [PubMed]
  129. P.J. Houghton, G.S. Germain, F.C. Harwood, J.D. Schuetz, C.F. Stewart, E. Buchdunger, P. Traxler. Imatinib mesylate is a potent inhibitor of the ABCG2 (BCRP) transporter and reverses resistance to Topotecan and SN-38 in vitro. Canc. Res., 64 (2004), No. 7, 2333–2337. [CrossRef]
  130. A. Iliadis, D. Barbolosi. Optimizing drug regimens in cancer chemotherapy by an efficacy-toxicity mathematical model. Computers Biomed. Res., 33 (2000), No. 3, 211–226. [CrossRef] [PubMed]
  131. A. Iliadis, D. Barbolosi. Optimising drug regimens in cancer chemotherapy: a simulation study using a PK-PD model. Computers Biol. Med., 31 (2001), No. 3, 157–172. [CrossRef] [PubMed]
  132. F. Innocenti, D.L. Kroetz, E. Schuetz, M.E. Dolan, J. Ramirez, M. Relling, P.X. Chen, S. Das, G.L. Rosner, M.J. Ratain. Comprehensive pharmacogenetic analysis of Irinotecan neutropenia and pharmacokinetics. J. Clin. Oncol., (2009), Apr. 6 [Epub ahead of print]. [doi: 10.1200/JCO.2008.20.6300].
  133. T.L. Jackson, H.M. Byrne. A mathematical model to study the effects of drug resistance and vasculature on the response of solid tumors to chemotherapy. Math. Biosci., 164 (2000), No. 1, 17–38. [CrossRef] [MathSciNet] [PubMed]
  134. A. Jemal, R. Siegel, E. Ward, T. Murray, J.Q. Xu, M.J. Thun. Cancer Statistics, 2007. CA Cancer J. Clin., 57 (2007), No. 1, 43–66. [CrossRef] [PubMed]
  135. B. Kang, Y.Y. Li, X. Chang, L. Liu, Y.X. Li. Modeling the effects of cell cycle M-phase transcriptional inhibition on circadian oscillation. PLoS Comput. Biol., (2008). [doi: 10.1371/journal.pcbi.1000019].
  136. M.B. Kastan, J. Bartek. Cell-cycle checkpoints and cancer. Nature, 432 (2004), No. 7015, 316–323. [CrossRef] [PubMed]
  137. J.P. Keener, J. Sneyd. Mathematical physiology. Springer, New York, 1998.
  138. Yu. Kheifetz, Yu. Kogan, Z. Agur. Long-range predictability in models of cell populations subjected to phase-specific drugs: Growth-rate approximation using properties of positive compact operators. Math. Models Meth. Appl. Sci., 16 (2006), No. 7, 1–18. [CrossRef]
  139. P.S. Kim, P.P. Lee, D. Levy. Modeling Imatinib-treated chronic myelogenous leukemia: reducing the complexity of agent-based models. Bull. Math. Biol. 70 (2008), No. 3, 728–744.
  140. P.S. Kim, P.P. Lee, D. Levy. A PDE model for Imatinib-treated chronic myelogenous leukemia. Bull. Math. Biol. 70 (2008), No. 7, 1994–2016.
  141. M. Kimmel, A. Swierniak. Control theory approach to cancer chemotherapy: Benefiting from phase dependence and overcoming drug resistance. In: Cell cycle, proliferation, and cancer (A. Friedman, Ed.), Springer LN 1872, pp. 185–216, Springer, New York, 2006.
  142. H. Kitano (Ed.). Foundations of Systems Biology. MIT Press, Cambridge (MA), 2001.
  143. H. Kitano. Computational systems biology. Nature, 420 (2002), No. 6912, 206–210. [CrossRef] [PubMed]
  144. H. Kitano. Cancer as a robust system: Implications for anticancer therapy. Nature Rev. Cancer, 4 ( 2004), No. 3, 227–235.
