Biology Reference
In-Depth Information
There are three pairs of opposing (mutually inhibiting) TFs that control binary decisions
at the three levels of pancreas differentiation. The first level of binary branching, between
the exocrine and endocrine lineage, is governed by the opposing pair of the TFs, Ptf1a
--
,
.
Ngn3.
46
The second-level branching is governed in a similar manner by the Pax4
,
--
.
Arx
-cell lineage, respectively.
46
The fate-
determining TFs for the third branching into the
circuit which determines the
β
/
δ
versus the
α
β
δ
cells have not fully been
characterized, but MafA has been shown to bias the decision to establishing the
-cells versus the
β
-cells,
whereas little information is available for the fate-determining factor for the
δ
cells. Thus, for
modeling purposes and for maintaining symmetry, we use a placeholder for the
δ
-cell
determining factor, called
'δ
factor
'
and then assume a third pair of opposing TFs: MafA
,
-
.
δ
factor, governing the determination of
cells, respectively (
Fig. 5.4A
). Below are the
ODEs for the network of regulatory influences described above:
β
versus
δ
x
4
1
x
7
1
x
8
1
x
10
Pdx1
:
x
1
5
_
a
s
k
x
1
1
ξ
1
ð
t
Þ
x
10
2
x
4
1
x
7
1
x
8
1
1
1
x
10
_
Ptf 1a
:
x
2
5
a
k
x
2
1
ξ
2
ð
t
Þ
x
3
2
x
10
1
1
1
x
10
Ngn3
:
x
3
5
_
a
k
x
3
1
ξ
3
ð
t
Þ
x
2
2
x
10
1
1
1
n
x
3
1
x
4
η
_
Pax6
:
x
4
5
a
x
4
2
k
x
4
1
ξ
4
ð
t
Þ
1
η
n
x
3
1
1
n
x
1
η
n
x
3
η
m
Pax4
:
x
5
5
_
a
e
k
x
5
1
ξ
5
ð
t
Þ
x
6
2
x
1
η
x
3
1
1
1
η
m
n
m
x
1
η
n
x
3
η
(5.21)
95
_
Arx
:
x
6
5
a
e
x
5
2
k
x
6
1
ξ
6
ð
t
Þ
1
1
η
m
x
1
η
n
x
3
1
m
x
1
η
n
x
3
x
5
1
x
7
η
MafA
:
x
7
5
_
a
k
x
7
1
ξ
7
ð
t
Þ
x
8
2
x
1
η
x
3
x
5
1
x
7
1
1
1
η
m
n
m
x
1
η
n
x
3
x
5
1
x
8
η
δ
gene
:
x
8
_
a
k
x
8
1
ξ
8
ð
t
Þ
5
x
8
2
1
1
η
m
x
1
η
n
x
3
x
5
1
x
7
1
n
x
6
1
x
9
η
Brn4
:
x
9
5
_
a
k
x
9
1
ξ
9
ð
t
Þ
x
9
2
x
6
1
1
1
η
n
1
_
Hnf 6
:
x
10
5
a
s
k
x
10
1
ξ
10
ð
t
Þ
x
11
2
n
n
x
2
1
1
1
η
ð
x
7
1
x
8
1
x
9
Þ
Maturity
:
x
11
_
m
5
Here, the variables
x
1
to
x
10
represent the expression levels of the 10 key genes involved
in pancreas cell differentiation. Equations represent the regulatory relationship among
these 10 genes, as shown in
Figure 5.4B
. Each equation has three terms which capture the:
(i) production of the gene expression in response to the upstream TFs; (ii) the linear
degradation; and (iii) contribution of the stochastic fluctuations to gene expression.
The production rate for the gene expression change is, as explained in Step 2 above,
a sigmoidal function of its upstream regulators. Hill function-like forms with uniform
exponents
n
(
n
4) were used (more details can be found in
46
).
5
Figure 5.4C
shows the three
of gene expression trajectories during normal
pancreas cell differentiation. The expression of
Hnf6
starts at a high level and gradually
decays, which activates the first switch between
Ptf1a
and
Ngn3
. The nondeterministic
property of stochastic dynamics allows the state trajectory to split into two cell lineages,
'
branchings
'
