Free Access
Math. Model. Nat. Phenom.
Volume 7, Number 6, 2012
Biological oscillations
Page(s) 107 - 125
Published online 12 December 2012
  1. P. Achermann, H. Kunz. Modeling circadian rhythm generation in the suprachiasmatic nucleus with locally coupled self-sustained oscillators: Phase shifts and phase response curves. J Biol Rhythm, 14(6):460–468, 1999. [CrossRef]
  2. S. Becker-Weimann, J. Wolf, H. Herzel, A. Kramer. Modeling feedback loops of the mammalian circadian oscillator. Biophys J, 87(5):3023–3034, 2004. [CrossRef] [PubMed]
  3. F. Bekkal Brikci, J. Clairambault, B. Perthame. Analysis of a molecular structured population model with possible polynomial growth for the cell division cycle. Math and Comp Modelling, 47(7–8): 699–713, 2008. [CrossRef] [MathSciNet]
  4. S. Bernard, H. Herzel. Why do cells cycle with a 24 hour period ? Genome Inform Ser., 17(1):72–79, 2006.
  5. S. Bernard, D. Gonze, B. Cǎjavec, H. Herzel, A. Kramer. Synchronization-induced rhythmicity of circadian oscillations in the suprachiasmatic nucleus. PLoS Comput Biol, 17(1):72–79, 2006.
  6. S. Bernard, B. Căjavec Bernard, F. Lévi, H. Herzel. Tumor growth rate determines the timing of optimal chronomodulated treatment schedules. LoS Comput Biol, 6(3):e1000712, 2010. doi:10.1371/journal.pcbi.1000712 [CrossRef]
  7. F. Billy, J. Clairambault, O. Fercoq. Optimisation of cancer drug treatments using cell population dynamics. Math Meth and Mod in Biomed, 257–299, 2012.
  8. A. Chauhan, S. Lorenzen, H. Herzel, S. Bernard. Regulation of mammalian cell cycle progression in the regenerating liver. J Theor Biol, 283(1):103–12, 2011. [CrossRef] [PubMed]
  9. J. Clairambault, S. Gaubert, T. Lepoutre. Circadian rhythm and cell population growth. Math Comput Model, 53(7-8):1558–1567, 2011. [CrossRef] [MathSciNet]
  10. J. Clairambault, S. Gaubert, T. Lepoutre. Comparison of Perron and Floquet eigenvalues in age structured cell division cycle models. Math Model Nat Phenom, 4(3):183–209, 2009. [CrossRef] [MathSciNet]
  11. J. Clairambault, S. Gaubert, B. Perthame. An inequality for the Perron and Floquet eigenvalues of monotone differential systems and age structured equations. C R Math, 345(10):549–554, 2007. [CrossRef] [MathSciNet]
  12. J. Clairambault, P. Michel, B. Perthame. Circadian rhythm and tumour growth. C R Math, 342(1):17–22, 2006. [CrossRef] [MathSciNet]
  13. C. Czeisler, R. Kronauer, J. Allan, J. Duffy, M. Jewett, E. Brown, J. Ronda. Bright light induction of strong (type 0) resetting of the human circadian pacemaker. science, 244(4910):1328–1333, 1989. [CrossRef] [PubMed]
  14. M. Davidich, S. Bornholdt. Boolean network model predicts cell cycle sequence of fission yeast. PLoS One, 3(2):e1672, 2008. [CrossRef] [PubMed]
  15. M. Doumic. Analysis of a population Model Structured by the Cells Molecular Contents. MMNP, 3(2): 121–152, 2007.
  16. J. E. Ferrell, T. Y.-c. Tsai, Q. Yang. Modeling the cell cycle: why do certain circuits oscillate ? Cell, 144(6):874–85, 2011. [CrossRef] [PubMed]
  17. PC. da Fonseca, J. He, EP. Morris. Molecular model of the human 26S proteasome. Mol Cell, 46(1):54-66, 2012. [CrossRef] [PubMed]
  18. D. Forger, M. Jewett, R. Kronauer. A simpler model of the human circadian pacemaker. J Biol Rhythm, 14(6):533–538, 1999. [CrossRef]
  19. D. Forger, R. Kronauer. Reconciling mathematical models of biological clocks by averaging on approximate manifolds. SIAM J Appl Math., pages 1281–1296, 2002.
