Free Access
Math. Model. Nat. Phenom.
Volume 4, Number 3, 2009
Cancer modelling (Part 2)
Page(s) 97 - 116
Published online 05 June 2009
  1. B. Alberts, A. Johnson, J. Lewis, K. Roberts, P. Walter. Molecular Biology of the Cell, Fourth Edition. Garland Science, Taylor and Francis Group Ltd, Oxford, 2002.
  2. E. Appella, C.W. Anderson. Post-transcriptional modifications and activation of p53 by genotoxic stresses. Eur. J. Biochem., 268 (2001), 2764–2772. [CrossRef] [PubMed]
  3. D. Bennett. Applications of Delay Differential Equations in Physiology and Epidemiology. PhD Thesis, University of Surrey, 2005.
  4. S. Bernard, B. Cajavec, L. Pujo-Menjouet, M.C. Mackey, H. Herzel. Modelling transcriptional feedback loops: the role of Gro/TLE1 in Hes1 oscillations. Phil. Trans. R. Soc. A, 364 (2006), 1155–1170. [CrossRef]
  5. A. Ciliberto, B. Novak, J.J. Tyson. Steady states and oscillations in the p53/mdm2 network. Cell Cycle, 4 (2005), 488–493. [CrossRef] [PubMed]
  6. M.L. Dequeant, E. Glynn, K. Gaudenz, M. Wahl, J. Chen, A. Mushegian, O. Pourquie. A complex oscillating network of signaling genes underlies the mouse segmentation clock. Science, 314 (2006), 1595–1598. [CrossRef] [PubMed]
  7. B. Ermentrout. Simulating, Analyzing, and Animating Dynamical Systems: A Guide to XPPAUT for Researchers and Students. Society for Industrial and Applied Mathematics, Philadelphia, 2002.
  8. C.P. Fall, E.S. Marland, J.M. Wagner, J.J. Tyson. Interdisciplinary Applied Mathematics, Mathematical Biology: Computational Cell Biology. Springer-Verlag, New York, 2002.
  9. R.S. Foo, Y.J. Nam, M.J. Ostreicher, M.D. Metzl, R.S. Whelan, C.F. Peng, A.W. Ashton, W. Fu, K. Mani, S.F. Chin, E. Provenzano, I. Ellis, N. Figg, S. Pinder, M.R. Bennett, C. Caldas, R.N. Kitsis. Regulation of p53 tetramerization and nuclear export by ARC. Proc. Natl. Acad. Sci. USA, 104 (2007), 20826–20831. [CrossRef]
  10. S.J. Gallagher, R.F. Kefford, H. Rizos. The ARF tumour suppressor. Intl. J. Biochem. Cell Biol., 38 (2006), 1637–1641. [CrossRef]
  11. Y. Haupt, R. Maya, A. Kazaz, M. Oren. Mdm2 promotes the rapid degradation of p53. Nature, 387 (1997), 296–299. [CrossRef] [PubMed]
  12. H. Hirata, S. Yoshiura, T. Ohtsuka, Y. Bessho, T. Harada, K. Yoshikawa, R. Kageyama R. Oscillatory expression of the bHLH factor Hes1 regulated by a negative feedback loop. Science, 298 (2002), 840–843. [CrossRef] [PubMed]
  13. T.R. Hupp, A. Sparks, D.P. Lane. Small peptides activate the latent sequence-specific DNA binding function of p53. Cell, 83 (1995), 237–245. [CrossRef] [PubMed]
  14. B.N. Kholodenko. Cell signalling dynamics in time and space. Nat. Rev. Mol. Cell Biol., 7 (2006), 165–176. [CrossRef] [PubMed]
  15. S. Krishna, M.H. Jensen, K. Sneppen. Minimal model of spiky oscillations in NF-κB. Proc. Natl. Acad. Sci. USA, 103 (2006), 10840–10845. [CrossRef]
  16. A. Kusumi, S. Yasushi, Y. Mutsuya. Confined lateral diffusion of membrane receptors as studied by single particle tracking (nanovid microscopy). Effects of calcium-induced differentiation in cultured epithelial cells. Biophys. J., 65 (1993), 2021–2040. [CrossRef] [PubMed]
  17. G. Lahav, N. Rosenfield, A. Sigal, N. Geva-Zatorsky, A.J. Levine, M.B. Elowitz, U. Alon. Dynamics of the p53-mdm2 feedback loop in individual cells. Nat. Gen., 36 (2004), 147–150. [CrossRef] [PubMed]
  18. R. Lev Bar-Or, R. Maya, L.A. Segel, U. Alon, A.J. Levine, M. Oren. Generation of oscillations by the p53-mdm2 feedback loop: a theoretical and experimental study. Proc. Natl. Acad. Sci. USA, 97 (2000), 11250–11255. [CrossRef]
  19. J. Lewis. Autoinhibition with transcriptional delay: a simple mechanism for the Zebrafish somitogenesis oscillator. Curr. Biol., 13 (2003), 1398–1408. [CrossRef] [PubMed]
  20. H. Lodish, A. Berk, P. Matsudaira, C.A. Kaiser, M. Krieger, M.P. Scott, S.L. Zipursky, J. Darnell. Molecular Cell Biology. W.F. Freeman and Company, New York, 2003.
