just two reports related to cancer glycolytic oscillations
[147, 148]. Despite the low existing information about this aspect,
we can assume as a hypothesis that cancer glycolysis is a self-
organized process far from thermodynamics equilibrium. In other
words, sustained oscillations in cancer glycolysis grant high robust-
ness and complexity. Consequently, a strategy aimed at exploiting
abnormalities in cancer glycolytic therapies would be focused on
recognizing those regions in which control parameters lead to a loss
in self-organization.
The first developed glycolysis models were made taking yeast as
experimental reference. Glycolysis in yeast exhibits periodic and
aperiodic oscillations [149]. In 1964, Higgins [150] proposed a
general oscillatory mechanism for yeast glycolytic intermediaries.
Higgins’ model has six reactions, with PFK in the center showing
this enzyme great oscillatory potential in yeast.
Sel’kov in 1968 [151] refers again to PFK oscillations, by using
a simple model of a monosubstrate enzymatic reaction with sub-
strate inhibition and product activation. In 1981, Termonia and
Ross proposed a glycolysis model for yeast, slightly more extensive,
which beholds the coupling between PFK and PYK and takes into
consideration the inhibition of the latest [152].
In 1982, Decroly and Goldbeter [153] established a model
describing the coupling between two allosteric enzymes E 1 and
E 2 activated by their own products. This model embraces a series
of different cases of stationary state stability, including complex
behaviors, periodic oscillations, and chaotic behavior. However,
that model is a generic one, intended for no specific biological
system. Although it refers to PFK and PYK as an example of
enzymes, that model is unable in portraying cancer as it does not
consider PYK’s inhibition by ATP.
In the 1990s, several models aroused, all of them referring to
oscillations in yeast cells [154–156], where the glycolytic mecha-
nism is in deep investigated alongside with its oscillatory behavior.
As noted before, in cancer, although there is proof of the
existence of oscillations [63, 148], to this moment, there is no
such model that, at least qualitatively, reproduces oscillatory behav-
ior in glycolysis, which would help in understanding the observed
robustness and complexity.
Based on the evidence discussed above, we propose a model
based on a simple biochemical network to describe the dynamics of
glycolytic oscillations in HeLa cancer cell lines (seeFig. 12).
The model is based on six reactions that are named after their
enzymes: HK, PFK, GAPDH, PYK, ATPase, and LDH. These
reactions have been selected by a sensitivity analysis and entropy
production rate method [106, 157], according to the glycolytic
mechanism proposed by Marı ́n et al. [140] for HeLa tumor cells.
The reactions identified as HK, PFK, and PYK are known as control
points due to their condition of allosteric enzymes, which regulateParameters Estimation in Phase-Space Landscape Reconstruction of Cell Fate... 159