Biology Reference
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model: decrease in the peak amplitudes of B, even though an inhibitor is
removed from the system.
3. Infusion of a system node
A typical approach to experimentally investigating the behavior of a
particular endocrine network is to monitor the response to infusion of
one of the system components. For example, if we want to explore the
feedback exerted by GH on its own release, the experimental design
would involve systemic administration of GH. If the infused hormone is
indistinguishable from the endogenously secreted hormone, we have to
estimate the amounts of hormone secreted internally by subtracting the
model-predicted concentration of the infused hormone from the total
measured hormone.
We start with an approximation of the concentration rate of change
of a hormone that is simultaneously secreted and infused. The correct
way to simulate infusion of a hormone, which is also a system node,
would be to add an infusion term to the right-hand side of the
corresponding ODE. This term should correspond to the infusion rate
profile in the real experiment. Mathematically, it might be interpreted as
change in the basal secretion. In terms of the model described by
Eq. (10-14), if we are simulating infusion of hormone B, the
corresponding equation becomes:
dC B
dt ¼b
C B
ð
t
Þþ
S B
ð
C A
ð
t
ÞÞ þ
inf
ð
t
Þ;
(10-20)
where inf(t) is the infusion rate term. The solution of the above equation
is the sum of both endogenous and exogenous concentrations of B. To
follow the distinction explicitly, a new equation should be added to the
system:
dC inf
dt ¼b
C inf
ð
t
Þþ
inf
ð
t
Þ
and C B ð
in all model equations, except
the one that describes the rate of change of the concentration of B.
To sum up, the core equations are:
t
Þ
is replaced by C B ð
t
Þþ
C inf ð
t
Þ
dC A
dt ¼a
C A ð
t
Þþ
S A
C B þ
C inf ð
t
D B Þg
dC B
dt ¼b
C B
ð
t
Þþ
S B
ð
C A
ð
t
ÞÞ
(10-21)
dC inf
dt ¼b
C inf
ð
t
Þþ
inf
ð
t
Þ:
The model defined by Eq. (10-21) is, in essence, a three-node/one-
feedback construct, where exogenous B is the new node. The model
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