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Tolerance vs Intolerance: How Anity Defines
Topology in an Idiotypic Network
Emma Hart 1 , Hugues Bersini 2 , and Francisco Santos 2
1 School of Computing,Napier University
e.hart@napier.ac.uk
2 IRIDIA, Universite de Bruxelles
{ bersini, fsantos } @ulb.ac.be
Abstract. Idiotypic network models of the immune system have long
attracted interest in immunology as they offer a potential explanation
for the maintenance of immunological memory. They also give a possi-
ble justification for the appearance of tolerance for a certain category
of cells while maintaining immunization for the others. In this paper,
we provide new evidence that the manner in which anity is defined in
an idiotypic network model imposes a definite topology on the connec-
tivity of the potential idiotypic network that can emerge. The resulting
topology is responsible for very different qualitative behaviour of the net-
work. We show that using a 2D shape-space model with anity based
on complementary regions, a cluster-free topology results that clearly di-
vides the space into tolerant and non-tolerant zones in which antigen are
maintained or rejected respectively. On the other hand, using a 2D shape-
space with an anity function based on cell similarity, a highly clustered
topology emerges in which there is no separation of the space into iso-
lated tolerant and non-tolerant zones. Using a binary shape-space, both
similar and complementary anity measures also result in highly clus-
tered networks. In the networks whose topologies exhibit high clustering,
the tolerant and intolerant zones are so intertwined that the networks
either reject all antigen or tolerate all antigen.
1
Introduction
Part of a Nobel lecture that Niels Jerne gave the 8th December 1984 in France
[7] focusing on idiotypic networks was also more specifically concerned with the
definition of anity between two clones. In this lecture, he compared this anity
with the matching problem between pieces of sentence (for example referring to
Chomsky's work on universal grammar). He suspected that the way this anity
would be defined might provide the final network of connected clones with very
different properties. From very early papers of Varela and Coutinho dedicated to
immune idiotypic networks [11,12], the in-depth attention paid to the topology
of the connectivity is obvious.
Despite the lack of empirical data relating to the connectivity matrix which
made it impossible to make any definitive statement on the analytical nature
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