Biomedical Engineering Reference
In-Depth Information
H
=
c
h
(
h
p
P
+
h
N
N
) -
g
h
H
.
[13]
Now harm from the pathogen (
H
p
) is not the same as harm inflicted indirectly
through the immune response (
H
I
). Estimate
H
p
=
H
/(1 +
k
p
N
) and assuming that
H
=
H
I
+
H
p
, then an adaptive
s
coefficient might change according to the
Michaelean rate law:
sKH
2
p
ss
=+
++
.
[14]
1
1
sH
sKH
31
4
p
An immune response making use of multiple sources of feedback information
can operate effectively over a far greater range of parameter values and variable
values than one without. This form of robustness through feedback control is
typical of biological systems.
One caveat to be observed at this point regards the arbitrary nature of the
functional response curves assumed in this model and in others like it. In other
words, constant non-saturating rates of immune effector proliferation and patho-
gen replication. To what extent is feedback destabilized by increasing nonlin-
earities in response functions? The purpose of these models is often concerned
with "proof of principle," establishing the plausibility of intuitive notions of con-
trol, rather than empirical fitting of experimental data.
4.3.2. Barkai and Leibler's Chemotaxis Network
Feedback is no less important in regulating reactions within a cell as among
populations of cells. As with variation in pathogen parameters in populations,
there can as easily be variation in inputs to a cell. This means that fine-tuning
parameters in advance (through evolution) to maximize a function for fixed pa-
rameters is likely to be far from robust.
Chemotaxis in bacteria describes the purposeful motion of bacteria swim-
ming towards increasing concentrations of nutritive chemicals. Bacteria swim in
alternating bouts of
smooth runs
, during which they move along a single vector,
and
tumbling
, during which they randomly reorient to a new vector. An ob-
served property of bacterial chemotaxis is
adaptation
, whereby the steady-state
tumbling frequency in a homogeneous chemical environment is independent of
the concentration of chemical. This is a means of ensuring constant responsive-
ness (3). Barkai and Leibler (5) ask whether feedback circuits in the putative
chemotactic network are responsible for this adaptive property.
A nutritive chemical, or
ligand L
, binds to an enzymatic receptor
E
. The
receptor transitions between a modified and unmodified state at a rate propor-
tional to the concentration of
L
, denoted
l
.
L
represents the input to a cellular
