15 Glycolytic Oscillations in Cancer Cells
251
Furthermore, prostate cancer cells are reported to show “reverse Warburg effect” in
which cancer-associated fibroblasts (CAFs) undergo aerobic glycolysis to produce
lactate, which is subsequently used as a metabolic substrate by adjacent cancer cells
in tumour tissues [48].
The above metabolic characteristics in prostate cancer, namely, low glycolytic
activities, were probably represented in the glycolytic oscillations in DU145 cells;
the periods of oscillations were longer and the oscillatory ratio was smaller than those
in HeLa cells, which exhibit the Warburg effect. In addition, prostate cancer has been
reported to have high five-year survival rates, for instance, close to 99% in 2013 in
the US [50]. On the other hand, cervical cancer, whose cell line (HeLa) exhibited
higher glycolytic activities than DU145 cells in the oscillations, was reported to have
five-year survival rates of 67% in 2009 in the US [50]. Thus, we might predict the
malignancy that is directly proportional to glycolytic activities in cancer cells by
using their oscillatory behaviours as a readout.
15.7 Mathematical Model for Glycolytic Oscillations
in Cancer Cells
Many mathematical models have been developed to reproduce glycolytic oscillations
in yeast cells based on the enzymatic reactions in cells. They include minimal models
with two variables [14, 22, 51, 52], those with five to nine variables [58, 61, 62], and
those with extensive mechanistic details [25, 47].
On the other hand, very detailed models for cancer glycolysis were developed
to study the basic cellular physiology such as enzymatic and transport properties
[32, 40, 41]; however, no glycolytic oscillations have been investigated in these
models. A kinetic model was proposed recently to reproduce glycolytic oscillations
of HeLa cells qualitatively [39]. The importance of interaction between glycolysis
and mitochondria was also pointed out [34].
We developed a simple mathematical model, as shown in Fig. 15.4, to describe the
heterogeneities in glycolytic oscillations in HeLa cells [4]. It is a six-variable model,
simple enough to be applied for a mathematical analysis and capture the core of
the glycolytic pathway and the activity of the glucose transporter (GLUT). We have
succeeded in quantitatively simulating the heterogeneous oscillatory behaviours by
considering the variations in the rate constants for the enzymatic reactions and the
flux of glucose uptake through GLUT.
Briefly, it considers the upstream (ATP-consuming) reactions of hexose and the
downstream (ATP-producing) reactions of triose. Allosteric reactions of PFK and
pyruvate kinase (PK) represent the upstream and downstream reactions, respectively.
This model describes Michaelis–Menten type mechanisms for the PFK and PK reactions, and a first-order reaction for the consumption of ATP and the final product [4].
It also considers the uptake of glucose into the cells through GLUT. Glucose uptake
is reported to enhance glycolysis more than 20-fold in HeLa cells under glucose
251
Furthermore, prostate cancer cells are reported to show “reverse Warburg effect” in
which cancer-associated fibroblasts (CAFs) undergo aerobic glycolysis to produce
lactate, which is subsequently used as a metabolic substrate by adjacent cancer cells
in tumour tissues [48].
The above metabolic characteristics in prostate cancer, namely, low glycolytic
activities, were probably represented in the glycolytic oscillations in DU145 cells;
the periods of oscillations were longer and the oscillatory ratio was smaller than those
in HeLa cells, which exhibit the Warburg effect. In addition, prostate cancer has been
reported to have high five-year survival rates, for instance, close to 99% in 2013 in
the US [50]. On the other hand, cervical cancer, whose cell line (HeLa) exhibited
higher glycolytic activities than DU145 cells in the oscillations, was reported to have
five-year survival rates of 67% in 2009 in the US [50]. Thus, we might predict the
malignancy that is directly proportional to glycolytic activities in cancer cells by
using their oscillatory behaviours as a readout.
15.7 Mathematical Model for Glycolytic Oscillations
in Cancer Cells
Many mathematical models have been developed to reproduce glycolytic oscillations
in yeast cells based on the enzymatic reactions in cells. They include minimal models
with two variables [14, 22, 51, 52], those with five to nine variables [58, 61, 62], and
those with extensive mechanistic details [25, 47].
On the other hand, very detailed models for cancer glycolysis were developed
to study the basic cellular physiology such as enzymatic and transport properties
[32, 40, 41]; however, no glycolytic oscillations have been investigated in these
models. A kinetic model was proposed recently to reproduce glycolytic oscillations
of HeLa cells qualitatively [39]. The importance of interaction between glycolysis
and mitochondria was also pointed out [34].
We developed a simple mathematical model, as shown in Fig. 15.4, to describe the
heterogeneities in glycolytic oscillations in HeLa cells [4]. It is a six-variable model,
simple enough to be applied for a mathematical analysis and capture the core of
the glycolytic pathway and the activity of the glucose transporter (GLUT). We have
succeeded in quantitatively simulating the heterogeneous oscillatory behaviours by
considering the variations in the rate constants for the enzymatic reactions and the
flux of glucose uptake through GLUT.
Briefly, it considers the upstream (ATP-consuming) reactions of hexose and the
downstream (ATP-producing) reactions of triose. Allosteric reactions of PFK and
pyruvate kinase (PK) represent the upstream and downstream reactions, respectively.
This model describes Michaelis–Menten type mechanisms for the PFK and PK reactions, and a first-order reaction for the consumption of ATP and the final product [4].
It also considers the uptake of glucose into the cells through GLUT. Glucose uptake
is reported to enhance glycolysis more than 20-fold in HeLa cells under glucose