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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. 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.
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    3. Lucia, Umberto, 2013. "Thermodynamics and cancer stationary states," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(17), pages 3648-3653.
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    5. 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.
    6. 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.
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