researchers understand the full scope of Warburg’s work [78, 84]
despite its great importance. Altered energy metabolism is proving
to be as widespread in cancer cells as many of the other cancer-
associated traits that have been accepted as hallmarks of cancer
[16]. The regulation of metabolism, relevant to senescence process,
would be a key to improve and identify new anti-cancer therapies in
the future.
In cancerous cells the glycolysis is the main process (see
Eq. (13)). Then according to Luo [77] the affinity of glycolytic
processes yields 52 kcal/mol and 1 mol of glucose produces 2 mol
of ATP. Accordingly, the affinity decrease isAGl¼ 52 7 : 3 fC½kcal=mol glucoseðÞð 33 Þ
In the cancer cell (the modifying factorfCcomes from the
dependence of standard free energy on the pH value of cancerous
cells), namely,fC¼0.83 [85], hence we haveAGl¼ 39 :9 kcal½¼=mol glucoseðÞ 6 :65 kcal½ð=mol OðÞ 2 34 Þ
Taking into account Eq. (10), Eq. (13) can be rewritten asS_iq_Gl
T¼1
TAGlξ_RR ð 35 Þwhereξ_RRis the respiration rate (RR) of cancer cells [86], andTis
the temperature in the physiological conditions used experimen-
tally [87]:T¼310 K. The entropy production rate, Eq. (35), was
determined for 16 human tumor cells from the data reported by
Moreno-Sa ́nchez et al. [88] for the respiration rate for different
cancer cells (seeTable3).
Tumor growth rate is usually characterized by the tumor vol-
ume doubling time (DT). The term DT was introduced 50 years
ago and a graphical method was proposed for its estimation
[89]. The doubling time is the period of time required for a
quantity to double in size or value.
As can be seen in Table3, the entropy production rate exhibits
no global correlation with doubling time. On the other hand, if
similar cells were compared (as HepG2 and Hep 3B or breast
carcinoma cells or leukemia cells) it can observed that the entropy
production rate increases with decreasing tumor volume doubling
time, and so increases tumor aggressiveness.
It is well known [93] that the aneuploid HTB-126 cell line
originated from a human mammary epithelial carcinoma grows
aggressively in soft agar, exhibits invasive properties at in vitro
matrigel outgrowth assays, and causes tumors that extensively
metastasize in immunodeficient nude mice. The human MCF-7
breast epithelial cell line is estrogen receptor positive and retains
many of the biochemical and phenotypic characteristics of normal
mammary epithelial cells. It has only a very limited ability to grow
in soft agar, is noninvasive in matrigel assays, and does not form146 Sheyla Montero et al.