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and T lymphocytes. A recent work presented in [16] discusses two hypotheses in
this context: the tuning of activation thresholds of self-reactive T lymphocytes,
making them reversibly “anergic”, and the control of the proliferation of these
cells by specific regulatory T cells.
4ModlDipon
As previously discussed, this paper is aimed at modelling the control of an ini-
tiated immune response through cytokine signalling, involving effector and reg-
ulatory cells. The proposed model is based on microscopic mechanisms, and,
due to the lack of numerical data from
in vivo
or
in vitro
experiments, most
of the governing equations were arbitrarily selected. However, even if numerical
data were available, it is important to emphasize that a complete modelling the
immune system is not trivial, given its complexity [17] [18].
Before modelling the actual process of controlling the immune response, some
considerations were made about the environment. The tissue where the response
would occur is approximated by a rectangular region, whose dimensions are
given as parameters to the simulation. Also, the number of iterations and the
time step are additional necessary parameters. Cytokines are represented by
two-dimensional matrices, equivalent to a discrete representation of the environ-
ment. In this sense, there are two cytokine matrices, which separately store the
concentrations of the stimulation and regulatory cytokines. Each cell occupies a
single square in the grid, and, currently, remains fixed in this position. Besides,
the simulations performed so far don't take cell clonning into consideration. Fi-
nally, all data presented in this paper is adimensional (i.e.: no physical units for
the concentrations or other variables are used), because this has no effects on
the simulation outcome. However, if the results are to be compared to real world
data, the introduction of physical units in the governing equations is necessary.
The simulation is started after an effector cell is stimulated, after, for example,
contact with a specific antigen. It is important to mention that this model doesn't
consider antigen dynamics, once the response has been initiated. This cell will
secrete an amount of an stimulation cytokine that will be diffused through the
environment. The remaining cells (both effector and regulatory) will, then, ab-
sorb some of this cytokine, and be activated, secreting, in turn, more cytokines,
until a steady state is reached. Effector cells secrete the stimulation cytokine,
while regulatory cells secrete the regulatory cytokine; on the other hand, effec-
tor cells absorb both stimulation and regulatory cytokines, while regulatory cells
absorb only the stimulation cytokine. Based on the discussion presented in [5],
the expected response should be an increase of the number of activated effector
cells, with little influence from regulatory cells, until the response suppression is
initiated, with the activation of regulatory cells and eventual termination of the
response. These steps are represented graphically in figure 1.
Each cell stores its position in the tissue and a value representing its acti-
vation level. This activation level reflects the immunological status of the cell,
and is a real number in the interval (0
,
1). The greater the activation level, the
