Oscillation and bistable switching dynamical behavior of p53 regulated by PTEN upon DNA damage


The tumor suppressor p53 plays a key regulatory role in the response of cells to various stresses. It have experimentally shown that p53 can exhibit rich dynamic behaviors under DNA damage. In order to study the meticulous mechanism, we construct a coupling model including p53-murine double minute 2 (Mdm2) negative feedback loop (NFL) and p53-phosphatase and tensin homolog (PTEN)-Mdm2 positive feedback loop (PFL). By making use of bifurcation analysis and Binomial \(\tau \)-leap algorithm, we confirm that PTEN is a essential condition for p53 oscillation or bistable switching dynamic behaviours. We investigate the p53 dynamics affected by PFL through studying the p53-dependent PTEN synthesis rate. The results suggest that PFL may enrich the dynamic behaviors of the p53 system. This work can promote the understanding of p53 dynamics mediated by PTEN and provide clues for cancer therapy.

Graphic Abstract

The dynamics model of tumor suppressor p53 system is employed to investigate how PTEN protein mediates p53 dynamics after DNA damage and it indicates that the moderate p53-dependent PTEN synthesis rate is required for p53 to oscillate, while the higher p53-dependent PTEN synthesis rate is needed for the p53 bi-stable switch.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12


  1. 1.

    Murray-Zmijewski, F., Slee, E., Lu, X.: A complex barcode underlies the heterogeneous response of p53 to stress. Nat. Rev. Mol. Cell. Biol. 9, 702–712 (2008)

    Article  Google Scholar 

  2. 2.

    Blagih, J., Buck, M., Vousden, K.: p53, cancer and the immune response. J. Cell. Sci. 133, 237453 (2020)

    Article  Google Scholar 

  3. 3.

    Vogelstein, B., Lane, D., Levine, A.: Surfing the p53 network. Nature 408, 307–310 (2000)

    Article  Google Scholar 

  4. 4.

    Lev, B., Maya, R., Segel, L., et al.: Generation of oscillations by the p53-Mdm2 feedback loop: a theoretical and experimental study. Proc. Natl. Acad. Sci. USA 97, 11250–11255 (2000)

    Article  Google Scholar 

  5. 5.

    Lahav, G., Rosenfeld, N., Sigal, A., et al.: Dynamics of the p53-Mdm2 feedback loop in individual cells. Nat. Genet. 36, 147–150 (2004)

    Article  Google Scholar 

  6. 6.

    Geva-Zatorsky, N., Rosenfeld, N., Itzkovitz, S., et al.: Oscillations and variability in the p53 system. Mol. Syst. Biol. 2, 2006.0033 (2006)

  7. 7.

    Zhang, X., Liu, F., Cheng, Z., et al.: Cell fate decision mediated by p53 pulses. Proc. Natl. Acad. Sci. USA 106, 12245–12250 (2009)

    Article  Google Scholar 

  8. 8.

    Sun, T., Chen, C., Wu, Y., et al.: Modeling the role of p53 pulses in DNA damage-induced cell death decision. BMC Bioinf. 10, 190 (2009)

    Article  Google Scholar 

  9. 9.

    Purvis, J., Karhohs, K., Caroline, M., et al.: p53 dynamics control cell fate. Science 336, 1440–1444 (2012)

    Article  Google Scholar 

  10. 10.

    Lahav, G.: Oscillations by the p53-mdm2 feedback loop. Adv. Exp. Med. Biol. 641, 28–38 (2008)

    MathSciNet  Article  Google Scholar 

  11. 11.

    Blagosklonny, M.: Loss of function and p53 protein stabilization. Oncogene 15, 1889–1893 (1997)

    Article  Google Scholar 

  12. 12.

    Zhang, T., Brazhnik, P., Tyson, J.: Exploring mechanisms of the DNA-damage response: p53 pulses and their possible relevance to apoptosis. Cell Cycle 6, 85–94 (2007)

    Article  Google Scholar 

  13. 13.

