Biology Reference
In-Depth Information
C. Simulation of Feedback Experiments
The success of any modeling effort is measured by the model's potential
to reproduce key feedback experiments. We now discuss ways for
modeling the system reaction to certain experimental approaches, aimed
at disclosing specific linkages within endocrine systems. We shall use
reference systems, such as in Figure 10-14, to illustrate the modeling of
three common lab techniques: administration of antibody to one of the
nodes, sensitivity alterations, and infusion of one of the system nodes
(hormones). We examine the corresponding model response and
demonstrate that all of these conditions might disrupt the periodicity of
the system.
1. Changes in sensitivity
Changes in the parameters of the Hill functions approximate alterations
in system sensitivity. In the model from Eq. (10-15), this would
correspond to changes in the threshold or in the Hill coefficient.
Reducing (increasing) a threshold results in sensitivity increase
(decrease). Changes in the Hill coefficient affect the slope of the control
function. In general, increasing the Hill coefficient causes minor
alterations in the frequency and does not disrupt the pulsatility of the
hormones. In contrast, a decrease could effectively obliterate the
oscillations by preventing the system from overshooting its steady state.
E
XERCISE
10-10
Use Eq. (10-17) to show that pulses gradually shrink with:
(a) Decrease of T
A
.
(b) Increase, but not decrease, of T
B
.
Provide a heuristic explanation for the observed changes in model
behavior.
Hint: Show that if T
A
!
0 then C
B
!
b
=b
; and if T
B
!1
then C
A
!
a
=a
.
With appropriate computer software, one can study the specific effect of
increases or decreases n
A
, n
B
, T
A
, and T
B
on the output. For the model
given by Eq. (10-15), for example, investigating the numerical solutions
indicates that:
1. Increases in n
B
and/or n
A
do not disrupt the pulsatility and yield
minor increases in frequency and peak amplitude.
2. Decreases in n
B
or n
A
may alter the output, causing pulse shrinking
and eventually loss of pulsatility.
