P53-Mdm2 Loop Stability and Oscillatory Dynamics with Mdm2-Induced Delay Effect in P53

Authors

DOI:

https://doi.org/10.5556/j.tkjm.52.2021.3714

Keywords:

P53, Mdm2, DDE, Time delays, Stability, Oscillations

Abstract

In this paper, we consider P53-Mdm2 negative feedback loop supposed to be the core circuit of genome. We study stability and the oscillatory dynamics of the loop. Many of the studies modeled this loop by delay-differential equations with P53-induced transcrip- tional delay in the production of Mdm2. We, however, highlight the importance of Mdm2- induced delay in the degradation of P53 protein. We consider two forms of P53 protein i.e., plain P53 and active P53 along with its principal antagonist protein Mdm2 to formulate a minimal model. Active P53 finds its inclusion in the loop in the presence of DNA damage represented by a Boolean variable ‘s’. The analysis of the model provides thresholds on delays using Nyquist criterion such that delays in the degradation of P53 lower than these thresholds guarantee stability of the loop in that all proteins plain P53, active P53 and Mdm2 approach to stable equilibrium state. The oscillatory dynamics in proteins, if any, would exist beyond these thresholds.

Author Biographies

Mohammad Saleem, Aligarh Muslim University

Professor, Department of Applied Mathematics, AMU Aligarh, India 202002.

Abdur Raheem

Assistant Professor, Department of MAthematics, AMU Aligarh India 202002.

References

Y. Haupt, R Maya, A. Kazaz and M. Oren, Mdm2 promotes the rapid degradation of p53, Nature 387(1997), 296–299.

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

W. P. Bennett, S. P. Hussain, K. H. Vahakangas, M. A. Khan, P. G. Shields and C. C. Harris, Molecular epidemiology of human cancer risk: gene–environment interactions and p53 mutation spectrum in human lung cancer. The Journal of pathology 187(1999), 8–18.

Y. Barak, T. Juven, R. Haffner and M. Oren, mdm2 expression is induced by wild type p53 activity, The EMBO journal 12(1993), 461–468.

I. L. Hayon and Y. Haupt, p53: an internal investigation, Cell Cycle 1(2002), 105–110.

D. Michael and M. Oren, The p53–Mdm2 module and the ubiquitin system, Seminars in Cancer Biology 13(2003), 49–58.

J. Momand, H. H. Wu and G. Dasgupta, MDM2—master regulator of the p53 tumor suppressor protein. Gene 242(2000), 15–29.

F. Toledoa and G. M. Wahl, Regulating the p53 pathway : in vitro hypotheses, in vivo veritas. Nature Reviews Cancer 12(2006), 909–923.

M. Um and O. Petrenko, The MDM2-p53 interaction. Mol. Cancer Res 1(2003),1001–1008.

J. J. Tyson, (2002) Biochemical Oscillations. In: C. P. Fall, E. S. Marland, J. M. Wagner, J. J. Tyson, (eds) Computational Cell Biology. Interdisciplinary Applied Mathematics, Vol. 20. Springer, New York.

A. Ciliberto, B. Novák and J. J. Tyson, Steady states and oscillations in the p53/Mdm2 network. Cell Cycle 4(2005), e107–e112.

D. A. Hamstra, M. S. Bhojani, L. B. Griffin, B. Laxman, B. D. Ross and A. Rehemtulla, Real- time evaluation of p53 oscillatory behavior in vivo using bioluminescent imaging, Cancer Research 66(2006), 7482–7489.

G.Lahav,N.Rosenfeld,A.Sigal,N.Geva-Zatorsky,A.J.Levine,M.B.ElowitzandU.Alon, Dynamics of the p53-Mdm2 feedback loop in individual cells, Nature Genetics 36(2004), 147–150.

N. G. Zatorsky, N. Rosenfeld, S. Itzkovitz, R. Milo, A. Sigal, E. Dekel, T. Yarnitzky, Y. Liron, P. Polak, G. Lahav and U. Alon, Oscillations and variability in the p53 system. Molecular Systems Biology 2(2006), 1–13.

