Stability and bifurcation analyses of p53 gene regulatory network with time delay

Jianmin Hou; Quansheng Liu; Hongwei Yang; Lixin Wang; Yuanhong Bi; Jianmin Hou; Quansheng Liu; Hongwei Yang; Lixin Wang; Yuanhong Bi

doi:10.3934/era.2022045

Electronic Research Archive

2022, Volume 30, Issue 3: 850-873. doi: 10.3934/era.2022045

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Research article

Stability and bifurcation analyses of p53 gene regulatory network with time delay

1.
School of Mathematical Sciences, Inner Mongolia University, Hohhot, 010021, China
2.
College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao, 266590, China
3.
School of Ecology and Environment, Inner Mongolia University, Hohhot, 010021, China
4.
School of Statistics and Mathematics, Inner Mongolia University of Finance and Economics, Hohhot, 010070, China

Received: 29 September 2021 Revised: 27 November 2021 Accepted: 28 November 2021 Published: 01 March 2022

In this paper, based on a p53 gene regulatory network regulated by Programmed Cell Death 5(PDCD5), a time delay in transcription and translation of Mdm2 gene expression is introduced into the network, the effects of the time delay on oscillation dynamics of p53 are investigated through stability and bifurcation analyses. The local stability of the positive equilibrium in the network is proved through analyzing the characteristic values of the corresponding linearized systems, which give the conditions on undergoing Hopf bifurcation without and with time delay, respectively. The theoretical results are verified through numerical simulations of time series, characteristic values and potential landscapes. Furthermore, combined effect of time delay and several typical parameters in the network on oscillation dynamics of p53 are explored through two-parameter bifurcation diagrams. The results show p53 reaches a lower stable steady state under smaller PDCD5 level, the production rates of p53 and Mdm2 while reaches a higher stable steady state under these larger ones. But the case is the opposite for the degradation rate of p53. Specially, p53 oscillates at a smaller Mdm2 degradation rate, but a larger one makes p53 reach a low stable steady state. Besides, moderate time delay can make the steady state switch from stable to unstable and induce p53 oscillation for moderate value of these parameters. Theses results reveal that time delay has a significant impact on p53 oscillation and may provide a useful insight into developing anti-cancer therapy.
- stability analysis,
- bifurcation,
- p53 gene regulatory network,
- time delay,
- oscillation dynamics
Citation: Jianmin Hou, Quansheng Liu, Hongwei Yang, Lixin Wang, Yuanhong Bi. Stability and bifurcation analyses of p53 gene regulatory network with time delay[J]. Electronic Research Archive, 2022, 30(3): 850-873. doi: 10.3934/era.2022045

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Abstract

In this paper, based on a p53 gene regulatory network regulated by Programmed Cell Death 5(PDCD5), a time delay in transcription and translation of Mdm2 gene expression is introduced into the network, the effects of the time delay on oscillation dynamics of p53 are investigated through stability and bifurcation analyses. The local stability of the positive equilibrium in the network is proved through analyzing the characteristic values of the corresponding linearized systems, which give the conditions on undergoing Hopf bifurcation without and with time delay, respectively. The theoretical results are verified through numerical simulations of time series, characteristic values and potential landscapes. Furthermore, combined effect of time delay and several typical parameters in the network on oscillation dynamics of p53 are explored through two-parameter bifurcation diagrams. The results show p53 reaches a lower stable steady state under smaller PDCD5 level, the production rates of p53 and Mdm2 while reaches a higher stable steady state under these larger ones. But the case is the opposite for the degradation rate of p53. Specially, p53 oscillates at a smaller Mdm2 degradation rate, but a larger one makes p53 reach a low stable steady state. Besides, moderate time delay can make the steady state switch from stable to unstable and induce p53 oscillation for moderate value of these parameters. Theses results reveal that time delay has a significant impact on p53 oscillation and may provide a useful insight into developing anti-cancer therapy.