  20. D. B. Forger, C. S. Peskin. A detailed predictive model of the mammalian circadian clock. Proc Natl Acad Sci USA, 100(25):14806–14811, 2003. [CrossRef]
  21. C. Gérard, A. Goldbeter. A skeleton model for the network of cyclin-dependent kinases driving the mammalian cell cycle. Interface Focus, 1(1):24–35, 2011. [CrossRef] [MathSciNet] [PubMed]
  22. S. Gery, HP Koeffler. Circadian rhythms and cancer. Cell Cycle, 9:1097–1103, 2010. [CrossRef] [PubMed]
  23. C. Gérard, A. Goldbeter. Entrainment of the Mammalian Cell Cycle by the Circadian Clock: Modeling Two Coupled Cellular Rhythms. Plos Comp Biol, 8(5): e1002516. [CrossRef] [PubMed]
  24. A. Goldbeter, C. Ge, C. Gérard. Temporal self-organization of the Cyclin/Cdk network driving the mammalian cell cycle. Proc Natl Acad Sci USA, 1–6, 2009.
  25. D. Gonze. Modeling circadian clocks: From equations to oscillations. Cent Eur J Biol, 6(5):699–711, 2011. [CrossRef]
  26. B.C. Goodwin. Temporal Organization in Cells. A Dynamic Theory of Cellular Control Processes. New York: Academic Press, 1963.
  27. B.C. Goodwin. Oscillatory behavior in enzymatic control processes. Advances in Enzyme Regulation, 3:425–438, 1965. [CrossRef] [PubMed]
  28. T. Hunt. The Life Scientific, BBC Radio 4 podcast, 13/12/2011.
  29. J.F.C. Kingman. A convexity property of positive matrices. Quart. J. Math. Oxford, (2)12:283–284, 1961. [CrossRef]
  30. T. Kubo, K. Ozasa, K. Mikami, K. Wakai, Y. Fujino, Y. Watanabe, T. Miki, M. Nakao, K. Hayashi, K. Suzuki, et al. Prospective cohort study of the risk of prostate cancer among rotating-shift workers: findings from the japan collaborative cohort study. Am J Epidemiol, 164(6):549–555, 2006. [CrossRef] [PubMed]
  31. H. Kunz, P. Achermann. Simulation of circadian rhythm generation in the suprachiasmatic nucleus with locally coupled self-sustained oscillators. J Theor Biol, 224(1):63–78, 2003. [CrossRef] [PubMed]
  32. J.-C. Leloup, A. Goldbeter. Toward a detailed computational model for the mammalian circadian clock. Proc Natl Acad Sci USA, 100(12):7051–7056, 2003. [CrossRef]
  33. T. Lepoutre. Analysis and modelling of growth and motion phenomenon from biology. PHD in applied mathematics. Université Pierre et Marie Curie Paris (France), 2007–2009.
  34. F. Lévi, Circadian chronotherapy for human cancers. The Lancet Oncology, 2(5), 307–315, 2001, doi:10.1016/S1470-2045(00)00326-0 [CrossRef] [PubMed]
  35. F. Lévi. Cancer chronotherapy. J of Pharmacy and Pharmacol, 51(8), 891–898, 1999. [CrossRef]
  36. E.S. Maywood, A.B. Reddy, G.K.Y. Wong, J.S. O’Neill, J.A. O’Brien, D.G. McMahon, A.J. Harmar, H. Okamura, M.H. Hastings. Synchronisation and maintenance of timekeeping in suprachiasmatic circadian clock cells by neuropeptidergic signaling. Curr Biol, 16:599–605, 2006. [CrossRef] [PubMed]
  37. M.C. Mackey. Unified hypothesis for the origin of aplastic anemia and periodic hematopoiesis. Blood, 51(5):941–56, 1978. [PubMed]
  38. H. Mirsky, A. Liu, D. Welsh, S. Kay, F. Doyle. A model of the cell-autonomous mammalian circadian clock. Proc Natl Acad Sci USA, 106(27):11107–11112, 2009. [CrossRef]
  39. B. Novak, Z. Pataki, A. Ciliberto, J.J. Tyson. Mathematical model of the cell division cycle of fission yeast. Chaos, 11(1):277–286, 2001. [CrossRef] [PubMed]
  40. B. Novak, J.J. Tyson. A model for restriction point control of the mammalian cell cycle. J Theor Biol, 230(4):563–579, 2004. [CrossRef] [PubMed]
  41. B.F. Pando, A. van Oudenaarden. Coupling cellular oscillators-circadian and cell division cycles in cyanobacterial cells. Curr Opin Genet Dev, 20:1–6, 2010. [CrossRef] [PubMed]
