Analysis of a minimal model for p53 oscillations.

Oscillatory behaviours in genetic networks are important examples for studying the principles underlying the dynamics of cellular regulation. Recently the team of Alon has reported a surprisingly rich oscillatory response of the p53 tumor suppressor to irradiation stress et al. [Lahav, G., Rosenfeld, N., Sigal, A., Geva-Zatorsky, N., Levine, A.J., Elowitz, M.B., Alon, U., 2004. Dynamics of the p53-Mdm2 feedback loop in individual cells. Nat. Genet. 36 (2), 147-150; Geva-Zatorsky, N., Rosenfeld, N., Itzkovitz, S., Milo, R., Sigal, A., Dekel, E., Yarnitzky, T., Liron, Y., Polak, P., Lahav, G., Alon, U., 2006. Oscillations and variability in the p53 system. Mol. Syst. Biol. 2, 2006.0033]. Several models for this system have been proposed by different groups, based essentially on negative feedback loops. In this paper we investigate in detail oscillations and stability in a deterministic time delayed differential model of the core circuit for p53 expression. This model is representative of a class of modelling approaches of this system, based on a "minimal" set of well-established biomolecular regulations. Depending on the protein degradation rates we show the existence of bifurcations between a stable steady state and oscillations both in presence and absence of stress.

[1]  D. Meek,et al.  Phosphorylation of p53 at the casein kinase II site selectively regulates p53-dependent transcriptional repression but not transactivation. , 1996, Nucleic acids research.

[2]  U. Moll,et al.  The MDM2-p53 interaction. , 2003, Molecular cancer research : MCR.

[3]  J. Ferrell.  Tripping the switch fantastic: how a protein kinase cascade can convert graded inputs into switch-like outputs. , 1996, Trends in biochemical sciences.

[4]  Stephen N. Jones,et al.  Regulation of p53 stability by Mdm2 , 1997, Nature.

[5]  T. Crook,et al.  Corrigendum: Human papillomavirus E6 proteins bind p53 in vivo and abrogate p53-mediated repression of transcription (The EMBO Journal(1992)11(3045-3052)) , 1992 .

[6]  M. Oren,et al.  mdm2 expression is induced by wild type p53 activity. , 1993, The EMBO journal.

[7]  H. Feng,et al.  Protein serine/threonine phosphatase-1 dephosphorylates p53 at Ser-15 and Ser-37 to modulate its transcriptional and apoptotic activities , 2006, Oncogene.

[8]  K. Wilkinson.  Ubiquitination and deubiquitination: targeting of proteins for degradation by the proteasome. , 2000, Seminars in cell & developmental biology.

[9]  Z. Ronai,et al.  p53-Mdm2--the affair that never ends. , 2002, Carcinogenesis.

[10]  John Jeremy Rice,et al.  A plausible model for the digital response of p53 to DNA damage. , 2005, Proceedings of the National Academy of Sciences of the United States of America.

[11]  Alnawaz Rehemtulla,et al.  Real-time evaluation of p53 oscillatory behavior in vivo using bioluminescent imaging. , 2006, Cancer research.

[12]  Paul Brazhnik,et al.  Exploring Mechanisms of the DNA-Damage Response: p53 Pulses and their Possible Relevance to Apoptosis , 2007, Cell cycle.

[13]  R. Milo,et al.  Oscillations and variability in the p53 system , 2006, Molecular systems biology.

[14]  A. Hoffmann,et al.  The I (cid:1) B –NF-(cid:1) B Signaling Module: Temporal Control and Selective Gene Activation , 2022 .

[15]  A. Levine,et al.  p53-Mdm2 loop controlled by a balance of its feedback strength and effective dampening using ATM and delayed feedback. , 2005, Systems biology.

[16]  Y Taya,et al.  DNA damage‐inducible phosphorylation of p53 at N‐terminal sites including a novel site, Ser20, requires tetramerization , 1999, The EMBO journal.

[17]  A. Jochemsen,et al.  Mutual Dependence of MDM2 and MDMX in Their Functional Inactivation of p53* , 2002, The Journal of Biological Chemistry.

[18]  W. Gu,et al.  Dynamics in the p53-Mdm2 Ubiquitination Pathway , 2004, Cell cycle.

[19]  J. Royds,et al.  The p53 story: layers of complexity. , 2005, Carcinogenesis.

[20]  J. Liao,et al.  A synthetic gene–metabolic oscillator , 2005, Nature.

[21]  A. Gronenborn,et al.  Four p53 DNA-binding domain peptides bind natural p53-response elements and bend the DNA. , 1995, Proceedings of the National Academy of Sciences of the United States of America.

[22]  A. Levine,et al.  Structure of the MDM2 Oncoprotein Bound to the p53 Tumor Suppressor Transactivation Domain , 1996, Science.

[23]  R. Weiss,et al.  Ultrasensitivity and noise propagation in a synthetic transcriptional cascade. , 2005, Proceedings of the National Academy of Sciences of the United States of America.

[24]  G. Wahl,et al.  A New Twist in the Feedback Loop: Stress-Activated MDM2 Destabilization is Required for p53 Activation , 2005, Cell cycle.

[25]  B. Ogunnaike.  Elucidating the digital control mechanism for DNA damage repair with the p53–Mdm2 system: single cell data analysis and ensemble modelling , 2006, Journal of The Royal Society Interface.

[26]  M. E. Perry,et al.  The p53 Tumor Suppressor Protein Does Not Regulate Expression of Its Own Inhibitor, MDM2, Except under Conditions of Stress , 2000, Molecular and Cellular Biology.

