Applied statistical and mathematical modelling of peripheral T-Lymphocyte homeostasis

In normal replete hosts, cell turnover within the naïve compartment is slow and the majority of naïve cells at any time are in a quiescent non-cycling state. However, in conditions of lymphopenia, naïve T cells can undergo divisions, termed homeostatic or lymphopenia induced proliferation (LIP). Induction of cell division is dependent on signals through the T cell antigen receptor (TCR) from self-peptide MHC (spMHC) complexes and also cytokines such as interleukin 7 (IL7). Studies of TCR transgenic models reveal a spectrum of responses with some TCR transgenics failing to proliferate in lymphopenia, some undergoing slow cell division while others undergo more rapid divisions accompanied by subtle changes in the cell surface phenotype (e.g. increased CD44) and effector function that imply a transit from naïve to memory phenotype. The contribution to the memory pool of the naive pool through LIP, however, remains unknown as are the specific criteria of cell division that govern such entry. Our key aim is to determine the minimal requirements for entry into the memory pool via LIP. Is there a critical number and/or rate of cell divisions associated with differentiation through LIP? How important is the LIP process in T cell homeostasis? To address these questions, we will take advantage of a system biology approach integrating immunology, mathematics and statistics. Data on cell divisions and phenotypic characteristics will come from experimentation using transgenic mice. Relevant mathematical models and statistical approaches will be developed and adapted for analysing these data. Identification of the parameters that define the naïve to memory transition during LIP is crucial for understanding how T cell memory is maintained and for building more comprehensive models of naïve and memory T cell homeostasis in the normal host.

T cell homeostasis will be studied by combining experimental data from lymphopenic induced T cell proliferation (LIP) with statistical and mathematical modelling. Two TCR transgenic models will be used (F5 and OT-I). Both T cell types undergo LIP with different proliferative responses in lymphopenic hosts. We will generate detailed time course data using CFSE to assess cell division. The LIP response will be manipulated in Rag1-/- strains with varying levels of IL-7. Conditions for LIP expansion of naïve cells only or conversion of naïve cells to memory for both F5 and OT-I T cells will be established and detailed kinetics obtained. We will then fit these data sets to different mathematical models that describe LIP. By including parameters that link the phenotype (i.e. gradual upregulation of CD44 expression) and functional conversion of cells to number and/or rate of cell divisions we can explore the LIP responses that generate memory cells. Using two different TCR transgenic models will also allow us to address the question of whether the criteria for entry to the memory pool via LIP are linked to TCR affinity for spMHC or whether there are TCR specificity independent conditions with the response linked to cell division instead. This project will require mathematical models from classical (Smith-Martin) to new models (delay differential equations, branching process) to be developed. We also aim to improve the estimation of model parameters by taking into account several statistical issues (uncertainty in the assignment of cells to generations, undetectability of CFSE dye, and hierarchical structure of the data). To achieve the objectives of this project, we are banking on a close collaboration of teams recognized in their own topics, that is T-cell homeostasis (B Seddon), Applied Mathematics in immunology (R Callard, A Yates), Mathematical analysis of dynamical models (CM Brauner) and estimation of parameters of dynamical models (D Commenges, R Thiébaut).