  145. H. Kitano. A robustness-based approach to systems-oriented drug design. Nature Rev. Drug Discovery, 6 (2007), No. 3, 202–210. [CrossRef]
  146. M. Kivisaar. Stationary phase mutagenesis: mechanisms that accelerate adaptation of microbial populations under environmental stress. Environm. Microbiol., 5 (2003), No. 10, 814–827. [CrossRef] [PubMed]
  147. M. von Kleist, W. Huisinga. Physiologically based pharmacokinetic modelling: a sub-compartmentalized model of tissue distribution. J Pharmacokinet Pharmacodyn., 34 (2007), No. 6, 789–806. [CrossRef] [PubMed]
  148. A.G. Knudson. Two genetic hits (more or less) to cancer. Nature Rev. Cancer, 1 (2001), No. 2, 157–162. [CrossRef] [PubMed]
  149. K. Kohn. Molecular interaction map of the mammalian cell cycle control and DNA repair systems. Mol. Biol. Cell, 10 (1999), No. 8, 2703–34. [CrossRef] [PubMed]
  150. K.W. Kohn, M.I. Aladjem, S. Kim, J.N. Weinstein, Y. Pommier. Depicting combinatorial complexity with the molecular interaction map notation. Mol. Sys. Biol., 51 (2006), 1–12. [doi:10.1038/msb4100088].
  151. K.W. Kohn, M.I. Aladjem, J.N. Weinstein, Y. Pommier. Molecular interaction maps of bioregulatory networks: a general rubric for systems biology. Mol. Biol. Cell, 17 (2006), No. 1, 1–13.
  152. F. Kozusko, P.H. Chen, S.G. Grant, B.W. Day, J.C. Panetta. A mathematical model of in vitro cancer cell growth and treatment with the antimitotic agent curacin A. Math. Biosci., 170 (2001), No. 1, 1–16. [CrossRef] [MathSciNet] [PubMed]
  153. F. Kozusko, Z. Bajzer. Combining Gompertzian growth and cell population dynamics. Math. Biosci., 185 (2003), No. 2, 153–67. [CrossRef] [MathSciNet] [PubMed]
  154. A. Kramer, F.C. Yang, P. Snodgrass, X. Li, T.E. Scammell. Regulation of daily locomotor activity and sleep by hypothalamic EGF receptor signaling. Science, 294 (2001), No. 5551, 2511–15. [CrossRef] [PubMed]
  155. J.-J. Kupiec. A Darwinian theory for the origin of cellular differentiation. Molecular and General Genetics, 255 (1997), No. 2, 201–208. [CrossRef] [PubMed]
  156. J.-J. Kupiec, P. Sonigo. Ni Dieu ni gène. Pour une autre théorie de l'hérédité. Seuil, Paris, 2000.
  157. J.-J. Kupiec. L'origine des individus. Fayard, Paris, 2008.
  158. D.M. Kweekel, H. Gelderblom, H.-J. Guchelaar. Pharmacology of oxaliplatin and the use of pharmacogenomics to individualize therapy. Canc. Treat. Rev., 31 (2005), No.2, 90–105. [CrossRef]
  159. D.M. Kweekel, H. Gelderblom, H.-J. Guchelaar. Clinical and pharmacogenetic factors associated with irinotecan toxicity. Canc. Treat. Rev., 34 (2008), No. 7, 655–669.
  160. E. Laconi. The evolving concept of tumor microenvironments. Bioessays, 29 (2007), No. 8, 738–44. [CrossRef] [PubMed]
  161. G. Lahav, N. Rosenfeld, A. Sigal, N. Geva-Zatorsky, A.J. Levine, M.B. Elowitz, U. Alon. Dynamics of the p53-Mdm2 feedback loop in individual cells. Nature Genet., 36 (2004), No. 2, 147–150. [CrossRef] [PubMed]
  162. L.G. Lajtha. On DNA labeling in the study of the dynamics of bone marrow cell populations. In: Stohlman, Jr., F. (Ed), The Kinetics of Cellular Proliferation, pp. 173-182, Grune and Stratton, New York, 1959.
  163. J.L. Lebowitz, S.I. Rubinow. A theory for the age and generation time distribution of a microbial population. J. Math. Biol., 1 (1974), No. 1, 17–36. [CrossRef] [MathSciNet]
  164. U. Ledzewicz, H. Schättler. Structure of optimal controls for a cancer chemotherapy model with PK/PD. In: Proceedings of the 43rd Conference on Decision and Control, Atlantis, Bahamas islands, pp. 1376–1381, IEEE Publishing, 2004.
