Biology Reference
In-Depth Information
the hormone concentration profile, the direct delay in this feedback must
be shorter than the interpulse interval.
We now briefly discuss some features of abstract endocrine networks
incorporating more than one delayed feedback loop. We shall consider
networks with two (delayed) feedback loops, and where each loop
accounts for its own oscillatory mechanism. Examples of two-feedback
constructs are shown in Figure 10-26.
Note that each of the two three-node networks, shown in the middle
panels of Figure 10-26, could be reduced to its corresponding two-node
network from the top panels of Figure 10-26. For example, consider
the three-node/two-feedback network shown in Figure 10-26, middle
left panel. Assuming that both B and C can fully suppress the release of
A (that is, when no basal secretion of A is assumed), we can describe
the formal network by the system of delayed ODE:
dC
A
dt
¼
1
1
ð
Þþ
3C
A
t
10000
3
3
½
C
B
ð
t
0
:
15
Þ=
100
þ
1
½
C
C
ð
t
Þ=
70
þ
1
2
½
ð
Þ=
dC
B
dt
¼
C
A
t
500
3C
B
ð
t
Þþ
4000
(10-24)
2
½
C
A
ð
t
Þ=
500
þ
1
2
dC
C
dt
¼
½
C
B
ð
t
4
Þ=
200
8C
C
ð
t
Þþ
13200
1
:
2
½
C
B
ð
t
4
Þ=
200
þ
(
−
)
(
−
)
(
−
)
(+)
A
A
D
2
D
1
(+)
D
1
(
−
)
D
2
B
B
(
−
)
(
−
)
(
−
)
(
−
)
C
A
A
C
(+)
(+)
D
2
D
1
D
1
(+)
(+)
D
2
B
B
(
−
)
(+)
A
C
D
2
(+)
D
1
(
−
)
(+)
B
FIGURE 10-26.
Examples of hypothetical endocrine networks with more than one delayed feedback loop. In addition
to the connections shown, all hormones are subject to elimination. (Reprinted from Farhy, L. S.
[2004]. Modeling of oscillations in endocrine networks with feedback, Methods in Enzymology, 384,
54-81. Copyright 2004, with permission from Elsevier.)
