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Approximate Equilibria for a T Cell and Treg Model |
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PP: 2221-2231 |
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Author(s) |
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Bruno M. P. M. Oliveira,
Isabel P. Figueiredo,
Nigel J. Burroughs,
Alberto A. Pinto,
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Abstract |
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| We analyse a model of immune response by T cells (CD4), where regulatory T cells (Tregs) act by inhibiting IL-2 secretion.
We introduced an asymmetry reflecting that the difference between the growth and death rates can be higher for the active T cells
and the active Tregs than for the inactive T cells and inactive Tregs. This asymmetry mimics the presence of memory T cells. In this
paper we start by analysing the model in the absence of Tregs. We obtain an explicit formula that gives approximately the antigenic
stimulation of T cells from the concentration of Tregs. Afterwards, we present an explicit formula that describes approximately the
balance between the concentration of T cells and the concentration of Tregs; and an explicit formula that relates approximately the
antigenic stimulation of T cells, the concentration of T cells and the concentration of Tregs. For our parameter values, the relation
between the antigenic stimulation of T cells and the concentration of T cells is an hysteresis that is unfold when some of the parameters
are changed. We also consider a linear tuning between the antigenic stimulation of T cells and the antigenic stimulation of Tregs. Again,
we have obtained an explicit formula relating approximately the antigenic stimulation of T cells, the concentration of T cells and the
concentration of Tregs. With it, we can explain the appearance of an isola and a transcritical bifurcation. |
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