  165. J.-C. Leloup, D. Gonze, A. Goldbeter. Limit cycle models for circadian rhythms based on transcriptional regulation in Drosophila and Neurospora. J. Biol. Rhythms, 14 (1999), No. 6, 433–448. [CrossRef] [PubMed]
  166. J.-C. Leloup, A. Goldbeter. Towards a detailed computational model for the mammalian circadian clock. Proc. Natl. Acad. Sci. USA, 100 (2003), No. 12, 7051–7056. [CrossRef]
  167. F. Lévi (Ed.). Cancer chronotherapeutics. Special issue of Chronobiology International, Vol. 19 (2002), No. 1.
  168. F. Lévi. Chronotherapeutics: the relevance of timing in cancer therapy. Cancer Causes Control, 17 (2006), No. 4, 611–621. [CrossRef] [PubMed]
  169. F. Lévi, G. Metzger, C. Massari, G. Milano. Oxaliplatin: Pharmacokinetics and Chronopharmacological Aspects. Clin. Pharmacokinet., 38 (2000), No. 1, 1–21. [CrossRef] [PubMed]
  170. F. Lévi , U. Schibler. Circadian Rhythms: Mechanisms and Therapeutic Implications. Ann. Rev. Pharmacol. Toxicol., 47 (2007), 493–528.
  171. F. Lévi, A. Altinok, J. Clairambault, A. Goldbeter. Implications of circadian clocks for the rhythmic delivery of cancer therapeutics. Phil. Trans. Roy. Soc. A, 366 (2008), No. 1880, 3575–3598.
  172. A.J. Levine, J. Momand, C.A. Finlay. The p53 tumor suppressor gene. Nature, 351 (1991), No. 6326, 453–456. [CrossRef] [PubMed]
  173. M. Loeffler, I. Roeder. Tissue stem cells: definition, plasticity, heterogeneity, self-organization and models - A conceptual approach. Cells Tissues Organs, 171 (2002), No. 1, 8–26. [CrossRef] [PubMed]
  174. X.M. Li, G. Metzger, E. Filipski, N. Boughattas, G. Lemaigre, B. Hecquet., E. Filipski, F. Lévi. Pharmacologic modulation of reduced glutathione circadian rhythms with buthionine sulfoximine: relationship with cisplatin toxicity in mice. Tox. Appl. Pharmacol., 143 (1997), No. 2, 281–290. [CrossRef]
  175. X.M. Li, G. Metzger, E. Filipski, G. Lemaigre, F. Lévi. Modulation of nonprotein sulphydryl compounds rhythm with buthionine sulphoximine: relationship with oxaliplatin toxicity in mice. Arch.Toxicol., 72 (1998), No. 9, 574–579. [CrossRef] [PubMed]
  176. D.B. Longley, D.P. Harkin, P.G. Johnston. 5-Fluorouracil: mechanisms of action and clinical strategies. Nature Rev. Cancer, 3 (2003), No. 5, 330–338. [CrossRef] [PubMed]
  177. R.A. Lockshin, Z. Zakeri, J.L. Tilly (Eds.). When cells die. Wiley, New York, 1998.
  178. R.A. Lockshin, Z. Zakeri (Eds.). When cells die II. Wiley, New York, 2004.
  179. H. Lodish. Ed. Molecular Cell Biology. Freeman, New York, 2003.
  180. T.G. Lugo, A.M. Pendergast, A.J. Muller, O.N. Witte. Tyrosine kinase activity and transformation potency of BCR-ABL oncogene products. Science, 247 (1990), No. 4946, 1079–1082. [CrossRef] [PubMed]
  181. A.G. McKendrick. Applications of mathematics to medical problems. Proc. Edinburgh Math. Soc., 54 (1926), 98–130.
  182. M.C. Mackey. Unified Hypothesis for the Origin of Aplastic Anemia and Periodic Hematopoiesis. Blood, 51 (1978), No. 5, 941–956. [PubMed]
  183. M.C. Mackey. Dynamic hematological disorders of stem cell origin. In: G. Vassileva-Popova and E.V. Jensen (Eds). Biophysical and Biochemical Information Transfer in Recognition, pp. 373-409, Plenum Press, New York, 1979.
  184. M.C. Mackey, R. Rudnicki. Global stability in a delayed partial differential equation describing cellular replication. J. Math. Biol., 33 (1994), No. 1, 89–109. [CrossRef] [MathSciNet] [PubMed]
  185. M.C. Mackey, R. Rudnicki.. A new criterion for the global stability of simultaneous cell replication and maturation process. J. Math. Biol., 38 (1999),195–219.
  186. M.C. Mackey. Cell kinetic status of haematopoietic stem cells. Cell Prolif., 34 (2001), No. 2, 71–83. [CrossRef] [PubMed]
  187. P. Macklin, S. McDougall, A.R.A Anderson, M.A. Chaplain, V. Cristini, J. Lowengrub. Multiscale modelling and nonlinear simulation of vascular tumour growth. J. Math. Biol., 58 (2009), No. 4-5, 765–98. [CrossRef] [MathSciNet] [PubMed]
  188. M.V. Maffini, J.M. Calabro, A.M. Soto, C. Sonnenschein. Stromal regulation of neoplastic development. Age-dependent normalization of neoplastic mammary cells by mammary stroma. Am. J. Pathol., 167 (2005), No. 5, 1405–1410. [CrossRef] [PubMed]
  189. P. Magal, S.G. Ruan (Eds.). Structured population models in biology and epidemiology. Springer LN in Mathematics 1936, Springer, New York, 2008.
