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Process equation as a model for the development of cells

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Abstract

This paper proposes a behavioral model for cells that shows their different dynamics from a high pluripotent stem cell to any distinct cell fate. The proposed model considers a cell as a black-box for a living system and tries to depict the presumed behaviors of the system. The model is a multistable iterated map with sensitive dependence on initial conditions. It indicates various stages of cell evolution in strict order from stem cells in embryos to differentiated cells functioning in an organ. The results show that the dynamical system inters to a situation with an infinite number of coexisting attractors by decreasing the parameter g. In the first stages of division, the system has a more complex dynamic, and so the model has chaotic attractor. Passing the time in the division process results in stronger cell-cell interactions and so the dynamic of the system becomes more ordered and simpler. Finally, at the end of the division process, the system has the simplest dynamic, which is an equilibrium in the model.

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References

  1. B. Alberts, D. Bray, K. Hopkin, A. Johnson, J. Lewis, M. Raff, et al.,, Essential cell biology (Garland Science, New York, 2013).

  2. Y. Wang, S. Li, P. Zhang, H. Bai, L. Feng, F. Lv, et al.,, Adv. Mater. 30, 1705418 (2018).

    Article  Google Scholar 

  3. S. Sell, Stem cells handbook (Springer, Berlin).

  4. H. Abdallah, D. Del Vecchio, Y. Qian, A dynamical model for the low efficiency of induced pluripotent stem cell reprogramming (2015), https://doi.org/10.1101/028266.

  5. B. Soria, E. Roche, G. Berna, T. León-Quinto, J.A. Reig, Diabetes 49, 157 (2000).

    Article  Google Scholar 

  6. J.W. McDonald, X.-Z. Liu, Y. Qu, S. Liu, S.K. Mickey, D. Turetsky, et al.,, Nat. Med. 5, 1410 (1999).

    Article  Google Scholar 

  7. K.-C. Sonntag, B. Song, N. Lee, J.H. Jung, Y. Cha, P. Leblanc, et al.,, Progr. Neurobiol. 168 1 (2018).

    Article  Google Scholar 

  8. G.R. Martin, Proc. Natl. Acad. Sci. 78, 7634 (1981).

    Article  ADS  Google Scholar 

  9. J.A. Thomson, J. Itskovitz-Eldor, S.S. Shapiro, M.A. Waknitz, J.J. Swiergiel, V.S. Marshall, et al.,, Science 282, 1145 (1998).

    Article  ADS  Google Scholar 

  10. K. Takahashi, K. Tanabe, M. Ohnuki, M. Narita, T. Ichisaka, K. Tomoda, et al.,, Cell 131, 861 (2007).

    Article  Google Scholar 

  11. P. Karagiannis, K. Takahashi, M. Saito, Y. Yoshida, K. Okita, A. Watanabe, et al.,, Physiol. Rev. 99, 79 (2018).

    Article  Google Scholar 

  12. L. Weinberger, M. Ayyash, N. Novershtern, J.H. Hanna, Nat. Rev. Mol. Cell Biol. 17, 155 (2016).

    Article  Google Scholar 

  13. J. Yu, M.A. Vodyanik, K. Smuga-Otto, J. Antosiewicz-Bourget, J.L. Frane, S. Tian, et al.,, Science 318, 1917 (2007).

    Article  ADS  Google Scholar 

  14. J.F. Rabajante, A.L. Babierra, Progr. Biophys, Mol. Biol. 117, 240 (2015).

    Google Scholar 

  15. I. Efroni, Plant Cell Physiol. 59, 696 (2017).

    Article  Google Scholar 

  16. C. Furusawa, K. Kaneko, Biol. Direct 4, 1 (2009).

    Article  Google Scholar 

  17. C.H. Waddington, The strategy of the genes. A discussion of some aspects of theoretical biology. With an appendix by H. Kacser. (1957), pp. ix+-262 .

  18. J.E. Ferrell, Curr. Biol. 22, R458 (2012).

    Article  Google Scholar 

  19. T.L. Davis, I. Rebay, Dev. Biol. 421, 93 (2017).

    Article  Google Scholar 

  20. S. Woodhouse, N. Piterman, C.M. Wintersteiger, B. Göttgens, J. Fisher, BMC Syst. Biol. 12, 59 (2018).

    Article  Google Scholar 

  21. K. Tsumoto, T. Yoshinaga, H. Iida, H. Kawakami, K. Aihara, J. Theor. Biol. 239, 101 (2006).

    Article  Google Scholar 

  22. Z. Aram, S. Jafari, J. Ma, J.C. Sprott, S. Zendehrouh, V.-T. Pham, Commun. Nonlinear Sci. Numer. Simul. 44, 449 (2017).

