Biology Reference
In-Depth Information
This system is capable of generating recurring multiphase volleys by the
mechanism described in Section IV, Part D, as illustrated in Figure 10-27.
In particular, the A/B two-node subsystem, which does not have a
periodic solution if C is taken out of the system, is perturbed by a
delayed system loop via the third node C. This removes the system from
its steady state and drives consecutive pulses during recurrent volleys.
The schematic diagram in the middle left panel of Figure 10-26,
represented by Eq. (10-24), shows that hormone B reduces the secretion
of A both directly and indirectly. The direct down-regulation occurs
with a delay D
1
and corresponds to the left link of the diagram. The
indirect effect of B is caused by up-regulating the secretion of a third
hormone C, with a delay D
2
. This third hormone then down-regulates
the secretion of A. This observation shows that the sequence of nodes
and conduits (B
FIGURE 10-27.
Computer-generated output [concentration of A
(dotted), B (black), and C (dashed)] of the core
system Eq. (10-24).
!
C
!
A
!
B) is essentially a negative two-node
delayed feedback loop: (B
B). Analogous model output can be
achieved by reducing the three-node network to a two-node model with
two feedbacks. Therefore, the system can be modeled by removing C
from the system and introducing a correct delay in the conduit (B
!
A
!
!
A).
The reduced network is the one shown in Figure 10-26, upper left
panel (with, of course, D
2
different from the delay used to describe the
B
!
C
!
A
!
B loop). A corresponding simplified system of delayed
ODEs could be:
dC
A
dt
¼
1
1
3C
A
ð
t
Þþ
10000
3
3
½
C
B
ð
t
0
:
15
Þ=
100
þ
1
½
C
B
ð
t
4
Þ=
10
þ
1
2
dC
B
dt
¼
½
C
A
ð
t
Þ=
500
3C
B
ð
t
Þþ
4000
2
½
C
A
ð
t
Þ=
500
þ
1
(10-25)
and the model output (Figure 10-28) is similar to the hormone profiles
shown in Figure 10-27.
Note that the schematic diagram in Figure 10-26 (upper left panel)
corresponds to a situation where hormone B down-regulates the
secretion of A through two different pathways. Therefore, additionally
reducing the number of conduits in this diagram to obtain a network
representation such as in Figure 10-14 (left panel) may not be possible.
As a broad rule, decisions for reducing the number of nodes or links in
the schematic diagrams should always be considered in the specific
context of the particular physiology that is being investigated.
2000
960
1000
0
480
0
Reducing the number of nodes and, therefore, the number of equations,
from three to two decreases the number of parameters to be determined
and the time needed for solving the equations numerically. This
would be most important if multiple computer runs are required.
Adding the third node to the formal network can only be justified if the
60
70
80
90
100
TIME
FIGURE 10-28.
Computer-generated output [concentration of
A (dashed) and B (black)] of the core system
Eq. (10-25).
