Biomedical Engineering Reference
In-Depth Information
was first introduced by Lee and Heinrich [
53
] and further extended and analyzed by
others (see review by [
46
]). The Notch pathway was also mathematically modeled
[
2
]. However, to our knowledge, the model presented in [
5
,
44
] is the first model
that specifically merges these pathways together. The approach used in this model
is supported by recent information about crosstalk between the pathways [
83
].
The model of a single BCSC [
5
,
44
] was built on the basis of the above biological
information. It comprises descriptions of the Wnt, Notch, and E-cadherin pathways,
including feedback loops and crosstalk between the pathways. This intracellular
network was implemented [
5
] within a tissue model, where SCs and non-SCs are
interconnected through signals in the microenvironment. The CA tissue model is
similar to that described in the previous section (Sect.
5.3
), except that the SC
decision to differentiate and its decision to enter the proliferation cycle are not
simply a function of numbers of neighbor cells. Rather, these decisions are dictated
deterministically by accumulation of proliferation factors (PF) and differentiation
factors (DF) above certain thresholds (
C
P
and
C
M
, respectively). These factors are
quantitatively estimated for each SC, taking into account the specific inter-cellular
signal intensities, as illustrated in the scheme shown in Fig. 5 [
5
].
In [
5
,
44
], the intracellular processes in a BCSC are modeled according to the
following assumptions: activated LEF/TCF transcription factors (denoted in the
equations as
L
) encourage proliferation by increasing PF levels (denoted as
P
).
The activation of LEF/TCF is positively controlled by the Wnt signal intensity
(denoted as
S
) and negatively controlled by the E-cadherins, which are bound to
E-cadherins in neighboring cells. (The levels of total and bound E-cadherins are
denoted as
E
and
E
b
, respectively.) E-cadherin synthesis is negatively regulated by
Wnt signal intensity. The Wnt pathway is assumed to be activated by the Wnt ligand
(
W
) in the close environment of the cell, while Dkk1 proteins (
D
) form a negative
feedback loop on the pathway, since their secretion is enhanced as a function of the
signal intensity, and they in turn inhibit the Wnt signal [
16
]. The Notch pathway
is activated by Notch receptors (
N
) binding to DSL proteins in neighboring cells,
which are assumed to be expressed by every cell in the model at a constant level.
An activated Notch receptor stimulates a sequence of molecular events that increases
Hes protein (
H
) synthesis, which inhibits cell differentiation by reducing
DF
(
M
).
The Notch pathway is also regulated by a positive feedback loop, as LEF/TCF
inhibits the degradation of the Notch receptor [
41
].
On the basis of these assumptions, a hybrid model was constructed, where cells
in the tissue were represented as automata cells, while the intracellular realm of
each SC in the tissue model was described by an ODE model of the protein-
protein interactions in the Wnt and Notch signaling pathways. The ODE system
is as follows:
f
F
W
t
(
f
S
D
t
(
S
(
t
)=
t
)
·
t
)
(7)
D
f
D
(
=
L
)
−
μ
D
·
D
(8)
L
f
L
(
=
S
·
E
b
)
−
μ
L
·
L
(9)
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