Mathematical Model of Naive T Cell Division and Survival IL-7 Thresholds - Molina-Paris, Carmen; Reynolds, Joseph; Lythe, Grant; Coles, Mark C. (Frontiers in Immunology, 2013)
We develop a mathematical model to describe the homeostasis of naive T~cells in the peripheral immune system of ageing humans, incorporating thymic output and the availability of interleukin-7 (IL-7). The model is formulated as three ordinary differential equations: two describe T~cell numbers, in a resting state and progressing through the cell cycle. The third is introduced to describe changes in IL-7 availability. Thymic output is a decreasing function of time, representative of thymic atrophy found in ageing humans. Each T~cell is assumed to possess two interleukin-7 receptor (IL-7R) signalling thresholds: a survival threshold and a second, higher, proliferation threshold. If the IL-7R signalling strength is below its survival threshold, a cell may undergo apoptosis. When the signalling strength is above the survival threshold, but below the proliferation threshold, the cell survives but does not divide. Signalling strength above the proliferation threshold enables entry into cell cycle. Assuming that individual cell thresholds are log-normally distributed, we derive population-average rates for apoptosis and entry into cell cycle. We have analysed the adiabatic change in homeostasis as thymic output decreases. With a parameter set representative of a healthy individual, the model predicts a unique equilibrium number of T~cells. In a parameter range representative of persistent virus or bacterial infection, where naive T~cell survival is impaired, a decrease in thymic output may result in the collapse of the naive T~cell repertoire.