    Tian, X., Zhang, X., Liu, F., et al.: Interlinking positive and negative feedback loops creates a tunable motif in gene regulatory networks. Phys. Rev. E 80, 011926 (2009)

    Article  Google Scholar 

  14. 14.

    Wang, L., Li, N., Chen, J., et al.: Modulation of dynamic modes by interplay between positive and negative feedback loops in gene regulatory networks. Phys. Rev. E 97, 042412 (2018)

    MathSciNet  Article  Google Scholar 

  15. 15.

    Chang, H., Cai, Z., Roberts, T.: The mechanisms underlying PTEN loss in human tumors suggest potential therapeutic opportunities. Biomolecules 9, 713 (2019)

    Article  Google Scholar 

  16. 16.

    Stambolic, V., MacPherson, D., Sas, D., et al.: Regulation of PTEN transcription by p53. Mol. Cell 8, 317–325 (2001)

    Article  Google Scholar 

  17. 17.

    Puszynski, K., Hat, B., Lipniacki, T.: Oscillations and bistability in the stochastic model of p53 regulation. J. Theor. Biol. 254, 452–465 (2008)

    Article  Google Scholar 

  18. 18.

    Pascual, J., Turner, N.: Targeting the PI3-kinase pathway in triple-negative breast cancer. Ann. Oncol. 30, 1051–1060 (2019)

    Article  Google Scholar 

  19. 19.

    Li, J., Jiang, D., Zhang, Q., et al.: MiR-301a promotes cell proliferation by repressing PTEN in renal cell carcinoma. Cancer Manag. Res. 12, 4309–4320 (2020)

    Article  Google Scholar 

  20. 20.

    Steck, P., Pershouse, M., Jasser, S., et al.: Identification of a candidate tumour suppressor gene, MMAC1, at chromosome 10q23.3 that is mutated in multiple advanced cancers. Nat. Genet. 15, 356–362 (1997)

    Article  Google Scholar 

  21. 21.

    Lee, Y., Chen, M., Lee, J., et al.: Reactivation of PTEN tumor suppressor for cancer treatment through inhibition of a MYC-WWP1 inhibitory pathway. Science 364, 0159 (2019)

    Google Scholar 

  22. 22.

    Ferrell, J., Xiong, W.: Bistability in cell signaling: how to make continuous processes discontinuous, and reversible processes irreversible. Chaos 11, 227–236 (2001)

    Article  Google Scholar 

  23. 23.

    Zhang, X., Cheng, Z., Liu, F., et al.: Linking fast and slow positive feedback loops creates an optimal bistable switch in cell signaling. Phys. Rev. E 76, 031924 (2007)

    Article  Google Scholar 

  24. 24.

    Wee, K., Aguda, B.: Akt versus p53 in a network of oncogenes and tumor suppressor genes regulating cell survival and death. Biophys. J. 91, 857–865 (2006)

    Article  Google Scholar 

  25. 25.

    Ciliberto, A., Novak, B., Tyson, J.: Steady states and oscillations in the p53/Mdm2 network. Cell Cycle 4, 488–493 (2005)

    Article  Google Scholar 

  26. 26.

    Tian, X., Liu, F., Zhang, X.: A two-step mechanism for cell fate decision by coordination of nuclear and mitochondrial p53 activities. PLoS ONE 7, e38164 (2012)

    Article  Google Scholar 

  27. 27.

    Stommel, J., Wahl, G.: Accelerated MDM2 auto-degradation induced by DNA-damage kinases is required for p53 activation. EMBO. J. 23, 1547C1556 (2004)

  28. 28.

    Zhang, X., Liu, F., Wang, W.: Two-phase dynamics of p53 in the DNA damage response. Proc. Natl. Acad. Sci. USA 108, 8990–8995 (2011)

    Article  Google Scholar 

  29. 29.

    Tyson, J.: Another turn for p53. Molecul. Syst. Biol. 2, 2006.0032 (2006)

  30. 30.

