case of a cell division event, I sig concentrations in the daughter
cells are updated using Eq. 5.
3. At the end of the Gillespie update, the concentrations of molecules in each cell in the population are updated. Let Δt be the
time interval between the last Gillespie update and the current
one. Then, the concentrations of molecules can be updated by
integrating the ordinary differential equations for the EMT
regulatory circuit [9] over the time period Δt.
Computer code for simulating the model dynamics can be
downloaded from GitHub (https://github.com/st35/cancerEMT-heterogeneity-noise).
We simulated the model dynamics for populations with
different initial phenotypic compositions. Figure 5 shows how
epithelial-mesenchymal heterogeneity can emerge in a phenotypically homogeneous population over a period of 2 weeks. While
epithelial and mesenchymal populations exhibit fairly stable phenotypic compositions, a hybrid E/M population can quickly give rise
to a mixed population with both epithelial and mesenchymal cells.
Such behavior has been confirmed in populations of mouse prostate
cancer cells [17] and a comparison of experimental dynamics with
the predictions from the model is shown in Fig. 5 (bottom panel).
The model thus shows that random partitioning of parent cell
proteins and RNAs among the daughter cells can generate
epithelial-mesenchymal heterogeneity in a population of cancer
cells. Arising from cell division, this heterogeneity can emerge and
be propagated from a small population, such as the one left after an
anticancer regime. Note that the model proposed here is not sensitive to the choice of the core EMT/MET regulatory circuit. Any
circuit topology can be used within the framework of this model as
long as the circuit dynamics is multi-stable which is a key feature of
EMT regulation.
6 Heterogeneity from Cell–Cell Communication Via Notch Signaling
In addition to the regulatory mechanism at the single-cell level,
cell–cell communication also plays a major role in modulating EMT
[6, 7]. Notch signaling [70, 71] is one such mechanism which
operates via the binding of Notch, a transmembrane receptor, to a
ligand expressed on the surface of a neighboring cell. This binding
event triggers the cleavage of the Notch intracellular domain
(NICD). NICD is then released into the cytoplasm where it can
act as a transcriptional cofactor thereby promoting or inhibiting the
expression of certain genes [70]. Notch signaling between neighboring cells can create varied spatial patterns in a population. The
pattern type depends on the type of Notch ligands that are active in
the population. NICD inhibits the expression of Delta ligands and
Mathematical Modelling of EMT
401
cells are updated using Eq. 5.
3. At the end of the Gillespie update, the concentrations of molecules in each cell in the population are updated. Let Δt be the
time interval between the last Gillespie update and the current
one. Then, the concentrations of molecules can be updated by
integrating the ordinary differential equations for the EMT
regulatory circuit [9] over the time period Δt.
Computer code for simulating the model dynamics can be
downloaded from GitHub (https://github.com/st35/cancerEMT-heterogeneity-noise).
We simulated the model dynamics for populations with
different initial phenotypic compositions. Figure 5 shows how
epithelial-mesenchymal heterogeneity can emerge in a phenotypically homogeneous population over a period of 2 weeks. While
epithelial and mesenchymal populations exhibit fairly stable phenotypic compositions, a hybrid E/M population can quickly give rise
to a mixed population with both epithelial and mesenchymal cells.
Such behavior has been confirmed in populations of mouse prostate
cancer cells [17] and a comparison of experimental dynamics with
the predictions from the model is shown in Fig. 5 (bottom panel).
The model thus shows that random partitioning of parent cell
proteins and RNAs among the daughter cells can generate
epithelial-mesenchymal heterogeneity in a population of cancer
cells. Arising from cell division, this heterogeneity can emerge and
be propagated from a small population, such as the one left after an
anticancer regime. Note that the model proposed here is not sensitive to the choice of the core EMT/MET regulatory circuit. Any
circuit topology can be used within the framework of this model as
long as the circuit dynamics is multi-stable which is a key feature of
EMT regulation.
6 Heterogeneity from Cell–Cell Communication Via Notch Signaling
In addition to the regulatory mechanism at the single-cell level,
cell–cell communication also plays a major role in modulating EMT
[6, 7]. Notch signaling [70, 71] is one such mechanism which
operates via the binding of Notch, a transmembrane receptor, to a
ligand expressed on the surface of a neighboring cell. This binding
event triggers the cleavage of the Notch intracellular domain
(NICD). NICD is then released into the cytoplasm where it can
act as a transcriptional cofactor thereby promoting or inhibiting the
expression of certain genes [70]. Notch signaling between neighboring cells can create varied spatial patterns in a population. The
pattern type depends on the type of Notch ligands that are active in
the population. NICD inhibits the expression of Delta ligands and
Mathematical Modelling of EMT
401