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the emerging architecture can be very complex. Typically, groups of nodes can
be distinguished with clearly distinct statistical properties. These groups are
linked together in a characteristic way which leads to the found architecture.
We achieved a detailed analytical understanding of the building principles of
these very complex structures emerging during the random evolution. Modules
of remarkable regularity serve as building blocks of the complex pattern. We
can calculate for instance size and connectivity of the idiotype groups in perfect
agreement with the empirical findings based on numerical simulations [12].
For a suitable parameter setting the network consists of a central and a periph-
eral part, as proposed in [15]. The central part of the immune system is thought
to play an essential role, e.g., in the control of autoreactive clones. In this view,
the peripheral part provides the response to external antigens and keeps a local-
ized memory. An
ad hoc
architecture similar to the one described here was used
in [21] to investigate the role of the idiotypic network in autoimmunity.
The analytical understanding opens the possibility to consider networks of
more realistic size and to investigate their scaling behaviour, e.g. exploiting
renormalization group techniques [22]. We are optimistic that we can explain
and predict many statistical results of the six-group structure for arbitrary pa-
rameters
d
and
m
, too, if we consider the idiotypes as situated in a mean field
created by its surrounding vertices, which in turn act according to the expected
behavior of their group.
Future steps will include to check whether a similar understanding can be
reached for more realistic models. For example, we think of matching rules al-
lowing bitstrings of different lengths, of links of different weight for varying
binding anities, of several degrees of population for each idiotype and a delay
of take-out of understimulated clones.
Furthermore, we are interested in the co-evolution of the network in the pres-
ence of self-antigens or an invading foreign antigen in terms of whether the net-
work tolerates them or rejects them, respectively. We also think about modeling
the development of the architecture during the life time of an organism.
References
1. Burnett, F.M.: The clonal selection theory of acquired immunity. Vanderbuilt Univ.
Press, Nashville, TN (1959)
2. Jerne, N.K.: Towards a network theory of the immune system. Ann. Inst. Pasteur
Immunol.
125C
(1974) 373-389
3. Shoenfeld, Y.: The idiotypic network in autoimmunity: Antibodies that bind anti-
bodies that bind antibodies. Nature Medicine
10(1)
(2004) 17-18
4. McGuire, K.L., Holmes, D.S.: Role of complementary proteins in autoimmunity: an
old idea re-emerges with new twists. Trends in Immunology
26(7)
(2005) 367-372
5. Carneiro, J.: Towards a comprehensive view of the immune system. PhD thesis,
University of Porto (1997)
6. Coutinho, A.: A walk with Francisco Varela from first- to second generation net-
works: In search of the structure, dynamics and metadynamics of an organism-
centered immune system. Biol. Res.
36
(2003) 17-26