  190. P. Magni, M. Simeoni, I. Poggesi, M. Rocchetti. A mathematical model to study the effects of drugs administration on tumor growth dynamics. Math. Biosci., 200 (2006), No. 2, 127–51. [CrossRef] [MathSciNet] [PubMed]
  191. M. Malumbres, M. Barbacid. To cycle or not to cycle: a critical decision in cancer. Nature Rev. Cancer, 1 (2001), No. 3, 222–231.
  192. A. Marciniak-Czochra, T. Stiehl, A.D. Ho, W. Jäger, W. Wagner. Modeling of asymmetric cell division in hematopoietic stem cells - Regulation of self-renewal is essential for efficient repopulation. Stem Cells Dev., 18 (2009), No. 3, 57–66. [CrossRef] [PubMed]
  193. J. Massagué. G1 cell-cycle control and cancer. Nature, 432 (2004), No. 7015, 298–306. [CrossRef] [PubMed]
  194. T. Matsuo, S. Yamaguchi, S. Mitsui, A. Emi, F. Shimoda, H. Okamura. Control mechanism of the circadian clock for timing of cell division in vivo. Science, 302 (2003), No. 5643, 255–259. [CrossRef] [PubMed]
  195. L. Mazelin, A. Bernet, C. Bonod-Bidaud, L. Pays, S. Arnaud, C. Gespach, D.E. Bredesen, J.-Y. Scoazec, P. Mehlen. Netrin-1 controls colorectal tumorigenesis by regulating apoptosis. Nature, 431 (2004), No. 7004, 80–4. [CrossRef] [PubMed]
  196. P. Mehlen, C. Thibert. Dependence receptors: between life and death. Cell Mol Life Sci., 61 (2004), No. 15, 1854–66. [PubMed]
  197. S. Méléard, V.C. Tran. Trait substitution sequence processes and canonical equation for age-structured populations. J. Math. Biol., 58 (2009), No. 6, 881–921. [CrossRef] [MathSciNet] [PubMed]
  198. J. Mendelsohn, J. Baselga. Status of Epidermal Growth Factor Receptor Antagonists in the Biology and Treatment of Cancer. J. Clin. Oncol., 21 (2003), No. 14, 2787–2799. [CrossRef] [PubMed]
  199. J.A.J. Metz, O. Diekmann. The dynamics of physiologically structured populations. LN in biomathematics 68, Springer, New York, 1986.
  200. P. Michel, S. Mischler, B. Perthame. The entropy structure of models of structured population dynamics. General relative entropy inequality: an illustration on growth models. J. Math. Pures et Appl., 84 (2005), No. 9, 1235–1260.
  201. G. Milano, J. Robert. Pharmaco génétique - pharmacogénomie, quelle est la différence ? Oncologie, 7 (2005), No. 1, 4–5.
  202. S. Mischler, B. Perthame, L. Ryzhik. Stability in a Nonlinear Population Maturation Model. Mathematical Models and Methods in Applied Sciences (M3AS), 12 (2002), No. 12, 1751–1772. [CrossRef]
  203. M. Mishima, G. Samimi, A. Kondo, X. Lin, S.B. Howell, The cellular pharmacology of oxaliplatin resistance. Eur. J. Cancer, 38 (2002), No. 10, 1405–1412.
  204. D. Morgan. The Cell Cycle: Principles of Control. Primers in Biology series, Oxford University Press, 2006.
  205. M.-C. Mormont, F. Lévi. Cancer chronotherapy: principles, applications and perspectives. Cancer, 97 (2003), No. 1,155–169.
