Biomedical Engineering Reference
In-Depth Information
particular that
k
is an increasing function of the concentration
N
of a noxious
chemical [
k
=
k
(
N
)] that is secreted by
E
at rate
s
. (Think of
E
as macrophages,
which require an intracellular but leaky "poison" such as nitric oxide to dispose
of ingested pathogens.) The proliferation rate of
E
is proportional to
P
(the pres-
ence of pathogens induces an immune response); both
E
and
N
are supposed to
have a finite half-life. We will assume that over evolutionary time immune sys-
tems that are described by our model would evolve to diminish the average harm
E that the body sustains by the joint presence of pathogens and noxious chemi-
cal. Suppose for simplicity that the rate of doing harm to the body by pathogens
P
and noxious chemical
N
is simply
h
P
P
+
h
N
N
, where
h
P
and
h
N
are constants.
The equations of this model are given in the Appendix. There the simplifying
assumption is made that
k
(
N
) =
aN
, where
a
is a constant.
Computer simulations of the model demonstrate that there is a rate of secre-
tion
s
* that minimizes E (4). If its secretion rate
s
is too large, noxious chemical
N
causes great harm; if
s
is too small, pathogens
P
are not controlled. Accord-
ingly, one indeed expects the existence of an optimal secretion rate
s
*. But
s
*
depends on the parameters of the model, particularly pathogen growth rate
r
.
The faster the pathogen grows (the bigger
r
) the more noxious chemical
N
should be secreted to kill them, in spite of the harm done by
N
. Consequently,
in the face of the shifting nature of the pathogen population, no "top-down"
fixed choice of the secretion rate
s
can provide effective and economical im-
mune response. Analogous difficulties are faced in selecting immune responses
of other types.
One way to deal with the difficulty is to evolve an immune system that can
detect telltale signs of a variety of pathogens and hence deal suitably with the
different types (6,7). In view of the fast mutability of which many pathogens are
capable, I have suggested that this "reflexive" response must be supplemented
by an ability to sense how well the response is working and to alter it in view of
this sensory information. As will now be shown, our simple model of the action
of a noxious but essential chemical
N
can be modified to illustrate the issues.
3.3. Chemicals that Supply Information Concerning Progress
toward Conflicting Goals
In our modified model, we shall assume that evolution has selected immune
systems that can be characterized by just two goals: killing harmful pathogens
and avoiding harm to self generated by the immune system. These goals are
partially contradictory; the pathogen-destroying inflammatory process harms the
host. In particular, intracellular pathogens are fought by destroying the cells
where the pathogens reside. Suppose that information is available concerning
immune performance in the form of a kill chemical
K
(whose presence is associ-
ated with pathogen destruction) and a harm chemical
H
(whose presence is asso-
ciated with harm to the host). Possible kill indicators
K
include N-formyl
peptides, palindromic DNA sequences, CD-1 ligating intracellular fragments
