Abstract : T lymphocytes are a fundamental component of the immune system that can recognise and respond to foreign antigens by virtue of their clonally expressed T cell antigen receptor (TCR). T cells that have yet to encounter the antigen they recognise are termed 'naive' as they have not been activated to respond. Homeostatic mechanisms maintain the number of T cells at an approximately constant level by controling cell division and death. In normal replete hosts, cell turnover within the naive compartment is very low and naive cells are maintained in a resting state.
However, disruption of the homeostatic balance can arise from a wide variety of causes (viral infection (e.g. HIV), or drugs used in peritransplant induction therapy or cancer chemotherapy) and can result in T cell de ciency or T lymphopenia. Under conditions of T lymphopenia, naive T cells undergo cell division with a subtle change in the cell surface phenotype (CD44 expression), termed homeostatic proliferation or lymphopenia induced proliferation (LIP). In this thesis, our purpose is to understand the process of T cell homeostatic through mathematical approach. At
fi rst, we build a new model that describes the proliferation of T cells in vitro under lymphopenic conditions. Our nonlinear model is composed of ordinary di erential equations and partial di erential equations structured by age (maturity of cell) and CD44 expression. To better understand the homeostasis of T cells, we identify the parameters that de ne T cell division by using experimental data. Next, we consider an age-structured model system describing the T cell homeostatic in vivo, and we investigate its asymptotic behaviour. Finally, an optimal strategy is applied in the
in vivo model to rebuild immunity under conditions of T lympopenia.
Résumé : Les lymphocytes T sont une composante essentielle du systeme immunitaire de l'organisme. Ils peuvent reconna^tre et repondre a un antigene etranger en vertu de leur recepteur d'antigene.
Dans le cas normal, le renouvellement des cellules T naives est tres faible et ces derniers restent approximativement dans un etat de repos. Cependant, une perturbation de l'equilibre homeostatique peut resulter d'une grande variete de causes (infection virale, ou les traitements de chimiotherapie), et peut entrainer une lymphopenie (i.e. Une carence en lymphocytes T). Dans ces conditions lymphopeniques, les cellules T naives subissent la division cellulaire avec un changement de l'expression de CD44 sur leur surface cellulaire. Ce processus est appele "proliferation homeostatique" ou en anglais "lymphopenia induced proliferation" (LIP). Ainsi, le CD44 est un marqueur naturel qui caracterise la transition des cellules du phenotype naf (CD44-) au phenotype memoire (CD44+) durant LIP.
L'objectif de cette these est de comprendre la relation complexe entre LIP et le passage du phenotype naif (CD44-) au phenotype memoire (CD44+) en utilisant des modeles mathematiques et des donnees experimentales. On s'interesse en plus au comportement asymptotique des cellules T durant le processus d'homeostasie in vivo.
