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activation level will remain constant. In this sense, each cell can be seen as
a processing unit with an activation level controlled by a given externally
received input
-
the steepness (
σ
in equation 6) is inversely proportional to the transition
region between 0 and 1 in figure 3. As an example, consider the first curve
(
α
0
=0
.
2
,σ
=0
.
1), where a resultant input equals to approximately 5.4 units
is needed to increase the activation level by 0.1, while, for the second curve,
this value is around 4.1 units. Therefore, the steepness, together with the
stimulation and regulation constants, can be seen a parameter representing
the anity for the absorbed cytokines.
Regulatory Cells.
Due to the fact that, in this proposal, regulatory cells react
only to IFN-
γ
, the resultant input (
χ
, according to equation 5) is either positive
or zero. Therefore, using equation 6 is not appropriate, because the activation
level would never decrease. Thus, update of the activation level for regulatory
cells is governed by equation 7.
2
1+
exp
(
α
(
χ
)=
χ
)
−
1
(7)
−
σ
·
According to equation 7, the new activation level for regulatory cells is not
dependant on the current activation level (
α
0
), in contrast to equation 6. In this
sense, regulatory cells have no memory of past states (in this case, the activation
level), and act based only on the current environment conditions.
4.4
Cytokine Secretion
In this step, each cell secretes an amount of a given cytokine. As previously
discussed, effector cells secrete IFN-
γ
(referred to as a stimulation cytokine),
while regulatory cells secrete IL-10 (referred to as a regulatory cytokine). The
amount of cytokine to be secreted is directly proportionally to the cell's acti-
vation level, and has been modelled according to equation 8, where
Δψ
is the
Fig. 4.
Plots of the cytokine secretion as a function of cell activation for two sensitivity
values
