Biomedical Engineering Reference
In-Depth Information
4.3. Feedback Control in Immune Regulation and Signal Transduction
4.3.1. Segel and Bar-Or's Adaptive Control Model for Immune Effector Action
The immune system is configured so as to maximize damage to pathogens
and minimize damage to
self
. These, however, are not orthogonal goals, and
hence the regulation of infection by the immune system requires feedback con-
trol in order to prevent an overenthusiastic immune response from destroying
healthy tissues.
Segel and Bar-Or (51,52) approach the problem as follows (see also this
volume, Part III, chapter 4, by Segel). Assume a population of immune effector
cells
E
, a population of pathogens
P
and a noxious chemical
N
.
E
are able to kill
P
, as is
N
. However,
N
can also damage the host and thereby compromise pro-
duction of
E
. It is assumed that the immune system seeks to minimize damage to
the host by maximizing the efficiency of the immune response. Damage to the
host E is calculated as the time averaged abundance of
P
and
N
, where damage
from
P
occurs at a rate
h
p
P
and damage from
N
at a rate
h
N
N
. Thus
1
T
¨
E
=
[
hPt
( )
+
hNt dt
( )]
.
[8]
p
N
T
0
Assuming the dynamical system:
N egN
=
,
[9]
N
P
=
rP
aEPN
,
[10]
E
=
EP EE
[
N
(1 /
)
g
].
[11]
p
max
E
where the crucial parameter,
s
, the secretion coefficient of noxious chemicals, in
response to immune activation, is assumed to be under constitutive control by
the host. The function E(
s
) has a unique minimum for any given value of the
pathogen proliferation coefficient
r
, moreover
d
(E(
s
))/
dr
> 0.
The problem for feedback control is to determine the optimal value of
s
for
a variety of pathogens with different proliferation rates. Segel and Bar-Or sug-
gest one way, which requires that the host employ two performance measures: a
kill indicator
chemical,
K
, produced in response to immune activity
NPE
, and a
harm indicator
chemical produced in response to instantaneous damage—
h
p
P
+
h
N
N
. Include these two chemicals in the dynamical system:
K
=
c
k
(
aEPN
) -
g
k
K
,
[12]