  21. J. Luo, M. Li, Y. Tang, M. Laszkowska, R.G. Roeder, W. Gu. Acetylation of p53 augments its site-specific DNA binding both in vitro and in vivo. Proc. Natl. Acad. Sci. USA, 101 (2004), 2259–2264. [CrossRef]
  22. L. Ma, J. Wagner, J.J. Rice, W. Hu, A.J. Levine, G.A. Stolovitzky. A plausible model for the digital response of p53 to DNA damage. Proc. Natl. Acad. Sci. USA, 102 (2005), 14266–14271. [CrossRef]
  23. S.M. Mendrysa, M.E. Perry. The p53 tumor suppressor protein does not regulate expression of is own inhibitor, MDM2, except under conditions of stress. Mol. Cell Biol., 20 (2000), 2023–2030. [CrossRef] [PubMed]
  24. J. Meyers, J. Craig, D.J. Odde. Potential for control of signaling pathways via cell size and shape. Curr. Biol., 16 (2006), 1685–1693. [CrossRef] [PubMed]
  25. G.I. Mihalas, Z. Simon, G. Balea, E. Popa. Possible oscillatory behaviour in p53-mdm2 interaction computer simulation. J. Biol. Syst., 8 (2000), 21–29.
  26. N.A.M. Monk. Oscillatory expression of Hes1, p53, and NF-kappaB driven by transcriptional time delays. Curr. Biol., 13 (2003), 1409–1413. [CrossRef] [PubMed]
  27. C.W. Mullineaux, A. Nenniger, N. Ray, C. Robinson. Diffusion of green fluorescent protein in three cell environments in Escherichia coli. J. Bacteriol., 188 (2006), 3442-3448. [CrossRef] [PubMed]
  28. D.E. Nelson, A.E. Ihekwaba, M. Elliott, J.R. Johnson, C.A. Gibney, B.E. Foreman, G. Nelson, V. See, C.A. Horton, D.G. Spiler, S.W. Edwards, H.P. McDowell, J.F. Unitt, E. Sullivan, R. Grimley, N. Benson, D. Broomhead, D.B. Kell, M.R. White. Oscillations in NF-κB signaling control de dynamics of gene expression. Science, 306 (2004), 704–708. [CrossRef] [PubMed]
  29. S.R. Neves, P. Tsokas, A. Sarkar, E.A. Grace, P. Rangamani, S.M. Taubenfeld, C.M. Alberini, J.C. Schaff, R.D. Blitzer, I.I. Moraru, R. Iyengar. Cell shape and negative links in regulatory motifs together control spatial information flow in signaling networks. Cell, 133 (2008), 666–680. [CrossRef] [PubMed]
  30. L. Nie, M. Sasaki, C.G. Maki C.G. Regulation of p53 nuclear export through sequential changes in conformation and ubiquitination. J. Biol. Chem., 282 (2007), 14616–14625. [CrossRef] [PubMed]
  31. B.A. Ogunnaike. Elucidating the digital control mechanism for DNA damage repair with the p53-mdm2 system: single cell data analysis and ensemble modelling. J. R. Soc. Interface, 3 (2006), 175–184. [CrossRef] [PubMed]
  32. J. Owen. Topological proteomics: a new approach to drug discovery. Drug Discovery Today, 6 (2001), 1081–1082. [CrossRef] [PubMed]
  33. I.G. Pearce, M.A.J. Chaplain, P.G. Schoeld, A.R.A. Anderson, S.F. Hubbard. Modelling the spatio-temporal dynamics of multi-species host-parasitoid interactions: heterogeneous patterns and ecological implications. J. Theor. Biol., 241 (2006), 876–886. [PubMed]
