IL-2 stimulation of regulatory T cells: a stochastic and algorithmic approach

Regulatory T cells express IL-2 receptor (IL-2R) complexes on their surface, but do not produce IL-2 molecules. Survival of a population of regulatory T cells depends on the production of IL-2 by other cells, such as effector T cells. We formulate a stochastic version of the model of Busse (Dynamics of the IL-2 cytokine network and T-cell proliferation, Logos, Berlin, 2010, [1]), for the synthesis of IL-2R by a regulatory T cell in constitutive (ligand-independent) and in ligand-induced conditions, with the assumption that synthesis is a function of the number of IL-2/IL-2R bound complexes present on the cell surface. Exact analysis of the stochastic Markov process, by considering its master equation, is usually not possible. Here, we develop an algorithmic approach, which leads to the analysis of suitable random variables. In particular, we focus on the time to reach a threshold number of IL-2/IL-2R bound complexes on the cell surface, and the number of receptors synthesised in this time. These descriptors provide a way to quantify the rates at which IL-2/IL-2R bound complexes and IL-2R free receptors are formed in the cell, and how these rates relate to each other. By following first-step arguments, the different order moments of these random variables are obtained. We illustrate our approach with numerical realisations. The contributions of the constitutive and the ligand-induced synthesis pathways are quantified under different signalling hypotheses.