[27]  M. Oren,et al.  The p53-Mdm2 module and the ubiquitin system. , 2003, Seminars in cancer biology.

[28]  M. Hollstein,et al.  p53 and human cancer: the first ten thousand mutations. , 2000, Advances in cancer research.

[29]  Kathy Chen,et al.  Network dynamics and cell physiology , 2001, Nature Reviews Molecular Cell Biology.

[30]  G. Stark,et al.  Limited role of N-terminal phosphoserine residues in the activation of transcription by p53 , 2004, Oncogene.

[31]  A. Fersht,et al.  Cooperative binding of tetrameric p53 to DNA. , 2004, Journal of molecular biology.

[32]  N. Monk.  Oscillatory Expression of Hes1, p53, and NF-κB Driven by Transcriptional Time Delays , 2003, Current Biology.

[33]  George I. Mihalas,et al.  POSSIBLE OSCILLATORY BEHAVIOR IN P53–MDM2 INTERACTION COMPUTER SIMULATION , 2000 .

[34]  A dynamic P53-MDM2 model with time delay , 2005, math/0507055.

[35]  D. Koshland,et al.  Ultrasensitivity in biochemical systems controlled by covalent modification. Interplay between zero-order and multistep effects. , 1984, The Journal of biological chemistry.

[36]  A. Levine,et al.  Surfing the p53 network , 2000, Nature.

[37]  K. Sneppen,et al.  Sustained oscillations and time delays in gene expression of protein Hes1 , 2003, FEBS letters.

[38]  T. Crook,et al.  Human papillomavirus E6 proteins bind p53 in vivo and abrogate p53‐mediated repression of transcription. , 1992, The EMBO journal.

[39]  K. Sneppen,et al.  Time delay as a key to apoptosis induction in the p53 network , 2002, cond-mat/0207236.

[40]  H. Sauro,et al.  A p53 Oscillator Model of DNA Break Repair Control , 2005, q-bio/0510002.

[41]  N. Gueven,et al.  The complexity of p53 stabilization and activation , 2006, Cell Death and Differentiation.

[42]  M. Oren,et al.  Mdm2 promotes the rapid degradation of p53 , 1997, Nature.

[43]  Margaret Ashcroft,et al.  Regulation of p53 stability , 1999, Oncogene.

[44]  O. Pourquié.  The Segmentation Clock: Converting Embryonic Time into Spatial Pattern , 2003, Science.

[45]  G. Wahl,et al.  Accelerated MDM2 auto‐degradation induced by DNA‐damage kinases is required for p53 activation , 2004, The EMBO journal.

[46]  J. Dunlap.  Molecular Bases for Circadian Clocks , 1999, Cell.

[47]  D. Faller,et al.  DNA-damaging Aryl Hydrocarbons Induce Mdm2 Expression via p53-independent Post-transcriptional Mechanisms* , 2000, The Journal of Biological Chemistry.

[48]  D. Meek,et al.  Serine 15 phosphorylation stimulates p53 transactivation but does not directly influence interaction with HDM2 , 1999, The EMBO journal.

[49]  A. Levine,et al.  Analysis of the degradation function of Mdm2. , 1999, Cell growth & differentiation : the molecular biology journal of the American Association for Cancer Research.

[50]  P. Hainaut,et al.  25 years of p53 research , 2005 .

[51]  P. Herrlich,et al.  DNA damage induced p53 stabilization: no indication for an involvement of p53 phosphorylation , 1999, Oncogene.

[52]  Hong Yang,et al.  Phosphorylation of p53 on Key Serines Is Dispensable for Transcriptional Activation and Apoptosis*♦ , 2004, Journal of Biological Chemistry.

[53]  U Alon,et al.  Generation of oscillations by the p53-Mdm2 feedback loop: a theoretical and experimental study. , 2000, Proceedings of the National Academy of Sciences of the United States of America.

[54]  K. Khanna,et al.  ATM, a central controller of cellular responses to DNA damage , 2001, Cell Death and Differentiation.

[55]  T. Unger,et al.  Critical role for Ser20 of human p53 in the negative regulation of p53 by Mdm2 , 1999, The EMBO journal.

[56]  Andrea Ciliberto,et al.  Steady States and Oscillations in the p53/Mdm2 Network , 2005, Cell cycle.

[57]  M. Kubbutat,et al.  Regulation of p53 Function and Stability by Phosphorylation , 1999, Molecular and Cellular Biology.

[58]  A. Levine,et al.  The p53-mdm-2 autoregulatory feedback loop. , 1993, Genes & development.

[59]  J E Ferrell,et al.  The biochemical basis of an all-or-none cell fate switch in Xenopus oocytes. , 1998, Science.

[60]  M. Elowitz,et al.  A synthetic oscillatory network of transcriptional regulators , 2000, Nature.

[61]  Uri Alon,et al.  Dynamics of the p53-Mdm2 feedback loop in individual cells , 2004, Nature Genetics.

[62]  L. Mayo,et al.  The PTEN, Mdm2, p53 tumor suppressor-oncoprotein network. , 2002, Trends in biochemical sciences.

[63]  M. E. Perry.  Mdm2 in the response to radiation. , 2004, Molecular cancer research : MCR.

[64]  D Gonze,et al.  Theoretical models for circadian rhythms in Neurospora and Drosophila. , 2000, Comptes rendus de l'Academie des sciences. Serie III, Sciences de la vie.