References

[1]	A. J. Levine, M. Oren, The first 30 years of p53: growing ever more complex, Nat. Rev. Cancer, 9 (2009), 749–758. https://doi.org/10.1038/nrc2723 doi: 10.1038/nrc2723
[2]	K. T. Bieging, S. S. Mello, L. D. Attardi, Unravelling mechanisms of p53-mediated tumour suppression, Nat. Rev. Cancer, 14 (2014), 359–370. https://doi.org/10.1038/nrc3711 doi: 10.1038/nrc3711
[3]	M. H. Kubbutat, S. N. Jones, K. H. Vousden, Regulation of p53 stability by Mdm2, Nature, 387 (1997), 299–303. https://doi.org/10.1038/387299a0 doi: 10.1038/387299a0
[4]	Y. Aylon, M. Oren, Living with p53, dying of p53, Cell, 130 (2007), 597–600. https://doi.org/10.1016/j.cell.2007.08.005 doi: 10.1016/j.cell.2007.08.005
[5]	R. L. 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., 97 (2000), 11250–11255.
[6]	Y. Wang, X. Li, L. Wang, P. Ding, Y. Zhang, W. Han, et al., An alternative form of paraptosis-like cell death, triggered by TAJ/TROY and enhanced by PDCD5 overexpression, J. Cell Sci., 117 (2004), 1525–1532. https://doi.org/10.1242/jcs.00994 doi: 10.1242/jcs.00994
[7]	X. Zhang, F. Liu, Z. Cheng, W. Wang, Cell fate decision mediated by p53 pulses, Proc. Natl. Acad. Sci., 106 (2009), 12245–12250.
[8]	X. Zhang, F. Liu, Z. Cheng, W. Wang, Two-phase dynamics of p53 in the DNA damage response, Proc. Natl. Acad. Sci., 108 (2011), 8990–8995. https://doi.org/10.1073/pnas.1100600108 doi: 10.1073/pnas.1100600108
[9]	E. Batchelor, C. S. Mock, I. Bhan, A. Loewer, G. Lahav, Recurrent initiation: a mechanism for triggering p53 pulses in response to DNA damage, Mol. Cell, 30 (2008), 277–289. https://doi.org/10.1016/j.molcel.2008.03.016 doi: 10.1016/j.molcel.2008.03.016
[10]	C. Wang, F. Yan, H. Hai, Y. Zhang, Theoretical study on the oscillation mechanism of p53-mdm2 network, Int. J. Biomath., 11 (2018), 1850112. https://doi.org/10.1142/S1793524518501127 doi: 10.1142/S1793524518501127
[11]	N. Geva-Zatorsky, N. Rosenfeld, S. Itzkovitz, R. Milo, A. Sigal, E. Dekel, et al., Oscillations and variability in the p53 system, Mol. Syst. Biol., 2 (2006), 0030. https://doi.org/10.1038/msb4100068 doi: 10.1038/msb4100068
[12]	L. Xu, J. Hu, Y. Zhao, J. Hu, J. Xiao, Y. Wang, et al., PDCD5 interacts with p53 and functions as a positive regulator in the p53 pathway, Apoptosis, 17 (2012), 1235–1245. https://doi.org/10.1007/s10495-012-0754-x doi: 10.1007/s10495-012-0754-x
[13]	Y. Bi, Q. Liu, L. Wang, W. Yang, X. Wu, Bifurcation and Potential Landscape of p53 Dynamics Depending on PDCD5 Level and ATM Degradation Rate, Int. J. Bifurcation Chaos Appl. Sci. Eng., 30 (2020), 2050134. https://doi.org/10.1142/S0218127420501345 doi: 10.1142/S0218127420501345
[14]	N. A. Monk, Oscillatory expression of Hes1, p53, and NF-B driven by transcriptional time delays, Curr. Biol., 13 (2003), 1409–1413. https://doi.org/10.1016/S0960-9822(03)00494-9 doi: 10.1016/S0960-9822(03)00494-9
[15]	Y. Cao, X. He, Y. Hao, Q. Wang, Transition Dynamics of Epileptic Seizures in the Coupled Thalamocortical Network Model, Int. J. Bifurcation Chaos Appl. Sci. Eng., 28 (2018), 1850104. https://doi.org/10.1142/S0218127418501043 doi: 10.1142/S0218127418501043