  206. J.D. Murray. Mathematical biology, 2 vol., 3rd edition, Springer, New York, 2002, 2003.
  207. J.M. Murray. Optimal drug regimens in cancer chemotherapy for single drugs that block progression through the cell cycle. Math. BioSci., 123 (1994), No. 2, 183–193. [CrossRef] [PubMed]
  208. I.A. Nestorov, L.J. Aarons, P.A. Arundel, M. Rowland. Lumping of whole-body physiologically based pharmacokinetic models. J Pharmacokinet Biopharm., 26 (1998), No.1, 21–46. [PubMed]
  209. B. Novak, Z. Pataki, A. Ciliberto, J.J. Tyson. Mathematical model of the cell division cycle of fission yeast. Chaos, 11 (2001), No. 1, 277–286. [CrossRef] [PubMed]
  210. B. Novak, J.J. Tyson. A model for restriction point control of the cell cycle. J. Theor. Biol., 230 (2004), No. 4, 563–579. [CrossRef] [PubMed]
  211. B. Novak, J.J. Tyson. Design principles of biochemical oscillators. Nature Rev. Mol. Cell Biol., 9 (2008), No. 12, 981–991. [CrossRef] [PubMed]
  212. T. Oguri, T. Isobe, K. Fujitaka, N. Ishikawa, N. Kohno. Association between expression of the MRP3 gene and exposure to platinum drugs in lung cancer. Int. J. Canc., 93 (2001), No. 4, 584–589. [CrossRef]
  213. T. Oguri, Y. Bessho, H. Achiwa, H. Ozasa, K. Maeno, H. Maeda, S. Sato, R. Ueda. MRP8/ABCC11 directly confers resistance to 5-fluorouracil. Mol. Canc. Therap., 6 (2007), No. 1, 122–127. [CrossRef] [MathSciNet] [PubMed]
  214. H. Okamura. Suprachiasmatic nucleus clock time in the mammalian circadian system. Cold Spring Harbor Symposia on quantitative biology, Vol. LXXII (2007), 551–556.
  215. J.M. Pacheco, A. Traulsen, D. Dingli. The allometry of chronic myeloid leukemia. J. Theor. Biol., (2009). [doi:10.1016/j.jtbi.2009.04.003].
  216. J.C. Panetta. A mechanistic model of temozolomide myelosuppression in children with high-grade gliomas. Math. Biosci., 186 (2003), No. 1, 29–41. [CrossRef] [MathSciNet] [PubMed]
  217. B. Perthame. Transport equations in biology. Birkhäuser, Boston, 2007.
  218. B. Perthame, S. Génieys. Concentration in the nonlocal Fisher equation: the Hamilton-Jacobi limit. Mathematical Modelling of Natural Phenomena, 2 (2007), No.4, 135–151.
  219. V.K. Piotrovsky. Population pharmacodynamic and pharmacokinetic modeling via mixed effects. Curr. Op. Drug Discov. Devel., 3 (2000), No. 3, 314–319.
  220. Y. Pommier. Topoisomerase I inhibitors: camptothecins and beyond. Nature Rev. Cancer, 6 (2006), No. 10, 789–802. [CrossRef]
  221. C.S. Potten, M. Loeffler. Stem cells: attributes, cycles, spirals, pitfalls and uncertainties. Lessons for and from the crypt. Development ,110 (1990), No. 4, 1001–1020.
  222. C.S. Potten, C. Booth, D.M. Pritchard. The intestinal epithelial stem cell: the mucosal governor. Int. J. Exp. Path., 78 (1997), No. 4, 219–243. [CrossRef]
  223. L. Preziosi (Ed.). Cancer modelling and simulation. Chapman and Hall / CRC, New York, 2003.
  224. A. Quintas-Cardama, H.M. Kantardjian, J.E. Cortes. Mechanisms of primary and secondary resistance to imatinib in chronic myeloid leukemia. Cancer Control,16 (2009), No. 2, 122–31.
  225. D.A. Rand. Mapping global sensitivity of cellular network dynamics: sensitivity heat maps and a global summation law. J. Roy. Soc. Interface, 5 (2008), Suppl. 1, S59–69.
  226. A. Rafii, et al. Oncologic trogocytosis of an original stromal cell induces chemoresistance of ovarian tumours. PLoS One, 3 (2008), No. 12, e3894, Dec. 2008. [doi:10.1371/journal.pone.0003894].
