Mathematical Models for the Immune System

In collaboration with the Division of Immunology and Allergy of Centre Hospitalier Universitaire Vaudois (CHUV), Lausanne, Switzerland.

We are presently working on regulatory T cells (Tregs). They are part of the adaptive immune system and are a subset of the CD4+ helper T cell family. They act as antagonists to immune responses by suppressing the activation and proliferation of CD4+ helper and CD8+ killer T cells. By this means, they are involved in self-tolerance, homeostasis and in the control of excessive immune reactions. They are identified by the surface expression of CD4, as well as by high levels of CD25, the alpha-chain of the IL-2 receptor. In addition, they express the forkhead/winged-helix transcription factor FoxP3, a negative modulator of IL-2 transcription and are therefore referenced as CD4+CD25+FoxP3+ Treg cells. Moreover, Tregs are difficult to activate through their T-cell receptor and require optimal stimulation conditions in order to initiate a clonal expansion. The limited activation and proliferation capacity of Tregs define their anergic nature. Two different origins of Treg cells have been identified: naturally occurring thymus-derived or activation-induced Tregs. It is difficult to study their separate evolution, as specific markers for each of these origins have not been identified yet.

Cells of the immune system



Statistical Analysis of In Vitro Experimental Data

Immunologists have performed in vitro cell cultures in order to evaluate the proliferation capacity of regulatory T cells. Because the blood collected from a donor is sufficient to make only one experiment, the latter is repeated with the blood of another donor in order to make statistics. Thus, the variability of the data is very large and statistical analysis is difficult to perform. The goal of this project is to define a robust statistical methodology that will allow us to extract a maximum information form the data. Our first approach is to study several error models and use them to compute maximum likelihood estimators that are fitted to the data.



Mathematical Modeling of In Vivo Dynamics of CD4+CD25+ Regulatory T Cells

The goal of this project is to test several hypotheses about the origins and the proliferation capacity of regulatory T cells (Tregs). From the immunological knowledge of Tregs, we define a mathematical model that includes all the events affecting their population size. The biological hypotheses are then tested and validated with immunological data.

Different types of Tregs


People

Jean-Yves Le Boudec
Irina Baltcheva (Ph.D. student)


References

Journal papers :

[1] Mathematical Modeling of the Development and Maintenance of a Stable Pool of Human CD4+CD25+ Regulatory T cells. Irina Baltcheva, Laura Codarri, Giuseppe Pantaleo and Jean-Yves Le Boudec. Under submission.