T.Zhang,P.BrazhnikandJ.J.Tyson,ExploringmechanismsoftheDNA-damageresponse: p53 pulses and their possible relevance to apoptosis. Cell Cycle 6(2007), 5–94.

R. L. Bar-Or, R. Maya, L. A. Segel, U. Alon, A. J. Levine and M. Oren, Generation of oscil- lations by the p53-Mdm2 feedback loop: a theoretical and experimental study. Proceedings of the National Academy of Sciences 97(2000), 11250–11255.

D. Brewer, Investigations of the p53 protein DNA damage network using mathematical models. University College London, London (UK). 2002 Oct.

E. Batchelor, C. S. Mock, I. Bhan, A. Loewer and G. Lahav, Recurrent initiation : a mechanism for triggering p53 pulses in response to DNA damage. Molecular Cell 30(2008), 277–289.

E. Batchelor, A. Loewer, C. Mock and G. Lahav, Stimulus-dependent dynamics of p53 in single cells. Molecular Systems Biology 7(2011), 1–8.

J. D. Murray, editor. Mathematical BiologyI. An Introduction, thirdedn. Springer, 2002.

T. F. Thingstad and T. I. Langeland, Dynamics of chemostat culture: The effect of a delay in cell response. Journal of Theoretical Biology 48(1974), 149–159.

J. D. Murray, editor. Mathematical Biology II. Spatial Models and Biomedical Applications. Springer, 2003.

G. I. Mihalas, Z. Simon, G. Balea and E. Popa, Possible oscillatory behavior in p53–Mdm2 interaction computer simulation. Journal of Biological Systems 8(2000), 21–29.

G. I. Mihalaş, M. Neamţu, S. D. Opriş and R. F. Horhat, A dynamic P53-MDM2 model with time delay. Chaos, Solitons and Fractals 30(2006), 936–945.

S. Bottani and B. Grammaticos, Analysis of a minimal model for p53 oscillations. Journal of Theoretical Biology 249(2007), 235–245.

R. K. Layek, A. Datta and E. R. Dougherty, From biological pathways to regulatory networks. Molecular BioSystems 7(2011), 843–851.

J. E. Purvis, K. W. Karhohs, C. Mock, E. Batchelor, A. Loewer and G. Lahav, p53 dynamics control cell fate. Science 336(2012), 1440–1444.

T. Sun, W. Yang, J. Liu and P. Shen, Modeling the basal dynamics of p53 system. PloS One 6(2011), 1–9.

K. H. Chong, S. Samarasinghe and D. Kulasiri, Mathematical modelling of p53 basal dynamics and DNA damage response. Mathematical Biosciences 259(2015), 27–42.

V. Pant and G. Lozano, Dissecting the p53-Mdm2 feedback loop in vivo : uncoupling the role in p53 stability and activity. Oncotarget 5(2014), 1149–1156.

L. Pecorino, Molecular biology of cancer: mechanisms, targets, and therapeutics. Oxford university press, 2012.

X. Yang, L. Chen and J. Chen, Permanence and positive periodic solution for the single- species nonautonomous delay diffusive models. Computers and Mathematics with Applica- tions 32(1996), 109–116.

Y. Kuang, editor. Delay differential equations: with applications in population dynamics. Academic Press, 1993.

H. I. Freedman and V. S. Rao, Stability criteria for a system involving two time delays. SIAM Journal on Applied Mathematics 46(1986), 552–560.

Downloads

Published

2021-10-30

How to Cite

Baba, M. Y., Saleem, M., & Raheem, A. (2021). P53-Mdm2 Loop Stability and Oscillatory Dynamics with Mdm2-Induced Delay Effect in P53. Tamkang Journal of Mathematics, 52(4), 509-533. https://doi.org/10.5556/j.tkjm.52.2021.3714

Issue

Section

Papers