Information Technology Reference
In-Depth Information
cell is reduced to below 10000, this is no longer sucient to cause any further
decrease in concentration of the cell (recall that concentration decreases by an
amount
stimulation/
(100
L
). Therefore, at this point, although its stimula-
tion continues to decrease, it's concentration remains constant from this point
onwards.
We can now offer an explanation for the observed results based on the cluster-
ing observed between cells that arises from the network topology. In a bit-string
space, the networks that emerge will necessarily have high cluster coecient due
to the nature of the anity function, whether it is defined in a complementary
or similar manner: if
a
interacts with
b
which interacts with
c
, there is a good
chance that
a
can also interact with
c
due to the anity measure which allows
such connections via a series of different matching sequences. Consider a trivial
example in a 3-bit universe; if the anity function is such that cells with 2-
mismatches can connect, then
a
= 000 can connect to
b
= 110 which connects to
c
=011whichinturnconnectsbackto
a
= 000. Thus, any antigen will always
find itself with two kinds of responding antibodies closely located in the space,
one in high and the other in low concentration. At the end, the response of the
network to any antigen intrusion just depends on the initial concentration of this
antigen and therefore no longer on the position of this antigen. The space has
been uniformly filled up with all kinds of antibodies. No clustering of antibodies
with similar concentration would be possible. Similarly, using a similarity anity
function in the 2D model, we also obtain highly clustered networks, in which it
is possible to form the triangle
a
∗
−
b
−
c
, therefore we observe the same effects
as just described for th binary network.
In 2D shape-space using a complementary anity function however, then it
is clear that the cluster-coecient is necessarily close to 0 and no clustering can
occur — if
a
stimulates
b
and
b
stimulates
c
,then
c
cannot stimulate
a
.Thiscan
easily be seen by drawing a simple diagram. The only exception to this is for cells
located very close to the centre of the space, where (
X
−
x, Y
−
y
) is approximately
equal to (
x, y
), and therefore the triangle
a
c
can occur for some values.
The network topology therefore prevents clusters, but facilitates the emergence of
chains of cells which are able to separate the space into distinct regions. This rea-
soning is confirmed by calculating the cluster coecients of the networks pictured
in figures 1 and 7 which exhibit cluster coecients of 0.012 and 0.566 respectively.
−
b
−
6Con lu on
We have shown the role played by the potential network (the network defined
by all possible cells and all possible interactions) in defining whether or not it is
possible for tolerant and intolerant zones to co-exist in a network. If the cluster
coecient of a network is zero (or close to 0), then it is possible for two distinct
zones to co-exist. Although since the origin of networks in immunology (essen-
tially with idiotypic networks) the topology has always raised a lot of interest,
this is the first time it has been shown how this topology influences an essen-
tial capability of the network: to separate zones of tolerance from immunisation
