IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v486y2017icp762-771.html
   My bibliography  Save this article

Phase transitions in tumor growth: V what can be expected from cancer glycolytic oscillations?

Author

Listed:
  • Martin, R.R.
  • Montero, S.
  • Silva, E.
  • Bizzarri, M.
  • Cocho, G.
  • Mansilla, R.
  • Nieto-Villar, J.M.

Abstract

Experimental evidence confirms the existence of glycolytic oscillations in cancer, which allows it to self-organize in time and space far from thermodynamic equilibrium, and provides it with high robustness, complexity and adaptability. A kinetic model is proposed for HeLa tumor cells grown in hypoxia conditions. It shows oscillations in a wide range of parameters. Two control parameters (glucose and inorganic phosphate concentration) were varied to explore the phase space, showing also the presence of limit cycles and bifurcations. The complexity of the system was evaluated by focusing on stationary state stability and Lempel–Ziv complexity. Moreover, the calculated entropy production rate was demonstrated behaving as a Lyapunov function.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:486:y:2017:i:c:p:762-771
    DOI: 10.1016/j.physa.2017.06.001
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437117306404
    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.2017.06.001?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. 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.
    2. 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.
    3. Lucia, Umberto, 2013. "Thermodynamics and cancer stationary states," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(17), pages 3648-3653.
    4. Lucia, Umberto & Ponzetto, Antonio & Deisboeck, Thomas S., 2015. "A thermodynamic approach to the ‘mitosis/apoptosis’ ratio in cancer," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 436(C), pages 246-255.
    5. Giuliani, Alessandro & Colafranceschi, Mauro & Webber, Charles L & Zbilut, Joseph P, 2001. "A complexity score derived from principal components analysis of nonlinear order measures," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 301(1), pages 567-588.
    6. Lucia, Umberto & Ponzetto, Antonio & Deisboeck, Thomas S., 2016. "Investigating the impact of electromagnetic fields on human cells: A thermodynamic perspective," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 443(C), pages 42-48.
    7. Lucia, Umberto, 2014. "Transport processes in biological systems: Tumoral cells and human brain," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 393(C), pages 327-336.
    8. Izquierdo-Kulich, E. & Rebelo, I. & Tejera, E. & Nieto-Villar, J.M., 2013. "Phase transition in tumor growth: I avascular development," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(24), pages 6616-6623.
    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. 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.
    2. Lucia, Umberto, 2014. "Thermodynamic approach to nano-properties of cell membrane," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 407(C), pages 185-191.
    3. Lucia, Umberto, 2014. "Entropy generation and cell growth with comments for a thermodynamic anticancer approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 406(C), pages 107-118.
    4. 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.
    5. Lucia, Umberto, 2014. "Entropy generation approach to cell systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 406(C), pages 1-11.
    6. 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.
    7. 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.
    8. Umberto Lucia, 2014. "The Gouy-Stodola Theorem in Bioenergetic Analysis of Living Systems (Irreversibility in Bioenergetics of Living Systems)," Energies, MDPI, vol. 7(9), pages 1-23, September.
    9. Belaire-Franch, Jorge, 2004. "Testing for non-linearity in an artificial financial market: a recurrence quantification approach," Journal of Economic Behavior & Organization, Elsevier, vol. 54(4), pages 483-494, August.
    10. Lucia, Umberto, 2014. "Transport processes in biological systems: Tumoral cells and human brain," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 393(C), pages 327-336.
    11. Kohestani, Havva & Totonkuban, Mahbubeh & Di Paola, Luisa & Todde, Virginia & Giuliani, Alessandro, 2018. "The basic principles of topology-dynamics relations in networks: An empirical approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 508(C), pages 584-594.
    12. Baggio, Rodolfo, 2015. "Looking into the future of complex dynamic systems," MPRA Paper 65549, University Library of Munich, Germany.
    13. González-Solís, José Luis & Guizar-Ruiz, Juan Ignacio & Martínez-Espinosa, Juan Carlos & Martínez-Zerega, Brenda Esmeralda & Juárez-López, Héctor Alfonso & Vargas-Rodríguez, Héctor & Gallegos-Infante,, 2016. "Cancer detection based on Raman spectra super-paramagnetic clustering," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 455(C), pages 52-64.
    14. Llanos-Pérez, J.A. & Betancourt-Mar, A. & De Miguel, M.P. & Izquierdo-Kulich, E. & Royuela-García, M. & Tejera, E. & Nieto-Villar, J.M., 2015. "Phase transitions in tumor growth: II prostate cancer cell lines," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 426(C), pages 88-92.
    15. Dünki, R.M. & Dressel, M., 2006. "Statistics of biophysical signal characteristics and state specificity of the human EEG," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 370(2), pages 632-650.
    16. Lucia, Umberto, 2016. "Electromagnetic waves and living cells: A kinetic thermodynamic approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 461(C), pages 577-585.
    17. Miranda, Luiza M.S. & Souza, Andre M.C., 2023. "Fractality in tumor growth at the avascular stage from a generalization of the logistic-Gompertz dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 618(C).
    18. Alessandro Giuliani & Alessandro Vici, 2024. "On the (Apparently) Paradoxical Role of Noise in the Recognition of Signal Character of Minor Principal Components," Stats, MDPI, vol. 7(1), pages 1-11, January.

    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:486:y:2017:i:c:p:762-771. 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.