IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v499y2018icp208-215.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437118300700
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2018.01.040?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    2. Lucia, Umberto & Ponzetto, Antonio, 2017. "Some thermodynamic considerations on low frequency electromagnetic waves effects on cancer invasion and metastasis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 467(C), pages 289-295.
    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Martin, R.R. & Montero, S. & Silva, E. & Bizzarri, M. & Cocho, G. & Mansilla, R. & Nieto-Villar, J.M., 2017. "Phase transitions in tumor growth: V what can be expected from cancer glycolytic oscillations?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 486(C), pages 762-771.
    3. Hanshuo Qiu & Xiangzi Zhang & Huaixiao Yue & Jizhao Liu, 2023. "A Novel Eighth-Order Hyperchaotic System and Its Application in Image Encryption," Mathematics, MDPI, vol. 11(19), pages 1-29, September.
    4. Lucia, Umberto & Grisolia, Giulia & Francia, Sabrina & Astori, Mariarosa, 2019. "Theoretical biophysical approach to cross-linking effects on eyes pressure," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 534(C).
    5. 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.
    6. Yadati, Yash & Mears, Nicholas & Chatterjee, Atanu, 2020. "Spatio-temporal characterization of thermal fluctuations in a non-turbulent Rayleigh–Bénard convection at steady state," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 547(C).
    7. Olkhov, Victor, 2018. "Expectations, Price Fluctuations and Lorenz Attractor," MPRA Paper 89105, University Library of Munich, Germany.
    8. Carlo Bianca & Marco Menale, 2019. "A Convergence Theorem for the Nonequilibrium States in the Discrete Thermostatted Kinetic Theory," Mathematics, MDPI, vol. 7(8), pages 1-13, July.
    9. Tianhai Tian & Jiangning Song, 2012. "Mathematical Modelling of the MAP Kinase Pathway Using Proteomic Datasets," PLOS ONE, Public Library of Science, vol. 7(8), pages 1-12, August.
    10. Horváth, D. & Brutovsky, B. & Kočišová, J. & Šprinc, S., 2010. "Manipulation with heterogeneity within a species population formulated as an inverse problem," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(21), pages 5028-5036.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:phsmap:v:499:y:2018:i:c:p:208-215. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.