Systems Biology (Methods in Molecular Biology)

emergence of limit cycle, and then through a cascade of bifur-

cations type saddle-foci Shilnikov’s bifurcation.

2. The entropy production rate may be used as a quantitative
   index of the metastatic potential of tumors.


3. A relationship between the production of entropy per unit
   time, the fractal dimension, and the tumor growth rate for
   human tumors cells has been derived.


4. In cancer glycolysis under hypoxia conditions, the entropy
   production rate is higher than the entropy production rate of
   normoxia that means more complexity and robustness. This
   conduces to the thesis that the employ of any type of therapy
   should be in normoxia conditions.


5. The total entropy production rate that is shown by cancer
   glycolysis in the hypoglycemic phenotype is greater than
   those of the other states. In fact, this metabolic condition
   exhibits more robustness.


6. A kinetic model is proposed using experimental data for HeLa
   tumor cells grown in hypoxia conditions which confirms the
   existence of glycolytic oscillations in cancer. This allows it to
   self-organize in time and space far from thermodynamic equi-
   librium, and provides it with high robustness, complexity, and
   adaptability. Glycolytic oscillations in cancer emerge through
   an Andronov-Hopf bifurcation as a “first order” phase transi-
   tion, and could be called “biologic phase transition.”

We hope to provide a better understanding of the dynamics of

the growth of cancerous tumors, resulting in better and more

effective therapies.

Acknowledgments

Prof. Dr. A. Alzolain memoriam. We would like to thank Prof.

M. Bizzarri for inviting us to write the Chapter. We would like to

thank E. Silva for aiding us with illustrations; we would also like to

thank the rest of our colleagues M. D. Mesa, D. J. Rodriguez,

I. Dura ́n, J. C. Jaime, and J. P. Pomuceno.

References

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2. Schmitz U, Wolkenhauer O (2016) Systems
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164 Sheyla Montero et al.