  227. F.I. Raynaud, et al. In vitro et in vivo pharmacokinetic-pharmacodynamic relationships for the trisubstituted aminopurine cyclin-dependent kinase inhibitors Olomoucine, Bohemine and CYC202. Clin. Canc. Res., 11 (2005), No. 113, 4875–4888. [CrossRef]
  228. D.C. Rees, E. Johnson, O. Lewinson. ABC transporters: the power to change. Nature Rev. Mol. Cell Biol., 10 (2009), No. 3, 218–227. [CrossRef] [PubMed]
  229. S.M. Reppert, D.R. Weaver. Coordination of circadian timing in mammals. Nature, 418 (2002), No. 6901, 935–941. [CrossRef] [PubMed]
  230. B. Ribba, O. Saut, T. Colin, D. Bresch, E. Grenier, J.-P. Boissel. A multiscale mathematical model of avascular tumor growth to investigate the therapeutic benefit of anti-invasive agents. J. Theor. Biol., 243 (2006), No. 4, 532–541. [CrossRef] [PubMed]
  231. T. Rich, P.F. Innominato, J. Boerner, M.-C. Mormont, S. Iacobelli, B. Baron, C. Jasmin, F. Lévi. Elevated serum cytokines correlated with altered behavior, serum cortisol rhythm, and dampened 24-hour rest-activity patterns in patients with metastatic colorectal cancer. Clin. Cancer Res., 11 (2005), No. 5, 1757–64. [CrossRef] [PubMed]
  232. N.R. Rodrigues, A. Rowan, M.E. Smith, I.B. Kerr, W.F. Bodmer, J.V. Gannon, D.P. Lane. p53 mutations in colorectal cancer. Proc. Natl. Acad. Sci. USA, 87 (1990), No. 19, 7555–7559. [CrossRef]
  233. I. Roeder, M. Loeffler. A novel dynamic model of hematopoietic stem cell organization based on the concept of within-tissue plasticicity. Exp. Hematol., 30 (2002), No. 8, 853–861. [CrossRef] [PubMed]
  234. M. Rotenberg. Transport theory for growing cell populations. J. Theor. Biol., 103 (1983), No. 2, 181–199. [CrossRef] [PubMed]
  235. P. Ruoff, S. Mohsenzadeh, L. Rensing. Circadian rhythms and protein turnover: the effect of temperature on the period lengths of clock mutants simulated by the Goodwin oscillator. Naturwissenschaften, 83 (1996), No. 11, 514–7. [CrossRef] [PubMed]
  236. P. Ruoff, M. Vinsjevik, C. Monnerjahn, L. Rensing. The Goodwin model: simulating the effect of light pulses on the circadian sporulation rhythm of Neurospora crassa. J. Theor. Biol., 209 (2001), No. 1, 29–42. [CrossRef] [PubMed]
  237. A. Sakaue-Sawano, H. Kurokawa, T. Morimura, A. Hanyu, H. Hama, H. Osawa, S. Kashiwagi, K. Fukami, T. Miyata, H. Miyoshi, T. Imamura, M. Ogawa, H. Masai, A. Miyawaki. Visualizing spatiotemporal dynamics of multicellular cell-cycle progression. Cell, 32 (2008), No. 3, 487–98. [CrossRef] [PubMed]
  238. A. Sakaue-Sawano, K. Ohtawa, H. Hama, M. Kawano, M. Ogawa, A. Miyawaki. Tracing the silhouette of individual cells in S/G2/M phases with fluorescence. Chem Biol., 15 (2008), No. 12, 1243–8. [CrossRef] [PubMed]
  239. U. Schibler. Liver regeneration clocks on. Science, 302 (2003), No. 5642, 234–235. [CrossRef] [PubMed]
  240. D. Schiffer. Radiotherapy by particle beams (hadrontherapy) of intracranial tumours: a survey on pathology. Neurol. Sci., 26 (2005), No. 1, 5–12. [CrossRef] [PubMed]
  241. R.L. Schilsky, G.M. Milano, M.J. Ratain (Eds.). Principles of Antineoplastic Drug Development and Pharmacology. Marcel Dekker, New York, 1996.
  242. L.B. Sheiner, J.-L. Steimer. Pharmacokinetic/pharmacodynamic modeling in drug development. Annu. Rev. Pharmacol. Toxicol., 40 (2000), 67–95. [CrossRef] [PubMed]
  243. J.A. Sherratt, M.A. Chaplain. A new mathematical model for avascular tumour growth. J. Math. Biol., 43 (2001), No. 4, 291–312. [CrossRef] [MathSciNet] [PubMed]
  244. Y. Shiloh. ATM and related kinases: Safeguarding genome integrity. Nature Rev. Cancer, 3 (2003), No. 3,155-168, 2003.
