Mathematical Model of Naive T Cell Division and Survival IL-7 Thresholds

Abstract

We develop a mathematical model of the peripheral naive T cell population to study the change in human naive T cell numbers from birth to adulthood, 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 the thymic atrophy observed in aging humans. Each T cell is assumed to possess two interleukin-7 receptor (IL-7R) signaling thresholds: a survival threshold and a second, higher, proliferation threshold. If the IL-7R signaling strength is below its survival threshold, a cell may undergo apoptosis. When the signaling strength is above the survival threshold, but below the proliferation threshold, the cell survives but does not divide. Signaling 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 analyzed 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 viral or bacterial infection, where naive T cell cycle progression is impaired, a decrease in thymic output may result in the collapse of the naive T cell repertoire.

The natural history of naive T cells from birth to maturity

“…Approximately 0.2‐1% of naive T cells are Ki67+ in young adult humans . Assuming a cell cycle duration of 12 hours and a Ki67 lifetime of 3.5 days, these observations imply that 0.03‐0.14% of naive cells are in cell cycle at any time, which is in broad agreement with the predictions of Reynolds et al.…”

“…Nevertheless, Reynolds et al modeled naive T‐cell homeostasis in humans assuming that quorum‐sensing does operate under normal conditions, mediated by competition for a finite resource of IL‐7 that regulates both cell survival and homeostatic proliferation. In this model cells possess different IL‐7 signaling thresholds for the 2 processes, which are both lognormally distributed across the population.…”

Naive T Cell Maintenance and Function in Human Aging

“…In modeling naïve T cell division and survival, Reynolds and colleagues propose that increased IL-7-driven proliferation, possibly due to a lower threshold for IL-7 receptor signaling, leads to abrupt declines in compartment size several years later (39). Taking this thought one step further, tonic TCR and homeostatic cytokine stimulation need to be optimally tuned to find the balance between providing sufficient signals for survival and replacement without triggering increased turnover (38).…”

Lymphocyte generation and population homeostasis throughout life

“…Lowering TCR and cytokine receptor thresholds or excess of cytokines may even accelerate aging, as proposed by Reynolds et. al., in which increased IL-7 driven proliferation leads to increased cell death, decreasing the cell compartment size several years later [19]. …”