  42. B. Perthame. Transport equations in biology. Birkhauser, 2007.
  43. J. R. Pomerening, E. D. Sontag, J. E. Ferrell. Building a cell cycle oscillator: hysteresis and bistability in the activation of Cdc2. Nat Cell Biol, 5(4):346–51, 2003. [CrossRef] [PubMed]
  44. K. Rompala, R. Rand, H. Howland. Dynamics of three coupled van der Pol oscillators with application to circadian rhythms. Commun Nonlinear Sci, 12(5):794–803, 2007. [CrossRef] [MathSciNet]
  45. P. Ruoff, C.M. M Vindjevik, L. Rensing. The Goodwin model simulating the effect of light pulses on the circadian sporulation rhythm of Neurospora crassa. J. Theor. Biol., 209:29–42, 2001. [CrossRef] [PubMed]
  46. S. Sahar, P. Sassone-Corsi. Circadian rhythms and memory formation: regulation by chromatin remodeling. Front Mol Neurosci, 5–37, 2006. Published online 2012 March 26. doi: 10.3389/fnmol.2012.00037.
  47. M. Swat, A. Kel, H. Herzel. Bifurcation analysis of the regulatory modules of the mammalian G1/S transition. Bioinformatics, 20(10):1506–1511, 2004. [CrossRef] [PubMed]
  48. J.J. Tyson, B. Novak. Temporal organization of the cell cycle. Curr Biol 18, R759-R768, 2008.
  49. J.J. Tyson, K.C. Chen, B. Novak. Sniffers, buzzers, toggles and blinkers: dynamics of regulatory and signaling pathways in the cell. Curr Op in Cell Biol, 15:221–231, 2003. [CrossRef] [PubMed]
  50. B. Van der Pol, J. Van der Mark. Frequency demultiplication. Nature, 120:363–364, 1927. [CrossRef]
  51. A.B. Webb, N. Angelo, J.E. Huettner, E.D. Herzog. Intrinsic, nondeterministic circadian rhythm generation in identified mammalian neurons. Proc Natl Acad Sci USA, 106(38):16493–16498, 2009. [CrossRef]
  52. D. Welsh, J. Takahashi, S. Kay. Suprachiasmatic nucleus: cell autonomy and network properties. Ann Rev Physiol, 72:551–577, 2010. [CrossRef] [PubMed]
  53. P.O. Westermark, D.K. Welsh, H. Okamura, H. Herzel. Quantification of Circadian Rhythms in Single Cells. PLoS Comput Biol, 5(11):e1000580, 2009. [CrossRef] [PubMed]
  54. R. Wever. Zum Mechanismus der Biologischen 24-Stunden-Periodik. Biol Cybern, 1(4):139–154, 1962.
  55. R. Wever. Zum Mechanismus der Biologischen 24-Stunden-Periodik II. Biol Cybern, 1(6):213–231, 1963.
  56. S. Yamaguchi, H. Isejima, T. Matsuo, R. Okura, K. Yagita, M. Kobayashi, H Okamura, H. Synchronization of cellular clocks in the suprachiasmatic nucleus. Science, 302:1408–1412, 2003. [CrossRef] [PubMed]
  57. E. E. Zhang, S. A. Kay. Clocks not winding down: unravelling circadian networks. Nat Rev Mol Cell Biol, 11(11):764–776, 2010. [CrossRef] [PubMed]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.