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Phase transitions in tumor growth VI: Epithelial–Mesenchymal transition

Author

Listed:
  • Guerra, A.
  • Rodriguez, D.J.
  • Montero, S.
  • Betancourt-Mar, J.A.
  • Martin, R.R.
  • Silva, E.
  • Bizzarri, M.
  • Cocho, G.
  • Mansilla, R.
  • Nieto-Villar, J.M.

Abstract

Herewith we discuss a network model of the epithelial–mesenchymal transition (EMT) based on our previous proposed framework. The EMT appears as a “first order” phase transition process, analogous to the transitions observed in the chemical–physical field. Chiefly, EMT should be considered a transition characterized by a supercritical Andronov–Hopf bifurcation, with the emergence of limit cycle and, consequently, a cascade of saddle-foci Shilnikov’s bifurcations. We eventually show that the entropy production rate is an EMT-dependent function and, as such, its formalism reminds the van der Waals equation.

Suggested Citation

  • Guerra, A. & Rodriguez, D.J. & Montero, S. & Betancourt-Mar, J.A. & Martin, R.R. & Silva, E. & Bizzarri, M. & Cocho, G. & Mansilla, R. & Nieto-Villar, J.M., 2018. "Phase transitions in tumor growth VI: Epithelial–Mesenchymal transition," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 499(C), pages 208-215.
    • Handle: RePEc:eee:phsmap:v:499:y:2018:i:c:p:208-215
    DOI: 10.1016/j.physa.2018.01.040
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    References listed on IDEAS

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    1. Lucia, Umberto & Grisolia, Giulia & Ponzetto, Antonio & Deisboeck, Thomas S., 2018. "Thermodynamic considerations on the role of heat and mass transfer in biochemical causes of carcinogenesis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 490(C), pages 1164-1170.
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    3. Betancourt-Mar, J.A. & Llanos-Pérez, J.A. & Cocho, G. & Mansilla, R. & Martin, R.R. & Montero, S. & Nieto-Villar, J.M., 2017. "Phase transitions in tumor growth: IV relationship between metabolic rate and fractal dimension of human tumor cells," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 473(C), pages 344-351.
    4. Llanos-Pérez, J.A. & Betancourt-Mar, J.A. & Cocho, G. & Mansilla, R. & Nieto-Villar, José Manuel, 2016. "Phase transitions in tumor growth: III vascular and metastasis behavior," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 462(C), pages 560-568.
    5. Hiroaki Kitano, 2003. "Cancer robustness: Tumour tactics," Nature, Nature, vol. 426(6963), pages 125-125, November.
    6. Anishchenko, V.S. & Vadivasova, T.E. & Okrokvertskhov, G.A. & Strelkova, G.I., 2003. "Correlation analysis of dynamical chaos," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 325(1), pages 199-212.
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