very high levels of OCT4 expression lead to loss of stemness, to
determine if a certain EMT-associated phenotype can acquire stemness, one can define a “stemness window”—range of expression
levels of OCT4 for which a cell can acquire stemness.
EMT-associated phenotypes that overlap with this stemness window can then acquire stemness. This overlap, and thus the set of
EMT-associated phenotypes that can acquire stemness can be
modulated by varying the strength of the coupling between the
two regulatory units. This coupling is modeled via two parameters—α 1 , the maximum fold change in the expression level of
LIN28 that miR-200 can cause, and α 2 , the maximum fold change
in the expression level of ZEB that let-7 can cause. Since miR-200
inhibits LIN28 and let-7 inhibits ZEB, 0
α 1 , α 2
1. A fold
change close to 1 indicates weak coupling while a fold change close
to 0 indicates strong coupling.
When there is no coupling between the two regulatory units
(α 1 ¼ 1, α 2 ¼ 1), cells can exhibit three distinct phenotypes associated with the EMT circuit (epithelial, mesenchymal, and hybrid
E/M) provided the concentration of the EMT-driver SNAIL is
within the range for which the EMT circuit can exhibit
tri-stability. Cells can further exhibit three distinct phenotypes
corresponding to the stemness circuit (low LIN28, high LIN28,
and intermediate LIN28). Thus, 9 (3 Â 3) total phenotypes are
possible. This number decreases when the strength of the coupling
between the circuits is increased. Which of the EMT-associated
phenotypes exist within the stemness window depends on the
relative values of α 1 and α 2 . When both α 1 and α 2 are close to
1 (weak coupling), all three EMT-associated phenotypes lie within
the “stemness window” and thus can acquire stemness. Upon
decreasing α 1 , the stemness window shifts toward the mesenchymal
phenotype. Epithelial cells can no longer acquire stemness in this
scenario. When α 2 is decreased while keeping α 1 close to 1, the
stemness window shifts toward the epithelial phenotype and mesenchymal cells cannot acquire stemness with such a coupling
between the regulatory units. The different scenarios have been
illustrated in Fig. 9.
The total number of phenotypes that may be exhibited by cells
in a population will further depend on the concentration of SNAIL.
For example, when the SNAIL concentration is very high, cells can
only exhibit the mesenchymal phenotype. These mesenchymal cells
can then acquire stemness provided the “stemness window” overlaps with the mesenchymal phenotype. Similarly, very low concentrations of SNAIL will lead to cells in the population exhibiting
only the epithelial phenotype. In such a scenario, two distinct
phenotypes may be acquired by tumor cells in the population—
epithelial stem-like and epithelial non-stem-like. The number of
phenotypes exhibited can further be tuned by varying the concentration of NF-κB which activates the expression of both LIN28 and
Mathematical Modelling of EMT
407
determine if a certain EMT-associated phenotype can acquire stemness, one can define a “stemness window”—range of expression
levels of OCT4 for which a cell can acquire stemness.
EMT-associated phenotypes that overlap with this stemness window can then acquire stemness. This overlap, and thus the set of
EMT-associated phenotypes that can acquire stemness can be
modulated by varying the strength of the coupling between the
two regulatory units. This coupling is modeled via two parameters—α 1 , the maximum fold change in the expression level of
LIN28 that miR-200 can cause, and α 2 , the maximum fold change
in the expression level of ZEB that let-7 can cause. Since miR-200
inhibits LIN28 and let-7 inhibits ZEB, 0
α 1 , α 2
1. A fold
change close to 1 indicates weak coupling while a fold change close
to 0 indicates strong coupling.
When there is no coupling between the two regulatory units
(α 1 ¼ 1, α 2 ¼ 1), cells can exhibit three distinct phenotypes associated with the EMT circuit (epithelial, mesenchymal, and hybrid
E/M) provided the concentration of the EMT-driver SNAIL is
within the range for which the EMT circuit can exhibit
tri-stability. Cells can further exhibit three distinct phenotypes
corresponding to the stemness circuit (low LIN28, high LIN28,
and intermediate LIN28). Thus, 9 (3 Â 3) total phenotypes are
possible. This number decreases when the strength of the coupling
between the circuits is increased. Which of the EMT-associated
phenotypes exist within the stemness window depends on the
relative values of α 1 and α 2 . When both α 1 and α 2 are close to
1 (weak coupling), all three EMT-associated phenotypes lie within
the “stemness window” and thus can acquire stemness. Upon
decreasing α 1 , the stemness window shifts toward the mesenchymal
phenotype. Epithelial cells can no longer acquire stemness in this
scenario. When α 2 is decreased while keeping α 1 close to 1, the
stemness window shifts toward the epithelial phenotype and mesenchymal cells cannot acquire stemness with such a coupling
between the regulatory units. The different scenarios have been
illustrated in Fig. 9.
The total number of phenotypes that may be exhibited by cells
in a population will further depend on the concentration of SNAIL.
For example, when the SNAIL concentration is very high, cells can
only exhibit the mesenchymal phenotype. These mesenchymal cells
can then acquire stemness provided the “stemness window” overlaps with the mesenchymal phenotype. Similarly, very low concentrations of SNAIL will lead to cells in the population exhibiting
only the epithelial phenotype. In such a scenario, two distinct
phenotypes may be acquired by tumor cells in the population—
epithelial stem-like and epithelial non-stem-like. The number of
phenotypes exhibited can further be tuned by varying the concentration of NF-κB which activates the expression of both LIN28 and
Mathematical Modelling of EMT
407