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of the topology, it is evident that Varela did not see the connectivity of this
system as simply random like in Erds graph, but rather well structured and
playing a key role in the functionality of the system. For instance, he discussed
the topology of this connectivity as a possible cause or signature of some auto-
immune diseases whose treatment was inspired by this new network perspective.
He showed, using again very scant data, that people suffering from auto-immune
disease could present a less densely connected network than healthy ones. This
default in connectivity could decrease the network effect and thereby provoke
homeostatic failure by perturbing the emergent regulatory effect of this network.
It is hard not to see in these studies (together with the critical quest for more
experimental data), a pioneering approach to discovering the structure and the
functionality of biological networks. Today, this is receiving renewed attention,
and advancements in our knowledge and understanding are being made by a
new generation of physicists enthusiastic about small-world effects and scale-free
topology [1,9]. This paper carries on this quest with new and very unexpected
findings.
A
nity: Complementarity or Similarity ?
1.1
The study of the effects of anity between cells was facilitated by by the no-
tion of shape-space introduced by [8] as a method for representing biological
molecules and therefore capturing anities between them. There have been nu-
merous attempts to exploit this simple idea. The most typical interpretations
(by both immunologists and computer scientists) utilise either a real-valued uni-
verse or bit-string universe to represent cells. Biologically, it is well established
that two cells
recognise
or have an
a
nity
with each other if the cells contain
complementary shaped regions that can “fit” together — the “lock and key”.
In a bit-string universe, it is straightforward to model the notion of a com-
plementary matching. Hence, a number of anity functions have been proposed
which are physiologically plausible based on finding complementary matching re-
gions between two strings [8]. For example, this could take the form of counting
complementary bits or identifying contiguous regions of complementary bitwise
matches along two strings. A study of the properties of a bit-string shape-space
with anity defined in terms of Hamming distance by Bersini in [3] suggested
that this model can give rise to tolerant and intolerant zones in the shape-space,
in which some antigens can be tolerated and others rejected, although this work
has not since been replicated.
Complementarity can also be defined in a real-valued universe. Bersini [2]
proposed a shape-space model implemented in 2D in which anity was based
upon complementary matching between cells by supposing that a cell exerts a
domain of anity in a zone which is situated in region obtained by reflecting
the cell through the centre of symmetry of the space. This is consistent with the
biological notion of a lock-and-key. [2] showed that this led to model in which
regions of tolerance and intolerance emerged naturally from the dynamics of the
idiotypic network, without need for pre-defining cells as being of a particular
type. This model was later explored in greater depth by Hart in [6,5] which
