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J Theor Biol. 2011 Jan 21;269(1):70-8. doi: 10.1016/j.jtbi.2010.10.013. Epub 2010 Oct 14.

Mathematical modeling of allergy and specific immunotherapy: Th1-Th2-Treg interactions.

Author information

1
Institute for Theoretical Physics, University of Leipzig, P.O.B. 100 920, D-04009 Leipzig, Germany. fridolin.gross@ifom-ieo-campus.it

Abstract

Regulatory T cells (Treg) have recently been identified as playing a central role in the immune response to allergens and during allergen-specific immunotherapy. We have extended our previous mathematical model describing the nonlinear dynamics of Th1-Th2 regulation by including Treg cells and their major cytokines. We hypothesize that immunotherapy mainly acts on the T cell level and that the decisive process can be regarded as a dynamical phenomenon. The model consists of nonlinear differential equations which describe the proliferation and mutual suppression of different T cell subsets. The old version of the model was based upon the Th1-Th2 paradigm and is successful in describing the "Th1-Th2 switch" which was considered to be the decisive event during specific immunotherapy. In recent years, however, the Th1-Th2 paradigm has been questioned and therefore, we have investigated a modified model in order to account for the influence of a regulatory T cell type. We examined the extended model by means of numerical simulations and analytical methods. As the modified model is more complex, we had to develop new methods to portray its characteristics. The concept of stable manifolds of fixed points of a stroboscobic map turned out to be especially important. We found that when including regulatory T cells, our model can describe the events in allergen-specific immunotherapy more accurately. Our results suggest that the decisive effect of immunotherapy, the increased proliferation of Treg and suppression of Th2 cells, crucially depends on the administration of high dose injections in short intervals right before the maintenance phase sets in. Empirical protocols could therefore be improved by optimizing this step of therapy.

PMID:
20951144
DOI:
10.1016/j.jtbi.2010.10.013
[Indexed for MEDLINE]

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