  34. S. Pigolotti, S. Krishna, M.H. Jensen. Oscillation patterns in negative feedback loops. Proc. Natl. Acad. Sci. USA, 104 (2007), 6533–6537. [CrossRef] [MathSciNet] [PubMed]
  35. W. Schubert. Cytomics in characterizing toponomes: towards the biological code of the cell. Cytometry, 69A (2006), 209–211. [CrossRef]
  36. J.A. Sherratt, M.A. Lewis, A.C. Fowler. Ecological chaos in the wake of invasion. Proc. Natl. Acad. Sci. USA, 92 (1995), 2524–2528. [CrossRef]
  37. J.A. Sherratt, B.T. Eagen, M.A. Lewis. Oscillations and chaos behind predatorprey invasion: mathematical artifact or ecological reality? Philos. Trans. R. Soc. London B, 52 (1997), 79–92.
  38. J.A. Sherratt. Periodic travelling waves in cyclic predatorprey systems, Ecol. Lett., 352 (2001), 21–38.
  39. Shieh S.Y., Ikeda M., Taya Y., Prives C. DNA damage-induced phosphorylation of p53 alleviates inhibition by MDM2. Cell, 91 (1997), 325–334. [CrossRef] [PubMed]
  40. Srividya, J., Gopinathan, M.S., Schnells, S. The effects of time delays in a phosphorylation-dephosphorylation pathway, Biophys. Chem., 125 (2007), 286–297. [CrossRef] [PubMed]
  41. Y. Tang, W. Zhao, Y. Chen, Y. Zhao, W. Gu. Acetylation is indispensable for p53 activation. Cell, 133 (2008), 612–626. [CrossRef] [PubMed]
  42. G. Tiana, M.H. Jensen, K. Sneppen. Time delay as a key to apoptosis induction in the p53 network, Eur. Phys. J. B, 29 (2002), 135–140. [CrossRef] [EDP Sciences]
  43. G. Tiana, S. Krishna, S. Pigolotti, M.H. Jensen, K. Sneppen. Oscillations and temporal signalling in cells. Phys. Biol., 4 (2007), R1–R17. [CrossRef] [PubMed]
  44. K.H. Vousden, D.P. Lane. p53 in health and disease. Nat. Mol. Cell Biol., 8 (2007), 275–283. [CrossRef]
  45. J. Wagner, L. Ma, J.J. Rice, W. Hu, A.J. Levine, G.A. Stolovitzky. p53-mdm2 loop controlled by a balance of its feedback strength and effective dampening using ATM and delayed feedback. I.E.E. Proc. Syst. Biol., 152 (2005), 109–118. [CrossRef]
  46. C. Wawra, M. Kuhl, H.A. Kestler. Extended analyses of the Wnt/β-catenin pathway: robustness and oscillatory behaviour. FEBS Lett., 581 (2007), 4043–4048. [CrossRef] [PubMed]
  47. O. Wolkenhauer, M. Ullah, P. Wellstead, K.H. Cho. The dynamic systems approach to control and regulation of intracellular networks. FEBS Lett., 579 (2005), 1846–1853. [CrossRef] [PubMed]
  48. A. Zauberman, D. Flusberg, Y. Haupt, Y. Barak, M. Oren. A functional p53-response intronic promoter is contained within the human mdm2 gene. Nucleic Acids Res., 23 (1995), 2584–2592. [CrossRef] [PubMed]
  49. W.B.J. Zimmerman. Multiphysics Modeling With Finite Element Methods, Series on Stability, Vibration and Control of Systems, Series A - Vol.18. World Scientific Publishing Company, London, 2006.

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.