Mathematical models of the roles of IL-2 and IL-7 in T cell homeostasis

We study the homeostasis of a peripheral naive T cell population through the use of deterministic mathematical models. A two compartment approach is used, where, naive T cells are assumed to be either in a resting state, or undergoing the cell cycle. We begin by assuming all rates are linear, then discuss the limitations in doing so. We next explore examples of published methods which improve this simple description. Finally, we introduce a model in which resting T cell survival and entry into the cell
cycle is assumed to be dependent on the amount of available IL-7.
To aid our description of T cell homeostasis, a stochastic model of IL-7 signalling is developed. In this model we consider the number of IL-7 receptors, either membrane bound or internalised, the extra-cellular
concentration of IL-7, and the amount of IL-7 induced signalling. The model is used to derive a relationship between the amount of IL-7 induced signalling to the extra-cellular concentration of IL-7. The survival and proliferative ability of the T cell population is then assumed to be dependent on the amount of IL-7 induced signalling with respect to IL-7 signalling thresholds for survival and division.
This signalling relation is then used with the model of T cell homeostasis. The model is fitted to experimental data measuring the expansion of transgenic naive T cells in lymphopenic mice. We show this approach can capture the homeostatic equilibrium, and notably, time scales required
to reach equilibrium. The model is then explored in the context of the human periphery.
In a separate piece of work we develop a stochastic Markov model of the peripheral CD4+ T cell pool, in which we consider sub-populations of naive, IL-2 producing, IL-2 non-producing and regulatory T cells. The balance between the IL-2 producing and regulatory sub-populations
is assumed to be determined by a recently proposed quorum-sensing hypothesis. This model is explored in scenarios where no antigen is presented to the CD4+ population, before and after a challenge, and when antigen is presented at a constant level. We show, amongst other results, that the number of regulatory T cells in equilibrium is greater
when antigen is presented, whilst the number of IL-2 producing T cells remains the same. We finally use the stochastic aspect of this model to explore probabilities of and times to extinction of the sub-populations.