  245. M. Simeoni, P. Magni P, C. Cammia, G. De Nicolao, V. Croci, E. Pesenti, M. Germani, I. Poggesi, M. Rocchetti. Predictive pharmacokinetic-pharmacodynamic modeling of tumor growth kinetics in xenograft models after administration of anticancer agents. Cancer Res., 64 (2004), No. 3, 1094–1101. [CrossRef] [PubMed]
  246. R. Smaaland, O.D. Laerum, K. Lote, O. Sletvold, R.B. Sothern, R. Bjerknes. DNA Synthesis in Human Bone Marrow is Circadian Stage Dependent. Blood, 77 (1991), No. 12, 2603–2611. [PubMed]
  247. C. Sonnenschein, A.M. Soto. Carcinogenesis and metastasis now in the third dimension - What's in it for pathologists? Am. J. Pathol., 168 (2006), No. 2, 363–366.
  248. C. Sonnenschein, A.M. Soto. Theories of carcinogenesis: an emerging perspective. Seminars in cancer biology, 18 (2008), No. 5, 372–377. [CrossRef] [PubMed]
  249. A.M. Soto, C. Sonnenschein. The somatic mutation theory of cancer: growing problems with the paradigm? BioEssays, 26 (2004), No. 10, 1097–1107.
  250. A.M. Soto, C. Sonnenschein, P.A. Miquel. On physicalism and downward causation in developmental and cancer biology. Acta biotheor., 56 (2008), No. 4, 257–74. [CrossRef] [PubMed]
  251. F.X. Su, X.Q. Hu, W.J. Jia, C. Gong, E.W. Song, P. Hamar. Glutathion S Transferase π indicates chemotherapy resistance in breast cancer. J. Surg. Res., 113 (2003), No. 1, 102–108. [CrossRef] [PubMed]
  252. G.W. Swan, T.L. Vincent. Optimal control analysis in the chemotherapy of IgG multiple myeloma. Bull. Math. Biol., 39 (1977), No. 3, 317–337. [PubMed]
  253. G.W. Swan. Applications of optimal control theory in biomedicine. Marcel Dekker, New York, 1984.
  254. K.R. Swanson, E.C. Alvord Jr, J.D. Murray. A quantitative model for differential motility of gliomas in grey and white matter. Cell Prolif., 33 (2000), No. 5, 317–29. [CrossRef] [PubMed]
  255. K.R. Swanson, C. Bridge, J.D. Murray, E.C. Alvord Jr. Virtual and real brain tumors: using mathematical modeling to quantify glioma growth and invasion. J Neurol. Sci., 16 (2003), No. 1, 1–10. [CrossRef]
  256. R. Tang, A.M. Faussat, J.-Y. Perrot, Z. Marjanovic, S. Cohen, T. Storme, H. Morjani, O. Legrand, J.-P. Marie. Zosuquidar restores drug sensitivity in P-glycoprotein expressing acute myeloid leukemia (AML). BMC Cancer, 8 (2008), 51. [doi:10.1186/1471-2407-8-51]. [CrossRef] [PubMed]
  257. T.N. Tozer, M. Rowland. Introduction to Pharmacokinetics and Pharmacodynamics: The Quantitative Basis of Drug Therapy. Lippincott, Philadelphia, 2006.
  258. Y. Tsukamoto, Y. Kato, M. Ura, I. Horii, T. Ishikawa, H. Ishitsuka, Y. Sugiyama. Investigation of 5-FU disposition after oral administration of capecitabine, a triple-prodrug of 5-FU, using a physiologically based pharmacokinetic model in a human cancer xenograft model: comparison of the simulated 5-FU exposures in the tumour tissue between human and xenograft model. Biopharm Drug Dispos., 22 (2001), No. 1, 1–14. [CrossRef] [PubMed]
  259. J.J. Tyson, C.I. Hong, C.D. Thron, B. Novak. A simple model of circadian rhythms based on dimerization and proteolysis of PER and TIM. Biophys J.,77 (1999), No. 5, 2411–7.
