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1. For the objects representing type of antibodies there exist two kinds of rela-
tion: to recognize anybody and to be recognized by anybody . In the first case
we can say that the object B 1 will recognize the object B 2 if the anity be-
tween B 1 paratope and B 2 epitope is above the specified threshold. In this
case B 1 will be activated. In the second case - B 1 will be recognized by B 2
if the anity between B 1 epitope and B 2 paratope is above specified thresh-
old. In this case B 1 will be suppressed. The thresholds for both relations do
not need to be equal.
2. If neither the objects's paratope nor the epitope interact with any other
object in the system (i.e. the given type of antibodies neither recognizes nor
is recognized by any other type of antibodies) it will be suppressed.
3. If the object representing type of antibodies recognizes any object repre-
senting type of antigens i.e. anity between the antibodies' paratope and
theantigens'epitopeisabovethespecified threshold the object represent-
ing types of antibodies will be activated and the object representing type of
antigens will be suppressed.
4. If the object representing type of antibodies neither is recognized by any
other type of antibodies in the system nor recognize any type of antigens the
object will be suppressed.
5. The real-world antigens try to proliferate continuously in the infected organ-
ism so for each of types of antigens a concentration growth proportional to
current level of concentration is evaluated in every iteration.
The five rules presented above require to define the anity measure and three
thresholds. The first threshold at controls the relation of the first type when B 1
recognizes B 2 and causes activation of B 1 . The second threshold st controls the
relation of the second type when B 1 is recognized by B 2 and causes suppression
of B 1 . The last threshold t controls the relation between types of antibodies and
types of antigens.
2.3
Evaluation of a New Concentration Level
To evaluate new values of concentrations of types of antibodies and types of
antigens in the time t of the process the first step is to check current relations
between them. For each of the types of antibodies B i the total number of other
types of antibodies which are recognized by B i (called A i B 2 B ( t )) and the total
number of types of antibodies which recognize B i (called S i B 2 B (t)) are evaluated
using the first rule. Then in case of presence of antigens the third rule is used
to evaluate the number of types of antigens which are recognized by B i (called
A B 2 A ( t )) and for each of the types of antigens the number of types of antibodies
which recognize them ( S B 2 A ( t )) is evaluated.
In the second step for each of B i a change of its concentration c i ( t )based
on each of the rules of interaction is evaluated. The change of concentration is
controlled by two factors: an activation factor η a where η a > 1, and a suppression
factor η s where η s < 1. There are four components of concentration change
Δc 1 ( t ), Δc 2 ( t ), Δc 3 ( t )and Δc 4 ( t ) which come from the former four rules:
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