Biomedical Engineering Reference
In-Depth Information
(2) The immune system has architectural features, which include a
single spleen and a single thymus in mammals of differing
size. Thus, at least some components of the immune system
are not modular.
(3) A larger animal lives longer than a smaller one. Hence, its im-
mune system has to do a better job of protecting it.
2.
SCALING LAWS IN IMMUNOLOGY
It has been observed that the average lifespan (
T
0
) of a mammal seems to
scale with its body mass (
M
) according to the scaling law
T
0
~
M
1/4
(cf. (2,3)). A
scaling law between a biological variable
Y
and body mass
M
is written in the
form
Y
~
M
b
, and
b
is called the scaling exponent. This is shorthand for an ap-
proximate, quantitative relation
b
-
Y
M
!
--
A
®
-
,
[1]
Y
M
0
0
where
Y
0
is a standard unit with the same dimension as
Y
,
M
0
is a standard unit of
mass, and
A
is a dimensionless constant. Here we shall take the point of view
that death is generally not due to failure of the immune system, and thus the
mammalian immune system should be designed in such a way that it can protect
an organism during a lifetime
T
0
~
M
1/4
.
If the immune system of a larger animal must help keep that animal alive
for longer periods than the immune system of a smaller animal, it must be more
reliable. A larger animal has more B and T lymphocytes. This implies either
more lymphocyte clones or more cells per clone, or both. This suggests the fol-
lowing question: what is the optimal way for the system to balance these two
modes of resource allocation—T and B cell diversity versus clone size?
2.1. Scaling of B and T Cell Clone Size
In order to derive the typical size of a lymphocyte clone as a function of
M
,
we follow the model of West et al. (2), in which the circulatory system is repre-
sented by a branching tree.
In the West, Brown, and Enquist (or WBE) model the organism is divided
into a certain number of small units, each of which is supplied by a single capil-
lary. These units, called
service volumes
or
service units
, are regions that a sin-