B Cell–Inspired Algorithms - Immunological Computation: Theory and Applications - page 123

Antigens

Antibodies

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.

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Figure 5.4 Illustration of an IN. Nodes, edges, and arrows represent antibod-
ies, interaction among them, and stimulation to the AIN by foreign antigens,
respectively.

5.2.1 Continuous Immune Network Models

Continuous IN models are defi ned as a set of diff erential equations that attempt
to predict the concentration of a fi nite number of antibodies in the IN at a certain
time, during or after an immune response. Models based on diff erential equations
do not focus on the structure of the IN, but on the antibody and foreign antigen
concentration, although they assume that all antibodies interact with one another
and the antigens interact with all antibodies as well.
h e change in the concentration of a specifi c antibody is represented as the sum
of two terms:

dx i / dt = ∆ x i = internal network dynamics + antigen driven dynamics (5.1)

where x i is the concentration of type i antibody at a given time. h e fi rst term
models the interaction among antibodies, that is, the eff ect of stimulation and
suppression of antibody paratopes by other antibody epitopes; this term describes
natural death of antibodies. In contrast, the second term models the stimulation of
antibodies by antigens.