B Cell–Inspired Algorithms - Immunological Computation: Theory and Applications - page 129

Also, the change in the concentration of Ig molecules is defi ned as

df
dt

i

…

k ( ,, b ) ( k k ) f , for i 1,, , N (5.14)

5 i i i 6 7 i i

where the fi rst term represents the growth (at the rate k 5 ) of the amount of soluble Ig
molecules as a proportion to the number of Ig-producing (activated) B cells (note that
the function β is the same as in Equation 5.14); k 6 is the rate at which antibodies pro-
duced by clone i decreases; the factor ( k 7 σ i ) is the change rate at which Ig molecules
produced by clone i are removed due to the formation of complexes with available
legends.

5.2.2 Discrete Immune Network Models

Diff erent variations of discrete IN models have been studied; each model is
distinguished by the abstractions of the network structure, its dynamics and
metadynamics, and data representation.

5.2.2.1 Hunt and Cooke's Immune Network Model

and Its Variation

h e fi rst AIN model (Hunt and Cooke, 1996) considers an IN of B cells that
interact with one another according to their a nities. B cells are represented as
binary strings, following some earlier works (Farmer et al., 1986); thus the a nity
between B cells is defi ned based on the Hamming distance. If B cell stimulation by
foreign antigens is above a certain threshold, then they will undergo cloning and
mutation. Cloning produces a certain number of exact copies of a B cell. h e num-
ber of copies, however, depends on the stimulation level of the B cell. Finally, in
the simple substitution operator, a small (less than half ) portion of the substring
representing a B cell is replaced by the corresponding elements of another randomly
selected B cell. Also, three types of mutation operators are introduced: multipoint
mutation, substring regeneration, and simple substitution; however, at each time,
only one of these operators is applied to a clone at random. In multipoint mutation,
each element of the antibody is mutated with a certain probability. In substring
regeneration, a substring of the antibody's paratope is selected at random to be
replaced by a randomly generated string.
h e training process is performed in an iterative fashion; at the end of each
iteration, a proportion of the less-stimulated B cells are removed and replaced with
newly generated B cells, which are incorporated in the network. A variation of
this model is called artifi cial immune network (AINE), which was introduced by
Timmis et al. (2000). In this model, B cells are represented by real-valued vectors,
instead of binary strings. A similarity measure is then defi ned by the Euclidean
distance between two B cells. h e dynamics of the network is similar to Hunt and