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work much better than random creation; we show that libraries give rise to many
more antibodies then random creation, due to increased efficiency (chance of
producing a valid antibody) - that is, reducing the cost of negative selection.
It is tempting to infer a causal link between efficiency and coverage, but in section
4 we show that concentrating purely on the cost of negative selection actually reduces
the number of antibodies produced, by reducing diversity. While these results confirm
what might be suspected from a simple combinatorial analysis, in both “real” immune
systems, and AIS applications, it is extremely rarely, if ever, the case that either the
self or non-self population to be matched is uniformly distributed.
In section 5 we turn our attention to non uniform spaces, and show how different
patterns of self and antigen clustering affect both coverage and efficiency. Choosing a
number of points in cluster space to analyze, in section 6, we show that gene libraries
not only produce more antibodies, but those they do produce are targeted around the
antigen clusters. Finally in Section 7 we conclude that gene libraries: provide
combinatorial efficiency, improve coverage and reduce the cost of negative selection.
Most importantly, they allow the targeting of fixed antigen populations.
2 Background and Related Work
In the biological immune system, both T cell receptors and antibodies are generated
by combining fragments from gene libraries. The gene library mechanism appears at
first to be wasteful: to make a protein of about 200 amino acids we require enough
DNA to make almost 12000 amino acids. However this 60-fold redundancy enables
2M combinations; this potential diversity is of course augmented by the well known
somatic hypermutation mechanism [2]. The expressed diversity is, of course, likely to
be somewhat lower not least become some combinations will be autoreactive (hence
screened out by negative selection or other mechanisms [3]). A more detailed account
is found in [1] where we speculate that gene libraries, shaped by evolution, are used to
guide the B cell creation process to create antibodies with a good chance of success,
while preserving the ability to respond to novel threats.
With regard to gene libraries in AIS, a seminal paper by Perelson et al [4] showed
that gene libraries can enhance coverage in the absence of a 'self' set. Hightower et al
[5] showed that the 'best' coverage was achieved by a high Hamming distance
(spread out antibodies) - but not too high. A maximal separation actually allows gaps
in coverage (analogous to gaps between disjoint spheres). Oprea & Forrest [6] showed
that as the pathogen set size decreases, the structure of the gene library changes,
moving from a 'coarse mapping' of antigen space towards a more focused targeting of
pathogenic clusters. We present complementary analyses to these papers by studying
clustering of both antibodies and antigens.
Other work by Hart and Ross [7,8] and Kim and Bentley [9,10,11] have used gene
libraries to improve performance of an AIS application; we argue in [1] that these
approaches use the gene library metaphor as an engineering artefact and would
benefit from a principled analysis of when and how to use gene libraries. We reiterate
our aim that we would like to build a bridge between the established theoretical
foundations and current AIS engineering practice.
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