[16]	A. Audibert, D. Weil, F. Dautry, In vivo kinetics of mRNA splicing and transport in mammalian cells, Mol. Cell. Biol., 22 (2002), 6706–6718.
[17]	Z. Wei, B. Zhu, J. Yang, M. Perc, M. Slavinec, Bifurcation analysis of two disc dynamos with viscous friction and multiple time delays, Appl. Math. Comput., 347 (2019), 265–281. https://doi.org/10.1016/j.amc.2018.10.090 doi: 10.1016/j.amc.2018.10.090
[18]	Y. Li, Z. Wei, W. Zhang, M. Perc, R. Repnik, Bogdanov - Takens singularity in the Hindmarsh - Rose neuron with time delay, Appl. Math. Comput., 354 (2019), 180–188. https://doi.org/10.1016/j.amc.2019.02.046 doi: 10.1016/j.amc.2019.02.046
[19]	X. Mao, X. Li, W. Ding, S. Wang, X. Zhou, L. Qiao, Dynamics of a multiplex neural network with delayed couplings, Appl. Math. Mech., 42 (2021), 441–456. https://doi.org/10.1007/S10483-021-2709-6 doi: 10.1007/S10483-021-2709-6
[20]	D. Michael, M. Oren, The p53-Mdm2 module and the ubiquitin system, in Semin. Cancer Biol., Academic Press, 13 (2003), 49–58.
[21]	C. Gao, F. Chen, Dynamics of p53 regulatory network in DNA damage response, Appl. Math. Model., 88 (2020), 701–714. https://doi.org/10.1016/j.apm.2020.06.057 doi: 10.1016/j.apm.2020.06.057
[22]	C. Zhuge, X. Sun, Y. Chen, J. Lei, PDCD5 functions as a regulator of p53 dynamics in the DNA damage response, J. Theor. Biol., 388 (2016), 1–10. https://doi.org/10.1016/j.jtbi.2015.09.025 doi: 10.1016/j.jtbi.2015.09.025
[23]	Y. Bi, Z. Yang, C. Zhuge, J. Lei, Bifurcation analysis and potential landscapes of the p53-Mdm2 module regulated by the co-activator programmed cell death 5, Chaos, 25 (2015), 113103. https://doi.org/10.1063/1.4934967 doi: 10.1063/1.4934967
[24]	C. Prives, Signaling to p53: breaking the MDM2-p53 circuit, Cell, 95 (1998), 5–8. https://doi.org/10.1016/S0092-8674(00)81774-2 doi: 10.1016/S0092-8674(00)81774-2
[25]	P. Chene, Inhibiting the p53-MDM2 interaction: an important target for cancer therapy, Nat. Rev. Cancer, 3 (2003), 102–109. https://doi.org/10.1038/nrc991 doi: 10.1038/nrc991
[26]	P. J. Hamard, J. J. Manfredi, Mdm2's dilemma: to degrade or to translate p53?, Cancer cell, 21 (2012), 3–5. https://doi.org/10.1016/j.ccr.2011.12.018 doi: 10.1016/j.ccr.2011.12.018
[27]	P. C. Parks, A new proof of of the Routh-Hurwitz stability criterion using the second method of Liapunov, Math. Proc. Cambridge Philos. Soc., 58 (1962), 694–702. https://doi.org/10.1017/S030500410004072X doi: 10.1017/S030500410004072X
[28]	T. Zhang, H. Jiang, Z. Teng, On the distribution of the roots of a fifth degree exponential polynomial with application to a delayed neural network model, Neurocomputing, 72 (2009), 1098–1104. https://doi.org/10.1016/j.neucom.2008.03.003 doi: 10.1016/j.neucom.2008.03.003
[29]	J. Wang, L. Xu, E. Wang, Potential landscape and flux framework of nonequilibrium networks: robustness, dissipation, and coherence of biochemical oscillations, Proc. Natl. Acad. Sci., 105 (2008), 12271–12276. https://doi.org/10.1016/B978-0-444-53835-2.00001-8 doi: 10.1016/B978-0-444-53835-2.00001-8

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