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n
. Furthermore, an antibody recognizes not only one
specific antigen, but several similar antigens which have a certain specificity —
this property is called cross-reactivity
2
. In [1] each antibody is represented as a
n
-dimensional point and its (cross-reactivity) recognition space is modeled as a
hypersphere — called an antibody recognition region. Antigens which lie within
the hypersphere are recognized by the associated antibody. From an immuno-
logical point of view, antibodies recognize antigens which have a complementary
binding site instead of similar binding regions (see Fig. 1(a)). This inspired Hart
et al. [10] to develop a simulation to investigate empirically complementary bind-
ing properties in a immune network, with regard to emerging recognition regions.
Hart et al. reported that the resultant immune network depended very much on
the anity metric employed (see [10] for further details).
point in the shape-space
R
ab
h
1
1
ab
ab
3
2
h
1
ab
2
h
3
h
h
h
3
2
ab
ab
1
3
(a) Complementary antibodies
recognition regions. Antibodies
ab
i
recognize all antigens which
lie within the complementary
hyperspheres
h
i
(b) Non-complementary an-
tibodies recognition regions.
Antibodies
ab
i
recognize all
antigens which lie within the
hyperspheres
h
i
Fig. 1.
Real-valued Shape-Space with complementer and non-complementer antibody
recognition regions (modeling cross-reactivity)
For solving information processing problems, like pattern recognition, anomaly
detection and clustering problems, the complementary recognition approach is
possibly less appropriate, as it less obvious how one might employ such an
idea. For such problems, it is useful to recognize points which are similar in-
stead of complementary and therefore, similarity antibody-antigen recognition
approaches are typically applied (see Fig. 1(b)). More precisely, an antibody
can be represented as a hypersphere with center
ab
n
∈
R
and a radius
r
∈
R
.
n
is recognized by an antibody
ab
, when it lies within the
hypersphere, i.e.
d
(
ab
,
ag
)
An antigen
ag
∈
R
≤
r
.
2
A well described explanation of the difference between cross-reactivity and multi-
specificity is provided in [1], page 661.