    Article  ADS  MathSciNet  Google Scholar 

  23. S.S. Hosseini, F. Nazarimehr, S. Jafari, Int. J. Bifurc. Chaos 27, 1750153 (2017).

    Article  Google Scholar 

  24. T.M. Khlebodarova, V.V. Kogai, S.I. Fadeev, V.A. Likhoshvai, J. Bioinf. Comput. Biol. 15, 1650042 (2017).

    Article  Google Scholar 

  25. M. Beigzadeh, S.H. Golpayegani, Comput. Sci. Eng. Electr. 22, 2492 (2015).

    Google Scholar 

  26. M. Moghtadaei, M.H. Golpayegani, Sci. Iran. 19, 733 (2012).

    Article  Google Scholar 

  27. D. Angeli, J.E. Ferrell, E.D. Sontag, Proc. Natl. Acad. Sci. 101, 1822 (2004).

    Article  ADS  Google Scholar 

  28. J. Ma, J.-H. Gao, C.-N. Wang, J.-Y. Su, Chaos Solitons Fractals 38, 521 (2008).

    Article  ADS  MathSciNet  Google Scholar 

  29. J. Ma, F. Wu, C. Wang, Int. J. Mod. Phys. B. 650251 (2016).

  30. D. Jercog, A. Roxin, P. Bartho, A. Luczak, A. Compte, J. de la Rocha, Elife 6, e22425 (2017).

    Article  Google Scholar 

  31. A.N. Pisarchik, U. Feudel, Phys. Rep. 540, 167 (2014).

    Article  ADS  MathSciNet  Google Scholar 

  32. Q. Lai, X.-W. Zhao, J.-N. Huang, V.-T. Pham, K. Rajagopal, Eur. Phys. J. Special Topics 227, 719 (2018).

    Article  ADS  Google Scholar 

  33. K. Kaneko, T. Yomo, Bull. Math. Biol. 59, 139 (1997).

    Article  Google Scholar 

  34. K. Kaneko, T. Yomo, Proc. R. Soc. London B: Biol. Sci. 267, 2367 (2000).

    Article  Google Scholar 

  35. S. Huang, G. Eichler, Y. Bar-Yam, D.E. Ingber, Phys. Rev. Lett. 94, 128701 (2005).

    Article  ADS  Google Scholar 

  36. S. Majhi, M. Perc, D. Ghosh, Chaos 27, 073109 (2017).

    Article  ADS  MathSciNet  Google Scholar 

  37. L. Kauffman, H. Sabelli, Bios: Creative organization beyond chaos (International Society for Systems Sciences, Atlanta, 1998).

  38. T. Geisel, J. Nierwetberg, Phys. Rev. Lett. 48, 7 (1982).

    Article  ADS  MathSciNet  Google Scholar 

  39. V.I. Arnol’d, Izvestiya Rossiiskoi Akademii Nauk Seriya, Matematicheskaya 25, 21 (1961).

    Google Scholar 

  40. H. Louis, K.H.C. Sabelli, Cybern. Syst. 29, 345 (1998).

    Article  Google Scholar 

  41. L. Kauffman, H. Sabelli, Cybern. Syst. 30, 261 (1999).

    Article  Google Scholar 

  42. F. Nazarimehr, S. Jafari, S.M.R.H. Golpayegani, L.H. Kauffman, Int. J. Bifurc. Chaos 27, 1750201 (2017).

    Article  Google Scholar 

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Authors and Affiliations

  1. Biomedical Engineering Department, Amirkabir University of Technology, Tehran, 15875-4413, Iran

    Fahimeh Nazarimehr & Sajad Jafari

  2. Department of Psychology, Florida International University, Miami, FL, USA

    Seyedeh Sanaz Hosseini

  3. Ministry of Higher Education and Scientific Research, Baghdad, Iraq

    Abdul Jalil M. Khalaf

  4. Department of Physics, University of Wisconsin, Madison, WI, 53706, USA

    Julien C. Sprott

Authors
  1. Fahimeh Nazarimehr
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  2. Seyedeh Sanaz Hosseini
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  3. Abdul Jalil M. Khalaf
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  4. Sajad Jafari
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  5. Julien C. Sprott
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Correspondence to Fahimeh Nazarimehr.

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Nazarimehr, F., Hosseini, S.S., Khalaf, A.J.M. et al. Process equation as a model for the development of cells. Eur. Phys. J. Spec. Top. 229, 921–927 (2020). https://doi.org/10.1140/epjst/e2020-900089-7

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  • DOI: https://doi.org/10.1140/epjst/e2020-900089-7

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