Biomedical Engineering Reference
In-Depth Information
Wnt(
W
)
Dkk1(
D
)
Bound
E-Cadherins(
E
)
Stem Cell
LEF/TCF
(
L
)
PF(
P
)
Stem Cell
P
>
C
P
DF(
M
)
Hes(
H
)
Notch(
N
)
DSL(
N
l
)
Proliferation
M
>
C
M
Differentiation
Fig. 5
Schematic representation of the mathematical model of an SC fate decision, regulated
by signals in the cell's microenvironment. In this model, the SC's decision to proliferate and to
differentiate is caused by the accumulation of proliferation and differentiation factors (PF and DF),
respectively, above certain thresholds (
C
P
and
C
M
, respectively). The regulation of these factors
by Wnt, Notch, and E-cadherin signaling pathways is represented, including feedback loops and
crosstalk between the pathways. The role of the proteins Wnt, Dickkopf1 (Dkk1), LEF/TCF and
Hes and of the cell-surface receptors Notch, Delta, Serrate, Lag-2 (DSL) and E-cadherin in these
pathways is demonstrated, using pointed arrows (
)
to represent inhibition. Neighboring cells increase the levels of Wnt, E-cadherins, and Notch-DSL
bindings. A stem neighbor may also increase Dkk1 levels. The threshold-dependent effects of PF
and DF, respectively, on the SC fate decision are also shown (
dashed arrows
). Notation for the
level of every factor/protein, as used in the equations, is written in parentheses [
5
]
→
) to represent activation and blunt arrows (
E
f
E
(
=
S
)
−
μ
E
·
E
(10)
max
E
b
,
i
(
E
b
,
i
(
)=
)
,
t
(
k
b
·
(
)
·
(
))
t
0
max
τ
≤
E
t
E
i
t
(11)
f
P
(
P
=
L
)
−
μ
P
·
P
(12)
f
N
(
N
=
p
N
−
L
)
·
N
(13)
f
H
(
H
=
N
r
)
−
μ
H
·
H
(14)
f
M
(
M
=
H
)
−
μ
M
·
M
,
(15)
where the dependence of each protein on another protein is described using a
sigmoid-shaped Hill function of the form:
f
a
m
x
m
u
·
+
v
·
x
m
. Different functions
(with different parameters
u
,
v
,
a
,
m
for each, which determine the exact shape
(
x
)=
a
m
+
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