Biology Reference
In-Depth Information
large, reboundlike, GH release (Clark et al. [1988]). An intuitive
explanation of this effect might be that because SRIF suppresses the
secretion, but not the synthesis, during the 4 hours of systemic SRIF
infusion, the releasable pool of GH has increased under persisting
GHRH drive.
To model-test this prediction, it is appropriate to separate, on a network
level, the hormone synthesis and storage from its release. This separation
is important, because major network components affect these processes
in different ways. Let us again consider the network from Figure 10-14
(left panel), in an attempt to explain a rebound release of B following a
withdrawal of continuous infusion of a certain substance C. Assume that
during the infusion of C the release of B was suppressed and we have
evidence that C is not affecting the release of A. A possible explanation
of the rebound phenomenon would be that C affects the release of B, but
not its synthesis. However, because all conduits in the network are
affected in this experiment, the intuitive reconstruction of all processes
involved is not trivial.
One way to model this situation mathematically is to introduce
a so-called storage pool, in which B is synthesized and held for
release and another pool (e.g., the bloodstream) in which B is
secreted. This adds a new equation to the model, describing the
dynamics of the concentration of B in the storage pool. Denote this
concentration by P
B
. The following basic model assumptions would be
appropriate:
Elimination
(-)
A
1. The total concentration of B in the storage pool, P
B
, is positively
affected by the synthesis and negatively affected by the release.
D
(+)
2. The concentration P
B
feedbacks on the synthesis of B and cannot
exceed a certain absolute limit P
max
.
B
Storage
3. The rate of release of B from the storage pool is stimulated by a
high pool concentration, but might be inhibited by the concentra-
tion of B in the bloodstream.
(+)
(-)
C
(+)
B
Secreted
4. B is subjected to elimination only after it is secreted.
Elimination
Next, we construct the schematic diagram incorporating these
assumptions. In the network from Figure 10-14 (left panel), in addition to
A and B, there is a new substance, C, that inhibits the secretion
(competing with A) but does not affect the synthesis and storage of B.
This is shown in Figure 10-24.
FIGURE 10-24.
Formal network that distinguishes between synthesis
and release of hormone B. Hormone A stimulates the
synthesis and secretion of B. A third hormone C
suppresses the release of B, but not its synthesis.
(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.)
Using Eq. (10-13) to approximate a ''competitive'' control function, we
can describe the network with the following system of delayed ordinary
differential equations:
