|
Article information
2021 , Volume 26, ¹ 6, p.33-53
Voropaeva O.F., Gavrilova K.S.
Mathematical modelling for the functioning of the p53 signaling pathway following DNA damage.I.The model of activation of the p53 - Mdm2 - Wip1 system
In the context of the survival and death of cells with DNA damage, a special role is assigned to the p53 protein. The management of p53 and its inhibitors can provide a protective effect in a wide range of degenerative diseases, such as cancer, infarctions, and dementia. Therefore, there are increased requirements for mathematical models designed to study the mechanism of functioning of the p53 signaling pathway. Our work is devoted to the study of the properties of the well-known mathematical model of the dynamics of the p53–Mdm2–Wip1 system under various influences leading to DNA damage. A simple modification of the model is proposed. The main attention is paid to the analysis of the sensitivity and qualitative properties of solutions, as well as the validation of the model before and after its modification. In numerical experiments, it was found that within the framework of the accepted models, the stationary state of the p53–Mdm2–Wip1 system can be unstable to negligible changes in the initial conditions, so that the system can function under the same parameter values according to the bifurcation scenario with a doubling of the period. The mathematical conditions under which the multiplicity of solutions and complex dynamic modes were detected allow for a biological interpretation as a reflection of the variability in the response of the p53 protein pathway to the damage signal. The range of applicability of the models was compared using the example of a wellknown laboratory experiment, in which the most complete set of observed in vitro and in vivo states of the p53–Wip1 system was demonstrated when irradiating cancer cells with wild-type p53. It is shown that the simplest modification of the original model significantly expands the scope of its applicability, allows describing the transition from normal to critical states of the system associated with known degenerative diseases. Thus, the modified model is a more effective tool for numerical analysis of a wide range of states of the p53–Mdm2–Wip1 system.
[full text]
Keywords: p53 - Mdm2 - Wip1, negative feedback, mathematical model, differential equation with delay, validation, sensitivity, scope of the model applicability, bifurcation, comparison with a laboratory experiment
doi: 10.25743/ICT.2021.26.6.004
Author(s):
Voropaeva Olga Falaleevna
Dr.
Position: Leading research officer
Office: Federal Research Centerfor Information and Computational Technologies
Address: 630090, Russia, Novosibirsk, ac. Lavrentyev Avenue, 6
Phone Office: (383) 330-85-70
E-mail: vorop@ict.nsc.ru
SPIN-code: 6550-0849Gavrilova Kseniya Sergeevna
Office: Novosibirsk State University
Address: 630090, Russia, Novosibirsk, Pirogova str., 1
E-mail: ksu483@yandex.ru
References:
1. Chumakov P.M. Versatile functions of p53 protein in multicellular organisms. Biochemistry (Moscow). 2007; 72(13):1399–421.
2. Almazov V.P., Kochetkov D.V., Chumakov P.M. Use of p53 for therapy of human cancer. Molecular Biology. 2007: 41(6):863–877.
3. Zheltukhin A.O., Chumakov P.M. Constitutive and induced functions of the p53 gene. Biochemistry (Moscow). 2010; 75(13):1692–1721.
4. Lane D., Levine A. p53 research: The past thirty years and the next thirty years. Cold Spring Harbor Perspectives in Biology. 2010; 2(12):10. Article No. a000893.
5. Lu X. Tied up in loops: Positive and negative autoregulation of p53. Cold Spring Harbor Perspectives in Biology. 2010; 2. Article No. a000984. DOI:10.1101/cshperspect.a000984.
6. Batchelor E., Mock C.S., Bhan I., Loewer A., Lahav G. Recurrent initiation: A mechanism for triggering p53 pulses in response to DNA damage. Molecular Cell. 2008; 30(3):277–289.
7. Purvis J.E., Mock C.S., Batchelor E., Loewer A., Lahav G. p53 dynamics control cell fate. Science. 2012; 336(6087):1440–1444.
8. Stewart-Ornstein J., Cheng H.W., Lahav G. Conservation and divergence of p53 oscillation dynamics across species. Cell Systems. 2017; (5):410–417.
9. Wang Z.-P., Tian Y., Lin J. Role of wild-type p53-induced phosphatase 1 in cancer. Oncology Letters. 2017; 14(4):3893–3898.
10. Wu M., Ye H., Tang Z., Shao C., Lu G., Chen B., Yang Y., Wang G., Hao H. p53 dynamics orchestrates with binding affinity to target genes for cell fate decision. Cell Death and Disease. 2017; 8(e3130). DOI:10.1038/cddis.2017.492.
11. Batchelor E., Loewer A. Recent progress and open challenges in modelling p53 dynamics in single cells. Current Opinion in Systems Biology. 2017; (3):54–59. DOI:10.1016/j.coisb.2017.04.007.
12. Voropaeva O.F., Senotrusova S.D., Shokin Yu.I. Deregulation of p53-dependent microRNAs: The results of mathematical modelling. Mathematical Biology and Bioinformatics. 2017; 12(1):151–175. (In Russ.)
13. Voropaeva O.F., Lisachev P.D., Senotrusova S.D., Shokin Yu.I. Hyperactivation of the p53– microRNA signaling pathway: Mathematical modelling of antitumor therapy options. Mathematical Biology and Bioinformatics. 2019; 14(1):355–372. (In Russ.)
14. Senotrusova S.D., Voropaeva O.F. Mathematical modelling of a positive connection in the p53–microRNA tumor marker system. Numerical Analysis and Applications. 2019; 12(3):270–283. (In Russ.)
15. Kim E., Kim J.-Y., Lee J.-Y. Mathematical modelling of p53 pathways. International Journal of Molecular Sciences. 2019; 20(20):5179.
