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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
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    References listed on IDEAS

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    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.
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    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.
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