  260. J.J. Tyson, K. Chen, B. Novak. Network dynamics and cell physiology. Nature Rev. Mol. Cell Biol., 2 (2001), No. 12, 908–916. [CrossRef] [PubMed]
  261. P. Ubezio. Unraveling the complexity of cell cycle effects of anticancer drugs in cell populations. Disc. Cont. Dyn. Syst. B, 4 (2004), No. 1, 323–335. [CrossRef]
  262. K. Vanselow, J.T. Vanselow, P.O. Westermark, S. Reischl, B. Maier, T. Korte, A. Herrmann, H. Herzel, A. Schlosser, A. Kramer. Differential effects of PER2 phosphorylation: molecular basis for the human familial advanced sleep phase syndrome (FASPS). Genes Dev., 20 (2006), No. 19, 2660–2672. [CrossRef] [PubMed]
  263. J. Viguier, et al. ERCC1 codon 118 polymorphism is a predictive factor for the tumor response to oxaliplatin/5-fluorouracil combination chemotherapy in patients with advanced colorectal cancer. Clin Cancer Res., 11 (2005), No. 17, 6212–7. [CrossRef] [PubMed]
  264. B. Vogelstein, D. Lane, A.J. Levine. Surfing the p53 network. Nature, 408 (2010), No. 6810, 307–310. [CrossRef] [PubMed]
  265. H.M. Warenius, L. Seabra, L. Kyritsi, R. White, R. Dormer, S. Anandappa, C. Thomas, A. Howarth. Theranostic proteomic profiling of cyclins, cyclin dependent kinases and Ras in human cancer cell lines is dependent on p53 mutational status. Int. J. Oncol., 32 (2008), No. 4, 895–907. [PubMed]
  266. F.M. Watt, B.L. Hogan. Out of Eden: stem cells and their niches. Science, 287 (2000), No. 5457, 1427–1430. [CrossRef] [PubMed]
  267. G.F. Webb. Resonance phenomena in cell population chemotherapy models. Rocky Mountain J. Math., 20 (1990), No. 4, 1195–1216. [CrossRef] [MathSciNet]
  268. R.A. Weinberg. One renegade cell: how cancer begins. Basic Books, New York, 1998.
  269. H.V. Westerhoff, B.O. Palsson. The evolution of molecular biology into systems biology. Nature Biotechnol., 22 (2004), No. 10, 1249–1252. [CrossRef] [PubMed]
  270. H.V. Westerhoff. Mathematical and theoretical biology for systems biology, and then...vice versa. J. Math. Biol., 54 (2007), No. 1, 147–150. [CrossRef] [MathSciNet] [PubMed]
  271. World Health Organisation (WHO). Preventing chronic diseases: a vital investment. (20055), Source: 2005
  272. D. Wodarz, D. Killer Cell Dynamics. Springer, New York, 2007.
  273. M.W. Wu, L.J. Xian, X.M. Li, P. Innominato, F. Lévi. Circadian expression of dihydropyrimidine dehydrogenase, thymidylate synthase, c-myc and p53 mRNA in mouse liver tissue. Ai Zheng (Chinese Journal of Cancer), 23 (2004), No. 3, 235–242.
  274. C. Wyman, R. Kanaar. DNA double-strand break repair: All's well that ends well. Annu. Rev. Genet., 40 (2006), 363–383. [CrossRef] [PubMed]
  275. J.H. Xing, J. Chen. The Goldbeter-Koshland switch in the first-order region and its response to dynamic disorder. PLoS ONE, 2008 May 14;3(5):e2140. [doi:10.1371/journal.pone.0002140].
  276. S. Yamaguchi, H. Isejima, T. Matsuo, R. Okura, K. Yagita, M. Kobayashi, H. Okamura. Synchronization of cellular clocks in the`suprachiasmatic nucleus. Science, 302 (2003), No. 5649, 1408–12. [CrossRef] [PubMed]
  277. S. You, P.A. Wood, Y. Xiong, M. Kobayashi, J. Du Quiton, W.J.M. Hrushesky. Daily coordination of cancer growth and circadian clock gene expression. Breast Canc. Res. Treatment, 91 (2005), No. 1, 47–60. [CrossRef]
  278. J. Zamborsky, C.I. Hong, A. Csikasz-Nagy. Computational analysis of mammalian cell division gated by a circadian clock: quantized cell cycles and cell size control. J. Biol. Rhythms, 22 (2007), 542–553. [CrossRef] [PubMed]
  279. A. Zetterberg, O. Larsson, K.G. Wiman. What is the restriction point? Curr. Opin. Cell Biol., 7 (1995), No. 6, 835–42.
  280. L. Zitvogel, A. Tesniere, G. Kroemer. Cancer despite immunosurveillance: immunoselection and immunosubversion. Nature Rev. Immunol., 6 (2006), No. 10, 715–727. [CrossRef] [PubMed]
  281. L. Zitvogel, L. Apetoh, F. Ghiringhelli, G. Kroemer. Immunological aspects of cancer chemotherapy. Nature Rev. Immunol., 8 (2008), No. 1, 59–73. [CrossRef] [PubMed]
  282. L. Zitvogel, L. Apetoh, F. Ghiringhelli, F. André, A. Tesniere, G. Kroemer. The anticancer immune response: indispensable for therapeutic success? J. Clin. Invest., 118 (2008), No. 6, 1991–2001.

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