Stochastic Model of T Cell Proliferation: A Calculus Revealing IL-2 Regulation of Precursor Frequencies, Cell Cycle Time, and Survival

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Abstract
The outcome of Ag exposure is dictated by complex regulation of T cell proliferation. The rates of proliferation and survival are altered by numerous signals that the cell receives and integrates to achieve a net response. We have illustrated previously how small changes in kinetic parameters can lead to large differences, even under conditions of saturating IL-2. In this study, we examine the effect of varying IL-2 concentration on T cell response and develop a model incorporating additional parameters of proliferation and survival. Strikingly, the proportion of cells that enter the first division, but not the time at which they enter, is dramatically altered by IL-2. Furthermore, the survival and average division time of cells in later divisions are also altered by IL-2 concentration. Together, the small simultaneous effects on these parameters result in large differences in total cell number. These results reveal how in vitro systems may exaggerate the contribution of IL-2, and thus how costimuli or additional helper cells that alter IL-2 concentration, even by relatively small amounts, will generate large in vitro differences in cell number and therefore appear obligatory. Furthermore, they illustrate how a quantitative model of T cell activation can clarify how complex signal integration is handled by T cells in situ, and therefore more appropriately aid development of a theory of behavior.

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