Biology Reference
In-Depth Information
stronger the presence of B, the lower the secretion of A, and the function
S
A
;
system
will be monotone decreasing. Monotone increase represents
positive control, and monotone decrease represents negative control.
Finally, the control function should be chosen to ensure that the
concentration C
A
will remain within its physiological range—between
the minimal and maximal possible concentrations of hormone A.
ð
C
B
Þ
From a physiological perspective, in order for a molecule of hormone B
to exert its effect, it should bind to a specific receptor on the cell that
produces and releases hormone A. As we saw in Chapter 7, hormone-
receptor interactions obey laws of mass action, and the dissociation
constant for the corresponding chemical reaction determines the affinity
of the receptor for its ligand (hormone B). The higher the affinity of the
receptor, the lower the hormone concentration required to elicit biological
response. Sometimes, we say that changes in affinity (or in sensitivity)
modulate the potency (power to produce the desired effect) of the
hormone. On the other side, the efficacy (responsiveness; maximal effect
that can be produced) of a hormone depends, among other things, on the
number of receptors. This number may vary under different physiological
conditions and affect the level of the response, but, generally, not the
affinity. Therefore, it is desirable that the control function S
A
;
system
Þ
explicitly embodies parameters corresponding to potency and efficacy.
ð
C
B
These properties of S
A
;
system
ð
C
B
Þ
can be represented in a mathematical
form by assuming that S
A
;
system
, where the parameter a
represents the efficacy of hormone B, and F is a properly chosen,
normalized (efficacy
ð
C
B
Þ¼
aF
ð
C
B
Þ
¼
1) version of the control function. The desired
criteria regarding S
A
;
system
will now be satisfied if the following
requirements are imposed on the normalized function:
ð
C
B
Þ
1. 0
F
ð
C
B
Þ
1
;
2. F is monotone; and
3. F includes parameters that correspond to the potency of the action
of B.
Among the various different functions satisfying the above properties,
many authors choose to use the following nonlinear, sigmoid functions,
known as up- and down-regulatory Hill functions to describe positive and
negative hormone relationships:
8
<
n
C
n
½
C
=
T
1
¼
ð
up
Þ
n
½
C
=
T
þ
C
n
þ
T
n
F
up
ð
down
Þ
ð
C
Þ¼
(10-5)
or
:
T
n
1
1
¼
ð
down
Þ:
n
½
C
=
T
þ
C
n
þ
T
n
As a justification for the name, consider the Hill equation given by
Eq. (4-8) of Chapter 4, which was derived based on the presumed
