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Randomly Evolving Idiotypic Networks:
Analysis of Building Principles
Holger Schmidtchen and Ulrich Behn
Institute for Theoretical Physics,
University of Leipzig, POB 100 920, 04009 Leipzig, Germany
Ulrich.Behn@itp.uni-leipzig.de
http://www.physik.uni-leipzig.de/~behn/
Abstract. We investigate a minimalistic model of the idiotypic network
of B-lymphocytes where idiotypes are represented by bitstrings encod-
ing the nodes of a network. A node is occupied if a lymphocyte clone
of the corresponding idiotype exists at the given moment, otherwise it
is empty. There is a continuous influx of B-lymphocytes of randomly
(by mutation) generated idiotype from the bone marrow. B-lymphocytes
are stimulated to proliferate if its receptors (antibodies) are cross-linked
by complementary structures. Unstimulated lymphocytes die. Thus, the
links of the network connect nodes encoded by complementary bitstrings
allowing for a few mismatches.
The random evolution leads to a network of highly organized archi-
tecture depending on only few parameters. The nodes can be classified
into different groups with clearly distinct properties. We report on the
building principles which allow to calculate analytically characteristics
as the size and the number of links between the groups previously found
by simulations.
1
Introduction
B-Lymphocytes express on their surface receptors, i.e. antibodies which are pro-
teins with highly specific binding sites, which enable them to bind to comple-
mentary sites of an antigen, which is thus marked for further processing, e.g., for
eating by macrophages. A given B-cell has exactly one specific type (the idiotype)
of antibody. When stimulated, i.e. crosslinked by complementary structures,
they proliferate and, after a few cell cycles, differentiate into plasma cells and
memory cells, the former secreting large amounts of the useful antibodies. Thus,
useful clones survive, while others, lacking stimulation, die [1].
B-lymphocytes are capable of mutual interaction if their receptors have com-
plementary specifity. Hence, the entirety of the B-lymphocyte system forms a
functional network, with nodes representing the idiotypes and links between
complementary idiotypes. This is the central idea behind the concept of idio-
typic network presented in 1974 by Jerne [2]. Jerne's idea got an immediate en-
thusiastic resonance. B-lymphocytes of a given idiotype and their anti-idiotypic
counterparts have been experimentally identified. However, the search for deeper
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