Abstract
Due to the heterogeneity of cells in a population, they react differently to the same stimuli. This diversification results in the population separating into subpopulations with different cell responses such as apoptosis, cell cycle blockade, or proliferation. Here we focus on the regulatory module of the protein p53, which is responsible for cell responses to DNA damage, and analyze a piece-wise linear model with switches discussed in our previous publications. The main goal of this work was to examine the influence of differences occurring between cells on the cellular response for different doses of external stress. We investigate the properties of the whole cell population in the case of three different types of cell diversity: diversity in sensitivity to stress, diversity in gene expression, and diversity in all the processes analyzed. The diversification of the cell population is acquired by stochastic localization of the switching thresholds. The results show that a population with high diversity in sensitivity to stress has a wide range of responses, so that almost all possible trajectories are present and consequently it is impossible, for example, to force all the cells to apoptosis. Differences in gene activation result in differences in the time courses. The apoptotic response can be activated much later and additional possible results appear. In the case of diversity in all processes analyzed, a variety of different responses can be observed even for a narrow range of the changes, and moreover additional stationary points appear. These results show that even minor changes in proper cell functioning can lead to abnormalities, which may lead to cancer.
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References
Vousden, K.H., Lu, X.: Live or let die: the cell’s response to p53. Nature 2, 594–604 (2002)
Sane, S., Rezvani, K.: Essential roles of E3 ubiquitin ligases in p53 regulation. Int. J. Mol. Sci. 18(2), 442 (2017)
Jonak, K., Kurpas, M., Szoltysek, K., Janus, P., Abramowicz, A., Puszynski, K.: A novel mathematical model of ATM/p53/NF-kB pathways points to the importance of the DDR switch-off mechanisms. BMC Syst. Biol. 10, 75 (2016)
Schmitt, C.A., Lowe, S.W.: Apoptosis and therapy. J. Pathol 187, 127–137 (1999)
Yang, P., Du, C.W., Kwan, M., Liang, S.X., Zhang, G.J.: The impact of p53 in predicting clinical outcome of breast cancer patients with visceral metastasis. Sci. R 3, 2246 (2013)
Liberzon, D.: Switchings in Systems and Control. University of Illionis at Urbana-Campaign, Urbana (2003)
Klamka, J., Czornik, A., Niezabitowski, M.: Stability and controllability of switched systems. Bull. Pol. Acad. Sci. Tech. Sci. 61(3), 547–555 (2013). (Online)
Mestl, T., Plahte, E., Omholt, S.W.: A mathematical framework for describing and analysing gene regulatory networks. J. Theor. Biol. 176, 291–300 (1995)
Ochab, M., Puszynski, K., Swierniak, A.: Application of the piece-wise linear models for description of nonlinear biological systems based on p53 regulatory unit. In: Proceedings of the XXI National Conference on Applications of Mathematics in Biology and Medicine, pp. 85–90 (2016)
Plahte, E., Mestl, T., Omholt, S.W.: Global analysis of steady points for systems of differential equations with sigmoid interactions. Dyn. Stab. Syst. 9(4), 275–291 (1994)
Plahte, E., Mestl, T., Omholt, S.W.: A methodological basis for description and analysis of the systems with complex switch-like interactions. J. Math. Biol. 36, 321–348 (1998)
Alberts, B., Johnson, A., Lewis, J., Raff, M., Roberts, K., Walter, P.: Molecular Biology of the Cell, 4th edn. Garland Science, New York (2002)
Kracikova, M., Akiri, G., George, A., Sachidanandam, R., Aaronson, S.A.: A threshold mechanism mediates p53 cell fate decision beteen growth arrest and apoptosis. Cell Death Differ. 20, 576–588 (2013)
Puszynski, K., Gandolfi, A., d’Onofrio, A.: The pharmacodynamics of the p53-Mdm2 targeting drug nutlin: the role of gene-switching noise. PLOS Comput. Biol. 10(12), e1003991 (2014)
Ochab, M., Puszynski, K., Swierniak, A., Klamka, J.: Variety behavior in the piece-wise linear model of the p53-regulatory module. In: International Conference on Bioinformatics and Biomedical Engineering, pp. 208–219. Springer, Cham (2017)
Kurpas, M., Jonak, K., Puszynski, K.: Simulation analysis of the ATR module as a detector of UV-induced DNA damage. Inf. Technol. Biomed. Adv. Intell. Syst. Comput. 283, 317–326 (2014)
Thor, AD., Moor II, DH., Edgerton, SM., Kawasaki, ES., Reihsaus, E., Lynch, HT., Marcus, JN., Schwarts, L., Chen, L-C. Mayall, BH., Smith, HS.: Accumulation of p53 tumor suppressor gene protein: an independent marker of prognosis in breast cancers. J. Natl. Cancer Inst. 84(11), 845–855 (1992)
Geva-Zatorsky, N., Rosenfeld, N., Itzkovitz, S., Milo, R., Sigal, A., Dekel, E., Yarnitzky, T., Liron, Y., Polak, P., Lahav, G., Alon, U.: Oscillations and variability in the p53 system. Mol. Syst. Biol. 2, 2006.0033 (2006)
Bar-Or, R.L., 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 97(21), 11250–11255 (2000)
Wee, K.B., Aguda, B.D.: Akt versus p53 in a network of oncogenes and tumor suppressor genes regulating cell survival and death. Biophys. J. 91, 857–865 (2006)
Weisz, L., Oren, M., Rotter, V.: Transcript regulation by mutant p53. Oncogene 26, 2202–2211 (2007)
Lu, C.-D., Altieri, D.C., Tanigawa, N.: Expression of a novel antiapoptosis gene, survivin, correlated with tumor cell apoptosis and p53 accumulation in gastric carcinomas. Cancer Res. 58, 1808–1812 (1998)
Acknowledgments
The research presented here was partially supported by the National Science Centre in Poland granted with decision number DEC-2013/11/B/ST7/01713 (for KP), DEC-2014/13/B/ST7/00755 (JK) and by Silesian University of Technology grant with decision number BK/213/RAU1/2016 t.3 (AS) and donation for young researchers BKM 2017 (MO).
The authors would like to thank Prof. Ronald Hacock for his assistance in preparation of the revised version of the manuscript.
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Ochab, M., Swierniak, A., Klamka, J., Puszynski, K. (2018). Influence of the Stochasticity in Threshold Localization on Cell Fate in the PLDE-Model of the P53 Module. In: Augustyniak, P., Maniewski, R., Tadeusiewicz, R. (eds) Recent Developments and Achievements in Biocybernetics and Biomedical Engineering. PCBBE 2017. Advances in Intelligent Systems and Computing, vol 647. Springer, Cham. https://doi.org/10.1007/978-3-319-66905-2_18
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DOI: https://doi.org/10.1007/978-3-319-66905-2_18
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