B Cell–Inspired Algorithms - Immunological Computation: Theory and Applications - page 128

h e explanation of immunology memory is as follows: assuming that antibody
Ab 1 is produced by modeling the stimulating antigen, the production of Ab 1 is
increased in the presence of Ab 2 . h at is, the lifetime of Ab 1 -producing cells is
increased and so the population of Ab 1 -specifi c helper T cells is also increased.
h us, Ab 2 , considered as the image of the stimulating antigen, remains after the
antigen is removed; thus, the presence of Ab 2 induces the survival of memory B
cells.

5.2.1.5 Stewart and Carneiro's Idiotypical Network

In addition to the immune elements considered in the earlier models, this model
introduces T cell cooperation (Stewart and Carneiro, 1999). h erefore, at a given
time, the variables considered are

z i —

=

the concentration of T lymphocyte clones of type i , for i 1, 2, … , L

b i —

the concentration of antibody of B lymphocyte clones of type i , for

=

i 1, 2, … , M

f i —

the concentration of Ig molecules (free antibodies) they produce, for

=

i 1, 2, … , N

y i —

=

the eff ective concentration of antigens of type i , for i 1, 2, … , R

h e following set of diff erential equations, which describe the dynamic behavior of
the IN are defi ned.

dz
dt

i

kz k (,,) z , for i 12 ,, , … L (5.12)

1 i 2 i i i i

where k 1 is the natural T cell death rate; α (•) the amount of activated T cells, which
is a function of both excitatory ( π i ) and inhibitory signals ( η i ) received by T clones;
and

i (•) the (thymic) production of T cell clones of type i .
Also, two sets of diff erential equations are introduced to describe the dynamic
behavior of both bound antibodies and free antibodies. Accordingly, the change
in antibodies bound to the surface of B cells follow the following diff erential
equation:

db
dt

i

k (,,) b k b (5.13)

3 i i i 4 i i

where β (•) denotes the number of activated B cells in the clone, which is a function
of the amount of both induction signals ( σ i ) and the number of specifi c activated
T lymphocytes available for cooperation ( τ i ); k 4 is the natural B cell death rate; and
i (•) represents the (thymic) production of T cell clones of type i .