16. Lev Bar-Or R., Maya R., Segel L.A., Alon U., Levine A.J., Oren M. Generation of oscillations by the p53–Mdm2 feedback loop: A theoretical and experimental study. PNAS. 2000; 97(21):11250–11255.
17. Tiana G., Jensen M.H., Sneppen K. Time delay as a key to apoptosis induction in the p53 network. The European Physical Journal B. 2002; 29:135–140.
18. Voropaeva O.F., Shokin Yu.I., Nepomnyashchikh L.M., Senchukova S.R. Matematicheskoe modelirovanie funktsionirovaniya i regulyatsii biologicheskoy sistemy p53–Mdm2 [A mathematical model for functioning and regulation of the p53–Mdm2 biological system]. Moscow: Izdatel’stvo RAMN; 2014: 176. (In Russ.)
19. Ciliberto A., Novak B., Tyson J.J. Steady states and oscillations in the p53–Mdm2 network. Cell Cycle. 2005; 4(3):488–493. DOI:10.4161/cc.4.3.1548.
20. Geva-Zatorsky N., Rosenfeld N., Itzkovitz Sh., Milo R., Sigal A., Dekel F., Yarnitzky T., Liron Yu., Polak P., Lahav G., Alon U. Oscillations and variability in the p53 system. Molecular Systems Biology. 2006; 2(1):2006.0033.
21. Chickarmane V., Ray A., Sauro H.M., Nadim A. A model for p53 dynamics triggered by damage. SIAM J. Applied Dynamical Systems. 2007; 6(1):61–78.
22. Hamada H., Tashima Y., Kisaka Y., Iwamoto K., Hanai T., Eguchi Y., Okamoto M. Sophisticated framework between cell cycle arrest and apoptosis induction based on p53 dynamics. PLOS ONE. 2009; 4(3):e4795. 7 p.
23. Sun T., Chen C., Shen P. Modelling the role of p53 pulses in DNA damage-induced cell death decision. BMC Bioinformatics. 2009; (10):190.
24. Zhang T., Brazhnik P., Tyson J. Exploring mechanisms of the DNA-damage response: p53 pulses and their possible relevance to apoptosis. Cell Cycle. 2007; (6):85–94.
25. Jolma I.W., Ni X.Y., Rensing L., Ruoff P. Harmonic oscillations in homeostatic controllers: Dynamics of the p53 regulatory system. Biophysical Journal. 2010; (98):743–752.
26. Lai X., Wolkenhauer O., Vera Ju. Modelling miRNA regulation in cancer signaling systems: miR-34a regulation of the p53/Sirt1 signaling module. Computational Modeling of Signaling Networks. Methods in Molecular Biology. 2012; (880):87–108.
27. Sun T., Cui J. A plausible model for bimodal p53 switch in DNA damage response. FEBS Letters. 2014; (588):815–821.
28. Moore R., Ooi H.K., Kang T., Bleris L., Ma L. MiR-192-mediated positive feedback loop controls the robustness of stress-induced p53 oscillations in breast cancer cells. PLoS Computational Biology. 2015; 11(12):e1004653.
29. Jonak K., Kurpas M., Szoltysek K., Janus P., Abramowicz A., Puszynski K. A novel mathematical model of ATM/p53/NF-B pathways points to the importance of the DDR switch-off mechanisms. BMC Systems Biology. 2016; 10(75):12.
30. Senotrusova S.D., Voropaeva O.F., Shokin Yu.I. Application of minimal mathematical models for the dynamics of the signaling pathway of the p53–miRNA to the analysis of laboratory data. Computational Technologies. 2020; 25(6):4–49. DOI:10.25743/ICT.2020.25.6.002.
31. Voropaeva O.F., Gavrilova K.S., Senotrusova S.D. Minimal mathematical models for the functioning of the protein the p53–Mdm2–Wip1–p21 network. Aktual’nye Problemy Prikladnoy Matematiki, Informatiki i Mekhaniki: Sbornik Trudov Mezhdunarodnoy Nauchno-Tekhnicheskoy Konferentsii [Actual Problems of Applied Mathematics, Computer Science and Mechanics: Proceedings of the International Scientific and Technical Conference]. Voronezh, 3–5 dekabrya 2018 g. Voronezh: Izdatel’stvo “Nauchno-issledovatel’skie publikatsii”; 2019: 672–679. (In Russ.)
32. Voropaeva O.F., Gavrilova K.S., Senotrusova S.D. Mathematical modelling of the dynamics of a network of biomarkers for degenerative diseases. Raspredelennye Informatsionno-Vychislitel’nye Resursy. Tsifrovye Dvoyniki i Bol’shie Dannye (DICR-2019): Trudy XVII Mezhdunarodnoy
Konferentsii [Distributed Information and Computing Resources. Digital Twins and Big Data (DICR2019): Proceedings of the XVII International Conference], Novosibirsk, 03.12–06.12.2019. Novosibirsk: IVT SO RAN; 2019: 185–190. (In Russ.)
33. Myshkis A.D. General theory of differential equations with retarded arguments. Uspekhi Matematicheskikh Nauk. 1949; 4(5(33)):99–141. (In Russ.)
34. Belykh L.N. Analiz matematicheskikh modeley v immunologii [Analysis of mathematical models in immunology]. Moscow: Nauka. Gl. red. fiz.-mat. lit.; 1988: 192. (In Russ.)
35. Oran E.S., Boris J.P. Numerical simulation of reactive flow. N.Y.: Elsevier Science Publishing Co.; 1987: 529
Bibliography link:
Voropaeva O.F., Gavrilova K.S. Mathematical modelling for the functioning of the p53 signaling pathway following DNA damage.I.The model of activation of the p53 - Mdm2 - Wip1 system // Computational technologies. 2021. V. 26. ¹ 6. P. 33-53
|