    Aguda, B., Kim, Y., Piper-Hunter, M., et al.: MicroRNA regulation of a cancer network: consequences of the feedback loops involving miR-17-92, E2F, and Myc. Proc. Natl. Acad. Sci. USA 105, 19678–19683 (2008)

    Article  Google Scholar 

  31. 31.

    Rostami, P., Marzbanrad, J.: Hybrid algorithms for handling the numerical noise in topology optimization. Acta. Mech. Sin. 36, 536–554 (2020)

    MathSciNet  Article  Google Scholar 

  32. 32.

    Ran, L., Ye, C., Wan, Z., et al.: Instability waves and low-frequency noise radiation in the subsonic chevron jet. Acta. Mech. Sin. 34, 421–430 (2018)

    Article  Google Scholar 

  33. 33.

    L\(\ddot{u}\), Q., Zhu, W., Deng, M.: Reliability of quasi integrable and non-resonant Hamiltonian systems under fractional Gaussian noise excitation. Acta Mech. Sin. 36, 902–909 (2020)

  34. 34.

    Gillespie, G.: Exact stochastic simulation of coupled chemical reactions. J. Phys. Chem. 81, 2340–2361 (1977)

    Article  Google Scholar 

  35. 35.

    Gillespie, G.: Approximate accelerated stochastic simulation of chemically reacting systems. J. Chem. Phys. 115, 1716–1733 (2001)

    Article  Google Scholar 

  36. 36.

    Chatterjee, A., Vlachos, D., Katsoulakis, A.: Binomial distribution based \(\tau \)-leap accelerated stochastic simulation. J. Chem. Phys. 122, 024112 (2005)

    Article  Google Scholar 

  37. 37.

    Wang, D., Wang, S., Huang, B., et al.: Roles of cellular heterogeneity, intrinsic and extrinsic noise in variability of p53 oscillation. Sci. Rep. 9, 5883 (2019)

    Article  Google Scholar 

  38. 38.

    Liu, N., Wang, D., Liu, H., et al.: Potential dynamic analysis of tumor suppressor p53 regulated by Wip1 protein. Chin. Phys. B 29, 068704 (2020)

    Article  Google Scholar 

  39. 39.

    Wang, D., Liu, N., Yang, H., et al.: Theoretical analysis of the delay on the p53 micronetwork. Adv. Differ. Equ. 2020, 340 (2020)

    MathSciNet  Article  Google Scholar 

  40. 40.

    Bi, Y., Yang, Z., Meng, X., et al.: Noise-induced bistable switching dynamics through a potential energy landscape. Acta. Mech. Sin. 2, 216–222 (2015)

    MathSciNet  Article  Google Scholar 

  41. 41.

    Bi, Y., Yang, Z., Zhuge, C., et al.: Bifurcation analysis and potential landscapes of the p53-Mdm2 module regulated by the co-activator programmed cell death 5. Chaos 25, 113103 (2015)

    MathSciNet  Article  Google Scholar 

  42. 42.

    Gao, C., Liu, H., Yan, F.: Dynamic behavior of p53 driven by delay and a Microrna-34a-mediated feedback loop. Int. J. Mol. Sci. 21, 1271 (2020)

    Article  Google Scholar 

  43. 43.

    Zhou, C., Zhang, X., Liu, F., et al.: Involvement of miR-605 and miR-34a in the DNA damage response promotes apoptosis induction. Biophys. J. 106, 1792–1800 (2014)

    Article  Google Scholar 

Download references


The authors are very grateful to the reviewers for their constructive suggestions. This work was supported by the National Natural Science Foundation of China (Grant 11762011).

Author information



Corresponding author

Correspondence to Hongli Yang.

Additional information

Executive Editor: Ji-Zeng Wang.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Liu, N., Yang, H., Li, S. et al. Oscillation and bistable switching dynamical behavior of p53 regulated by PTEN upon DNA damage. Acta Mech. Sin. (2021). https://doi.org/10.1007/s10409-020-01041-3

Download citation


  • p53 dynamics
  • Phosphatase and tensin homolog
  • Bifurcation
  • Noise